{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_27942/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_27942","id":"gutenberg_27942","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/27942","summary":null,"tags":["Banned Books from Anne Haight's list","Category: Philosophy & Ethics","Knowledge, Theory of","Logic","Philosophy","Science -- Methodology"],"text":"A SYSTEM OF LOGIC,\n\n                       RATIOCINATIVE AND INDUCTIVE,\n\n                      BEING A CONNECTED VIEW OF THE\n\n                         PRINCIPLES OF EVIDENCE,\n\n                                 AND THE\n\n                   METHODS OF SCIENTIFIC INVESTIGATION.\n\n                                    by\n\n                            JOHN STUART MILL.\n\n                             Eighth Edition.\n\n                                New York:\n\n                      Harper & Brothers, Publishers,\n\n                             Franklin Square.\n\n                                  1882.\n\n\n\n\nCONTENTS\n\n\nPreface To The First Edition.\nPreface To The Third And Fourth Editions.\nIntroduction.\nBook I. Of Names And Propositions.\n   Chapter I. Of The Necessity Of Commencing With An Analysis Of Language.\n   Chapter II. Of Names.\n   Chapter III. Of The Things Denoted By Names.\n   Chapter IV. Of Propositions.\n   Chapter V. Of The Import Of Propositions.\n   Chapter VI. Of Propositions Merely Verbal.\n   Chapter VII. Of The Nature Of Classification, And The Five Predicables.\n   Chapter VIII. Of Definition.\nBook II. On Reasoning.\n   Chapter I. Of Inference, Or Reasoning, In General.\n   Chapter II. Of Ratiocination, Or Syllogism.\n   Chapter III. Of The Functions And Logical Value Of The Syllogism.\n   Chapter IV. Of Trains Of Reasoning, And Deductive Sciences.\n   Chapter V. Of Demonstration, And Necessary Truths.\n   Chapter VI. The Same Subject Continued.\n   Chapter VII. Examination Of Some Opinions Opposed To The Preceding\n   Doctrines.\nBook III. Of Induction.\n   Chapter I. Preliminary Observations On Induction In General.\n   Chapter II. Of Inductions Improperly So Called.\n   Chapter III. Of The Ground Of Induction.\n   Chapter IV. Of Laws Of Nature.\n   Chapter V. Of The Law Of Universal Causation.\n   Chapter VI. On The Composition Of Causes.\n   Chapter VII. On Observation And Experiment.\n   Chapter VIII. Of The Four Methods Of Experimental Inquiry.\n   Chapter IX. Miscellaneous Examples Of The Four Methods.\n   Chapter X. Of Plurality Of Causes, And Of The Intermixture Of Effects.\n   Chapter XI. Of The Deductive Method.\n   Chapter XII. Of The Explanation Of Laws Of Nature.\n   Chapter XIII. Miscellaneous Examples Of The Explanation Of Laws Of\n   Nature.\n   Chapter XIV. Of The Limits To The Explanation Of Laws Of Nature; And Of\n   Hypotheses.\n   Chapter XV. Of Progressive Effects; And Of The Continued Action Of\n   Causes.\n   Chapter XVI. Of Empirical Laws.\n   Chapter XVII. Of Chance And Its Elimination.\n   Chapter XVIII. Of The Calculation Of Chances.\n   Chapter XIX. Of The Extension Of Derivative Laws To Adjacent Cases.\n   Chapter XX. Of Analogy.\n   Chapter XXI. Of The Evidence Of The Law Of Universal Causation.\n   Chapter XXII. Of Uniformities Of Co-Existence Not Dependent On\n   Causation.\n   Chapter XXIII. Of Approximate Generalizations, And Probable Evidence.\n   Chapter XXIV. Of The Remaining Laws Of Nature.\n   Chapter XXV. Of The Grounds Of Disbelief.\nBook IV. Of Operations Subsidiary To Induction.\n   Chapter I. Of Observation And Description.\n   Chapter II. Of Abstraction, Or The Formation Of Conceptions.\n   Chapter III. Of Naming, As Subsidiary To Induction.\n   Chapter IV. Of The Requisites Of A Philosophical Language, And The\n   Principles Of Definition.\n   Chapter V. On The Natural History Of The Variations In The Meaning Of\n   Terms.\n   Chapter VI. The Principles Of A Philosophical Language Further\n   Considered.\n   Chapter VII. Of Classification, As Subsidiary To Induction.\n   Chapter VIII. Of Classification By Series.\nBook V. On Fallacies.\n   Chapter I. Of Fallacies In General.\n   Chapter II. Classification Of Fallacies.\n   Chapter III. Fallacies Of Simple Inspection; Or A Priori Fallacies.\n   Chapter IV. Fallacies Of Observation.\n   Chapter V. Fallacies Of Generalization.\n   Chapter VI. Fallacies Of Ratiocination.\n   Chapter VII. Fallacies Of Confusion.\nBook VI. On The Logic Of The Moral Sciences.\n   Chapter I. Introductory Remarks.\n   Chapter II. Of Liberty And Necessity.\n   Chapter III. That There Is, Or May Be, A Science Of Human Nature.\n   Chapter IV. Of The Laws Of Mind.\n   Chapter V. Of Ethology, Or The Science Of The Formation Of Character.\n   Chapter VI. General Considerations On The Social Science.\n   Chapter VII. Of The Chemical, Or Experimental, Method In The Social\n   Science.\n   Chapter VIII. Of The Geometrical, Or Abstract, Method.\n   Chapter IX. Of The Physical, Or Concrete Deductive, Method.\n   Chapter X. Of The Inverse Deductive, Or Historical, Method.\n   Chapter XI. Additional Elucidations Of The Science Of History.\n   Chapter XII. Of The Logic Of Practice, Or Art; Including Morality And\n   Policy.\nFootnotes\n\n\n\n\nPREFACE TO THE FIRST EDITION.\n\n\nThis book makes no pretense of giving to the world a new theory of the\nintellectual operations. Its claim to attention, if it possess any, is\ngrounded on the fact that it is an attempt, not to supersede, but to\nembody and systematize, the best ideas which have been either promulgated\non its subject by speculative writers, or conformed to by accurate\nthinkers in their scientific inquiries.\n\nTo cement together the detached fragments of a subject, never yet treated\nas a whole; to harmonize the true portions of discordant theories, by\nsupplying the links of thought necessary to connect them, and by\ndisentangling them from the errors with which they are always more or less\ninterwoven, must necessarily require a considerable amount of original\nspeculation. To other originality than this, the present work lays no\nclaim. In the existing state of the cultivation of the sciences, there\nwould be a very strong presumption against any one who should imagine that\nhe had effected a revolution in the theory of the investigation of truth,\nor added any fundamentally new process to the practice of it. The\nimprovement which remains to be effected in the methods of philosophizing\n(and the author believes that they have much need of improvement) can only\nconsist in performing more systematically and accurately operations with\nwhich, at least in their elementary form, the human intellect, in some one\nor other of its employments, is already familiar.\n\nIn the portion of the work which treats of Ratiocination, the author has\nnot deemed it necessary to enter into technical details which may be\nobtained in so perfect a shape from the existing treatises on what is\ntermed the Logic of the Schools. In the contempt entertained by many\nmodern philosophers for the syllogistic art, it will be seen that he by no\nmeans participates; though the scientific theory on which its defense is\nusually rested appears to him erroneous: and the view which he has\nsuggested of the nature and functions of the Syllogism may, perhaps,\nafford the means of conciliating the principles of the art with as much as\nis well grounded in the doctrines and objections of its assailants.\n\nThe same abstinence from details could not be observed in the First Book,\non Names and Propositions; because many useful principles and distinctions\nwhich were contained in the old Logic have been gradually omitted from the\nwritings of its later teachers; and it appeared desirable both to revive\nthese, and to reform and rationalize the philosophical foundation on which\nthey stood. The earlier chapters of this preliminary Book will\nconsequently appear, to some readers, needlessly elementary and\nscholastic. But those who know in what darkness the nature of our\nknowledge, and of the processes by which it is obtained, is often involved\nby a confused apprehension of the import of the different classes of Words\nand Assertions, will not regard these discussions as either frivolous, or\nirrelevant to the topics considered in the later Books.\n\nOn the subject of Induction, the task to be performed was that of\ngeneralizing the modes of investigating truth and estimating evidence, by\nwhich so many important and recondite laws of nature have, in the various\nsciences, been aggregated to the stock of human knowledge. That this is\nnot a task free from difficulty may be presumed from the fact that even at\na very recent period, eminent writers (among whom it is sufficient to name\nArchbishop Whately, and the author of a celebrated article on Bacon in the\n_Edinburgh Review_) have not scrupled to pronounce it impossible.(1) The\nauthor has endeavored to combat their theory in the manner in which\nDiogenes confuted the skeptical reasonings against the possibility of\nmotion; remembering that Diogenes\u2019s argument would have been equally\nconclusive, though his individual perambulations might not have extended\nbeyond the circuit of his own tub.\n\nWhatever may be the value of what the author has succeeded in effecting on\nthis branch of his subject, it is a duty to acknowledge that for much of\nit he has been indebted to several important treatises, partly historical\nand partly philosophical, on the generalities and processes of physical\nscience, which have been published within the last few years. To these\ntreatises, and to their authors, he has endeavored to do justice in the\nbody of the work. But as with one of these writers, Dr. Whewell, he has\noccasion frequently to express differences of opinion, it is more\nparticularly incumbent on him in this place to declare, that without the\naid derived from the facts and ideas contained in that gentleman\u2019s\n\u201cHistory of the Inductive Sciences,\u201d the corresponding portion of this\nwork would probably not have been written.\n\nThe concluding Book is an attempt to contribute toward the solution of a\nquestion which the decay of old opinions, and the agitation that disturbs\nEuropean society to its inmost depths, render as important in the present\nday to the practical interests of human life, as it must at all times be\nto the completeness of our speculative knowledge\u2014viz.: Whether moral and\nsocial phenomena are really exceptions to the general certainty and\nuniformity of the course of nature; and how far the methods by which so\nmany of the laws of the physical world have been numbered among truths\nirrevocably acquired and universally assented to, can be made instrumental\nto the formation of a similar body of received doctrine in moral and\npolitical science.\n\n\n\n\nPREFACE TO THE THIRD AND FOURTH EDITIONS.\n\n\nSeveral criticisms, of a more or less controversial character, on this\nwork, have appeared since the publication of the second edition; and Dr.\nWhewell has lately published a reply to those parts of it in which some of\nhis opinions were controverted.(2)\n\nI have carefully reconsidered all the points on which my conclusions have\nbeen assailed. But I have not to announce a change of opinion on any\nmatter of importance. Such minor oversights as have been detected, either\nby myself or by my critics, I have, in general silently, corrected: but it\nis not to be inferred that I agree with the objections which have been\nmade to a passage, in every instance in which I have altered or canceled\nit. I have often done so, merely that it might not remain a\nstumbling-block, when the amount of discussion necessary to place the\nmatter in its true light would have exceeded what was suitable to the\noccasion.\n\nTo several of the arguments which have been urged against me, I have\nthought it useful to reply with some degree of minuteness; not from any\ntaste for controversy, but because the opportunity was favorable for\nplacing my own conclusions, and the grounds of them, more clearly and\ncompletely before the reader. Truth on these subjects is militant, and can\nonly establish itself by means of conflict. The most opposite opinions can\nmake a plausible show of evidence while each has the statement of its own\ncase; and it is only possible to ascertain which of them is in the right,\nafter hearing and comparing what each can say against the other, and what\nthe other can urge in its defense.\n\nEven the criticisms from which I most dissent have been of great service\nto me, by showing in what places the exposition most needed to be\nimproved, or the argument strengthened. And I should have been well\npleased if the book had undergone a much greater amount of attack; as in\nthat case I should probably have been enabled to improve it still more\nthan I believe I have now done.\n\n                  \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\nIn the subsequent editions, the attempt to improve the work by additions\nand corrections, suggested by criticism or by thought, has been continued.\nThe additions and corrections in the present (eighth) edition, which are\nnot very considerable, are chiefly such as have been suggested by\nProfessor Bain\u2019s \u201cLogic,\u201d a book of great merit and value. Mr. Bain\u2019s view\nof the science is essentially the same with that taken in the present\ntreatise, the differences of opinion being few and unimportant compared\nwith the agreements; and he has not only enriched the exposition by many\napplications and illustrative details, but has appended to it a minute and\nvery valuable discussion of the logical principles specially applicable to\neach of the sciences\u2014a task for which the encyclopedical character of his\nknowledge peculiarly qualified him. I have in several instances made use\nof his exposition to improve my own, by adopting, and occasionally by\ncontroverting, matter contained in his treatise.\n\nThe longest of the additions belongs to the chapter on Causation, and is a\ndiscussion of the question how far, if at all, the ordinary mode of\nstating the law of Cause and Effect requires modification to adapt it to\nthe new doctrine of the Conservation of Force\u2014a point still more fully and\nelaborately treated in Mr. Bain\u2019s work.\n\n\n\n\nINTRODUCTION.\n\n\n\u00a7 1. There is as great diversity among authors in the modes which they\nhave adopted of defining logic, as in their treatment of the details of\nit. This is what might naturally be expected on any subject on which\nwriters have availed themselves of the same language as a means of\ndelivering different ideas. Ethics and jurisprudence are liable to the\nremark in common with logic. Almost every writer having taken a different\nview of some of the particulars which these branches of knowledge are\nusually understood to include; each has so framed his definition as to\nindicate beforehand his own peculiar tenets, and sometimes to beg the\nquestion in their favor.\n\nThis diversity is not so much an evil to be complained of, as an\ninevitable and in some degree a proper result of the imperfect state of\nthose sciences. It is not to be expected that there should be agreement\nabout the definition of any thing, until there is agreement about the\nthing itself. To define, is to select from among all the properties of a\nthing, those which shall be understood to be designated and declared by\nits name; and the properties must be well known to us before we can be\ncompetent to determine which of them are fittest to be chosen for this\npurpose. Accordingly, in the case of so complex an aggregation of\nparticulars as are comprehended in any thing which can be called a\nscience, the definition we set out with is seldom that which a more\nextensive knowledge of the subject shows to be the most appropriate. Until\nwe know the particulars themselves, we can not fix upon the most correct\nand compact mode of circumscribing them by a general description. It was\nnot until after an extensive and accurate acquaintance with the details of\nchemical phenomena, that it was found possible to frame a rational\ndefinition of chemistry; and the definition of the science of life and\norganization is still a matter of dispute. So long as the sciences are\nimperfect, the definitions must partake of their imperfection; and if the\nformer are progressive, the latter ought to be so too. As much, therefore,\nas is to be expected from a definition placed at the commencement of a\nsubject, is that it should define the scope of our inquiries: and the\ndefinition which I am about to offer of the science of logic, pretends to\nnothing more than to be a statement of the question which I have put to\nmyself, and which this book is an attempt to resolve. The reader is at\nliberty to object to it as a definition of logic; but it is at all events\na correct definition of the subject of this volume.\n\n\u00a7 2. Logic has often been called the Art of Reasoning. A writer(3) who has\ndone more than any other person to restore this study to the rank from\nwhich it had fallen in the estimation of the cultivated class in our own\ncountry, has adopted the above definition with an amendment; he has\ndefined Logic to be the Science, as well as the Art, of reasoning; meaning\nby the former term, the analysis of the mental process which takes place\nwhenever we reason, and by the latter, the rules, grounded on that\nanalysis, for conducting the process correctly. There can be no doubt as\nto the propriety of the emendation. A right understanding of the mental\nprocess itself, of the conditions it depends on, and the steps of which it\nconsists, is the only basis on which a system of rules, fitted for the\ndirection of the process, can possibly be founded. Art necessarily\npresupposes knowledge; art, in any but its infant state, presupposes\nscientific knowledge: and if every art does not bear the name of a\nscience, it is only because several sciences are often necessary to form\nthe groundwork of a single art. So complicated are the conditions which\ngovern our practical agency, that to enable one thing to be _done_, it is\noften requisite to _know_ the nature and properties of many things.\n\nLogic, then, comprises the science of reasoning, as well as an art,\nfounded on that science. But the word Reasoning, again, like most other\nscientific terms in popular use, abounds in ambiguities. In one of its\nacceptations, it means syllogizing; or the mode of inference which may be\ncalled (with sufficient accuracy for the present purpose) concluding from\ngenerals to particulars. In another of its senses, to reason is simply to\ninfer any assertion, from assertions already admitted: and in this sense\ninduction is as much entitled to be called reasoning as the demonstrations\nof geometry.\n\nWriters on logic have generally preferred the former acceptation of the\nterm: the latter, and more extensive signification is that in which I mean\nto use it. I do this by virtue of the right I claim for every author, to\ngive whatever provisional definition he pleases of his own subject. But\nsufficient reasons will, I believe, unfold themselves as we advance, why\nthis should be not only the provisional but the final definition. It\ninvolves, at all events, no arbitrary change in the meaning of the word;\nfor, with the general usage of the English language, the wider\nsignification, I believe, accords better than the more restricted one.\n\n\u00a7 3. But reasoning, even in the widest sense of which the word is\nsusceptible, does not seem to comprehend all that is included, either in\nthe best, or even in the most current, conception of the scope and\nprovince of our science. The employment of the word Logic to denote the\ntheory of Argumentation, is derived from the Aristotelian, or, as they are\ncommonly termed, the scholastic, logicians. Yet even with them, in their\nsystematic treatises, Argumentation was the subject only of the third\npart: the two former treated of Terms, and of Propositions; under one or\nother of which heads were also included Definition and Division. By some,\nindeed, these previous topics were professedly introduced only on account\nof their connection with reasoning, and as a preparation for the doctrine\nand rules of the syllogism. Yet they were treated with greater minuteness,\nand dwelt on at greater length, than was required for that purpose alone.\nMore recent writers on logic have generally understood the term as it was\nemployed by the able author of the Port Royal Logic; viz., as equivalent\nto the Art of Thinking. Nor is this acceptation confined to books, and\nscientific inquiries. Even in ordinary conversation, the ideas connected\nwith the word Logic include at least precision of language, and accuracy\nof classification: and we perhaps oftener hear persons speak of a logical\narrangement, or of expressions logically defined, than of conclusions\nlogically deduced from premises. Again, a man is often called a great\nlogician, or a man of powerful logic, not for the accuracy of his\ndeductions, but for the extent of his command over premises; because the\ngeneral propositions required for explaining a difficulty or refuting a\nsophism, copiously and promptly occur to him: because, in short, his\nknowledge, besides being ample, is well under his command for\nargumentative use. Whether, therefore, we conform to the practice of those\nwho have made the subject their particular study, or to that of popular\nwriters and common discourse, the province of logic will include several\noperations of the intellect not usually considered to fall within the\nmeaning of the terms Reasoning and Argumentation.\n\nThese various operations might be brought within the compass of the\nscience, and the additional advantage be obtained of a very simple\ndefinition, if, by an extension of the term, sanctioned by high\nauthorities, we were to define logic as the science which treats of the\noperations of the human understanding in the pursuit of truth. For to this\nultimate end, naming, classification, definition, and all other operations\nover which logic has ever claimed jurisdiction, are essentially\nsubsidiary. They may all be regarded as contrivances for enabling a person\nto know the truths which are needful to him, and to know them at the\nprecise moment at which they are needful. Other purposes, indeed, are also\nserved by these operations; for instance, that of imparting our knowledge\nto others. But, viewed with regard to this purpose, they have never been\nconsidered as within the province of the logician. The sole object of\nLogic is the guidance of one\u2019s own thoughts: the communication of those\nthoughts to others falls under the consideration of Rhetoric, in the large\nsense in which that art was conceived by the ancients; or of the still\nmore extensive art of Education. Logic takes cognizance of our\nintellectual operations only as they conduce to our own knowledge, and to\nour command over that knowledge for our own uses. If there were but one\nrational being in the universe, that being might be a perfect logician;\nand the science and art of logic would be the same for that one person as\nfor the whole human race.\n\n\u00a7 4. But, if the definition which we formerly examined included too\nlittle, that which is now suggested has the opposite fault of including\ntoo much.\n\nTruths are known to us in two ways: some are known directly, and of\nthemselves; some through the medium of other truths. The former are the\nsubject of Intuition, or Consciousness;(4) the latter, of Inference. The\ntruths known by intuition are the original premises from which all others\nare inferred. Our assent to the conclusion being grounded on the truth of\nthe premises, we never could arrive at any knowledge by reasoning, unless\nsomething could be known antecedently to all reasoning.\n\nExamples of truths known to us by immediate consciousness, are our own\nbodily sensations and mental feelings. I know directly, and of my own\nknowledge, that I was vexed yesterday, or that I am hungry to-day.\nExamples of truths which we know only by way of inference, are occurrences\nwhich took place while we were absent, the events recorded in history, or\nthe theorems of mathematics. The two former we infer from the testimony\nadduced, or from the traces of those past occurrences which still exist;\nthe latter, from the premises laid down in books of geometry, under the\ntitle of definitions and axioms. Whatever we are capable of knowing must\nbelong to the one class or to the other; must be in the number of the\nprimitive data, or of the conclusions which can be drawn from these.\n\nWith the original data, or ultimate premises of our knowledge; with their\nnumber or nature, the mode in which they are obtained, or the tests by\nwhich they may be distinguished; logic, in a direct way at least, has, in\nthe sense in which I conceive the science, nothing to do. These questions\nare partly not a subject of science at all, partly that of a very\ndifferent science.\n\nWhatever is known to us by consciousness is known beyond possibility of\nquestion. What one sees or feels, whether bodily or mentally, one can not\nbut be sure that one sees or feels. No science is required for the purpose\nof establishing such truths; no rules of art can render our knowledge of\nthem more certain than it is in itself. There is no logic for this portion\nof our knowledge.\n\nBut we may fancy that we see or feel what we in reality infer. A truth, or\nsupposed truth, which is really the result of a very rapid inference, may\nseem to be apprehended intuitively. It has long been agreed by thinkers of\nthe most opposite schools, that this mistake is actually made in so\nfamiliar an instance as that of the eyesight. There is nothing of which we\nappear to ourselves to be more directly conscious than the distance of an\nobject from us. Yet it has long been ascertained, that what is perceived\nby the eye, is at most nothing more than a variously colored surface; that\nwhen we fancy we see distance, all we really see is certain variations of\napparent size, and degrees of faintness of color; that our estimate of the\nobject\u2019s distance from us is the result partly of a rapid inference from\nthe muscular sensations accompanying the adjustment of the focal distance\nof the eye to objects unequally remote from us, and partly of a comparison\n(made with so much rapidity that we are unconscious of making it) between\nthe size and color of the object as they appear at the time, and the size\nand color of the same or of similar objects as they appeared when close at\nhand, or when their degree of remoteness was known by other evidence. The\nperception of distance by the eye, which seems so like intuition, is thus,\nin reality, an inference grounded on experience; an inference, too, which\nwe learn to make; and which we make with more and more correctness as our\nexperience increases; though in familiar cases it takes place so rapidly\nas to appear exactly on a par with those perceptions of sight which are\nreally intuitive, our perceptions of color.(5)\n\nOf the science, therefore, which expounds the operations of the human\nunderstanding in the pursuit of truth, one essential part is the inquiry:\nWhat are the facts which are the objects of intuition or consciousness,\nand what are those which we merely infer? But this inquiry has never been\nconsidered a portion of logic. Its place is in another and a perfectly\ndistinct department of science, to which the name metaphysics more\nparticularly belongs: that portion of mental philosophy which attempts to\ndetermine what part of the furniture of the mind belongs to it originally,\nand what part is constructed out of materials furnished to it from\nwithout. To this science appertain the great and much debated questions of\nthe existence of matter; the existence of spirit, and of a distinction\nbetween it and matter; the reality of time and space, as things without\nthe mind, and distinguishable from the objects which are said to exist in\nthem. For in the present state of the discussion on these topics, it is\nalmost universally allowed that the existence of matter or of spirit, of\nspace or of time, is in its nature unsusceptible of being proved; and that\nif any thing is known of them, it must be by immediate intuition. To the\nsame science belong the inquiries into the nature of Conception,\nPerception, Memory, and Belief; all of which are operations of the\nunderstanding in the pursuit of truth; but with which, as phenomena of the\nmind, or with the possibility which may or may not exist of analyzing any\nof them into simpler phenomena, the logician as such has no concern. To\nthis science must also be referred the following, and all analogous\nquestions: To what extent our intellectual faculties and our emotions are\ninnate\u2014to what extent the result of association: Whether God and duty are\nrealities, the existence of which is manifest to us _a priori_ by the\nconstitution of our rational faculty; or whether our ideas of them are\nacquired notions, the origin of which we are able to trace and explain;\nand the reality of the objects themselves a question not of consciousness\nor intuition, but of evidence and reasoning.\n\nThe province of logic must be restricted to that portion of our knowledge\nwhich consists of inferences from truths previously known; whether those\nantecedent data be general propositions, or particular observations and\nperceptions. Logic is not the science of Belief, but the science of Proof,\nor Evidence. In so far as belief professes to be founded on proof, the\noffice of logic is to supply a test for ascertaining whether or not the\nbelief is well grounded. With the claims which any proposition has to\nbelief on the evidence of consciousness\u2014that is, without evidence in the\nproper sense of the word\u2014logic has nothing to do.\n\n\u00a7 5. By far the greatest portion of our knowledge, whether of general\ntruths or of particular facts, being avowedly matter of inference, nearly\nthe whole, not only of science, but of human conduct, is amenable to the\nauthority of logic. To draw inferences has been said to be the great\nbusiness of life. Every one has daily, hourly, and momentary need of\nascertaining facts which he has not directly observed; not from any\ngeneral purpose of adding to his stock of knowledge, but because the facts\nthemselves are of importance to his interests or to his occupations. The\nbusiness of the magistrate, of the military commander, of the navigator,\nof the physician, of the agriculturist, is merely to judge of evidence,\nand to act accordingly. They all have to ascertain certain facts, in order\nthat they may afterward apply certain rules, either devised by themselves\nor prescribed for their guidance by others; and as they do this well or\nill, so they discharge well or ill the duties of their several callings.\nIt is the only occupation in which the mind never ceases to be engaged;\nand is the subject, not of logic, but of knowledge in general.\n\nLogic, however, is not the same thing with knowledge, though the field of\nlogic is co-extensive with the field of knowledge. Logic is the common\njudge and arbiter of all particular investigations. It does not undertake\nto find evidence, but to determine whether it has been found. Logic\nneither observes, nor invents, nor discovers; but judges. It is no part of\nthe business of logic to inform the surgeon what appearances are found to\naccompany a violent death. This he must learn from his own experience and\nobservation, or from that of others, his predecessors in his peculiar\npursuit. But logic sits in judgment on the sufficiency of that observation\nand experience to justify his rules, and on the sufficiency of his rules\nto justify his conduct. It does not give him proofs, but teaches him what\nmakes them proofs, and how he is to judge of them. It does not teach that\nany particular fact proves any other, but points out to what conditions\nall facts must conform, in order that they may prove other facts. To\ndecide whether any given fact fulfills these conditions, or whether facts\ncan be found which fulfill them in a given case, belongs exclusively to\nthe particular art or science, or to our knowledge of the particular\nsubject.\n\nIt is in this sense that logic is, what it was so expressively called by\nthe schoolmen and by Bacon, _ars artium_; the science of science itself.\nAll science consists of data and conclusions from those data, of proofs\nand what they prove: now logic points out what relations must subsist\nbetween data and whatever can be concluded from them, between proof and\nevery thing which it can prove. If there be any such indispensable\nrelations, and if these can be precisely determined, every particular\nbranch of science, as well as every individual in the guidance of his\nconduct, is bound to conform to those relations, under the penalty of\nmaking false inferences\u2014of drawing conclusions which are not grounded in\nthe realities of things. Whatever has at any time been concluded justly,\nwhatever knowledge has been acquired otherwise than by immediate\nintuition, depended on the observance of the laws which it is the province\nof logic to investigate. If the conclusions are just, and the knowledge\nreal, those laws, whether known or not, have been observed.\n\n\u00a7 6. We need not, therefore, seek any further for a solution of the\nquestion, so often agitated, respecting the utility of logic. If a science\nof logic exists, or is capable of existing, it must be useful. If there be\nrules to which every mind consciously or unconsciously conforms in every\ninstance in which it infers rightly, there seems little necessity for\ndiscussing whether a person is more likely to observe those rules, when he\nknows the rules, than when he is unacquainted with them.\n\nA science may undoubtedly be brought to a certain, not inconsiderable,\nstage of advancement, without the application of any other logic to it\nthan what all persons, who are said to have a sound understanding, acquire\nempirically in the course of their studies. Mankind judged of evidence,\nand often correctly, before logic was a science, or they never could have\nmade it one. And they executed great mechanical works before they\nunderstood the laws of mechanics. But there are limits both to what\nmechanicians can do without principles of mechanics, and to what thinkers\ncan do without principles of logic. A few individuals, by extraordinary\ngenius, or by the accidental acquisition of a good set of intellectual\nhabits, may work without principles in the same way, or nearly the same\nway, in which they would have worked if they had been in possession of\nprinciples. But the bulk of mankind require either to understand the\ntheory of what they are doing, or to have rules laid down for them by\nthose who have understood the theory. In the progress of science from its\neasiest to its more difficult problems, each great step in advance has\nusually had either as its precursor, or as its accompaniment and necessary\ncondition, a corresponding improvement in the notions and principles of\nlogic received among the most advanced thinkers. And if several of the\nmore difficult sciences are still in so defective a state; if not only so\nlittle is proved, but disputation has not terminated even about the little\nwhich seemed to be so; the reason perhaps is, that men\u2019s logical notions\nhave not yet acquired the degree of extension, or of accuracy, requisite\nfor the estimation of the evidence proper to those particular departments\nof knowledge.\n\n\u00a7 7. Logic, then, is the science of the operations of the understanding\nwhich are subservient to the estimation of evidence: both the process\nitself of advancing from known truths to unknown, and all other\nintellectual operations in so far as auxiliary to this. It includes,\ntherefore, the operation of Naming; for language is an instrument of\nthought, as well as a means of communicating our thoughts. It includes,\nalso, Definition, and Classification. For, the use of these operations\n(putting all other minds than one\u2019s own out of consideration) is to serve\nnot only for keeping our evidences and the conclusions from them permanent\nand readily accessible in the memory, but for so marshaling the facts\nwhich we may at any time be engaged in investigating, as to enable us to\nperceive more clearly what evidence there is, and to judge with fewer\nchances of error whether it be sufficient. These, therefore, are\noperations specially instrumental to the estimation of evidence, and, as\nsuch, are within the province of Logic. There are other more elementary\nprocesses, concerned in all thinking, such as Conception, Memory, and the\nlike; but of these it is not necessary that Logic should take any peculiar\ncognizance, since they have no special connection with the problem of\nEvidence, further than that, like all other problems addressed to the\nunderstanding, it presupposes them.\n\nOur object, then, will be, to attempt a correct analysis of the\nintellectual process called Reasoning or Inference, and of such other\nmental operations as are intended to facilitate this: as well as, on the\nfoundation of this analysis, and _pari passu_ with it, to bring together\nor frame a set of rules or canons for testing the sufficiency of any given\nevidence to prove any given proposition.\n\nWith respect to the first part of this undertaking, I do not attempt to\ndecompose the mental operations in question into their ultimate elements.\nIt is enough if the analysis as far as it goes is correct, and if it goes\nfar enough for the practical purposes of logic considered as an art. The\nseparation of a complicated phenomenon into its component parts is not\nlike a connected and interdependent chain of proof. If one link of an\nargument breaks, the whole drops to the ground; but one step toward an\nanalysis holds good and has an independent value, though we should never\nbe able to make a second. The results which have been obtained by\nanalytical chemistry are not the less valuable, though it should be\ndiscovered that all which we now call simple substances are really\ncompounds. All other things are at any rate compounded of those elements:\nwhether the elements themselves admit of decomposition, is an important\ninquiry, but does not affect the certainty of the science up to that\npoint.\n\nI shall, accordingly, attempt to analyze the process of inference, and the\nprocesses subordinate to inference, so far only as may be requisite for\nascertaining the difference between a correct and an incorrect performance\nof those processes. The reason for thus limiting our design, is evident.\nIt has been said by objectors to logic, that we do not learn to use our\nmuscles by studying their anatomy. The fact is not quite fairly stated;\nfor if the action of any of our muscles were vitiated by local weakness,\nor other physical defect, a knowledge of their anatomy might be very\nnecessary for effecting a cure. But we should be justly liable to the\ncriticism involved in this objection, were we, in a treatise on logic, to\ncarry the analysis of the reasoning process beyond the point at which any\ninaccuracy which may have crept into it must become visible. In learning\nbodily exercises (to carry on the same illustration) we do, and must,\nanalyze the bodily motions so far as is necessary for distinguishing those\nwhich ought to be performed from those which ought not. To a similar\nextent, and no further, it is necessary that the logician should analyze\nthe mental processes with which Logic is concerned. Logic has no interest\nin carrying the analysis beyond the point at which it becomes apparent\nwhether the operations have in any individual case been rightly or wrongly\nperformed: in the same manner as the science of music teaches us to\ndiscriminate between musical notes, and to know the combinations of which\nthey are susceptible, but not what number of vibrations in a second\ncorrespond to each; which, though useful to be known, is useful for\ntotally different purposes. The extension of Logic as a Science is\ndetermined by its necessities as an Art: whatever it does not need for its\npractical ends, it leaves to the larger science which may be said to\ncorrespond, not to any particular art, but to art in general; the science\nwhich deals with the constitution of the human faculties; and to which, in\nthe part of our mental nature which concerns Logic, as well as in all\nother parts, it belongs to decide what are ultimate facts, and what are\nresolvable into other facts. And I believe it will be found that most of\nthe conclusions arrived at in this work have no necessary connection with\nany particular views respecting the ulterior analysis. Logic is common\nground on which the partisans of Hartley and of Reid, of Locke and of\nKant, may meet and join hands. Particular and detached opinions of all\nthese thinkers will no doubt occasionally be controverted, since all of\nthem were logicians as well as metaphysicians; but the field on which\ntheir principal battles have been fought, lies beyond the boundaries of\nour science.\n\nIt can not, indeed, be pretended that logical principles can be altogether\nirrelevant to those more abstruse discussions; nor is it possible but that\nthe view we are led to take of the problem which logic proposes, must have\na tendency favorable to the adoption of some one opinion, on these\ncontroverted subjects, rather than another. For metaphysics, in\nendeavoring to solve its own peculiar problem, must employ means, the\nvalidity of which falls under the cognizance of logic. It proceeds, no\ndoubt, as far as possible, merely by a closer and more attentive\ninterrogation of our consciousness, or more properly speaking, of our\nmemory; and so far is not amenable to logic. But wherever this method is\ninsufficient to attain the end of its inquiries, it must proceed, like\nother sciences, by means of evidence. Now, the moment this science begins\nto draw inferences from evidence, logic becomes the sovereign judge\nwhether its inferences are well grounded, or what other inferences would\nbe so.\n\nThis, however, constitutes no nearer or other relation between logic and\nmetaphysics, than that which exists between logic and every other science.\nAnd I can conscientiously affirm that no one proposition laid down in this\nwork has been adopted for the sake of establishing, or with any reference\nto its fitness for being employed in establishing, preconceived opinions\nin any department of knowledge or of inquiry on which the speculative\nworld is still undecided.(6)\n\n\n\n\n                                 Book I.\n\n\nOF NAMES AND PROPOSITIONS.\n\n\n\u201cLa scolastique, qui produisit dans la logique, comme dans la morale, et\ndans une partie de la m\u00e9taphysique, une subtilit\u00e9, une pr\u00e9cision d\u2019id\u00e9es,\ndont l\u2019habitude inconnue aux anciens, a contribu\u00e9 plus qu\u2019on ne croit au\nprogr\u00e8s de la bonne philosophie.\u201d\u2014CONDORCET, _Vie de Turgot_.\n\n\u201cTo the schoolmen the vulgar languages are principally indebted for what\nprecision and analytic subtlety they possess.\u201d\u2014SIR W. HAMILTON,\n_Discussions in Philosophy_.\n\n\n\n\n                                Chapter I.\n\n\nOf The Necessity Of Commencing With An Analysis Of Language.\n\n\n\u00a7 1. It is so much the established practice of writers on logic to\ncommence their treatises by a few general observations (in most cases, it\nis true, rather meagre) on Terms and their varieties, that it will,\nperhaps, scarcely be required from me, in merely following the common\nusage, to be as particular in assigning my reasons, as it is usually\nexpected that those should be who deviate from it.\n\nThe practice, indeed, is recommended by considerations far too obvious to\nrequire a formal justification. Logic is a portion of the Art of Thinking:\nLanguage is evidently, and by the admission of all philosophers, one of\nthe principal instruments or helps of thought; and any imperfection in the\ninstrument, or in the mode of employing it, is confessedly liable, still\nmore than in almost any other art, to confuse and impede the process, and\ndestroy all ground of confidence in the result. For a mind not previously\nversed in the meaning and right use of the various kinds of words, to\nattempt the study of methods of philosophizing, would be as if some one\nshould attempt to become an astronomical observer, having never learned to\nadjust the focal distance of his optical instruments so as to see\ndistinctly.\n\nSince Reasoning, or Inference, the principal subject of logic, is an\noperation which usually takes place by means of words, and in complicated\ncases can take place in no other way; those who have not a thorough\ninsight into the signification and purposes of words, will be under\nchances, amounting almost to certainty, of reasoning or inferring\nincorrectly. And logicians have generally felt that unless, in the very\nfirst stage, they removed this source of error; unless they taught their\npupil to put away the glasses which distort the object, and to use those\nwhich are adapted to his purpose in such a manner as to assist, not\nperplex, his vision; he would not be in a condition to practice the\nremaining part of their discipline with any prospect of advantage.\nTherefore it is that an inquiry into language, so far as is needful to\nguard against the errors to which it gives rise, has at all times been\ndeemed a necessary preliminary to the study of logic.\n\nBut there is another reason, of a still more fundamental nature, why the\nimport of words should be the earliest subject of the logician\u2019s\nconsideration: because without it he can not examine into the import of\nPropositions. Now this is a subject which stands on the very threshold of\nthe science of logic.\n\nThe object of logic, as defined in the Introductory Chapter, is to\nascertain how we come by that portion of our knowledge (much the greatest\nportion) which is not intuitive: and by what criterion we can, in matters\nnot self-evident, distinguish between things proved and things not proved,\nbetween what is worthy and what is unworthy of belief. Of the various\nquestions which present themselves to our inquiring faculties, some\nreceive an answer from direct consciousness, others, if resolved at all,\ncan only be resolved by means of evidence. Logic is concerned with these\nlast. But before inquiring into the mode of resolving questions, it is\nnecessary to inquire what are those which offer themselves; what questions\nare conceivable; what inquiries are there, to which mankind have either\nobtained, or been able to imagine it possible that they should obtain, an\nanswer. This point is best ascertained by a survey and analysis of\nPropositions.\n\n\u00a7 2. The answer to every question which it is possible to frame, must be\ncontained in a Proposition, or Assertion. Whatever can be an object of\nbelief, or even of disbelief, must, when put into words, assume the form\nof a proposition. All truth and all error lie in propositions. What, by a\nconvenient misapplication of an abstract term, we call a Truth, means\nsimply a True Proposition; and errors are false propositions. To know the\nimport of all possible propositions would be to know all questions which\ncan be raised, all matters which are susceptible of being either believed\nor disbelieved. How many kinds of inquiries can be propounded; how many\nkinds of judgments can be made; and how many kinds of propositions it is\npossible to frame with a meaning, are but different forms of one and the\nsame question. Since, then, the objects of all Belief and of all Inquiry\nexpress themselves in propositions, a sufficient scrutiny of Propositions\nand of their varieties will apprise us what questions mankind have\nactually asked of themselves, and what, in the nature of answers to those\nquestions, they have actually thought they had grounds to believe.\n\nNow the first glance at a proposition shows that it is formed by putting\ntogether two names. A proposition, according to the common simple\ndefinition, which is sufficient for our purpose is, _discourse, in which\nsomething is affirmed or denied of something_. Thus, in the proposition,\nGold is yellow, the quality yellow is affirmed of the substance _gold_. In\nthe proposition, Franklin was not born in England, the fact expressed by\nthe words _born in England_ is denied of the man Franklin.\n\nEvery proposition consists of three parts: the Subject, the Predicate, and\nthe Copula. The predicate is the name denoting that which is affirmed or\ndenied. The subject is the name denoting the person or thing which\nsomething is affirmed or denied of. The copula is the sign denoting that\nthere is an affirmation or denial, and thereby enabling the hearer or\nreader to distinguish a proposition from any other kind of discourse.\nThus, in the proposition, The earth is round, the Predicate is the word\n_round_, which denotes the quality affirmed, or (as the phrase is)\npredicated: _the earth_, words denoting the object which that quality is\naffirmed of, compose the Subject; the word _is_, which serves as the\nconnecting mark between the subject and predicate, to show that one of\nthem is affirmed of the other, is called the Copula.\n\nDismissing, for the present, the copula, of which more will be said\nhereafter, every proposition, then, consists of at least two names\u2014brings\ntogether two names, in a particular manner. This is already a first step\ntoward what we are in quest of. It appears from this, that for an act of\nbelief, _one_ object is not sufficient; the simplest act of belief\nsupposes, and has something to do with, _two_ objects\u2014two names, to say\nthe least; and (since the names must be names of something) two _namable\nthings_. A large class of thinkers would cut the matter short by saying,\ntwo _ideas_. They would say, that the subject and predicate are both of\nthem names of ideas; the idea of gold, for instance, and the idea of\nyellow; and that what takes place (or part of what takes place) in the act\nof belief consists in bringing (as it is often expressed) one of these\nideas under the other. But this we are not yet in a condition to say:\nwhether such be the correct mode of describing the phenomenon, is an after\nconsideration. The result with which for the present we must be contented,\nis, that in every act of belief _two_ objects are in some manner taken\ncognizance of; that there can be no belief claimed, or question\npropounded, which does not embrace two distinct (either material or\nintellectual) subjects of thought; each of them capable, or not, of being\nconceived by itself, but incapable of being believed by itself.\n\nI may say, for instance, \u201cthe sun.\u201d The word has a meaning, and suggests\nthat meaning to the mind of any one who is listening to me. But suppose I\nask him, Whether it is true: whether he believes it? He can give no\nanswer. There is as yet nothing to believe, or to disbelieve. Now,\nhowever, let me make, of all possible assertions respecting the sun, the\none which involves the least of reference to any object besides itself;\nlet me say, \u201cthe sun exists.\u201d Here, at once, is something which a person\ncan say he believes. But here, instead of only one, we find two distinct\nobjects of conception: the sun is one object; existence is another. Let it\nnot be said that this second conception, existence, is involved in the\nfirst; for the sun may be conceived as no longer existing. \u201cThe sun\u201d does\nnot convey all the meaning that is conveyed by \u201cthe sun exists:\u201d \u201cmy\nfather\u201d does not include all the meaning of \u201cmy father exists,\u201d for he may\nbe dead; \u201ca round square\u201d does not include the meaning of \u201ca round square\nexists,\u201d for it does not and can not exist. When I say \u201cthe sun,\u201d \u201cmy\nfather,\u201d or a \u201cround square,\u201d I do not call upon the hearer for any belief\nor disbelief, nor can either the one or the other be afforded me; but if I\nsay, \u201cthe sun exists,\u201d \u201cmy father exists,\u201d or \u201ca round square exists,\u201d I\ncall for belief; and should, in the first of the three instances, meet\nwith it; in the second, with belief or disbelief, as the case might be; in\nthe third, with disbelief.\n\n\u00a7 3. This first step in the analysis of the object of belief, which,\nthough so obvious, will be found to be not unimportant, is the only one\nwhich we shall find it practicable to make without a preliminary survey of\nlanguage. If we attempt to proceed further in the same path, that is, to\nanalyze any further the import of Propositions; we find forced upon us, as\na subject of previous consideration, the import of Names. For every\nproposition consists of two names; and every proposition affirms or denies\none of these names, of the other. Now what we do, what passes in our mind,\nwhen we affirm or deny two names of one another, must depend on what they\nare names of; since it is with reference to that, and not to the mere\nnames themselves, that we make the affirmation or denial. Here, therefore,\nwe find a new reason why the signification of names, and the relation\ngenerally between names and the things signified by them, must occupy the\npreliminary stage of the inquiry we are engaged in.\n\nIt may be objected that the meaning of names can guide us at most only to\nthe opinions, possibly the foolish and groundless opinions, which mankind\nhave formed concerning things, and that as the object of philosophy is\ntruth, not opinion, the philosopher should dismiss words and look into\nthings themselves, to ascertain what questions can be asked and answered\nin regard to them. This advice (which no one has it in his power to\nfollow) is in reality an exhortation to discard the whole fruits of the\nlabors of his predecessors, and conduct himself as if he were the first\nperson who had ever turned an inquiring eye upon nature. What does any\none\u2019s personal knowledge of Things amount to, after subtracting all which\nhe has acquired by means of the words of other people? Even after he has\nlearned as much as people usually do learn from others, will the notions\nof things contained in his individual mind afford as sufficient a basis\nfor a _catalogue raisonn\u00e9_ as the notions which are in the minds of all\nmankind?\n\nIn any enumeration and classification of Things, which does not set out\nfrom their names, no varieties of things will of course be comprehended\nbut those recognized by the particular inquirer; and it will still remain\nto be established, by a subsequent examination of names, that the\nenumeration has omitted nothing which ought to have been included. But if\nwe begin with names, and use them as our clue to the things, we bring at\nonce before us all the distinctions which have been recognized, not by a\nsingle inquirer, but by all inquirers taken together. It doubtless may,\nand I believe it will, be found, that mankind have multiplied the\nvarieties unnecessarily, and have imagined distinctions among things,\nwhere there were only distinctions in the manner of naming them. But we\nare not entitled to assume this in the commencement. We must begin by\nrecognizing the distinctions made by ordinary language. If some of these\nappear, on a close examination, not to be fundamental, the enumeration of\nthe different kinds of realities may be abridged accordingly. But to\nimpose upon the facts in the first instance the yoke of a theory, while\nthe grounds of the theory are reserved for discussion in a subsequent\nstage, is not a course which a logician can reasonably adopt.\n\n\n\n\n                               Chapter II.\n\n\nOf Names.\n\n\n\u00a7 1. \u201cA name,\u201d says Hobbes,(7) \u201cis a word taken at pleasure to serve for a\nmark which may raise in our mind a thought like to some thought we had\nbefore, and which being pronounced to others, may be to them a sign of\nwhat thought the speaker had(8) before in his mind.\u201d This simple\ndefinition of a name, as a word (or set of words) serving the double\npurpose of a mark to recall to ourselves the likeness of a former thought,\nand a sign to make it known to others, appears unexceptionable. Names,\nindeed, do much more than this; but whatever else they do, grows out of,\nand is the result of this: as will appear in its proper place.\n\nAre names more properly said to be the names of things, or of our ideas of\nthings? The first is the expression in common use; the last is that of\nsome metaphysicians, who conceived that in adopting it they were\nintroducing a highly important distinction. The eminent thinker, just\nquoted, seems to countenance the latter opinion. \u201cBut seeing,\u201d he\ncontinues, \u201cnames ordered in speech (as is defined) are signs of our\nconceptions, it is manifest they are not signs of the things themselves;\nfor that the sound of this word _stone_ should be the sign of a stone, can\nnot be understood in any sense but this, that he that hears it collects\nthat he that pronounces it thinks of a stone.\u201d\n\nIf it be merely meant that the conception alone, and not the thing itself,\nis recalled by the name, or imparted to the hearer, this of course can not\nbe denied. Nevertheless, there seems good reason for adhering to the\ncommon usage, and calling (as indeed Hobbes himself does in other places)\nthe word _sun_ the name of the sun, and not the name of our idea of the\nsun. For names are not intended only to make the hearer conceive what we\nconceive, but also to inform him what we believe. Now, when I use a name\nfor the purpose of expressing a belief, it is a belief concerning the\nthing itself, not concerning my idea of it. When I say, \u201cthe sun is the\ncause of day,\u201d I do not mean that my idea of the sun causes or excites in\nme the idea of day; or in other words, that thinking of the sun makes me\nthink of day. I mean, that a certain physical fact, which is called the\nsun\u2019s presence (and which, in the ultimate analysis, resolves itself into\nsensations, not ideas) causes another physical fact, which is called day.\nIt seems proper to consider a word as the _name_ of that which we intend\nto be understood by it when we use it; of that which any fact that we\nassert of it is to be understood of; that, in short, concerning which,\nwhen we employ the word, we intend to give information. Names, therefore,\nshall always be spoken of in this work as the names of things themselves,\nand not merely of our ideas of things.\n\nBut the question now arises, of what things? and to answer this it is\nnecessary to take into consideration the different kinds of names.\n\n\u00a7 2. It is usual, before examining the various classes into which names\nare commonly divided, to begin by distinguishing from names of every\ndescription, those words which are not names, but only parts of names.\nAmong such are reckoned particles, as _of_, _to_, _truly_, _often_; the\ninflected cases of nouns substantive, as _me_, _him_, _John\u2019s_; and even\nadjectives, as _large_, _heavy_. These words do not express things of\nwhich any thing can be affirmed or denied. We can not say, Heavy fell, or\nA heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the\nroom. Unless, indeed, we are speaking of the mere words themselves, as\nwhen we say, Truly is an English word, or, Heavy is an adjective. In that\ncase they are complete names\u2014viz., names of those particular sounds, or of\nthose particular collections of written characters. This employment of a\nword to denote the mere letters and syllables of which it is composed, was\ntermed by the schoolmen the _suppositio materialis_ of the word. In any\nother sense we can not introduce one of these words into the subject of a\nproposition, unless in combination with other words; as, A heavy _body_\nfell, A truly _important fact_ was asserted, A _member_ of _parliament_\nwas in the room.\n\nAn adjective, however, is capable of standing by itself as the predicate\nof a proposition; as when we say, Snow is white; and occasionally even as\nthe subject, for we may say, White is an agreeable color. The adjective is\noften said to be so used by a grammatical ellipsis: Snow is white, instead\nof Snow is a white object; White is an agreeable color, instead of, A\nwhite color, or, The color white, is agreeable. The Greeks and Romans were\nallowed, by the rules of their language, to employ this ellipsis\nuniversally in the subject as well as in the predicate of a proposition.\nIn English this can not, generally speaking, be done. We may say, The\nearth is round; but we can not say, Round is easily moved; we must say, A\nround object. This distinction, however, is rather grammatical than\nlogical. Since there is no difference of meaning between _round_, and _a\nround object_, it is only custom which prescribes that on any given\noccasion one shall be used, and not the other. We shall, therefore,\nwithout scruple, speak of adjectives as names, whether in their own right,\nor as representative of the more circuitous forms of expression above\nexemplified. The other classes of subsidiary words have no title whatever\nto be considered as names. An adverb, or an accusative case, can not under\nany circumstances (except when their mere letters and syllables are spoken\nof) figure as one of the terms of a proposition.\n\nWords which are not capable of being used as names, but only as parts of\nnames, were called by some of the schoolmen Syncategorematic terms: from\n\u03c3\u1f7a\u03bd, with, and \u03ba\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03ad\u03c9, to predicate, because it was only _with_ some\nother word that they could be predicated. A word which could be used\neither as the subject or predicate of a proposition without being\naccompanied by any other word, was termed by the same authorities a\nCategorematic term. A combination of one or more Categorematic, and one or\nmore Syncategorematic words, as A heavy body, or A court of justice, they\nsometimes called a _mixed_ term; but this seems a needless multiplication\nof technical expressions. A mixed term is, in the only useful sense of the\nword, Categorematic. It belongs to the class of what have been called\nmany-worded names.\n\nFor, as one word is frequently not a name, but only part of a name, so a\nnumber of words often compose one single name, and no more. These words,\n\u201cThe place which the wisdom or policy of antiquity had destined for the\nresidence of the Abyssinian princes,\u201d form in the estimation of the\nlogician only one name; one Categorematic term. A mode of determining\nwhether any set of words makes only one name, or more than one, is by\npredicating something of it, and observing whether, by this predication,\nwe make only one assertion or several. Thus, when we say, John Nokes, who\nwas the mayor of the town, died yesterday\u2014by this predication we make but\none assertion; whence it appears that \u201cJohn Nokes, who was the mayor of\nthe town,\u201d is no more than one name. It is true that in this proposition,\nbesides the assertion that John Nokes died yesterday, there is included\nanother assertion, namely, that John Nokes was mayor of the town. But this\nlast assertion was already made: we did not make it by adding the\npredicate, \u201cdied yesterday.\u201d Suppose, however, that the words had been,\nJohn Nokes _and_ the mayor of the town, they would have formed two names\ninstead of one. For when we say, John Nokes and the mayor of the town died\nyesterday, we make two assertions: one, that John Nokes died yesterday;\nthe other, that the mayor of the town died yesterday.\n\nIt being needless to illustrate at any greater length the subject of\nmany-worded names, we proceed to the distinctions which have been\nestablished among names, not according to the words they are composed of,\nbut according to their signification.\n\n\u00a7 3. All names are names of something, real or imaginary; but all things\nhave not names appropriated to them individually. For some individual\nobjects we require, and consequently have, separate distinguishing names;\nthere is a name for every person, and for every remarkable place. Other\nobjects, of which we have not occasion to speak so frequently, we do not\ndesignate by a name of their own; but when the necessity arises for naming\nthem, we do so by putting together several words, each of which, by\nitself, might be and is used for an indefinite number of other objects; as\nwhen I say, _this stone_: \u201cthis\u201d and \u201cstone\u201d being, each of them, names\nthat may be used of many other objects besides the particular one meant,\nthough the only object of which they can both be used at the given moment,\nconsistently with their signification, may be the one of which I wish to\nspeak.\n\nWere this the sole purpose for which names, that are common to more things\nthan one, could be employed; if they only served, by mutually limiting\neach other, to afford a designation for such individual objects as have no\nnames of their own: they could only be ranked among contrivances for\neconomizing the use of language. But it is evident that this is not their\nsole function. It is by their means that we are enabled to assert\n_general_ propositions; to affirm or deny any predicate of an indefinite\nnumber of things at once. The distinction, therefore, between _general_\nnames, and _individual_ or _singular_ names, is fundamental; and may be\nconsidered as the first grand division of names.\n\nA general name is familiarly defined, a name which is capable of being\ntruly affirmed, in the same sense, of each of an indefinite number of\nthings. An individual or singular name is a name which is only capable of\nbeing truly affirmed, in the same sense, of one thing.\n\nThus, _man_ is capable of being truly affirmed of John, George, Mary, and\nother persons without assignable limit; and it is affirmed of all of them\nin the same sense; for the word man expresses certain qualities, and when\nwe predicate it of those persons, we assert that they all possess those\nqualities. But _John_ is only capable of being truly affirmed of one\nsingle person, at least in the same sense. For, though there are many\npersons who bear that name, it is not conferred upon them to indicate any\nqualities, or any thing which belongs to them in common; and can not be\nsaid to be affirmed of them in any _sense_ at all, consequently not in the\nsame sense. \u201cThe king who succeeded William the Conqueror,\u201d is also an\nindividual name. For, that there can not be more than one person of whom\nit can be truly affirmed, is implied in the meaning of the words. Even\n\u201c_the_ king,\u201d when the occasion or the context defines the individual of\nwhom it is to be understood, may justly be regarded as an individual name.\n\nIt is not unusual, by way of explaining what is meant by a general name,\nto say that it is the name of a _class_. But this, though a convenient\nmode of expression for some purposes, is objectionable as a definition,\nsince it explains the clearer of two things by the more obscure. It would\nbe more logical to reverse the proposition, and turn it into a definition\nof the word _class_: \u201cA class is the indefinite multitude of individuals\ndenoted by a general name.\u201d\n\nIt is necessary to distinguish _general_ from _collective_ names. A\ngeneral name is one which can be predicated of _each_ individual of a\nmultitude; a collective name can not be predicated of each separately, but\nonly of all taken together. \u201cThe 76th regiment of foot in the British\narmy,\u201d which is a collective name, is not a general but an individual\nname; for though it can be predicated of a multitude of individual\nsoldiers taken jointly, it can not be predicated of them severally. We may\nsay, Jones is a soldier, and Thompson is a soldier, and Smith is a\nsoldier, but we can not say, Jones is the 76th regiment, and Thompson is\nthe 76th regiment, and Smith is the 76th regiment. We can only say, Jones,\nand Thompson, and Smith, and Brown, and so forth (enumerating all the\nsoldiers), are the 76th regiment.\n\n\u201cThe 76th regiment\u201d is a collective name, but not a general one: \u201ca\nregiment\u201d is both a collective and a general name. General with respect to\nall individual regiments, of each of which separately it can be affirmed:\ncollective with respect to the individual soldiers of whom any regiment is\ncomposed.\n\n\u00a7 4. The second general division of names is into _concrete_ and\n_abstract_. A concrete name is a name which stands for a thing; an\nabstract name is a name which stands for an attribute of a thing. Thus\n_John_, _the sea_, _this table_, are names of things. _White_, also, is a\nname of a thing, or rather of things. Whiteness, again, is the name of a\nquality or attribute of those things. Man is a name of many things;\nhumanity is a name of an attribute of those things. _Old_ is a name of\nthings: _old age_ is a name of one of their attributes.\n\nI have used the words concrete and abstract in the sense annexed to them\nby the schoolmen, who, notwithstanding the imperfections of their\nphilosophy, were unrivaled in the construction of technical language, and\nwhose definitions, in logic at least, though they never went more than a\nlittle way into the subject, have seldom, I think, been altered but to be\nspoiled. A practice, however, has grown up in more modern times, which, if\nnot introduced by Locke, has gained currency chiefly from his example, of\napplying the expression \u201cabstract name\u201d to all names which are the result\nof abstraction or generalization, and consequently to all general names,\ninstead of confining it to the names of attributes. The metaphysicians of\nthe Condillac school\u2014whose admiration of Locke, passing over the\nprofoundest speculations of that truly original genius, usually fastens\nwith peculiar eagerness upon his weakest points\u2014have gone on imitating him\nin this abuse of language, until there is now some difficulty in restoring\nthe word to its original signification. A more wanton alteration in the\nmeaning of a word is rarely to be met with; for the expression _general\nname_, the exact equivalent of which exists in all languages I am\nacquainted with, was already available for the purpose to which _abstract_\nhas been misappropriated, while the misappropriation leaves that important\nclass of words, the names of attributes, without any compact distinctive\nappellation. The old acceptation, however, has not gone so completely out\nof use as to deprive those who still adhere to it of all chance of being\nunderstood. By _abstract_, then, I shall always, in Logic proper, mean the\nopposite of _concrete_; by an abstract name, the name of an attribute; by\na concrete name, the name of an object.\n\nDo abstract names belong to the class of general, or to that of singular\nnames? Some of them are certainly general. I mean those which are names\nnot of one single and definite attribute, but of a class of attributes.\nSuch is the word _color_, which is a name common to whiteness, redness,\netc. Such is even the word whiteness, in respect of the different shades\nof whiteness to which it is applied in common: the word magnitude, in\nrespect of the various degrees of magnitude and the various dimensions of\nspace; the word weight, in respect of the various degrees of weight. Such\nalso is the word _attribute_ itself, the common name of all particular\nattributes. But when only one attribute, neither variable in degree nor in\nkind, is designated by the name; as visibleness; tangibleness; equality;\nsquareness; milk-whiteness; then the name can hardly be considered\ngeneral; for though it denotes an attribute of many different objects, the\nattribute itself is always conceived as one, not many.(9) To avoid\nneedless logomachies, the best course would probably be to consider these\nnames as neither general nor individual, and to place them in a class\napart.\n\nIt may be objected to our definition of an abstract name, that not only\nthe names which we have called abstract, but adjectives, which we have\nplaced in the concrete class, are names of attributes; that _white_, for\nexample, is as much the name of the color as _whiteness_ is. But (as\nbefore remarked) a word ought to be considered as the name of that which\nwe intend to be understood by it when we put it to its principal use, that\nis, when we employ it in predication. When we say snow is white, milk is\nwhite, linen is white, we do not mean it to be understood that snow, or\nlinen, or milk, is a color. We mean that they are things having the color.\nThe reverse is the case with the word whiteness; what we affirm to _be_\nwhiteness is not snow, but the color of snow. Whiteness, therefore, is the\nname of the color exclusively: white is a name of all things whatever\nhaving the color; a name, not of the quality whiteness, but of every white\nobject. It is true, this name was given to all those various objects on\naccount of the quality; and we may therefore say, without impropriety,\nthat the quality forms part of its signification; but a name can only be\nsaid to stand for, or to be a name of, the things of which it can be\npredicated. We shall presently see that all names which can be said to\nhave any signification, all names by applying which to an individual we\ngive any information respecting that individual, may be said to _imply_ an\nattribute of some sort; but they are not names of the attribute; it has\nits own proper abstract name.\n\n\u00a7 5. This leads to the consideration of a third great division of names,\ninto _connotative_ and _non-connotative_, the latter sometimes, but\nimproperly, called _absolute_. This is one of the most important\ndistinctions which we shall have occasion to point out, and one of those\nwhich go deepest into the nature of language.\n\nA non-connotative term is one which signifies a subject only, or an\nattribute only. A connotative term is one which denotes a subject, and\nimplies an attribute. By a subject is here meant any thing which possesses\nattributes. Thus John, or London, or England, are names which signify a\nsubject only. Whiteness, length, virtue, signify an attribute only. None\nof these names, therefore, are connotative. But _white_, _long_,\n_virtuous_, are connotative. The word white, denotes all white things, as\nsnow, paper, the foam of the sea, etc., and implies, or in the language of\nthe schoolmen, _connotes_,(10) the attribute _whiteness_. The word white\nis not predicated of the attribute, but of the subjects, snow, etc.; but\nwhen we predicate it of them, we convey the meaning that the attribute\nwhiteness belongs to them. The same may be said of the other words above\ncited. Virtuous, for example, is the name of a class, which includes\nSocrates, Howard, the Man of Ross, and an undefinable number of other\nindividuals, past, present, and to come. These individuals, collectively\nand severally, can alone be said with propriety to be denoted by the word:\nof them alone can it properly be said to be a name. But it is a name\napplied to all of them in consequence of an attribute which they are\nsupposed to possess in common, the attribute which has received the name\nof virtue. It is applied to all beings that are considered to possess this\nattribute; and to none which are not so considered.\n\nAll concrete general names are connotative. The word _man_, for example,\ndenotes Peter, Jane, John, and an indefinite number of other individuals,\nof whom, taken as a class, it is the name. But it is applied to them,\nbecause they possess, and to signify that they possess, certain\nattributes. These seem to be, corporeity, animal life, rationality, and a\ncertain external form, which for distinction we call the human. Every\nexisting thing, which possessed all these attributes, would be called a\nman; and any thing which possessed none of them, or only one, or two, or\neven three of them without the fourth, would not be so called. For\nexample, if in the interior of Africa there were to be discovered a race\nof animals possessing reason equal to that of human beings, but with the\nform of an elephant, they would not be called men. Swift\u2019s Houyhnhnms\nwould not be so called. Or if such newly-discovered beings possessed the\nform of man without any vestige of reason, it is probable that some other\nname than that of man would be found for them. How it happens that there\ncan be any doubt about the matter, will appear hereafter. The word _man_,\ntherefore, signifies all these attributes, and all subjects which possess\nthese attributes. But it can be predicated only of the subjects. What we\ncall men, are the subjects, the individual Stiles and Nokes; not the\nqualities by which their humanity is constituted. The name, therefore, is\nsaid to signify the subjects _directly_, the attributes _indirectly_; it\n_denotes_ the subjects, and implies, or involves, or indicates, or as we\nshall say henceforth _connotes_, the attributes. It is a connotative name.\n\nConnotative names have hence been also called _denominative_, because the\nsubject which they denote is denominated by, or receives a name from the\nattribute which they connote. Snow, and other objects, receive the name\nwhite, because they possess the attribute which is called whiteness;\nPeter, James, and others receive the name man because they possess the\nattributes which are considered to constitute humanity. The attribute, or\nattributes, may therefore be said to denominate those objects, or to give\nthem a common name.(11)\n\nIt has been seen that all concrete general names are connotative. Even\nabstract names, though the names only of attributes, may in some instances\nbe justly considered as connotative; for attributes themselves may have\nattributes ascribed to them; and a word which denotes attributes may\nconnote an attribute of those attributes. Of this description, for\nexample, is such a word as _fault_; equivalent to _bad_ or _hurtful\nquality_. This word is a name common to many attributes, and connotes\nhurtfulness, an attribute of those various attributes. When, for example,\nwe say that slowness, in a horse, is a fault, we do not mean that the slow\nmovement, the actual change of pace of the slow horse, is a bad thing, but\nthat the property or peculiarity of the horse, from which it derives that\nname, the quality of being a slow mover, is an undesirable peculiarity.\n\nIn regard to those concrete names which are not general but individual, a\ndistinction must be made.\n\nProper names are not connotative: they denote the individuals who are\ncalled by them; but they do not indicate or imply any attributes as\nbelonging to those individuals. When we name a child by the name Paul, or\na dog by the name C\u00e6sar, these names are simply marks used to enable those\nindividuals to be made subjects of discourse. It may be said, indeed, that\nwe must have had some reason for giving them those names rather than any\nothers; and this is true; but the name, once given, is independent of the\nreason. A man may have been named John, because that was the name of his\nfather; a town may have been named Dartmouth, because it is situated at\nthe mouth of the Dart. But it is no part of the signification of the word\nJohn, that the father of the person so called bore the same name; nor even\nof the word Dartmouth, to be situated at the mouth of the Dart. If sand\nshould choke up the mouth of the river, or an earthquake change its\ncourse, and remove it to a distance from the town, the name of the town\nwould not necessarily be changed. That fact, therefore, can form no part\nof the signification of the word; for otherwise, when the fact confessedly\nceased to be true, no one would any longer think of applying the name.\nProper names are attached to the objects themselves, and are not dependent\non the continuance of any attribute of the object.\n\nBut there is another kind of names, which, although they are individual\nnames\u2014that is, predicable only of one object\u2014are really connotative. For,\nthough we may give to an individual a name utterly unmeaning, which we\ncall a proper name\u2014a word which answers the purpose of showing what thing\nit is we are talking about, but not of telling any thing about it; yet a\nname peculiar to an individual is not necessarily of this description. It\nmay be significant of some attribute, or some union of attributes, which,\nbeing possessed by no object but one, determines the name exclusively to\nthat individual. \u201cThe sun\u201d is a name of this description; \u201cGod,\u201d when used\nby a monotheist, is another. These, however, are scarcely examples of what\nwe are now attempting to illustrate, being, in strictness of language,\ngeneral, not individual names: for, however they may be _in fact_\npredicable only of one object, there is nothing in the meaning of the\nwords themselves which implies this: and, accordingly, when we are\nimagining and not affirming, we may speak of many suns; and the majority\nof mankind have believed, and still believe, that there are many gods. But\nit is easy to produce words which are real instances of connotative\nindividual names. It may be part of the meaning of the connotative name\nitself, that there can exist but one individual possessing the attribute\nwhich it connotes: as, for instance, \u201cthe _only_ son of John Stiles;\u201d \u201cthe\n_first_ emperor of Rome.\u201d Or the attribute connoted may be a connection\nwith some determinate event, and the connection may be of such a kind as\nonly one individual could have; or may at least be such as only one\nindividual actually had; and this may be implied in the form of the\nexpression. \u201cThe father of Socrates\u201d is an example of the one kind (since\nSocrates could not have had two fathers); \u201cthe author of the Iliad,\u201d \u201cthe\nmurderer of Henri Quatre,\u201d of the second. For, though it is conceivable\nthat more persons than one might have participated in the authorship of\nthe Iliad, or in the murder of Henri Quatre, the employment of the article\n_the_ implies that, in fact, this was not the case. What is here done by\nthe word _the_, is done in other cases by the context: thus, \u201cC\u00e6sar\u2019s\narmy\u201d is an individual name, if it appears from the context that the army\nmeant is that which C\u00e6sar commanded in a particular battle. The still more\ngeneral expressions, \u201cthe Roman army,\u201d or \u201cthe Christian army,\u201d may be\nindividualized in a similar manner. Another case of frequent occurrence\nhas already been noticed; it is the following: The name, being a\nmany-worded one, may consist, in the first place, of a _general_ name,\ncapable therefore in itself of being affirmed of more things than one, but\nwhich is, in the second place, so limited by other words joined with it,\nthat the entire expression can only be predicated of one object,\nconsistently with the meaning of the general term. This is exemplified in\nsuch an instance as the following: \u201cthe present prime minister of\nEngland.\u201d Prime Minister of England is a general name; the attributes\nwhich it connotes may be possessed by an indefinite number of persons: in\nsuccession however, not simultaneously; since the meaning of the name\nitself imports (among other things) that there can be only one such person\nat a time. This being the case, and the application of the name being\nafterward limited by the article and the word _present_, to such\nindividuals as possess the attributes at one indivisible point of time, it\nbecomes applicable only to one individual. And as this appears from the\nmeaning of the name, without any extrinsic proof, it is strictly an\nindividual name.\n\nFrom the preceding observations it will easily be collected, that whenever\nthe names given to objects convey any information\u2014that is, whenever they\nhave properly any meaning\u2014the meaning resides not in what they _denote_,\nbut in what they _connote_. The only names of objects which connote\nnothing are _proper_ names; and these have, strictly speaking, no\nsignification.(12)\n\nIf, like the robber in the Arabian Nights, we make a mark with chalk on a\nhouse to enable us to know it again, the mark has a purpose, but it has\nnot properly any meaning. The chalk does not declare any thing about the\nhouse; it does not mean, This is such a person\u2019s house, or This is a house\nwhich contains booty. The object of making the mark is merely distinction.\nI say to myself, All these houses are so nearly alike that if I lose sight\nof them I shall not again be able to distinguish that which I am now\nlooking at, from any of the others; I must therefore contrive to make the\nappearance of this one house unlike that of the others, that I may\nhereafter know when I see the mark\u2014not indeed any attribute of the\nhouse\u2014but simply that it is the same house which I am now looking at.\nMorgiana chalked all the other houses in a similar manner, and defeated\nthe scheme: how? simply by obliterating the difference of appearance\nbetween that house and the others. The chalk was still there, but it no\nlonger served the purpose of a distinctive mark.\n\nWhen we impose a proper name, we perform an operation in some degree\nanalogous to what the robber intended in chalking the house. We put a\nmark, not indeed upon the object itself, but, so to speak, upon the idea\nof the object. A proper name is but an unmeaning mark which we connect in\nour minds with the idea of the object, in order that whenever the mark\nmeets our eyes or occurs to our thoughts, we may think of that individual\nobject. Not being attached to the thing itself, it does not, like the\nchalk, enable us to distinguish the object when we see it; but it enables\nus to distinguish it when it is spoken of, either in the records of our\nown experience, or in the discourse of others; to know that what we find\nasserted in any proposition of which it is the subject, is asserted of the\nindividual thing with which we were previously acquainted.\n\nWhen we predicate of any thing its proper name; when we say, pointing to a\nman, this is Brown or Smith, or pointing to a city, that it is York, we do\nnot, merely by so doing, convey to the reader any information about them,\nexcept that those are their names. By enabling him to identify the\nindividuals, we may connect them with information previously possessed by\nhim; by saying, This is York, we may tell him that it contains the\nMinster. But this is in virtue of what he has previously heard concerning\nYork; not by any thing implied in the name. It is otherwise when objects\nare spoken of by connotative names. When we say, The town is built of\nmarble, we give the hearer what may be entirely new information, and this\nmerely by the signification of the many-worded connotative name, \u201cbuilt of\nmarble.\u201d Such names are not signs of the mere objects, invented because we\nhave occasion to think and speak of those objects individually; but signs\nwhich accompany an attribute; a kind of livery in which the attribute\nclothes all objects which are recognized as possessing it. They are not\nmere marks, but more, that is to say, significant marks; and the\nconnotation is what constitutes their significance.\n\nAs a proper name is said to be the name of the one individual which it is\npredicated of, so (as well from the importance of adhering to analogy, as\nfor the other reasons formerly assigned) a connotative name ought to be\nconsidered a name of all the various individuals which it is predicable\nof, or in other words _denotes_, and not of what it connotes. But by\nlearning what things it is a name of, we do not learn the meaning of the\nname: for to the same thing we may, with equal propriety, apply many\nnames, not equivalent in meaning. Thus, I call a certain man by the name\nSophroniscus: I call him by another name, The father of Socrates. Both\nthese are names of the same individual, but their meaning is altogether\ndifferent; they are applied to that individual for two different purposes:\nthe one, merely to distinguish him from other persons who are spoken of;\nthe other to indicate a fact relating to him, the fact that Socrates was\nhis son. I further apply to him these other expressions: a man, a Greek,\nan Athenian, a sculptor, an old man, an honest man, a brave man. All these\nare, or may be, names of Sophroniscus, not indeed of him alone, but of him\nand each of an indefinite number of other human beings. Each of these\nnames is applied to Sophroniscus for a different reason, and by each\nwhoever understands its meaning is apprised of a distinct fact or number\nof facts concerning him; but those who knew nothing about the names except\nthat they were applicable to Sophroniscus, would be altogether ignorant of\ntheir meaning. It is even possible that I might know every single\nindividual of whom a given name could be with truth affirmed, and yet\ncould not be said to know the meaning of the name. A child knows who are\nits brothers and sisters, long before it has any definite conception of\nthe nature of the facts which are involved in the signification of those\nwords.\n\nIn some cases it is not easy to decide precisely how much a particular\nword does or does not connote; that is, we do not exactly know (the case\nnot having arisen) what degree of difference in the object would occasion\na difference in the name. Thus, it is clear that the word man, besides\nanimal life and rationality, connotes also a certain external form; but it\nwould be impossible to say precisely what form; that is, to decide how\ngreat a deviation from the form ordinarily found in the beings whom we are\naccustomed to call men, would suffice in a newly-discovered race to make\nus refuse them the name of man. Rationality, also, being a quality which\nadmits of degrees, it has never been settled what is the lowest degree of\nthat quality which would entitle any creature to be considered a human\nbeing. In all such cases, the meaning of the general name is so far\nunsettled and vague; mankind have not come to any positive agreement about\nthe matter. When we come to treat of Classification, we shall have\noccasion to show under what conditions this vagueness may exist without\npractical inconvenience; and cases will appear in which the ends of\nlanguage are better promoted by it than by complete precision; in order\nthat, in natural history for instance, individuals or species of no very\nmarked character may be ranged with those more strongly characterized\nindividuals or species to which, in all their properties taken together,\nthey bear the nearest resemblance.\n\nBut this partial uncertainty in the connotation of names can only be free\nfrom mischief when guarded by strict precautions. One of the chief\nsources, indeed, of lax habits of thought, is the custom of using\nconnotative terms without a distinctly ascertained connotation, and with\nno more precise notion of their meaning than can be loosely collected from\nobserving what objects they are used to denote. It is in this manner that\nwe all acquire, and inevitably so, our first knowledge of our vernacular\nlanguage. A child learns the meaning of the words _man_, or _white_, by\nhearing them applied to a variety of individual objects, and finding out,\nby a process of generalization and analysis which he could not himself\ndescribe, what those different objects have in common. In the case of\nthese two words the process is so easy as to require no assistance from\nculture; the objects called human beings, and the objects called white,\ndiffering from all others by qualities of a peculiarly definite and\nobvious character. But in many other cases, objects bear a general\nresemblance to one another, which leads to their being familiarly classed\ntogether under a common name, while, without more analytic habits than the\ngenerality of mankind possess, it is not immediately apparent what are the\nparticular attributes, upon the possession of which in common by them all,\ntheir general resemblance depends. When this is the case, people use the\nname without any recognized connotation, that is, without any precise\nmeaning; they talk, and consequently think, vaguely, and remain contented\nto attach only the same degree of significance to their own words, which a\nchild three years old attaches to the words brother and sister. The child\nat least is seldom puzzled by the starting up of new individuals, on whom\nhe is ignorant whether or not to confer the title; because there is\nusually an authority close at hand competent to solve all doubts. But a\nsimilar resource does not exist in the generality of cases; and new\nobjects are continually presenting themselves to men, women, and children,\nwhich they are called upon to class _proprio motu_. They, accordingly, do\nthis on no other principle than that of superficial similarity, giving to\neach new object the name of that familiar object, the idea of which it\nmost readily recalls, or which, on a cursory inspection, it seems to them\nmost to resemble: as an unknown substance found in the ground will be\ncalled, according to its texture, earth, sand, or a stone. In this manner,\nnames creep on from subject to subject, until all traces of a common\nmeaning sometimes disappear, and the word comes to denote a number of\nthings not only independently of any common attribute, but which have\nactually no attribute in common; or none but what is shared by other\nthings to which the name is capriciously refused.(13) Even scientific\nwriters have aided in this perversion of general language from its\npurpose; sometimes because, like the vulgar, they knew no better; and\nsometimes in deference to that aversion to admit new words, which induces\nmankind, on all subjects not considered technical, to attempt to make the\noriginal stock of names serve with but little augmentation to express a\nconstantly increasing number of objects and distinctions, and,\nconsequently, to express them in a manner progressively more and more\nimperfect.\n\nTo what a degree this loose mode of classing and denominating objects has\nrendered the vocabulary of mental and moral philosophy unfit for the\npurposes of accurate thinking, is best known to whoever has most meditated\non the present condition of those branches of knowledge. Since, however,\nthe introduction of a new technical language as the vehicle of\nspeculations on subjects belonging to the domain of daily discussion, is\nextremely difficult to effect, and would not be free from inconvenience\neven if effected, the problem for the philosopher, and one of the most\ndifficult which he has to resolve, is, in retaining the existing\nphraseology, how best to alleviate its imperfections. This can only be\naccomplished by giving to every general concrete name which there is\nfrequent occasion to predicate, a definite and fixed connotation; in order\nthat it may be known what attributes, when we call an object by that name,\nwe really mean to predicate of the object. And the question of most nicety\nis, how to give this fixed connotation to a name, with the least possible\nchange in the objects which the name is habitually employed to denote;\nwith the least possible disarrangement, either by adding or subtraction,\nof the group of objects which, in however imperfect a manner, it serves to\ncircumscribe and hold together; and with the least vitiation of the truth\nof any propositions which are commonly received as true.\n\nThis desirable purpose, of giving a fixed connotation where it is wanting,\nis the end aimed at whenever any one attempts to give a definition of a\ngeneral name already in use; every definition of a connotative name being\nan attempt either merely to declare, or to declare and analyze, the\nconnotation of the name. And the fact, that no questions which have arisen\nin the moral sciences have been subjects of keener controversy than the\ndefinitions of almost all the leading expressions, is a proof how great an\nextent the evil to which we have adverted has attained.\n\nNames with indeterminate connotation are not to be confounded with names\nwhich have more than one connotation, that is to say, ambiguous words. A\nword may have several meanings, but all of them fixed and recognized ones;\nas the word _post_, for example, or the word _box_, the various senses of\nwhich it would be endless to enumerate. And the paucity of existing names,\nin comparison with the demand for them, may often render it advisable and\neven necessary to retain a name in this multiplicity of acceptations,\ndistinguishing these so clearly as to prevent their being confounded with\none another. Such a word may be considered as two or more names,\naccidentally written and spoken alike.(14)\n\n\u00a7 6. The fourth principal division of names, is into _positive_ and\n_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,\n_not-tree_, _not-good_. To every positive concrete name, a corresponding\nnegative one might be framed. After giving a name to any one thing, or to\nany plurality of things, we might create a second name which should be a\nname of all things whatever, except that particular thing or things. These\nnegative names are employed whenever we have occasion to speak\ncollectively of all things other than some thing or class of things. When\nthe positive name is connotative, the corresponding negative name is\nconnotative likewise; but in a peculiar way, connoting not the presence\nbut the absence of an attribute. Thus, _not-white_ denotes all things\nwhatever except white things; and connotes the attribute of not possessing\nwhiteness. For the non-possession of any given attribute is also an\nattribute, and may receive a name as such; and thus negative concrete\nnames may obtain negative abstract names to correspond to them.(15)\n\nNames which are positive in form are often negative in reality, and others\nare really positive though their form is negative. The word\n_inconvenient_, for example, does not express the mere absence of\nconvenience; it expresses a positive attribute\u2014that of being the cause of\ndiscomfort or annoyance. So the word _unpleasant_, notwithstanding its\nnegative form, does not connote the mere absence of pleasantness, but a\nless degree of what is signified by the word _painful_, which, it is\nhardly necessary to say, is positive. _Idle_, on the other hand, is a word\nwhich, though positive in form, expresses nothing but what would be\nsignified either by the phrase _not working_, or by the phrase _not\ndisposed to work_; and _sober_, either by _not drunk_ or by _not drunken_.\n\nThere is a class of names called _privative_. A privative name is\nequivalent in its signification to a positive and a negative name taken\ntogether; being the name of something which has once had a particular\nattribute, or for some other reason might have been expected to have it,\nbut which has it not. Such is the word _blind_, which is not equivalent to\n_not seeing_, or to _not capable of seeing_, for it would not, except by a\npoetical or rhetorical figure, be applied to stocks and stones. A thing is\nnot usually said to be blind, unless the class to which it is most\nfamiliarly referred, or to which it is referred on the particular\noccasion, be chiefly composed of things which can see, as in the case of a\nblind man, or a blind horse; or unless it is supposed for any reason that\nit ought to see; as in saying of a man, that he rushed blindly into an\nabyss, or of philosophers or the clergy that the greater part of them are\nblind guides. The names called privative, therefore, connote two things;\nthe absence of certain attributes, and the presence of others, from which\nthe presence also of the former might naturally have been expected.\n\n\u00a7 7. The fifth leading division of names is into _relative_ and\n_absolute_, or let us rather say, _relative_ and _non-relative_; for the\nword absolute is put upon much too hard duty in metaphysics, not to be\nwillingly spared when its services can be dispensed with. It resembles the\nword _civil_ in the language of jurisprudence, which stands for the\nopposite of criminal, the opposite of ecclesiastical, the opposite of\nmilitary, the opposite of political\u2014in short, the opposite of any positive\nword which wants a negative.\n\nRelative names are such as father, son; ruler, subject; like; equal;\nunlike; unequal; longer, shorter; cause, effect. Their characteristic\nproperty is, that they are always given in pairs. Every relative name\nwhich is predicated of an object, supposes another object (or objects), of\nwhich we may predicate either that same name or another relative name\nwhich is said to be the _correlative_ of the former. Thus, when we call\nany person a son, we suppose other persons who must be called parents.\nWhen we call any event a cause, we suppose another event which is an\neffect. When we say of any distance that it is longer, we suppose another\ndistance which is shorter. When we say of any object that it is like, we\nmean that it is like some other object, which is also said to be like the\nfirst. In this last case both objects receive the same name; the relative\nterm is its own correlative.\n\nIt is evident that these words, when concrete, are, like other concrete\ngeneral names, connotative; they denote a subject, and connote an\nattribute; and each of them has, or might have, a corresponding abstract\nname, to denote the attribute connoted by the concrete. Thus the concrete\n_like_ has its abstract _likeness_; the concretes, father and son, have,\nor might have, the abstracts, paternity, and filiety, or sonship. The\nconcrete name connotes an attribute, and the abstract name which answers\nto it denotes that attribute. But of what nature is the attribute? Wherein\nconsists the peculiarity in the connotation of a relative name?\n\nThe attribute signified by a relative name, say some, is a relation; and\nthis they give, if not as a sufficient explanation, at least as the only\none attainable. If they are asked, What then is a relation? they do not\nprofess to be able to tell. It is generally regarded as something\npeculiarly recondite and mysterious. I can not, however, perceive in what\nrespect it is more so than any other attribute; indeed, it appears to me\nto be so in a somewhat less degree. I conceive rather, that it is by\nexamining into the signification of relative names, or, in other words,\ninto the nature of the attribute which they connote, that a clear insight\nmay best be obtained into the nature of all attributes: of all that is\nmeant by an attribute.\n\nIt is obvious, in fact, that if we take any two correlative names,\n_father_ and _son_ for instance, though the objects _de_noted by the names\nare different, they both, in a certain sense, connote the same thing. They\ncan not, indeed, be said to connote the same _attribute_: to be a father,\nis not the same thing as to be a son. But when we call one man a father,\nanother a son, what we mean to affirm is a set of facts, which are exactly\nthe same in both cases. To predicate of A that he is the father of B, and\nof B that he is the son of A, is to assert one and the same fact in\ndifferent words. The two propositions are exactly equivalent: neither of\nthem asserts more or asserts less than the other. The paternity of A and\nthe filiety of B are not two facts, but two modes of expressing the same\nfact. That fact, when analysed, consists of a series of physical events or\nphenomena, in which both A and B are parties concerned, and from which\nthey both derive names. What those names really connote, is this series of\nevents: that is the meaning, and the whole meaning, which either of them\nis intended to convey. The series of events may be said to _constitute_\nthe relation; the schoolmen called it the foundation of the relation,\n_fundamentum relationis_.\n\nIn this manner any fact, or series of facts, in which two different\nobjects are implicated, and which is therefore predicable of both of them,\nmay be either considered as constituting an attribute of the one, or an\nattribute of the other. According as we consider it in the former, or in\nthe latter aspect, it is connoted by the one or the other of the two\ncorrelative names. _Father_ connotes the fact, regarded as constituting an\nattribute of A; _son_ connotes the same fact, as constituting an attribute\nof B. It may evidently be regarded with equal propriety in either light.\nAnd all that appears necessary to account for the existence of relative\nnames, is, that whenever there is a fact in which two individuals are\nconcerned, an attribute grounded on that fact may be ascribed to either of\nthese individuals.\n\nA name, therefore, is said to be relative, when, over and above the object\nwhich it denotes, it implies in its signification the existence of another\nobject, also deriving a denomination from the same fact which is the\nground of the first name. Or (to express the same meaning in other words)\na name is relative, when, being the name of one thing, its signification\ncan not be explained but by mentioning another. Or we may state it\nthus\u2014when the name can not be employed in discourse so as to have a\nmeaning, unless the name of some other thing than what it is itself the\nname of, be either expressed or understood. These definitions are all, at\nbottom, equivalent, being modes of variously expressing this one\ndistinctive circumstance\u2014that every other attribute of an object might,\nwithout any contradiction, be conceived still to exist if no object\nbesides that one had ever existed;(16) but those of its attributes which\nare expressed by relative names, would on that supposition be swept away.\n\n\u00a7 8. Names have been further distinguished into _univocal_ and\n_\u00e6quivocal_: these, however, are not two kinds of names, but two different\nmodes of employing names. A name is univocal, or applied univocally, with\nrespect to all things of which it can be predicated _in the same sense_;\nit is \u00e6quivocal, or applied \u00e6quivocally, as respects those things of which\nit is predicated in different senses. It is scarcely necessary to give\ninstances of a fact so familiar as the double meaning of a word. In\nreality, as has been already observed, an \u00e6quivocal or ambiguous word is\nnot one name, but two names, accidentally coinciding in sound. _File_\nmeaning a steel instrument, and _file_ meaning a line of soldiers, have no\nmore title to be considered one word, because written alike, than _grease_\nand _Greece_ have, because they are pronounced alike. They are one sound,\nappropriated to form two different words.\n\nAn intermediate case is that of a name used _analogically_ or\nmetaphorically; that is, a name which is predicated of two things, not\nunivocally, or exactly in the same signification, but in significations\nsomewhat similar, and which being derived one from the other, one of them\nmay be considered the primary, and the other a secondary signification. As\nwhen we speak of a brilliant light and a brilliant achievement. The word\nis not applied in the same sense to the light and to the achievement; but\nhaving been applied to the light in its original sense, that of brightness\nto the eye, it is transferred to the achievement in a derivative\nsignification, supposed to be somewhat like the primitive one. The word,\nhowever, is just as properly two names instead of one, in this case, as in\nthat of the most perfect ambiguity. And one of the commonest forms of\nfallacious reasoning arising from ambiguity, is that of arguing from a\nmetaphorical expression as if it were literal; that is, as if a word, when\napplied metaphorically, were the same name as when taken in its original\nsense: which will be seen more particularly in its place.\n\n\n\n\n                               Chapter III.\n\n\nOf The Things Denoted By Names.\n\n\n\u00a7 1. Looking back now to the commencement of our inquiry, let us attempt\nto measure how far it has advanced. Logic, we found, is the Theory of\nProof. But proof supposes something provable, which must be a Proposition\nor Assertion; since nothing but a Proposition can be an object of belief,\nor therefore of proof. A Proposition is, discourse which affirms or denies\nsomething of some other thing. This is one step: there must, it seems, be\ntwo things concerned in every act of belief. But what are these Things?\nThey can be no other than those signified by the two names, which being\njoined together by a copula constitute the Proposition. If, therefore, we\nknew what all names signify, we should know every thing which, in the\nexisting state of human knowledge, is capable either of being made a\nsubject of affirmation or denial, or of being itself affirmed or denied of\na subject. We have accordingly, in the preceding chapter, reviewed the\nvarious kinds of Names, in order to ascertain what is signified by each of\nthem. And we have now carried this survey far enough to be able to take an\naccount of its results, and to exhibit an enumeration of all kinds of\nThings which are capable of being made predicates, or of having any thing\npredicated of them: after which to determine the import of Predication,\nthat is, of Propositions, can be no arduous task.\n\nThe necessity of an enumeration of Existences, as the basis of Logic, did\nnot escape the attention of the schoolmen, and of their master Aristotle,\nthe most comprehensive, if not also the most sagacious, of the ancient\nphilosophers. The Categories, or Predicaments\u2014the former a Greek word, the\nlatter its literal translation in the Latin language\u2014were believed to be\nan enumeration of all things capable of being named; an enumeration by the\n_summa genera_, _i.e._, the most extensive classes into which things could\nbe distributed; which, therefore, were so many highest Predicates, one or\nother of which was supposed capable of being affirmed with truth of every\nnamable thing whatsoever. The following are the classes into which,\naccording to this school of philosophy, Things in general might be\nreduced:\n\n\u039f\u1f50\u03c3\u03af\u03b1, Substantia.\n\u03a0\u03bf\u03c3\u1f78\u03bd, Quantitas.\n\u03a0\u03bf\u03b9\u03cc\u03bd, Qualitas.\n\u03a0\u03c1\u03cc\u03c2 \u03c4\u03b9, Relatio.\n\u03a0\u03bf\u03b9\u03b5\u1fd6\u03bd, Actio.\n\u03a0\u03ac\u03c3\u03c7\u03b5\u03b9\u03bd, Passio.\n\u03a0\u03bf\u1fe6, Ubi.\n\u03a0\u03cc\u03c4\u03b5, Quando.\n\u039a\u03b5\u1fd6\u03c3\u03b8\u03b1\u03ba, Situs.\n\u1f1c\u03c7\u03b5\u03b9\u03bd, Habitus.\n\nThe imperfections of this classification are too obvious to require, and\nits merits are not sufficient to reward, a minute examination. It is a\nmere catalogue of the distinctions rudely marked out by the language of\nfamiliar life, with little or no attempt to penetrate, by philosophic\nanalysis, to the _rationale_ even of those common distinctions. Such an\nanalysis, however superficially conducted, would have shown the\nenumeration to be both redundant and defective. Some objects are omitted,\nand others repeated several times under different heads. It is like a\ndivision of animals into men, quadrupeds, horses, asses, and ponies. That,\nfor instance, could not be a very comprehensive view of the nature of\nRelation which could exclude action, passivity, and local situation from\nthat category. The same observation applies to the categories Quando (or\nposition in time), and Ubi (or position in space); while the distinction\nbetween the latter and Situs is merely verbal. The incongruity of erecting\ninto a _summum genus_ the class which forms the tenth category is\nmanifest. On the other hand, the enumeration takes no notice of any thing\nbesides substances and attributes. In what category are we to place\nsensations, or any other feelings and states of mind; as hope, joy, fear;\nsound, smell, taste; pain, pleasure; thought, judgment, conception, and\nthe like? Probably all these would have been placed by the Aristotelian\nschool in the categories of _actio_ and _passio_; and the relation of such\nof them as are active, to their objects, and of such of them as are\npassive, to their causes, would rightly be so placed; but the things\nthemselves, the feelings or states of mind, wrongly. Feelings, or states\nof consciousness, are assuredly to be accounted among realities, but they\ncan not be reckoned either among substances or attributes.(17)\n\n\u00a7 2. Before recommencing, under better auspices, the attempt made with\nsuch imperfect success by the early logicians, we must take notice of an\nunfortunate ambiguity in all the concrete names which correspond to the\nmost general of all abstract terms, the word Existence. When we have\noccasion for a name which shall be capable of denoting whatever exists, as\ncontradistinguished from non-entity or Nothing, there is hardly a word\napplicable to the purpose which is not also, and even more familiarly,\ntaken in a sense in which it denotes only substances. But substances are\nnot all that exists; attributes, if such things are to be spoken of, must\nbe said to exist; feelings certainly exist. Yet when we speak of an\n_object_, or of a _thing_, we are almost always supposed to mean a\nsubstance. There seems a kind of contradiction in using such an expression\nas that one _thing_ is merely an attribute of another thing. And the\nannouncement of a Classification of Things would, I believe, prepare most\nreaders for an enumeration like those in natural history, beginning with\nthe great divisions of animal, vegetable, and mineral, and subdividing\nthem into classes and orders. If, rejecting the word Thing, we endeavor to\nfind another of a more general import, or at least more exclusively\nconfined to that general import, a word denoting all that exists, and\nconnoting only simple existence; no word might be presumed fitter for such\na purpose than _being_: originally the present participle of a verb which\nin one of its meanings is exactly equivalent to the verb _exists_; and\ntherefore suitable, even by its grammatical formation, to be the concrete\nof the abstract _existence_. But this word, strange as the fact may\nappear, is still more completely spoiled for the purpose which it seemed\nexpressly made for, than the word Thing. _Being_ is, by custom, exactly\nsynonymous with substance; except that it is free from a slight taint of a\nsecond ambiguity; being implied impartially to matter and to mind, while\nsubstance, though originally and in strictness applicable to both, is apt\nto suggest in preference the idea of matter. Attributes are never called\nBeings; nor are feelings. A Being is that which excites feelings, and\nwhich possesses attributes. The soul is called a Being; God and angels are\ncalled Beings; but if we were to say, extension, color, wisdom, virtue,\nare beings, we should perhaps be suspected of thinking with some of the\nancients, that the cardinal virtues are animals; or, at the least, of\nholding with the Platonic school the doctrine of self-existent Ideas, or\nwith the followers of Epicurus that of Sensible Forms, which detach\nthemselves in every direction from bodies, and by coming in contact with\nour organs, cause our perceptions. We should be supposed, in short, to\nbelieve that Attributes are Substances.\n\nIn consequence of this perversion of the word Being, philosophers looking\nabout for something to supply its place, laid their hands upon the word\nEntity, a piece of barbarous Latin, invented by the schoolmen to be used\nas an abstract name, in which class its grammatical form would seem to\nplace it: but being seized by logicians in distress to stop a leak in\ntheir terminology, it has ever since been used as a concrete name. The\nkindred word _essence_, born at the same time and of the same parents,\nscarcely underwent a more complete transformation when, from being the\nabstract of the verb _to be_, it came to denote something sufficiently\nconcrete to be inclosed in a glass bottle. The word Entity, since it\nsettled down into a concrete name, has retained its universality of\nsignification somewhat less impaired than any of the names before\nmentioned. Yet the same gradual decay to which, after a certain age, all\nthe language of psychology seems liable, has been at work even here. If\nyou call virtue an _entity_, you are indeed somewhat less strongly\nsuspected of believing it to be a substance than if you called it a\n_being_; but you are by no means free from the suspicion. Every word which\nwas originally intended to connote mere existence, seems, after a time, to\nenlarge its connotation to _separate_ existence, or existence freed from\nthe condition of belonging to a substance; which condition being precisely\nwhat constitutes an attribute, attributes are gradually shut out; and\nalong with them feelings, which in ninety-nine cases out of a hundred have\nno other name than that of the attribute which is grounded on them.\nStrange that when the greatest embarrassment felt by all who have any\nconsiderable number of thoughts to express, is to find a sufficient\nvariety of precise words fitted to express them, there should be no\npractice to which even scientific thinkers are more addicted than that of\ntaking valuable words to express ideas which are sufficiently expressed by\nother words already appropriated to them.\n\nWhen it is impossible to obtain good tools, the next best thing is to\nunderstand thoroughly the defects of those we have. I have therefore\nwarned the reader of the ambiguity of the names which, for want of better,\nI am necessitated to employ. It must now be the writer\u2019s endeavor so to\nemploy them as in no case to leave the meaning doubtful or obscure. No one\nof the above terms being altogether unambiguous, I shall not confine\nmyself to any one, but shall employ on each occasion the word which seems\nleast likely in the particular case to lead to misunderstanding; nor do I\npretend to use either these or any other words with a rigorous adherence\nto one single sense. To do so would often leave us without a word to\nexpress what is signified by a known word in some one or other of its\nsenses: unless authors had an unlimited license to coin new words,\ntogether with (what it would be more difficult to assume) unlimited power\nof making readers understand them. Nor would it be wise in a writer, on a\nsubject involving so much of abstraction, to deny himself the advantage\nderived from even an improper use of a term, when, by means of it, some\nfamiliar association is called up which brings the meaning home to the\nmind, as it were by a flash.\n\nThe difficulty both to the writer and reader, of the attempt which must be\nmade to use vague words so as to convey a precise meaning, is not wholly a\nmatter of regret. It is not unfitting that logical treatises should afford\nan example of that, to facilitate which is among the most important uses\nof logic. Philosophical language will for a long time, and popular\nlanguage still longer, retain so much of vagueness and ambiguity, that\nlogic would be of little value if it did not, among its other advantages,\nexercise the understanding in doing its work neatly and correctly with\nthese imperfect tools.\n\nAfter this preamble it is time to proceed to our enumeration. We shall\ncommence with Feelings, the simplest class of namable things; the term\nFeeling being of course understood in its most enlarged sense.\n\n\nI. Feelings, Or States of Consciousness.\n\n\n\u00a7 3. A Feeling and a State of consciousness are, in the language of\nphilosophy, equivalent expressions: every thing is a feeling of which the\nmind is conscious; every thing which it _feels_, or, in other words, which\nforms a part of its own sentient existence. In popular language Feeling is\nnot always synonymous with State of Consciousness; being often taken more\npeculiarly for those states which are conceived as belonging to the\nsensitive, or to the emotional, phasis of our nature, and sometimes, with\na still narrower restriction, to the emotional alone, as distinguished\nfrom what are conceived as belonging to the percipient or to the\nintellectual phasis. But this is an admitted departure from correctness of\nlanguage; just as, by a popular perversion the exact converse of this, the\nword Mind is withdrawn from its rightful generality of signification, and\nrestricted to the intellect. The still greater perversion by which Feeling\nis sometimes confined not only to bodily sensations, but to the sensations\nof a single sense, that of touch, needs not be more particularly adverted\nto.\n\nFeeling, in the proper sense of the term, is a genus, of which Sensation,\nEmotion, and Thought, are subordinate species. Under the word Thought is\nhere to be included whatever we are internally conscious of when we are\nsaid to think; from the consciousness we have when we think of a red color\nwithout having it before our eyes, to the most recondite thoughts of a\nphilosopher or poet. Be it remembered, however, that by a thought is to be\nunderstood what passes in the mind itself, and not any object external to\nthe mind, which the person is commonly said to be thinking of. He may be\nthinking of the sun, or of God, but the sun and God are not thoughts; his\nmental image, however, of the sun, and his idea of God, are thoughts;\nstates of his mind, not of the objects themselves; and so also is his\nbelief of the existence of the sun, or of God; or his disbelief, if the\ncase be so. Even imaginary objects (which are said to exist only in our\nideas) are to be distinguished from our ideas of them. I may think of a\nhobgoblin, as I may think of the loaf which was eaten yesterday, or of the\nflower which will bloom to-morrow. But the hobgoblin which never existed\nis not the same thing with my idea of a hobgoblin, any more than the loaf\nwhich once existed is the same thing with my idea of a loaf, or the flower\nwhich does not yet exist, but which will exist, is the same with my idea\nof a flower. They are all, not thoughts, but objects of thought; though at\nthe present time all the objects are alike non-existent.\n\nIn like manner, a Sensation is to be carefully distinguished from the\nobject which causes the sensation; our sensation of white from a white\nobject: nor is it less to be distinguished from the attribute whiteness,\nwhich we ascribe to the object in consequence of its exciting the\nsensation. Unfortunately for clearness and due discrimination in\nconsidering these subjects, our sensations seldom receive separate names.\nWe have a name for the objects which produce in us a certain sensation:\nthe word _white_. We have a name for the quality in those objects, to\nwhich we ascribe the sensation: the name _whiteness_. But when we speak of\nthe sensation itself (as we have not occasion to do this often except in\nour scientific speculations), language, which adapts itself for the most\npart only to the common uses of life, has provided us with no\nsingle-worded or immediate designation; we must employ a circumlocution,\nand say, The sensation of white, or The sensation of whiteness; we must\ndenominate the sensation either from the object, or from the attribute, by\nwhich it is excited. Yet the sensation, though it never _does_, might very\nwell be _conceived_ to exist, without any thing whatever to excite it. We\ncan conceive it as arising spontaneously in the mind. But if it so arose,\nwe should have no name to denote it which would not be a misnomer. In the\ncase of our sensations of hearing we are better provided; we have the word\nSound, and a whole vocabulary of words to denote the various kinds of\nsounds. For as we are often conscious of these sensations in the absence\nof any perceptible object, we can more easily conceive having them in the\nabsence of any object whatever. We need only shut our eyes and listen to\nmusic, to have a conception of a universe with nothing in it except\nsounds, and ourselves hearing them: and what is easily conceived\nseparately, easily obtains a separate name. But in general our names of\nsensations denote indiscriminately the sensation and the attribute. Thus,\n_color_ stands for the sensations of white, red, etc., but also for the\nquality in the colored object. We talk of the colors of things as among\ntheir _properties_.\n\n\u00a7 4. In the case of sensations, another distinction has also to be kept in\nview, which is often confounded, and never without mischievous\nconsequences. This is, the distinction between the sensation itself, and\nthe state of the bodily organs which precedes the sensation, and which\nconstitutes the physical agency by which it is produced. One of the\nsources of confusion on this subject is the division commonly made of\nfeelings into Bodily and Mental. Philosophically speaking, there is no\nfoundation at all for this distinction: even sensations are states of the\nsentient mind, not states of the body, as distinguished from it. What I am\nconscious of when I see the color blue, is a feeling of blue color, which\nis one thing; the picture on my retina, or the phenomenon of hitherto\nmysterious nature which takes place in my optic nerve or in my brain, is\nanother thing, of which I am not at all conscious, and which scientific\ninvestigation alone could have apprised me of. These are states of my\nbody; but the sensation of blue, which is the consequence of these states\nof body, is not a state of body: that which perceives and is conscious is\ncalled Mind. When sensations are called bodily feelings, it is only as\nbeing the class of feelings which are immediately occasioned by bodily\nstates; whereas the other kinds of feelings, thoughts, for instance, or\nemotions, are immediately excited not by any thing acting upon the bodily\norgans, but by sensations, or by previous thoughts. This, however, is a\ndistinction not in our feelings, but in the agency which produces our\nfeelings: all of them when actually produced are states of mind.\n\nBesides the affection of our bodily organs from without, and the sensation\nthereby produced in our minds, many writers admit a third link in the\nchain of phenomena, which they call a Perception, and which consists in\nthe recognition of an external object as the exciting cause of the\nsensation. This perception, they say, is an _act_ of the mind, proceeding\nfrom its own spontaneous activity; while in a sensation the mind is\npassive, being merely acted upon by the outward object. And according to\nsome metaphysicians, it is by an act of the mind, similar to perception,\nexcept in not being preceded by any sensation, that the existence of God,\nthe soul, and other hyperphysical objects, is recognized.\n\nThese acts of what is termed perception, whatever be the conclusion\nultimately come to respecting their nature, must, I conceive, take their\nplace among the varieties of feelings or states of mind. In so classing\nthem, I have not the smallest intention of declaring or insinuating any\ntheory as to the law of mind in which these mental processes may be\nsupposed to originate, or the conditions under which they may be\nlegitimate or the reverse. Far less do I mean (as Dr. Whewell seems to\nsuppose must be meant in an analogous case(18)) to indicate that as they\nare \u201c_merely_ states of mind,\u201d it is superfluous to inquire into their\ndistinguishing peculiarities. I abstain from the inquiry as irrelevant to\nthe science of logic. In these so-called perceptions, or direct\nrecognitions by the mind, of objects, whether physical or spiritual, which\nare external to itself, I can see only cases of belief; but of belief\nwhich claims to be intuitive, or independent of external evidence. When a\nstone lies before me, I am conscious of certain sensations which I receive\nfrom it; but if I say that these sensations come to me from an external\nobject which I _perceive_, the meaning of these words is, that receiving\nthe sensations, I intuitively _believe_ that an external cause of those\nsensations exists. The laws of intuitive belief, and the conditions under\nwhich it is legitimate, are a subject which, as we have already so often\nremarked, belongs not to logic, but to the science of the ultimate laws of\nthe human mind.\n\nTo the same region of speculation belongs all that can be said respecting\nthe distinction which the German metaphysicians and their French and\nEnglish followers so elaborately draw between the _acts_ of the mind and\nits merely passive _states_; between what it receives from, and what it\ngives to, the crude materials of its experience. I am aware that with\nreference to the view which those writers take of the primary elements of\nthought and knowledge, this distinction is fundamental. But for the\npresent purpose, which is to examine, not the original groundwork of our\nknowledge, but how we come by that portion of it which is not original;\nthe difference between active and passive states of mind is of secondary\nimportance. For us, they all are states of mind, they all are feelings; by\nwhich, let it be said once more, I mean to imply nothing of passivity, but\nsimply that they are psychological facts, facts which take place in the\nmind, and are to be carefully distinguished from the external or physical\nfacts with which they may be connected either as effects or as causes.\n\n\u00a7 5. Among active states of mind, there is, however, one species which\nmerits particular attention, because it forms a principal part of the\nconnotation of some important classes of names. I mean _volitions_, or\nacts of the will. When we speak of sentient beings by relative names, a\nlarge portion of the connotation of the name usually consists of the\nactions of those beings; actions past, present, and possible or probable\nfuture. Take, for instance, the words Sovereign and Subject. What meaning\ndo these words convey, but that of innumerable actions, done or to be done\nby the sovereign and the subjects, to or in regard to one another\nreciprocally? So with the words physician and patient, leader and\nfollower, tutor and pupil. In many cases the words also connote actions\nwhich would be done under certain contingencies by persons other than\nthose denoted: as the words mortgagor and mortgagee, obligor and obligee,\nand many other words expressive of legal relation, which connote what a\ncourt of justice would do to enforce the legal obligation if not\nfulfilled. There are also words which connote actions previously done by\npersons other than those denoted either by the name itself or by its\ncorrelative; as the word brother. From these instances, it may be seen how\nlarge a portion of the connotation of names consists of actions. Now what\nis an action? Not one thing, but a series of two things: the state of mind\ncalled a volition, followed by an effect. The volition or intention to\nproduce the effect, is one thing; the effect produced in consequence of\nthe intention, is another thing; the two together constitute the action. I\nform the purpose of instantly moving my arm; that is a state of my mind:\nmy arm (not being tied or paralytic) moves in obedience to my purpose;\nthat is a physical fact, consequent on a state of mind. The intention,\nfollowed by the fact, or (if we prefer the expression) the fact when\npreceded and caused by the intention, is called the action of moving my\narm.\n\n\u00a7 6. Of the first leading division of namable things, viz., Feelings or\nStates of Consciousness, we began by recognizing three subdivisions;\nSensations, Thoughts, and Emotions. The first two of these we have\nillustrated at considerable length; the third, Emotions, not being\nperplexed by similar ambiguities, does not require similar\nexemplification. And, finally, we have found it necessary to add to these\nthree a fourth species, commonly known by the name Volitions. We shall now\nproceed to the two remaining classes of namable things; all things which\nare regarded as external to the mind being considered as belonging either\nto the class of Substances or to that of Attributes.\n\n\nII. Substances.\n\n\nLogicians have endeavored to define Substance and Attribute; but their\ndefinitions are not so much attempts to draw a distinction between the\nthings themselves, as instructions what difference it is customary to make\nin the grammatical structure of the sentence, according as we are speaking\nof substances or of attributes. Such definitions are rather lessons of\nEnglish, or of Greek, Latin, or German, than of mental philosophy. An\nattribute, say the school logicians, must be the attribute _of_ something;\ncolor, for example, must be the color _of_ something; goodness must be the\ngoodness _of_ something; and if this something should cease to exist, or\nshould cease to be connected with the attribute, the existence of the\nattribute would be at an end. A substance, on the contrary, is\nself-existent; in speaking about it, we need not put _of_ after its name.\nA stone is not the stone of any thing; the moon is not the moon _of_ any\nthing, but simply the moon. Unless, indeed, the name which we choose to\ngive to the substance be a relative name; if so, it must be followed\neither by _of_, or by some other particle, implying, as that preposition\ndoes, a reference to something else: but then the other characteristic\npeculiarity of an attribute would fail; the _something_ might be\ndestroyed, and the substance might still subsist. Thus, a father must be\nthe father _of_ something, and so far resembles an attribute, in being\nreferred to something besides himself: if there were no child, there would\nbe no father: but this, when we look into the matter, only means that we\nshould not call him father. The man called father might still exist though\nthere were no child, as he existed before there was a child; and there\nwould be no contradiction in supposing him to exist, though the whole\nuniverse except himself were destroyed. But destroy all white substances,\nand where would be the attribute whiteness? Whiteness, without any white\nthing, is a contradiction in terms.\n\nThis is the nearest approach to a solution of the difficulty, that will be\nfound in the common treatises on logic. It will scarcely be thought to be\na satisfactory one. If an attribute is distinguished from a substance by\nbeing the attribute _of_ something, it seems highly necessary to\nunderstand what is meant by _of_; a particle which needs explanation too\nmuch itself, to be placed in front of the explanation of any thing else.\nAnd as for the self-existence of substance, it is very true that a\nsubstance may be conceived to exist without any other substance, but so\nalso may an attribute without any other attribute: and we can no more\nimagine a substance without attributes than we can imagine attributes\nwithout a substance.\n\nMetaphysicians, however, have probed the question deeper, and given an\naccount of Substance considerably more satisfactory than this. Substances\nare usually distinguished as Bodies or Minds. Of each of these,\nphilosophers have at length provided us with a definition which seems\nunexceptionable.\n\n\u00a7 7. A body, according to the received doctrine of modern metaphysicians,\nmay be defined, the external cause to which we ascribe our sensations.\nWhen I see and touch a piece of gold, I am conscious of a sensation of\nyellow color, and sensations of hardness and weight; and by varying the\nmode of handling, I may add to these sensations many others completely\ndistinct from them. The sensations are all of which I am directly\nconscious; but I consider them as produced by something not only existing\nindependently of my will, but external to my bodily organs and to my mind.\nThis external something I call a body.\n\nIt may be asked, how come we to ascribe our sensations to any external\ncause? And is there sufficient ground for so ascribing them? It is known,\nthat there are metaphysicians who have raised a controversy on the point;\nmaintaining that we are not warranted in referring our sensations to a\ncause such as we understand by the word Body, or to any external cause\nwhatever. Though we have no concern here with this controversy, nor with\nthe metaphysical niceties on which it turns, one of the best ways of\nshowing what is meant by Substance is, to consider what position it is\nnecessary to take up, in order to maintain its existence against\nopponents.\n\nIt is certain, then, that a part of our notion of a body consists of the\nnotion of a number of sensations of our own, or of other sentient beings,\nhabitually occurring simultaneously. My conception of the table at which I\nam writing is compounded of its visible form and size, which are complex\nsensations of sight; its tangible form and size, which are complex\nsensations of our organs of touch and of our muscles; its weight, which is\nalso a sensation of touch and of the muscles; its color, which is a\nsensation of sight; its hardness, which is a sensation of the muscles; its\ncomposition, which is another word for all the varieties of sensation\nwhich we receive under various circumstances from the wood of which it is\nmade, and so forth. All or most of these various sensations frequently\nare, and, as we learn by experience, always might be, experienced\nsimultaneously, or in many different orders of succession at our own\nchoice: and hence the thought of any one of them makes us think of the\nothers, and the whole becomes mentally amalgamated into one mixed state of\nconsciousness, which, in the language of the school of Locke and Hartley,\nis termed a Complex Idea.\n\nNow, there are philosophers who have argued as follows: If we conceive an\norange to be divested of its natural color without acquiring any new one;\nto lose its softness without becoming hard, its roundness without becoming\nsquare or pentagonal, or of any other regular or irregular figure\nwhatever; to be deprived of size, of weight, of taste, of smell; to lose\nall its mechanical and all its chemical properties, and acquire no new\nones; to become, in short, invisible, intangible, imperceptible not only\nby all our senses, but by the senses of all other sentient beings, real or\npossible; nothing, say these thinkers, would remain. For of what nature,\nthey ask, could be the residuum? and by what token could it manifest its\npresence? To the unreflecting its existence seems to rest on the evidence\nof the senses. But to the senses nothing is apparent except the\nsensations. We know, indeed, that these sensations are bound together by\nsome law; they do not come together at random, but according to a\nsystematic order, which is part of the order established in the universe.\nWhen we experience one of these sensations, we usually experience the\nothers also, or know that we have it in our power to experience them. But\na fixed law of connection, making the sensations occur together, does not,\nsay these philosophers, necessarily require what is called a substratum to\nsupport them. The conception of a substratum is but one of many possible\nforms in which that connection presents itself to our imagination; a mode\nof, as it were, realizing the idea. If there be such a substratum, suppose\nit at this instant miraculously annihilated, and let the sensations\ncontinue to occur in the same order, and how would the substratum be\nmissed? By what signs should we be able to discover that its existence had\nterminated? Should we not have as much reason to believe that it still\nexisted as we now have? And if we should not then be warranted in\nbelieving it, how can we be so now? A body, therefore, according to these\nmetaphysicians, is not any thing intrinsically different from the\nsensations which the body is said to produce in us; it is, in short, a set\nof sensations, or rather, of possibilities of sensation, joined together\naccording to a fixed law.\n\nThe controversies to which these speculations have given rise, and the\ndoctrines which have been developed in the attempt to find a conclusive\nanswer to them, have been fruitful of important consequences to the\nScience of Mind. The sensations (it was answered) which we are conscious\nof, and which we receive, not at random, but joined together in a certain\nuniform manner, imply not only a law or laws of connection, but a cause\nexternal to our mind, which cause, by its own laws, determines the laws\naccording to which the sensations are connected and experienced. The\nschoolmen used to call this external cause by the name we have already\nemployed, a _substratum_; and its attributes (as they expressed\nthemselves) _inhered_, literally _stuck_, in it. To this substratum the\nname Matter is usually given in philosophical discussions. It was soon,\nhowever, acknowledged by all who reflected on the subject, that the\nexistence of matter can not be proved by extrinsic evidence. The answer,\ntherefore, now usually made to Berkeley and his followers, is, that the\nbelief is intuitive; that mankind, in all ages, have felt themselves\ncompelled, by a necessity of their nature, to refer their sensations to an\nexternal cause: that even those who deny it in theory, yield to the\nnecessity in practice, and both in speech, thought, and feeling, do,\nequally with the vulgar, acknowledge their sensations to be the effects of\nsomething external to them: this knowledge, therefore, it is affirmed, is\nas evidently intuitive as our knowledge of our sensations themselves is\nintuitive. And here the question merges in the fundamental problem of\nmetaphysics properly so called: to which science we leave it.\n\nBut although the extreme doctrine of the Idealist metaphysicians, that\nobjects are nothing but our sensations and the laws which connect them,\nhas not been generally adopted by subsequent thinkers; the point of most\nreal importance is one on which those metaphysicians are now very\ngenerally considered to have made out their case: viz., that _all we know_\nof objects is the sensations which they give us, and the order of the\noccurrence of those sensations. Kant himself, on this point, is as\nexplicit as Berkeley or Locke. However firmly convinced that there exists\na universe of \u201cThings in themselves,\u201d totally distinct from the universe\nof phenomena, or of things as they appear to our senses; and even when\nbringing into use a technical expression (_Noumenon_) to denote what the\nthing is in itself, as contrasted with the _representation_ of it in our\nminds; he allows that this representation (the matter of which, he says,\nconsists of our sensations, though the form is given by the laws of the\nmind itself) is all we know of the object: and that the real nature of the\nThing is, and by the constitution of our faculties ever must remain, at\nleast in the present state of existence, an impenetrable mystery to us.\n\u201cOf things absolutely or in themselves,\u201d says Sir William Hamilton,(19)\n\u201cbe they external, be they internal, we know nothing, or know them only as\nincognizable; and become aware of their incomprehensible existence, only\nas this is indirectly and accidentally revealed to us, through certain\nqualities related to our faculties of knowledge, and which qualities,\nagain, we can not think as unconditional, irrelative, existent in and of\nourselves. All that we know is therefore phenomenal\u2014phenomenal of the\nunknown.\u201d(20) The same doctrine is laid down in the clearest and strongest\nterms by M. Cousin, whose observations on the subject are the more worthy\nof attention, as, in consequence of the ultra-German and ontological\ncharacter of his philosophy in other respects, they may be regarded as the\nadmissions of an opponent.(21)\n\nThere is not the slightest reason for believing that what we call the\nsensible qualities of the object are a type of any thing inherent in\nitself, or bear any affinity to its own nature. A cause does not, as such,\nresemble its effects; an east wind is not like the feeling of cold, nor\nheat like the steam of boiling water. Why then should matter resemble our\nsensations? Why should the inmost nature of fire or water resemble the\nimpressions made by those objects upon our senses?(22) Or on what\nprinciple are we authorized to deduce from the effects, any thing\nconcerning the cause, except that it is a cause adequate to produce those\neffects? It may, therefore, safely be laid down as a truth both obvious in\nitself, and admitted by all whom it is at present necessary to take into\nconsideration, that, of the outward world, we know and can know absolutely\nnothing, except the sensations which we experience from it.(23)\n\n\u00a7 8. Body having now been defined the external cause, and (according to\nthe more reasonable opinion) the unknown external cause, to which we refer\nour sensations; it remains to frame a definition of Mind. Nor, after the\npreceding observations, will this be difficult. For, as our conception of\na body is that of an unknown exciting cause of sensations, so our\nconception of a mind is that of an unknown recipient or percipient, of\nthem; and not of them alone, but of all our other feelings. As body is\nunderstood to be the mysterious something which excites the mind to feel,\nso mind is the mysterious something which feels and thinks. It is\nunnecessary to give in the case of mind, as we gave in the case of matter,\na particular statement of the skeptical system by which its existence as a\nThing in itself, distinct from the series of what are denominated its\nstates, is called in question. But it is necessary to remark, that on the\ninmost nature (whatever be meant by inmost nature) of the thinking\nprinciple, as well as on the inmost nature of matter, we are, and with our\nfaculties must always remain, entirely in the dark. All which we are aware\nof, even in our own minds, is (in the words of James Mill) a certain\n\u201cthread of consciousness;\u201d a series of feelings, that is, of sensations,\nthoughts, emotions, and volitions, more or less numerous and complicated.\nThere is a something I call Myself, or, by another form of expression, my\nmind, which I consider as distinct from these sensations, thoughts, etc.;\na something which I conceive to be not the thoughts, but the being that\nhas the thoughts, and which I can conceive as existing forever in a state\nof quiescence, without any thoughts at all. But what this being is, though\nit is myself, I have no knowledge, other than the series of its states of\nconsciousness. As bodies manifest themselves to me only through the\nsensations of which I regard them as the causes, so the thinking\nprinciple, or mind, in my own nature, makes itself known to me only by the\nfeelings of which it is conscious. I know nothing about myself, save my\ncapacities of feeling or being conscious (including, of course, thinking\nand willing): and were I to learn any thing new concerning my own nature,\nI can not with my present faculties conceive this new information to be\nany thing else, than that I have some additional capacities, as yet\nunknown to me, of feeling, thinking, or willing.\n\nThus, then, as body is the unsentient cause to which we are naturally\nprompted to refer a certain portion of our feelings, so mind may be\ndescribed as the sentient _subject_ (in the scholastic sense of the term)\nof all feelings; that which has or feels them. But of the nature of either\nbody or mind, further than the feelings which the former excites, and\nwhich the latter experiences, we do not, according to the best existing\ndoctrine, know any thing; and if any thing, logic has nothing to do with\nit, or with the manner in which the knowledge is acquired. With this\nresult we may conclude this portion of our subject, and pass to the third\nand only remaining class or division of Namable Things.\n\n\nIII. Attributes: and, first, Qualities.\n\n\n\u00a7 9. From what has already been said of Substance, what is to be said of\nAttribute is easily deducible. For if we know not, and can not know, any\nthing of bodies but the sensations which they excite in us or in others,\nthose sensations must be all that we can, at bottom, mean by their\nattributes; and the distinction which we verbally make between the\nproperties of things and the sensations we receive from them, must\noriginate in the convenience of discourse rather than in the nature of\nwhat is signified by the terms.\n\nAttributes are usually distributed under the three heads of Quality,\nQuantity, and Relation. We shall come to the two latter presently: in the\nfirst place we shall confine ourselves to the former.\n\nLet us take, then, as our example, one of what are termed the sensible\nqualities of objects, and let that example be whiteness. When we ascribe\nwhiteness to any substance, as, for instance, snow; when we say that snow\nhas the quality whiteness, what do we really assert? Simply, that when\nsnow is present to our organs, we have a particular sensation, which we\nare accustomed to call the sensation of white. But how do I know that snow\nis present? Obviously by the sensations which I derive from it, and not\notherwise. I infer that the object is present, because it gives me a\ncertain assemblage or series of sensations. And when I ascribe to it the\nattribute whiteness, my meaning is only, that, of the sensations composing\nthis group or series, that which I call the sensation of white color is\none.\n\nThis is one view which may be taken of the subject. But there is also\nanother and a different view. It may be said, that it is true we _know_\nnothing of sensible objects, except the sensations they excite in us; that\nthe fact of our receiving from snow the particular sensation which is\ncalled a sensation of white, is the _ground_ on which we ascribe to that\nsubstance the quality whiteness; the sole proof of its possessing that\nquality. But because one thing may be the sole evidence of the existence\nof another thing, it does not follow that the two are one and the same.\nThe attribute whiteness (it may be said) is not the fact of receiving the\nsensation, but something in the object itself; a _power_ inherent in it;\nsomething _in virtue_ of which the object produces the sensation. And when\nwe affirm that snow possesses the attribute whiteness, we do not merely\nassert that the presence of snow produces in us that sensation, but that\nit does so through, and by reason of, that power or quality.\n\nFor the purposes of logic it is not of material importance which of these\nopinions we adopt. The full discussion of the subject belongs to the other\ndepartment of scientific inquiry, so often alluded to under the name of\nmetaphysics; but it may be said here, that for the doctrine of the\nexistence of a peculiar species of entities called qualities, I can see no\nfoundation except in a tendency of the human mind which is the cause of\nmany delusions. I mean, the disposition, wherever we meet with two names\nwhich are not precisely synonymous, to suppose that they must be the names\nof two different things; whereas in reality they may be names of the same\nthing viewed in two different lights, or under different suppositions as\nto surrounding circumstances. Because _quality_ and _sensation_ can not be\nput indiscriminately one for the other, it is supposed that they can not\nboth signify the same thing, namely, the impression or feeling with which\nwe are affected through our senses by the presence of an object; though\nthere is at least no absurdity in supposing that this identical impression\nor feeling may be called a sensation when considered merely in itself, and\na quality when looked at in relation to any one of the numerous objects,\nthe presence of which to our organs excites in our minds that among\nvarious other sensations or feelings. And if this be admissible as a\nsupposition, it rests with those who contend for an entity _per se_ called\na quality, to show that their opinion is preferable, or is any thing in\nfact but a lingering remnant of the old doctrine of occult causes; the\nvery absurdity which Moli\u00e8re so happily ridiculed when he made one of his\npedantic physicians account for the fact that opium produces sleep by the\nmaxim, Because it has a soporific virtue.\n\nIt is evident that when the physician stated that opium has a soporific\nvirtue, he did not account for, but merely asserted over again, the fact\nthat it produces sleep. In like manner, when we say that snow is white\nbecause it has the quality of whiteness, we are only re-asserting in more\ntechnical language the fact that it excites in us the sensation of white.\nIf it be said that the sensation must have some cause, I answer, its cause\nis the presence of the assemblage of phenomena which is termed the object.\nWhen we have asserted that as often as the object is present, and our\norgans in their normal state, the sensation takes place, we have stated\nall that we know about the matter. There is no need, after assigning a\ncertain and intelligible cause, to suppose an occult cause besides, for\nthe purpose of enabling the real cause to produce its effect. If I am\nasked, why does the presence of the object cause this sensation in me, I\ncan not tell: I can only say that such is my nature, and the nature of the\nobject; that the fact forms a part of the constitution of things. And to\nthis we must at last come, even after interpolating the imaginary entity.\nWhatever number of links the chain of causes and effects may consist of,\nhow any one link produces the one which is next to it, remains equally\ninexplicable to us. It is as easy to comprehend that the object should\nproduce the sensation directly and at once, as that it should produce the\nsame sensation by the aid of something else called the _power_ of\nproducing it.\n\nBut, as the difficulties which may be felt in adopting this view of the\nsubject can not be removed without discussions transcending the bounds of\nour science, I content myself with a passing indication, and shall, for\nthe purposes of logic, adopt a language compatible with either view of the\nnature of qualities. I shall say\u2014what at least admits of no dispute\u2014that\nthe quality of whiteness ascribed to the object snow, is _grounded_ on its\nexciting in us the sensation of white; and adopting the language already\nused by the school logicians in the case of the kind of attributes called\nRelations, I shall term the sensation of white the _foundation_ of the\nquality whiteness. For logical purposes the sensation is the only\nessential part of what is meant by the word; the only part which we ever\ncan be concerned in proving. When that is proved, the quality is proved;\nif an object excites a sensation, it has, of course, the power of exciting\nit.\n\n\nIV. Relations.\n\n\n\u00a7 10. The _qualities_ of a body, we have said, are the attributes grounded\non the sensations which the presence of that particular body to our organs\nexcites in our minds. But when we ascribe to any object the kind of\nattribute called a Relation, the foundation of the attribute must be\nsomething in which other objects are concerned besides itself and the\npercipient.\n\nAs there may with propriety be said to be a relation between any two\nthings to which two correlative names are or may be given, we may expect\nto discover what constitutes a relation in general, if we enumerate the\nprincipal cases in which mankind have imposed correlative names, and\nobserve what these cases have in common.\n\nWhat, then, is the character which is possessed in common by states of\ncircumstances so heterogeneous and discordant as these: one thing _like_\nanother; one thing _unlike_ another; one thing _near_ another; one thing\n_far from_ another; one thing _before_, _after_, _along with_ another; one\nthing _greater_, _equal_, _less_, than another; one thing the _cause_ of\nanother, the _effect_ of another; one person the _master_, _servant_,\n_child_, _parent_, _debtor_, _creditor_, _sovereign_, _subject_,\n_attorney_, _client_, of another, and so on?\n\nOmitting, for the present, the case of Resemblance, (a relation which\nrequires to be considered separately,) there seems to be one thing common\nto all these cases, and only one; that in each of them there exists or\noccurs, or has existed or occurred, or may be expected to exist or occur,\nsome fact or phenomenon, into which the two things which are said to be\nrelated to each other, both enter as parties concerned. This fact, or\nphenomenon, is what the Aristotelian logicians called the _fundamentum\nrelationis_. Thus in the relation of greater and less between two\nmagnitudes, the _fundamentum relationis_ is the fact that one of the two\nmagnitudes could, under certain conditions, be included in, without\nentirely filling, the space occupied by the other magnitude. In the\nrelation of master and servant, the _fundamentum relationis_ is the fact\nthat the one has undertaken, or is compelled, to perform certain services\nfor the benefit and at the bidding of the other. Examples might be\nindefinitely multiplied; but it is already obvious that whenever two\nthings are said to be related, there is some fact, or series of facts,\ninto which they both enter; and that whenever any two things are involved\nin some one fact, or series of facts, we may ascribe to those two things a\nmutual relation grounded on the fact. Even if they have nothing in common\nbut what is common to all things, that they are members of the universe,\nwe call that a relation, and denominate them fellow-creatures,\nfellow-beings, or fellow-denizens of the universe. But in proportion as\nthe fact into which the two objects enter as parts is of a more special\nand peculiar, or of a more complicated nature, so also is the relation\ngrounded upon it. And there are as many conceivable relations as there are\nconceivable kinds of fact in which two things can be jointly concerned.\n\nIn the same manner, therefore, as a quality is an attribute grounded on\nthe fact that a certain sensation or sensations are produced in us by the\nobject, so an attribute grounded on some fact into which the object enters\njointly with another object, is a relation between it and that other\nobject. But the fact in the latter case consists of the very same kind of\nelements as the fact in the former; namely, states of consciousness. In\nthe case, for example, of any legal relation, as debtor and creditor,\nprincipal and agent, guardian and ward, the _fundamentum relationis_\nconsists entirely of thoughts, feelings, and volitions (actual or\ncontingent), either of the persons themselves or of other persons\nconcerned in the same series of transactions; as, for instance, the\nintentions which would be formed by a judge, in case a complaint were made\nto his tribunal of the infringement of any of the legal obligations\nimposed by the relation; and the acts which the judge would perform in\nconsequence; acts being (as we have already seen) another word for\nintentions followed by an effect, and that effect being but another word\nfor sensations, or some other feelings, occasioned either to the agent\nhimself or to somebody else. There is no part of what the names expressive\nof the relation imply, that is not resolvable into states of\nconsciousness; outward objects being, no doubt, supposed throughout as the\ncauses by which some of those states of consciousness are excited, and\nminds as the subjects by which all of them are experienced, but neither\nthe external objects nor the minds making their existence known otherwise\nthan by the states of consciousness.\n\nCases of relation are not always so complicated as those to which we last\nalluded. The simplest of all cases of relation are those expressed by the\nwords antecedent and consequent, and by the word simultaneous. If we say,\nfor instance, that dawn preceded sunrise, the fact in which the two\nthings, dawn and sunrise, were jointly concerned, consisted only of the\ntwo things themselves; no third thing entered into the fact or phenomenon\nat all. Unless, indeed, we choose to call the succession of the two\nobjects a third thing; but their succession is not something added to the\nthings themselves; it is something involved in them. Dawn and sunrise\nannounce themselves to our consciousness by two successive sensations. Our\nconsciousness of the succession of these sensations is not a third\nsensation or feeling added to them; we have not first the two feelings,\nand then a feeling of their succession. To have two feelings at all,\nimplies having them either successively, or else simultaneously.\nSensations, or other feelings, being given, succession and\nsimultaneousness are the two conditions, to the alternative of which they\nare subjected by the nature of our faculties; and no one has been able, or\nneeds expect, to analyze the matter any further.\n\n\u00a7 11. In a somewhat similar position are two other sorts of relations,\nLikeness and Unlikeness. I have two sensations; we will suppose them to be\nsimple ones; two sensations of white, or one sensation of white and\nanother of black. I call the first two sensations _like_; the last two\n_unlike_. What is the fact or phenomenon constituting the _fundamentum_ of\nthis relation? The two sensations first, and then what we call a feeling\nof resemblance, or of want of resemblance. Let us confine ourselves to the\nformer case. Resemblance is evidently a feeling; a state of the\nconsciousness of the observer. Whether the feeling of the resemblance of\nthe two colors be a third state of consciousness, which I have _after_\nhaving the two sensations of color, or whether (like the feeling of their\nsuccession) it is involved in the sensations themselves, may be a matter\nof discussion. But in either case, these feelings of resemblance, and of\nits opposite dissimilarity, are parts of our nature; and parts so far from\nbeing capable of analysis, that they are presupposed in every attempt to\nanalyze any of our other feelings. Likeness and unlikeness, therefore, as\nwell as antecedence, sequence, and simultaneousness, must stand apart\namong relations, as things _sui generis_. They are attributes grounded on\nfacts, that is, on states of consciousness, but on states which are\npeculiar, unresolvable, and inexplicable.\n\nBut, though likeness or unlikeness can not be resolved into any thing\nelse, complex cases of likeness or unlikeness can be resolved into simpler\nones. When we say of two things which consist of parts, that they are like\none another, the likeness of the wholes does admit of analysis; it is\ncompounded of likenesses between the various parts respectively, and of\nlikeness in their arrangement. Of how vast a variety of resemblances of\nparts must that resemblance be composed, which induces us to say that a\nportrait, or a landscape, is like its original. If one person mimics\nanother with any success, of how many simple likenesses must the general\nor complex likeness be compounded: likeness in a succession of bodily\npostures; likeness in voice, or in the accents and intonations of the\nvoice; likeness in the choice of words, and in the thoughts or sentiments\nexpressed, whether by word, countenance, or gesture.\n\nAll likeness and unlikeness of which we have any cognizance, resolve\nthemselves into likeness and unlikeness between states of our own, or some\nother, mind. When we say that one body is like another, (since we know\nnothing of bodies but the sensations which they excite,) we mean really\nthat there is a resemblance between the sensations excited by the two\nbodies, or between some portions at least of those sensations. If we say\nthat two attributes are like one another (since we know nothing of\nattributes except the sensations or states of feeling on which they are\ngrounded), we mean really that those sensations, or states of feeling,\nresemble each other. We may also say that two relations are alike. The\nfact of resemblance between relations is sometimes called _analogy_,\nforming one of the numerous meanings of that word. The relation in which\nPriam stood to Hector, namely, that of father and son, resembles the\nrelation in which Philip stood to Alexander; resembles it so closely that\nthey are called the same relation. The relation in which Cromwell stood to\nEngland resembles the relation in which Napoleon stood to France, though\nnot so closely as to be called the same relation. The meaning in both\nthese instances must be, that a resemblance existed between the facts\nwhich constituted the _fundamentum relationis_.\n\nThis resemblance may exist in all conceivable gradations, from perfect\nundistinguishableness to something extremely slight. When we say, that a\nthought suggested to the mind of a person of genius is like a seed cast\ninto the ground, because the former produces a multitude of other\nthoughts, and the latter a multitude of other seeds, this is saying that\nbetween the relation of an inventive mind to a thought contained in it,\nand the relation of a fertile soil to a seed contained in it, there exists\na resemblance: the real resemblance being in the two _fundamenta\nrelationis_, in each of which there occurs a germ, producing by its\ndevelopment a multitude of other things similar to itself. And as,\nwhenever two objects are jointly concerned in a phenomenon, this\nconstitutes a relation between those objects, so, if we suppose a second\npair of objects concerned in a second phenomenon, the slightest\nresemblance between the two phenomena is sufficient to admit of its being\nsaid that the two relations resemble; provided, of course, the points of\nresemblance are found in those portions of the two phenomena respectively\nwhich are connoted by the relative names.\n\nWhile speaking of resemblance, it is necessary to take notice of an\nambiguity of language, against which scarcely any one is sufficiently on\nhis guard. Resemblance, when it exists in the highest degree of all,\namounting to undistinguishableness, is often called identity, and the two\nsimilar things are said to be the same. I say often, not always; for we do\nnot say that two visible objects, two persons, for instance, are the same,\nbecause they are so much alike that one might be mistaken for the other:\nbut we constantly use this mode of expression when speaking of feelings;\nas when I say that the sight of any object gives me the _same_ sensation\nor emotion to-day that it did yesterday, or the _same_ which it gives to\nsome other person. This is evidently an incorrect application of the word\n_same_; for the feeling which I had yesterday is gone, never to return;\nwhat I have to-day is another feeling, exactly like the former, perhaps,\nbut distinct from it; and it is evident that two different persons can not\nbe experiencing the same feeling, in the sense in which we say that they\nare both sitting at the same table. By a similar ambiguity we say, that\ntwo persons are ill of the _same_ disease; that two persons hold the\n_same_ office; not in the sense in which we say that they are engaged in\nthe same adventure, or sailing in the same ship, but in the sense that\nthey fill offices exactly similar, though, perhaps, in distant places.\nGreat confusion of ideas is often produced, and many fallacies engendered,\nin otherwise enlightened understandings, by not being sufficiently alive\nto the fact (in itself not always to be avoided), that they use the same\nname to express ideas so different as those of identity and\nundistinguishable resemblance. Among modern writers, Archbishop Whately\nstands almost alone in having drawn attention to this distinction, and to\nthe ambiguity connected with it.\n\nSeveral relations, generally called by other names, are really cases of\nresemblance. As, for example, equality; which is but another word for the\nexact resemblance commonly called identity, considered as subsisting\nbetween things in respect of their _quantity_. And this example forms a\nsuitable transition to the third and last of the three heads under which,\nas already remarked, Attributes are commonly arranged.\n\n\nV. Quantity.\n\n\n\u00a7 12. Let us imagine two things, between which there is no difference\n(that is, no dissimilarity), except in quantity alone; for instance, a\ngallon of water, and more than a gallon of water. A gallon of water, like\nany other external object, makes its presence known to us by a set of\nsensations which it excites. Ten gallons of water are also an external\nobject, making its presence known to us in a similar manner; and as we do\nnot mistake ten gallons of water for a gallon of water, it is plain that\nthe set of sensations is more or less different in the two cases. In like\nmanner, a gallon of water, and a gallon of wine, are two external objects,\nmaking their presence known by two sets of sensations, which sensations\nare different from each other. In the first case, however, we say that the\ndifference is in quantity; in the last there is a difference in quality,\nwhile the quantity of the water and of the wine is the same. What is the\nreal distinction between the two cases? It is not within the province of\nLogic to analyze it; nor to decide whether it is susceptible of analysis\nor not. For us the following considerations are sufficient: It is evident\nthat the sensations I receive from the gallon of water, and those I\nreceive from the gallon of wine, are not the same, that is, not precisely\nalike; neither are they altogether unlike: they are partly similar, partly\ndissimilar; and that in which they resemble is precisely that in which\nalone the gallon of water and the ten gallons do not resemble. That in\nwhich the gallon of water and the gallon of wine are like each other, and\nin which the gallon and the ten gallons of water are unlike each other, is\ncalled their quantity. This likeness and unlikeness I do not pretend to\nexplain, no more than any other kind of likeness or unlikeness. But my\nobject is to show, that when we say of two things that they differ in\nquantity, just as when we say that they differ in quality, the assertion\nis always grounded on a difference in the sensations which they excite.\nNobody, I presume, will say, that to see, or to lift, or to drink, ten\ngallons of water, does not include in itself a different set of sensations\nfrom those of seeing, lifting, or drinking one gallon; or that to see or\nhandle a foot-rule, and to see or handle a yard-measure made exactly like\nit, are the same sensations. I do not undertake to say what the difference\nin the sensations is. Every body knows, and nobody can tell; no more than\nany one could tell what white is to a person who had never had the\nsensation. But the difference, so far as cognizable by our faculties, lies\nin the sensations. Whatever difference we say there is in the things\nthemselves, is, in this as in all other cases, grounded, and grounded\nexclusively, on a difference in the sensations excited by them.\n\n\nVI. Attributes Concluded.\n\n\n\u00a7 13. Thus, then, all the attributes of bodies which are classed under\nQuality or Quantity, are grounded on the sensations which we receive from\nthose bodies, and may be defined, the powers which the bodies have of\nexciting those sensations. And the same general explanation has been found\nto apply to most of the attributes usually classed under the head of\nRelation. They, too, are grounded on some fact or phenomenon into which\nthe related objects enter as parts; that fact or phenomenon having no\nmeaning and no existence to us, except the series of sensations or other\nstates of consciousness by which it makes itself known; and the relation\nbeing simply the power or capacity which the object possesses of taking\npart along with the correlated object in the production of that series of\nsensations or states of consciousness. We have been obliged, indeed, to\nrecognize a somewhat different character in certain peculiar relations,\nthose of succession and simultaneity, of likeness and unlikeness. These,\nnot being grounded on any fact or phenomenon distinct from the related\nobjects themselves, do not admit of the same kind of analysis. But these\nrelations, though not, like other relations, grounded on states of\nconsciousness, are themselves states of consciousness: resemblance is\nnothing but our feeling of resemblance; succession is nothing but our\nfeeling of succession. Or, if this be disputed (and we can not, without\ntransgressing the bounds of our science, discuss it here), at least our\nknowledge of these relations, and even our possibility of knowledge, is\nconfined to those which subsist between sensations, or other states of\nconsciousness; for, though we ascribe resemblance, or succession, or\nsimultaneity, to objects and to attributes, it is always in virtue of\nresemblance or succession or simultaneity in the sensations or states of\nconsciousness which those objects excite, and on which those attributes\nare grounded.\n\n\u00a7 14. In the preceding investigation we have, for the sake of simplicity,\nconsidered bodies only, and omitted minds. But what we have said, is\napplicable, _mutatis mutandis_, to the latter. The attributes of minds, as\nwell as those of bodies, are grounded on states of feeling or\nconsciousness. But in the case of a mind, we have to consider its own\nstates, as well as those which it produces in other minds. Every attribute\nof a mind consists either in being itself affected in a certain way, or\naffecting other minds in a certain way. Considered in itself, we can\npredicate nothing of it but the series of its own feelings. When we say of\nany mind, that it is devout, or superstitious, or meditative, or cheerful,\nwe mean that the ideas, emotions, or volitions implied in those words,\nform a frequently recurring part of the series of feelings, or states of\nconsciousness, which fill up the sentient existence of that mind.\n\nIn addition, however, to those attributes of a mind which are grounded on\nits own states of feeling, attributes may also be ascribed to it, in the\nsame manner as to a body, grounded on the feelings which it excites in\nother minds. A mind does not, indeed, like a body, excite sensations, but\nit may excite thoughts or emotions. The most important example of\nattributes ascribed on this ground, is the employment of terms expressive\nof approbation or blame. When, for example, we say of any character, or\n(in other words) of any mind, that it is admirable, we mean that the\ncontemplation of it excites the sentiment of admiration; and indeed\nsomewhat more, for the word implies that we not only feel admiration, but\napprove that sentiment in ourselves. In some cases, under the semblance of\na single attribute, two are really predicated: one of them, a state of the\nmind itself; the other, a state with which other minds are affected by\nthinking of it. As when we say of any one that he is generous. The word\ngenerosity expresses a certain state of mind, but being a term of praise,\nit also expresses that this state of mind excites in us another mental\nstate, called approbation. The assertion made, therefore, is twofold, and\nof the following purport: Certain feelings form habitually a part of this\nperson\u2019s sentient existence; and the idea of those feelings of his,\nexcites the sentiment of approbation in ourselves or others.\n\nAs we thus ascribe attributes to minds on the ground of ideas and\nemotions, so may we to bodies on similar grounds, and not solely on the\nground of sensations: as in speaking of the beauty of a statue; since this\nattribute is grounded on the peculiar feeling of pleasure which the statue\nproduces in our minds; which is not a sensation, but an emotion.\n\n\nVII. General Results.\n\n\n\u00a7 15. Our survey of the varieties of Things which have been, or which are\ncapable of being, named\u2014which have been, or are capable of being, either\npredicated of other Things, or themselves made the subject of\npredications\u2014is now concluded.\n\nOur enumeration commenced with Feelings. These we scrupulously\ndistinguished from the objects which excite them, and from the organs by\nwhich they are, or may be supposed to be, conveyed. Feelings are of four\nsorts: Sensations, Thoughts, Emotions, and Volitions. What are called\nPerceptions are merely a particular case of Belief, and Belief is a kind\nof thought. Actions are merely volitions followed by an effect.\n\nAfter Feelings we proceeded to Substances. These are either Bodies or\nMinds. Without entering into the grounds of the metaphysical doubts which\nhave been raised concerning the existence of Matter and Mind as objective\nrealities, we stated as sufficient for us the conclusion in which the best\nthinkers are now for the most part agreed, that all we can know of Matter\nis the sensations which it gives us, and the order of occurrence of those\nsensations; and that while the substance Body is the unknown cause of our\nsensations, the substance Mind is the unknown recipient.\n\nThe only remaining class of Namable Things is Attributes; and these are of\nthree kinds, Quality, Relation, and Quantity. Qualities, like substances,\nare known to us no otherwise than by the sensations or other states of\nconsciousness which they excite: and while, in compliance with common\nusage, we have continued to speak of them as a distinct class of Things,\nwe showed that in predicating them no one means to predicate any thing but\nthose sensations or states of consciousness, on which they may be said to\nbe grounded, and by which alone they can be defined or described.\nRelations, except the simple cases of likeness and unlikeness, succession\nand simultaneity, are similarly grounded on some fact or phenomenon, that\nis, on some series of sensations or states of consciousness, more or less\ncomplicated. The third species of Attribute, Quantity, is also manifestly\ngrounded on something in our sensations or states of feeling, since there\nis an indubitable difference in the sensations excited by a larger and a\nsmaller bulk, or by a greater or a less degree of intensity, in any object\nof sense or of consciousness. All attributes, therefore, are to us nothing\nbut either our sensations and other states of feeling, or something\ninextricably involved therein; and to this even the peculiar and simple\nrelations just adverted to are not exceptions. Those peculiar relations,\nhowever, are so important, and, even if they might in strictness be\nclassed among states of consciousness, are so fundamentally distinct from\nany other of those states, that it would be a vain subtlety to bring them\nunder that common description, and it is necessary that they should be\nclassed apart.(24)\n\nAs the result, therefore, of our analysis, we obtain the following as an\nenumeration and classification of all Namable Things:\n\n1st. Feelings, or States of Consciousness.\n\n2d. The Minds which experience those feelings.\n\n3d. The Bodies, or external objects which excite certain of those\nfeelings, together with the powers or properties whereby they excite them;\nthese latter (at least) being included rather in compliance with common\nopinion, and because their existence is taken for granted in the common\nlanguage from which I can not prudently deviate, than because the\nrecognition of such powers or properties as real existences appears to be\nwarranted by a sound philosophy.\n\n4th, and last. The Successions and Co-existences, the Likenesses and\nUnlikenesses, between feelings or states of consciousness. Those\nrelations, when considered as subsisting between other things, exist in\nreality only between the states of consciousness which those things, if\nbodies, excite, if minds, either excite or experience.\n\nThis, until a better can be suggested, may serve as a substitute for the\nCategories of Aristotle considered as a classification of Existences. The\npractical application of it will appear when we commence the inquiry into\nthe Import of Propositions; in other words, when we inquire what it is\nwhich the mind actually believes, when it gives what is called its assent\nto a proposition.\n\nThese four classes comprising, if the classification be correct, all\nNamable Things, these or some of them must of course compose the\nsignification of all names: and of these, or some of them, is made up\nwhatever we call a fact.\n\nFor distinction\u2019s sake, every fact which is solely composed of feelings or\nstates of consciousness considered as such, is often called a\nPsychological or Subjective fact; while every fact which is composed,\neither wholly or in part, of something different from these, that is, of\nsubstances and attributes, is called an Objective fact. We may say, then,\nthat every objective fact is grounded on a corresponding subjective one;\nand has no meaning to us (apart from the subjective fact which corresponds\nto it), except as a name for the unknown and inscrutable process by which\nthat subjective or psychological fact is brought to pass.\n\n\n\n\n                               Chapter IV.\n\n\nOf Propositions.\n\n\n\u00a7 1. In treating of Propositions, as already in treating of Names, some\nconsiderations of a comparatively elementary nature respecting their form\nand varieties must be premised, before entering upon that analysis of the\nimport conveyed by them, which is the real subject and purpose of this\npreliminary book.\n\nA proposition, we have before said, is a portion of discourse in which a\npredicate is affirmed or denied of a subject. A predicate and a subject\nare all that is necessarily required to make up a proposition: but as we\ncan not conclude from merely seeing two names put together, that they are\na predicate and a subject, that is, that one of them is intended to be\naffirmed or denied of the other, it is necessary that there should be some\nmode or form of indicating that such is the intention; some sign to\ndistinguish a predication from any other kind of discourse. This is\nsometimes done by a slight alteration of one of the words, called an\n_inflection_; as when we say, Fire burns; the change of the second word\nfrom _burn_ to _burns_ showing that we mean to affirm the predicate burn\nof the subject fire. But this function is more commonly fulfilled by the\nword _is_, when an affirmation is intended, _is not_, when a negation; or\nby some other part of the verb _to be_. The word which thus serves the\npurpose of a sign of predication is called, as we formerly observed, the\n_copula_. It is important that there should be no indistinctness in our\nconception of the nature and office of the copula; for confused notions\nrespecting it are among the causes which have spread mysticism over the\nfield of logic, and perverted its speculations into logomachies.\n\nIt is apt to be supposed that the copula is something more than a mere\nsign of predication; that it also signifies existence. In the proposition,\nSocrates is just, it may seem to be implied not only that the quality\n_just_ can be affirmed of Socrates, but moreover that Socrates _is_, that\nis to say, exists. This, however, only shows that there is an ambiguity in\nthe word _is_; a word which not only performs the function of the copula\nin affirmations, but has also a meaning of its own, in virtue of which it\nmay itself be made the predicate of a proposition. That the employment of\nit as a copula does not necessarily include the affirmation of existence,\nappears from such a proposition as this, A centaur is a fiction of the\npoets; where it can not possibly be implied that a centaur exists, since\nthe proposition itself expressly asserts that the thing has no real\nexistence.\n\nMany volumes might be filled with the frivolous speculations concerning\nthe nature of Being (\u03c4\u03bf \u1f44\u03bd, \u03bf\u1f50\u03c3\u03af\u03b1, Ens, Entitas, Essentia, and the like),\nwhich have arisen from overlooking this double meaning of the word _to\nbe_; from supposing that when it signifies _to exist_, and when it\nsignifies to _be_ some specified thing, as to _be_ a man, to _be_\nSocrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a\nnonentity, it must still, at bottom, answer to the same idea; and that a\nmeaning must be found for it which shall suit all these cases. The fog\nwhich rose from this narrow spot diffused itself at an early period over\nthe whole surface of metaphysics. Yet it becomes us not to triumph over\nthe great intellects of Plato and Aristotle because we are now able to\npreserve ourselves from many errors into which they, perhaps inevitably,\nfell. The fire-teazer of a modern steam-engine produces by his exertions\nfar greater effects than Milo of Crotona could, but he is not therefore a\nstronger man. The Greeks seldom knew any language but their own. This\nrendered it far more difficult for them than it is for us, to acquire a\nreadiness in detecting ambiguities. One of the advantages of having\naccurately studied a plurality of languages, especially of those languages\nwhich eminent thinkers have used as the vehicle of their thoughts, is the\npractical lesson we learn respecting the ambiguities of words, by finding\nthat the same word in one language corresponds, on different occasions, to\ndifferent words in another. When not thus exercised, even the strongest\nunderstandings find it difficult to believe that things which have a\ncommon name, have not in some respect or other a common nature; and often\nexpend much labor very unprofitably (as was frequently done by the two\nphilosophers just mentioned) in vain attempts to discover in what this\ncommon nature consists. But, the habit once formed, intellects much\ninferior are capable of detecting even ambiguities which are common to\nmany languages: and it is surprising that the one now under consideration,\nthough it exists in the modern languages as well as in the ancient, should\nhave been overlooked by almost all authors. The quantity of futile\nspeculation which had been caused by a misapprehension of the nature of\nthe copula, was hinted at by Hobbes; but Mr. James Mill(25) was, I\nbelieve, the first who distinctly characterized the ambiguity, and pointed\nout how many errors in the received systems of philosophy it has had to\nanswer for. It has, indeed, misled the moderns scarcely less than the\nancients, though their mistakes, because our understandings are not yet so\ncompletely emancipated from their influence, do not appear equally\nirrational.\n\nWe shall now briefly review the principal distinctions which exist among\npropositions, and the technical terms most commonly in use to express\nthose distinctions.\n\n\u00a7 2. A proposition being a portion of discourse in which something is\naffirmed or denied of something, the first division of propositions is\ninto affirmative and negative. An affirmative proposition is that in which\nthe predicate is _affirmed_ of the subject; as, C\u00e6sar is dead. A negative\nproposition is that in which the predicate is _denied_ of the subject; as,\nC\u00e6sar is not dead. The copula, in this last species of proposition,\nconsists of the words _is not_, which are the sign of negation; _is_ being\nthe sign of affirmation.\n\nSome logicians, among whom may be mentioned Hobbes, state this distinction\ndifferently; they recognize only one form of copula, _is_, and attach the\nnegative sign to the predicate. \u201cC\u00e6sar is dead,\u201d and \u201cC\u00e6sar is not dead,\u201d\naccording to these writers, are propositions agreeing not in the subject\nand predicate, but in the subject only. They do not consider \u201cdead,\u201d but\n\u201cnot dead,\u201d to be the predicate of the second proposition, and they\naccordingly define a negative proposition to be one in which the predicate\nis a negative name. The point, though not of much practical moment,\ndeserves notice as an example (not unfrequent in logic) where by means of\nan apparent simplification, but which is merely verbal, matters are made\nmore complex than before. The notion of these writers was, that they could\nget rid of the distinction between affirming and denying, by treating\nevery case of denying as the affirming of a negative name. But what is\nmeant by a negative name? A name expressive of the _absence_ of an\nattribute. So that when we affirm a negative name, what we are really\npredicating is absence and not presence; we are asserting not that any\nthing is, but that something is not; to express which operation no word\nseems so proper as the word denying. The fundamental distinction is\nbetween a fact and the non-existence of that fact; between seeing\nsomething and not seeing it, between C\u00e6sar\u2019s being dead and his not being\ndead; and if this were a merely verbal distinction, the generalization\nwhich brings both within the same form of assertion would be a real\nsimplification: the distinction, however, being real, and in the facts, it\nis the generalization confounding the distinction that is merely verbal;\nand tends to obscure the subject, by treating the difference between two\nkinds of truths as if it were only a difference between two kinds of\nwords. To put things together, and to put them or keep them asunder, will\nremain different operations, whatever tricks we may play with language.\n\nA remark of a similar nature may be applied to most of those distinctions\namong propositions which are said to have reference to their _modality_;\nas, difference of tense or time; the sun _did_ rise, the sun _is_ rising,\nthe sun _will_ rise. These differences, like that between affirmation and\nnegation, might be glossed over by considering the incident of time as a\nmere modification of the predicate: thus, The sun is _an object having\nrisen_, The sun is _an object now rising_, The sun is _an object to rise\nhereafter_. But the simplification would be merely verbal. Past, present,\nand future, do not constitute so many different kinds of rising; they are\ndesignations belonging to the event asserted, to the _sun\u2019s_ rising\nto-day. They affect, not the predicate, but the applicability of the\npredicate to the particular subject. That which we affirm to be past,\npresent, or future, is not what the subject signifies, nor what the\npredicate signifies, but specifically and expressly what the predication\nsignifies; what is expressed only by the proposition as such, and not by\neither or both of the terms. Therefore the circumstance of time is\nproperly considered as attaching to the copula, which is the sign of\npredication, and not to the predicate. If the same can not be said of such\nmodifications as these, C\u00e6sar _may_ be dead; C\u00e6sar is _perhaps_ dead; it\nis _possible_ that C\u00e6sar is dead; it is only because these fall altogether\nunder another head, being properly assertions not of any thing relating to\nthe fact itself, but of the state of our own mind in regard to it; namely,\nour absence of disbelief of it. Thus \u201cC\u00e6sar may be dead\u201d means \u201cI am not\nsure that C\u00e6sar is alive.\u201d\n\n\u00a7 3. The next division of propositions is into Simple and Complex; more\naptly (by Professor Bain(26)) termed Compound. A simple proposition is\nthat in which one predicate is affirmed or denied of one subject. A\ncompound proposition is that in which there is more than one predicate, or\nmore than one subject, or both.\n\nAt first sight this division has the air of an absurdity; a solemn\ndistinction of things into one and more than one; as if we were to divide\nhorses into single horses and teams of horses. And it is true that what is\ncalled a complex (or compound) proposition is often not a proposition at\nall, but several propositions, held together by a conjunction. Such, for\nexample, is this: C\u00e6sar is dead, and Brutus is alive: or even this, C\u00e6sar\nis dead, _but_ Brutus is alive. There are here two distinct assertions;\nand we might as well call a street a complex house, as these two\npropositions a complex proposition. It is true that the syncategorematic\nwords _and_ and _but_ have a meaning; but that meaning is so far from\nmaking the two propositions one, that it adds a third proposition to them.\nAll particles are abbreviations, and generally abbreviations of\npropositions; a kind of short-hand, whereby something which, to be\nexpressed fully, would have required a proposition or a series of\npropositions, is suggested to the mind at once. Thus the words, C\u00e6sar is\ndead and Brutus is alive, are equivalent to these: C\u00e6sar is dead; Brutus\nis alive; it is desired that the two preceding propositions should be\nthought of together. If the words were, C\u00e6sar is dead, _but_ Brutus is\nalive, the sense would be equivalent to the same three propositions\ntogether with a fourth; \u201cbetween the two preceding propositions there\nexists a contrast:\u201d viz., either between the two facts themselves, or\nbetween the feelings with which it is desired that they should be\nregarded.\n\nIn the instances cited the two propositions are kept visibly distinct,\neach subject having its separate predicate, and each predicate its\nseparate subject. For brevity, however, and to avoid repetition, the\npropositions are often blended together: as in this, \u201cPeter and James\npreached at Jerusalem and in Galilee,\u201d which contains four propositions:\nPeter preached at Jerusalem, Peter preached in Galilee, James preached at\nJerusalem, James preached in Galilee.\n\nWe have seen that when the two or more propositions comprised in what is\ncalled a complex proposition are stated absolutely, and not under any\ncondition or proviso, it is not a proposition at all, but a plurality of\npropositions; since what it expresses is not a single assertion, but\nseveral assertions, which, if true when joined, are true also when\nseparated. But there is a kind of proposition which, though it contains a\nplurality of subjects and of predicates, and may be said in one sense of\nthe word to consist of several propositions, contains but one assertion;\nand its truth does not at all imply that of the simple propositions which\ncompose it. An example of this is, when the simple propositions are\nconnected by the particle _or_; as, either A is B or C is D; or by the\nparticle _if_; as, A is B if C is D. In the former case, the proposition\nis called _disjunctive_, in the latter, _conditional_: the name\n_hypothetical_ was originally common to both.\n\nAs has been well remarked by Archbishop Whately and others, the\ndisjunctive form is resolvable into the conditional; every disjunctive\nproposition being equivalent to two or more conditional ones. \u201cEither A is\nB or C is D,\u201d means, \u201cif A is not B, C is D; and if C is not D, A is B.\u201d\nAll hypothetical propositions, therefore, though disjunctive in form, are\nconditional in meaning; and the words hypothetical and conditional may be,\nas indeed they generally are, used synonymously. Propositions in which the\nassertion is not dependent on a condition, are said, in the language of\nlogicians, to be _categorical_.\n\nA hypothetical proposition is not, like the pretended complex propositions\nwhich we previously considered, a mere aggregation of simple propositions.\nThe simple propositions which form part of the words in which it is\ncouched, form no part of the assertion which it conveys. When we say, If\nthe Koran comes from God, Mohammed is the prophet of God, we do not intend\nto affirm either that the Koran does come from God, or that Mohammed is\nreally his prophet. Neither of these simple propositions may be true, and\nyet the truth of the hypothetical proposition may be indisputable. What is\nasserted is not the truth of either of the propositions, but the\ninferribility of the one from the other. What, then, is the subject, and\nwhat the predicate of the hypothetical proposition? \u201cThe Koran\u201d is not the\nsubject of it, nor is \u201cMohammed:\u201d for nothing is affirmed or denied either\nof the Koran or of Mohammed. The real subject of the predication is the\nentire proposition, \u201cMohammed is the prophet of God;\u201d and the affirmation\nis, that this is a legitimate inference from the proposition, \u201cThe Koran\ncomes from God.\u201d The subject and predicate, therefore, of a hypothetical\nproposition are names of propositions. The subject is some one\nproposition. The predicate is a general relative name applicable to\npropositions; of this form\u2014\u201can inference from so and so.\u201d A fresh instance\nis here afforded of the remark, that particles are abbreviations; since\n\u201c_If_ A is B, C is D,\u201d is found to be an abbreviation of the following:\n\u201cThe proposition C is D, is a legitimate inference from the proposition A\nis B.\u201d\n\nThe distinction, therefore, between hypothetical and categorical\npropositions is not so great as it at first appears. In the conditional,\nas well as in the categorical form, one predicate is affirmed of one\nsubject, and no more: but a conditional proposition is a proposition\nconcerning a proposition; the subject of the assertion is itself an\nassertion. Nor is this a property peculiar to hypothetical propositions.\nThere are other classes of assertions concerning propositions. Like other\nthings, a proposition has attributes which may be predicated of it. The\nattribute predicated of it in a hypothetical proposition, is that of being\nan inference from a certain other proposition. But this is only one of\nmany attributes that might be predicated. We may say, That the whole is\ngreater than its part, is an axiom in mathematics: That the Holy Ghost\nproceeds from the Father alone, is a tenet of the Greek Church: The\ndoctrine of the divine right of kings was renounced by Parliament at the\nRevolution: The infallibility of the Pope has no countenance from\nScripture. In all these cases the subject of the predication is an entire\nproposition. That which these different predicates are affirmed of, is\n_the proposition_, \u201cthe whole is greater than its part;\u201d _the\nproposition_, \u201cthe Holy Ghost proceeds from the Father alone;\u201d _the\nproposition_, \u201ckings have a divine right;\u201d _the proposition_, \u201cthe Pope is\ninfallible.\u201d\n\nSeeing, then, that there is much less difference between hypothetical\npropositions and any others, than one might be led to imagine from their\nform, we should be at a loss to account for the conspicuous position which\nthey have been selected to fill in treatises on logic, if we did not\nremember that what they predicate of a proposition, namely, its being an\ninference from something else, is precisely that one of its attributes\nwith which most of all a logician is concerned.\n\n\u00a7 4. The next of the common divisions of Propositions is into Universal,\nParticular, Indefinite, and Singular: a distinction founded on the degree\nof generality in which the name, which is the subject of the proposition,\nis to be understood. The following are examples:\n\n_All men_ are mortal\u2014Universal.\n_Some men_ are mortal\u2014Particular.\n_Man_ is mortal\u2014Indefinite.\n_Julius C\u00e6sar_ is mortal\u2014Singular.\n\nThe proposition is Singular, when the subject is an individual name. The\nindividual name needs not be a proper name. \u201cThe Founder of Christianity\nwas crucified,\u201d is as much a singular proposition as \u201cChrist was\ncrucified.\u201d\n\nWhen the name which is the subject of the proposition is a general name,\nwe may intend to affirm or deny the predicate, either of all the things\nthat the subject denotes, or only of some. When the predicate is affirmed\nor denied of all and each of the things denoted by the subject, the\nproposition is universal; when of some undefined portion of them only, it\nis particular. Thus, All men are mortal; Every man is mortal; are\nuniversal propositions. No man is immortal, is also a universal\nproposition, since the predicate, immortal, is denied of each and every\nindividual denoted by the term man; the negative proposition being exactly\nequivalent to the following, Every man is not-immortal. But \u201csome men are\nwise,\u201d \u201csome men are not wise,\u201d are particular propositions; the predicate\n_wise_ being in the one case affirmed and in the other denied not of each\nand every individual denoted by the term man, but only of each and every\none of some portion of those individuals, without specifying what portion;\nfor if this were specified, the proposition would be changed either into a\nsingular proposition, or into a universal proposition with a different\nsubject; as, for instance, \u201call _properly instructed_ men are wise.\u201d There\nare other forms of particular propositions; as, \u201c_Most_ men are\nimperfectly educated:\u201d it being immaterial how large a portion of the\nsubject the predicate is asserted of, as long as it is left uncertain how\nthat portion is to be distinguished from the rest.(27)\n\nWhen the form of the expression does not clearly show whether the general\nname which is the subject of the proposition is meant to stand for all the\nindividuals denoted by it, or only for some of them, the proposition is,\nby some logicians, called Indefinite; but this, as Archbishop Whately\nobserves, is a solecism, of the same nature as that committed by some\ngrammarians when in their list of genders they enumerate the _doubtful_\ngender. The speaker must mean to assert the proposition either as a\nuniversal or as a particular proposition, though he has failed to declare\nwhich: and it often happens that though the words do not show which of the\ntwo he intends, the context, or the custom of speech, supplies the\ndeficiency. Thus, when it is affirmed that \u201cMan is mortal,\u201d nobody doubts\nthat the assertion is intended of all human beings; and the word\nindicative of universality is commonly omitted, only because the meaning\nis evident without it. In the proposition, \u201cWine is good,\u201d it is\nunderstood with equal readiness, though for somewhat different reasons,\nthat the assertion is not intended to be universal, but particular.(28) As\nis observed by Professor Bain,(29) the chief examples of Indefinite\npropositions occur \u201cwith names of material, which are the subjects\nsometimes of universal, and at other times of particular predication.\n\u2018Food is chemically constituted by carbon, oxygen, etc.,\u2019 is a proposition\nof universal quantity; the meaning is all food\u2014all kinds of food. \u2018Food is\nnecessary to animal life\u2019 is a case of particular quantity; the meaning is\nsome sort of food, not necessarily all sorts. \u2018Metal is requisite in order\nto strength\u2019 does not mean all kinds of metal. \u2018Gold will make a way,\u2019\nmeans a portion of gold.\u201d\n\nWhen a general name stands for each and every individual which it is a\nname of, or in other words, which it denotes, it is said by logicians to\nbe _distributed_, or taken distributively. Thus, in the proposition, All\nmen are mortal, the subject, Man, is distributed, because mortality is\naffirmed of each and every man. The predicate, Mortal, is not distributed,\nbecause the only mortals who are spoken of in the proposition are those\nwho happen to be men; while the word may, for aught that appears, and in\nfact does, comprehend within it an indefinite number of objects besides\nmen. In the proposition, Some men are mortal, both the predicate and the\nsubject are undistributed. In the following, No men have wings, both the\npredicate and the subject are distributed. Not only is the attribute of\nhaving wings denied of the entire class Man, but that class is severed and\ncast out from the whole of the class Winged, and not merely from some part\nof that class.\n\nThis phraseology, which is of great service in stating and demonstrating\nthe rules of the syllogism, enables us to express very concisely the\ndefinitions of a universal and a particular proposition. A universal\nproposition is that of which the subject is distributed; a particular\nproposition is that of which the subject is undistributed.\n\nThere are many more distinctions among propositions than those we have\nhere stated, some of them of considerable importance. But, for explaining\nand illustrating these, more suitable opportunities will occur in the\nsequel.\n\n\n\n\n                                Chapter V.\n\n\nOf The Import Of Propositions.\n\n\n\u00a7 1. An inquiry into the nature of propositions must have one of two\nobjects: to analyze the state of mind called Belief, or to analyze what is\nbelieved. All language recognizes a difference between a doctrine or\nopinion, and the fact of entertaining the opinion; between assent, and\nwhat is assented to.\n\nLogic, according to the conception here formed of it, has no concern with\nthe nature of the act of judging or believing; the consideration of that\nact, as a phenomenon of the mind, belongs to another science.\nPhilosophers, however, from Descartes downward, and especially from the\nera of Leibnitz and Locke, have by no means observed this distinction; and\nwould have treated with great disrespect any attempt to analyze the import\nof Propositions, unless founded on an analysis of the act of Judgment. A\nproposition, they would have said, is but the expression in words of a\nJudgment. The thing expressed, not the mere verbal expression, is the\nimportant matter. When the mind assents to a proposition, it judges. Let\nus find out what the mind does when it judges, and we shall know what\npropositions mean, and not otherwise.\n\nConformably to these views, almost all the writers on Logic in the last\ntwo centuries, whether English, German, or French, have made their theory\nof Propositions, from one end to the other, a theory of Judgments. They\nconsidered a Proposition, or a Judgment, for they used the two words\nindiscriminately, to consist in affirming or denying one _idea_ of\nanother. To judge, was to put two ideas together, or to bring one idea\nunder another, or to compare two ideas, or to perceive the agreement or\ndisagreement between two ideas: and the whole doctrine of Propositions,\ntogether with the theory of Reasoning (always necessarily founded on the\ntheory of Propositions), was stated as if Ideas, or Conceptions, or\nwhatever other term the writer preferred as a name for mental\nrepresentations generally, constituted essentially the subject-matter and\nsubstance of those operations.\n\nIt is, of course, true, that in any case of judgment, as for instance when\nwe judge that gold is yellow, a process takes place in our minds, of which\nsome one or other of these theories is a partially correct account. We\nmust have the idea of gold and the idea of yellow, and these two ideas\nmust be brought together in our mind. But in the first place, it is\nevident that this is only a part of what takes place; for we may put two\nideas together without any act of belief; as when we merely imagine\nsomething, such as a golden mountain; or when we actually disbelieve: for\nin order even to disbelieve that Mohammed was an apostle of God, we must\nput the idea of Mohammed and that of an apostle of God together. To\ndetermine what it is that happens in the case of assent or dissent besides\nputting two ideas together, is one of the most intricate of metaphysical\nproblems. But whatever the solution may be, we may venture to assert that\nit can have nothing whatever to do with the import of propositions; for\nthis reason, that propositions (except sometimes when the mind itself is\nthe subject treated of) are not assertions respecting our ideas of things,\nbut assertions respecting the things themselves. In order to believe that\ngold is yellow, I must, indeed, have the idea of gold, and the idea of\nyellow, and something having reference to those ideas must take place in\nmy mind; but my belief has not reference to the ideas, it has reference to\nthe things. What I believe, is a fact relating to the outward thing, gold,\nand to the impression made by that outward thing upon the human organs;\nnot a fact relating to my conception of gold, which would be a fact in my\nmental history, not a fact of external nature. It is true, that in order\nto believe this fact in external nature, another fact must take place in\nmy mind, a process must be performed upon my ideas; but so it must in\nevery thing else that I do. I can not dig the ground unless I have the\nidea of the ground, and of a spade, and of all the other things I am\noperating upon, and unless I put those ideas together.(30) But it would be\na very ridiculous description of digging the ground to say that it is\nputting one idea into another. Digging is an operation which is performed\nupon the things themselves, though it can not be performed unless I have\nin my mind the ideas of them. And in like manner, believing is an act\nwhich has for its subject the facts themselves, though a previous mental\nconception of the facts is an indispensable condition. When I say that\nfire causes heat, do I mean that my idea of fire causes my idea of heat?\nNo: I mean that the natural phenomenon, fire, causes the natural\nphenomenon, heat. When I mean to assert any thing respecting the ideas, I\ngive them their proper name, I call them ideas: as when I say, that a\nchild\u2019s idea of a battle is unlike the reality, or that the ideas\nentertained of the Deity have a great effect on the characters of mankind.\n\nThe notion that what is of primary importance to the logician in a\nproposition, is the relation between the two _ideas_ corresponding to the\nsubject and predicate (instead of the relation between the two _phenomena_\nwhich they respectively express), seems to me one of the most fatal errors\never introduced into the philosophy of Logic; and the principal cause why\nthe theory of the science has made such inconsiderable progress during the\nlast two centuries. The treatises on Logic, and on the branches of Mental\nPhilosophy connected with Logic, which have been produced since the\nintrusion of this cardinal error, though sometimes written by men of\nextraordinary abilities and attainments, almost always tacitly imply a\ntheory that the investigation of truth consists in contemplating and\nhandling our ideas, or conceptions of things, instead of the things\nthemselves: a doctrine tantamount to the assertion, that the only mode of\nacquiring knowledge of nature is to study it at second hand, as\nrepresented in our own minds. Meanwhile, inquiries into every kind of\nnatural phenomena were incessantly establishing great and fruitful truths\non most important subjects, by processes upon which these views of the\nnature of Judgment and Reasoning threw no light, and in which they\nafforded no assistance whatever. No wonder that those who knew by\npractical experience how truths are arrived at, should deem a science\nfutile, which consisted chiefly of such speculations. What has been done\nfor the advancement of Logic since these doctrines came into vogue, has\nbeen done not by professed logicians, but by discoverers in the other\nsciences; in whose methods of investigation many principles of logic, not\npreviously thought of, have successively come forth into light, but who\nhave generally committed the error of supposing that nothing whatever was\nknown of the art of philosophizing by the old logicians, because their\nmodern interpreters have written to so little purpose respecting it.\n\nWe have to inquire, then, on the present occasion, not into Judgment, but\njudgments; not into the act of believing, but into the thing believed.\nWhat is the immediate object of belief in a Proposition? What is the\nmatter of fact signified by it? What is it to which, when I assert the\nproposition, I give my assent, and call upon others to give theirs? What\nis that which is expressed by the form of discourse called a Proposition,\nand the conformity of which to fact constitutes the truth of the\nproposition?\n\n\u00a7 2. One of the clearest and most consecutive thinkers whom this country\nor the world has produced, I mean Hobbes, has given the following answer\nto this question. In every proposition (says he) what is signified is, the\nbelief of the speaker that the predicate is a name of the same thing of\nwhich the subject is a name; and if it really is so, the proposition is\ntrue. Thus the proposition, All men are living beings (he would say) is\ntrue, because _living being_ is a name of every thing of which _man_ is a\nname. All men are six feet high, is not true, because _six feet high_ is\nnot a name of every thing (though it is of some things) of which _man_ is\na name.\n\nWhat is stated in this theory as the definition of a true proposition,\nmust be allowed to be a property which all true propositions possess. The\nsubject and predicate being both of them names of things, if they were\nnames of quite different things the one name could not, consistently with\nits signification, be predicated of the other. If it be true that some men\nare copper-colored, it must be true\u2014and the proposition does really\nassert\u2014that among the individuals denoted by the name man, there are some\nwho are also among those denoted by the name copper-colored. If it be true\nthat all oxen ruminate, it must be true that all the individuals denoted\nby the name ox are also among those denoted by the name ruminating; and\nwhoever asserts that all oxen ruminate, undoubtedly does assert that this\nrelation subsists between the two names.\n\nThe assertion, therefore, which, according to Hobbes, is the only one made\nin any proposition, really is made in every proposition: and his analysis\nhas consequently one of the requisites for being the true one. We may go a\nstep further; it is the only analysis that is rigorously true of all\npropositions without exception. What he gives as the meaning of\npropositions, is part of the meaning of all propositions, and the whole\nmeaning of some. This, however, only shows what an extremely minute\nfragment of meaning it is quite possible to include within the logical\nformula of a proposition. It does not show that no proposition means more.\nTo warrant us in putting together two words with a copula between them, it\nis really enough that the thing or things denoted by one of the names\nshould be capable, without violation of usage, of being called by the\nother name also. If, then, this be all the meaning necessarily implied in\nthe form of discourse called a Proposition, why do I object to it as the\nscientific definition of what a proposition means? Because, though the\nmere collocation which makes the proposition a proposition, conveys no\nmore than this scanty amount of meaning, that same collocation combined\nwith other circumstances, that _form_ combined with other _matter_, does\nconvey more, and the proposition in those other circumstances does assert\nmore, than merely that relation between the two names.\n\nThe only propositions of which Hobbes\u2019s principle is a sufficient account,\nare that limited and unimportant class in which both the predicate and the\nsubject are proper names. For, as has already been remarked, proper names\nhave strictly no meaning; they are mere marks for individual objects: and\nwhen a proper name is predicated of another proper name, all the\nsignification conveyed is, that both the names are marks for the same\nobject. But this is precisely what Hobbes produces as a theory of\npredication in general. His doctrine is a full explanation of such\npredications as these: Hyde was Clarendon, or, Tully is Cicero. It\nexhausts the meaning of those propositions. But it is a sadly inadequate\ntheory of any others. That it should ever have been thought of as such,\ncan be accounted for only by the fact, that Hobbes, in common with the\nother Nominalists, bestowed little or no attention upon the _connotation_\nof words; and sought for their meaning exclusively in what they _denote_:\nas if all names had been (what none but proper names really are) marks put\nupon individuals; and as if there were no difference between a proper and\na general name, except that the first denotes only one individual, and the\nlast a greater number.\n\nIt has been seen, however, that the meaning of all names, except proper\nnames and that portion of the class of abstract names which are not\nconnotative, resides in the connotation. When, therefore, we are analyzing\nthe meaning of any proposition in which the predicate and the subject, or\neither of them, are connotative names, it is to the connotation of those\nterms that we must exclusively look, and not to what they _denote_, or in\nthe language of Hobbes (language so far correct) are names of.\n\nIn asserting that the truth of a proposition depends on the conformity of\nimport between its terms, as, for instance, that the proposition, Socrates\nis wise, is a true proposition, because Socrates and wise are names\napplicable to, or, as he expresses it, names of, the same person; it is\nvery remarkable that so powerful a thinker should not have asked himself\nthe question, But how came they to be names of the same person? Surely not\nbecause such was the intention of those who invented the words. When\nmankind fixed the meaning of the word wise, they were not thinking of\nSocrates, nor, when his parents gave him the name of Socrates, were they\nthinking of wisdom. The names _happen_ to fit the same person because of a\ncertain _fact_, which fact was not known, nor in being, when the names\nwere invented. If we want to know what the fact is, we shall find the clue\nto it in the _connotation_ of the names.\n\nA bird or a stone, a man, or a wise man, means simply, an object having\nsuch and such attributes. The real meaning of the word man, is those\nattributes, and not Smith, Brown, and the remainder of the individuals.\nThe word _mortal_, in like manner connotes a certain attribute or\nattributes; and when we say, All men are mortal, the meaning of the\nproposition is, that all beings which possess the one set of attributes,\npossess also the other. If, in our experience, the attributes connoted by\n_man_ are always accompanied by the attribute connoted by _mortal_, it\nwill follow as a consequence, that the class _man_ will be wholly included\nin the class _mortal_, and that _mortal_ will be a name of all things of\nwhich _man_ is a name: but why? Those objects are brought under the name,\nby possessing the attributes connoted by it: but their possession of the\nattributes is the real condition on which the truth of the proposition\ndepends; not their being called by the name. Connotative names do not\nprecede, but follow, the attributes which they connote. If one attribute\nhappens to be always found in conjunction with another attribute, the\nconcrete names which answer to those attributes will of course be\npredicable of the same subjects, and may be said, in Hobbes\u2019s language (in\nthe propriety of which on this occasion I fully concur), to be two names\nfor the same things. But the possibility of a concurrent application of\nthe two names, is a mere consequence of the conjunction between the two\nattributes, and was, in most cases, never thought of when the names were\nintroduced and their signification fixed. That the diamond is combustible,\nwas a proposition certainly not dreamed of when the words Diamond and\nCombustible first received their meaning; and could not have been\ndiscovered by the most ingenious and refined analysis of the signification\nof those words. It was found out by a very different process, namely, by\nexerting the senses, and learning from them, that the attribute of\ncombustibility existed in the diamonds upon which the experiment was\ntried; the number or character of the experiments being such, that what\nwas true of those individuals might be concluded to be true of all\nsubstances \u201ccalled by the name,\u201d that is, of all substances possessing the\nattributes which the name connotes. The assertion, therefore, when\nanalyzed, is, that wherever we find certain attributes, there will be\nfound a certain other attribute: which is not a question of the\nsignification of names, but of laws of nature; the order existing among\nphenomena.\n\n\u00a7 3. Although Hobbes\u2019s theory of Predication has not, in the terms in\nwhich he stated it, met with a very favorable reception from subsequent\nthinkers, a theory virtually identical with it, and not by any means so\nperspicuously expressed, may almost be said to have taken the rank of an\nestablished opinion. The most generally received notion of Predication\ndecidedly is that it consists in referring something to a class, _i.e._,\neither placing an individual under a class, or placing one class under\nanother class. Thus, the proposition, Man is mortal, asserts, according to\nthis view of it, that the class man is included in the class mortal.\n\u201cPlato is a philosopher,\u201d asserts that the individual Plato is one of\nthose who compose the class philosopher. If the proposition is negative,\nthen instead of placing something in a class, it is said to exclude\nsomething from a class. Thus, if the following be the proposition, The\nelephant is not carnivorous; what is asserted (according to this theory)\nis, that the elephant is excluded from the class carnivorous, or is not\nnumbered among the things comprising that class. There is no real\ndifference, except in language, between this theory of Predication and the\ntheory of Hobbes. For a class _is_ absolutely nothing but an indefinite\nnumber of individuals denoted by a general name. The name given to them in\ncommon, is what makes them a class. To refer any thing to a class,\ntherefore, is to look upon it as one of the things which are to be called\nby that common name. To exclude it from a class, is to say that the common\nname is not applicable to it.\n\nHow widely these views of predication have prevailed, is evident from\nthis, that they are the basis of the celebrated _dictum de omni et nullo_.\nWhen the syllogism is resolved, by all who treat of it, into an inference\nthat what is true of a class is true of all things whatever that belong to\nthe class; and when this is laid down by almost all professed logicians as\nthe ultimate principle to which all reasoning owes its validity; it is\nclear that in the general estimation of logicians, the propositions of\nwhich reasonings are composed can be the expression of nothing but the\nprocess of dividing things into classes, and referring every thing to its\nproper class.\n\nThis theory appears to me a signal example of a logical error very often\ncommitted in logic, that of \u1f55\u03c3\u03c4\u03b5\u03c1\u03bf\u03bd \u03c0\u03c1\u03bf\u03c4\u03ad\u03c1\u03bf\u03bd, or explaining a thing by\nsomething which presupposes it. When I say that snow is white, I may and\nought to be thinking of snow as a class, because I am asserting a\nproposition as true of all snow: but I am certainly not thinking of white\nobjects as a class; I am thinking of no white object whatever except snow,\nbut only of that, and of the sensation of white which it gives me. When,\nindeed, I have judged, or assented to the propositions, that snow is\nwhite, and that several other things are also white, I gradually begin to\nthink of white objects as a class, including snow and those other things.\nBut this is a conception which followed, not preceded, those judgments,\nand therefore can not be given as an explanation of them. Instead of\nexplaining the effect by the cause, this doctrine explains the cause by\nthe effect, and is, I conceive, founded on a latent misconception of the\nnature of classification.\n\nThere is a sort of language very generally prevalent in these discussions,\nwhich seems to suppose that classification is an arrangement and grouping\nof definite and known individuals: that when names were imposed, mankind\ntook into consideration all the individual objects in the universe,\ndistributed them into parcels or lists, and gave to the objects of each\nlist a common name, repeating this operation _toties quoties_ until they\nhad invented all the general names of which language consists; which\nhaving been once done, if a question subsequently arises whether a certain\ngeneral name can be truly predicated of a certain particular object, we\nhave only (as it were) to read the roll of the objects upon which that\nname was conferred, and see whether the object about which the question\narises is to be found among them. The framers of language (it would seem\nto be supposed) have predetermined all the objects that are to compose\neach class, and we have only to refer to the record of an antecedent\ndecision.\n\nSo absurd a doctrine will be owned by nobody when thus nakedly stated; but\nif the commonly received explanations of classification and naming do not\nimply this theory, it requires to be shown how they admit of being\nreconciled with any other.\n\nGeneral names are not marks put upon definite objects; classes are not\nmade by drawing a line round a given number of assignable individuals. The\nobjects which compose any given class are perpetually fluctuating. We may\nframe a class without knowing the individuals, or even any of the\nindividuals, of which it may be composed; we may do so while believing\nthat no such individuals exist. If by the _meaning_ of a general name are\nto be understood the things which it is the name of, no general name,\nexcept by accident, has a fixed meaning at all, or ever long retains the\nsame meaning. The only mode in which any general name has a definite\nmeaning, is by being a name of an indefinite variety of things; namely, of\nall things, known or unknown, past, present, or future, which possess\ncertain definite attributes. When, by studying not the meaning of words,\nbut the phenomena of nature, we discover that these attributes are\npossessed by some object not previously known to possess them (as when\nchemists found that the diamond was combustible), we include this new\nobject in the class; but it did not already belong to the class. We place\nthe individual in the class because the proposition is true; the\nproposition is not true because the object is placed in the class.(31)\n\nIt will appear hereafter, in treating of reasoning, how much the theory of\nthat intellectual process has been vitiated by the influence of these\nerroneous notions, and by the habit which they exemplify of assimilating\nall the operations of the human understanding which have truth for their\nobject, to processes of mere classification and naming. Unfortunately, the\nminds which have been entangled in this net are precisely those which have\nescaped the other cardinal error commented upon in the beginning of the\npresent chapter. Since the revolution which dislodged Aristotle from the\nschools, logicians may almost be divided into those who have looked upon\nreasoning as essentially an affair of Ideas, and those who have looked\nupon it as essentially an affair of Names.\n\nAlthough, however, Hobbes\u2019s theory of Predication, according to the\nwell-known remark of Leibnitz, and the avowal of Hobbes himself,(32)\nrenders truth and falsity completely arbitrary, with no standard but the\nwill of men, it must not be concluded that either Hobbes, or any of the\nother thinkers who have in the main agreed with him, did in fact consider\nthe distinction between truth and error as less real, or attached less\nimportance to it, than other people. To suppose that they did so would\nargue total unacquaintance with their other speculations. But this shows\nhow little hold their doctrine possessed over their own minds. No person,\nat bottom, ever imagined that there was nothing more in truth than\npropriety of expression; than using language in conformity to a previous\nconvention. When the inquiry was brought down from generals to a\nparticular case, it has always been acknowledged that there is a\ndistinction between verbal and real questions; that some false\npropositions are uttered from ignorance of the meaning of words, but that\nin others the source of the error is a misapprehension of things; that a\nperson who has not the use of language at all may form propositions\nmentally, and that they may be untrue\u2014that is, he may believe as matters\nof fact what are not really so. This last admission can not be made in\nstronger terms than it is by Hobbes himself,(33) though he will not allow\nsuch erroneous belief to be called falsity, but only error. And he has\nhimself laid down, in other places, doctrines in which the true theory of\npredication is by implication contained. He distinctly says that general\nnames are given to things on account of their attributes, and that\nabstract names are the names of those attributes. \u201cAbstract is that which\nin any subject denotes the cause of the concrete name.... And these causes\nof names are the same with the causes of our conceptions, namely, some\npower of action, or affection, of the thing conceived, which some call the\nmanner by which any thing works upon our senses, but by most men they are\ncalled _accidents_.\u201d(34) It is strange that having gone so far, he should\nnot have gone one step further, and seen that what he calls the cause of\nthe concrete name, is in reality the meaning of it; and that when we\npredicate of any subject a name which is given _because_ of an attribute\n(or, as he calls it, an accident), our object is not to affirm the name,\nbut, by means of the name, to affirm the attribute.\n\n\u00a7 4. Let the predicate be, as we have said, a connotative term; and to\ntake the simplest case first, let the subject be a proper name: \u201cThe\nsummit of Chimborazo is white.\u201d The word white connotes an attribute which\nis possessed by the individual object designated by the words \u201csummit of\nChimborazo;\u201d which attribute consists in the physical fact, of its\nexciting in human beings the sensation which we call a sensation of white.\nIt will be admitted that, by asserting the proposition, we wish to\ncommunicate information of that physical fact, and are not thinking of the\nnames, except as the necessary means of making that communication. The\nmeaning of the proposition, therefore, is, that the individual thing\ndenoted by the subject, has the attributes connoted by the predicate.\n\nIf we now suppose the subject also to be a connotative name, the meaning\nexpressed by the proposition has advanced a step further in complication.\nLet us first suppose the proposition to be universal, as well as\naffirmative: \u201cAll men are mortal.\u201d In this case, as in the last, what the\nproposition asserts (or expresses a belief of) is, of course, that the\nobjects denoted by the subject (man) possess the attributes connoted by\nthe predicate (mortal). But the characteristic of this case is, that the\nobjects are no longer _individually_ designated. They are pointed out only\nby some of their attributes: they are the objects called men, that is,\npossessing the attributes connoted by the name man; and the only thing\nknown of them may be those attributes: indeed, as the proposition is\ngeneral, and the objects denoted by the subject are therefore indefinite\nin number, most of them are not known individually at all. The assertion,\ntherefore, is not, as before, that the attributes which the predicate\nconnotes are possessed by any given individual, or by any number of\nindividuals previously known as John, Thomas, etc., but that those\nattributes are possessed by each and every individual possessing certain\nother attributes; that whatever has the attributes connoted by the\nsubject, has also those connoted by the predicate; that the latter set of\nattributes _constantly accompany_ the former set. Whatever has the\nattributes of man has the attribute of mortality; mortality constantly\naccompanies the attributes of man.(35)\n\nIf it be remembered that every attribute is _grounded_ on some fact or\nphenomenon, either of outward sense or of inward consciousness, and that\nto _possess_ an attribute is another phrase for being the cause of, or\nforming part of, the fact or phenomenon upon which the attribute is\ngrounded; we may add one more step to complete the analysis. The\nproposition which asserts that one attribute always accompanies another\nattribute, really asserts thereby no other thing than this, that one\nphenomenon always accompanies another phenomenon; insomuch that where we\nfind the latter, we have assurance of the existence of the former. Thus,\nin the proposition, All men are mortal, the word man connotes the\nattributes which we ascribe to a certain kind of living creatures, on the\nground of certain phenomena which they exhibit, and which are partly\nphysical phenomena, namely the impressions made on our senses by their\nbodily form and structure, and partly mental phenomena, namely the\nsentient and intellectual life which they have of their own. All this is\nunderstood when we utter the word man, by any one to whom the meaning of\nthe word is known. Now, when we say, Man is mortal, we mean that wherever\nthese various physical and mental phenomena are all found, there we have\nassurance that the other physical and mental phenomenon, called death,\nwill not fail to take place. The proposition does not affirm _when_; for\nthe connotation of the word _mortal_ goes no further than to the\noccurrence of the phenomenon at some time or other, leaving the particular\ntime undecided.\n\n\u00a7 5. We have already proceeded far enough, not only to demonstrate the\nerror of Hobbes, but to ascertain the real import of by far the most\nnumerous class of propositions. The object of belief in a proposition,\nwhen it asserts any thing more than the meaning of words, is generally, as\nin the cases which we have examined, either the co-existence or the\nsequence of two phenomena. At the very commencement of our inquiry, we\nfound that every act of belief implied two Things: we have now ascertained\nwhat, in the most frequent case, these two things are, namely, two\nPhenomena; in other words, two states of consciousness; and what it is\nwhich the proposition affirms (or denies) to subsist between them, namely,\neither succession or co-existence. And this case includes innumerable\ninstances which no one, previous to reflection, would think of referring\nto it. Take the following example: A generous person is worthy of honor.\nWho would expect to recognize here a case of co-existence between\nphenomena? But so it is. The attribute which causes a person to be termed\ngenerous, is ascribed to him on the ground of states of his mind, and\nparticulars of his conduct: both are phenomena: the former are facts of\ninternal consciousness; the latter, so far as distinct from the former,\nare physical facts, or perceptions of the senses. Worthy of honor admits\nof a similar analysis. Honor, as here used, means a state of approving and\nadmiring emotion, followed on occasion by corresponding outward acts.\n\u201cWorthy of honor\u201d connotes all this, together with our approval of the act\nof showing honor. All these are phenomena; states of internal\nconsciousness, accompanied or followed by physical facts. When we say, A\ngenerous person is worthy of honor, we affirm co-existence between the two\ncomplicated phenomena connoted by the two terms respectively. We affirm,\nthat wherever and whenever the inward feelings and outward facts implied\nin the word generosity have place, then and there the existence and\nmanifestation of an inward feeling, honor, would be followed in our minds\nby another inward feeling, approval.\n\nAfter the analysis, in a former chapter, of the import of names, many\nexamples are not needed to illustrate the import of propositions. When\nthere is any obscurity, or difficulty, it does not lie in the meaning of\nthe proposition, but in the meaning of the names which compose it; in the\nextremely complicated connotation of many words; the immense multitude and\nprolonged series of facts which often constitute the phenomenon connoted\nby a name. But where it is seen what the phenomenon is, there is seldom\nany difficulty in seeing that the assertion conveyed by the proposition\nis, the co-existence of one such phenomenon with another; or the\nsuccession of one such phenomenon to another: so that where the one is\nfound, we may calculate on finding the other, though perhaps not\nconversely.\n\nThis, however, though the most common, is not the only meaning which\npropositions are ever intended to convey. In the first place, sequences\nand co-existences are not only asserted respecting Phenomena; we make\npropositions also respecting those hidden causes of phenomena, which are\nnamed substances and attributes. A substance, however, being to us nothing\nbut either that which causes, or that which is conscious of, phenomena;\nand the same being true, _mutatis mutandis_, of attributes; no assertion\ncan be made, at least with a meaning, concerning these unknown and\nunknowable entities, except in virtue of the Phenomena by which alone they\nmanifest themselves to our faculties. When we say Socrates was\ncontemporary with the Peloponnesian war, the foundation of this assertion,\nas of all assertions concerning substances, is an assertion concerning the\nphenomena which they exhibit\u2014namely, that the series of facts by which\nSocrates manifested himself to mankind, and the series of mental states\nwhich constituted his sentient existence, went on simultaneously with the\nseries of facts known by the name of the Peloponnesian war. Still, the\nproposition as commonly understood does not assert that alone; it asserts\nthat the Thing in itself, the _noumenon_ Socrates, was existing, and doing\nor experiencing those various facts during the same time. Co-existence and\nsequence, therefore, may be affirmed or denied not only between phenomena,\nbut between noumena, or between a noumenon and phenomena. And both of\nnoumena and of phenomena we may affirm simple existence. But what is a\nnoumenon? An unknown cause. In affirming, therefore, the existence of a\nnoumenon, we affirm causation. Here, therefore, are two additional kinds\nof fact, capable of being asserted in a proposition. Besides the\npropositions which assert Sequence or Co-existence, there are some which\nassert simple Existence;(36) and others assert Causation, which, subject\nto the explanations which will follow in the Third Book, must be\nconsidered provisionally as a distinct and peculiar kind of assertion.\n\n\u00a7 6. To these four kinds of matter-of-fact or assertion, must be added a\nfifth, Resemblance. This was a species of attribute which we found it\nimpossible to analyze; for which no _fundamentum_, distinct from the\nobjects themselves, could be assigned. Besides propositions which assert a\nsequence or co-existence between two phenomena, there are therefore also\npropositions which assert resemblance between them; as, This color is like\nthat color; The heat of to-day is _equal_ to the heat of yesterday. It is\ntrue that such an assertion might with some plausibility be brought within\nthe description of an affirmation of sequence, by considering it as an\nassertion that the simultaneous contemplation of the two colors is\n_followed_ by a specific feeling termed the feeling of resemblance. But\nthere would be nothing gained by incumbering ourselves, especially in this\nplace, with a generalization which may be looked upon as strained. Logic\ndoes not undertake to analyze mental facts into their ultimate elements.\nResemblance between two phenomena is more intelligible in itself than any\nexplanation could make it, and under any classification must remain\nspecifically distinct from the ordinary cases of sequence and\nco-existence.\n\nIt is sometimes said, that all propositions whatever, of which the\npredicate is a general name, do, in point of fact, affirm or deny\nresemblance. All such propositions affirm that a thing belongs to a class;\nbut things being classed together according to their resemblance, every\nthing is of course classed with the things which it is supposed to\nresemble most; and thence, it may be said, when we affirm that Gold is a\nmetal, or that Socrates is a man, the affirmation intended is, that gold\nresembles other metals, and Socrates other men, more nearly than they\nresemble the objects contained in any other of the classes co-ordinate\nwith these.\n\nThere is some slight degree of foundation for this remark, but no more\nthan a slight degree. The arrangement of things into classes, such as the\nclass _metal_, or the class _man_, is grounded indeed on a resemblance\namong the things which are placed in the same class, but not on a mere\ngeneral resemblance: the resemblance it is grounded on consists in the\npossession by all those things, of certain common peculiarities; and those\npeculiarities it is which the terms connote, and which the propositions\nconsequently assert; not the resemblance. For though when I say, Gold is a\nmetal, I say by implication that if there be any other metals it must\nresemble them, yet if there were no other metals I might still assert the\nproposition with the same meaning as at present, namely, that gold has the\nvarious properties implied in the word metal; just as it might be said,\nChristians are men, even if there were no men who were not Christians.\nPropositions, therefore, in which objects are referred to a class because\nthey possess the attributes constituting the class, are so far from\nasserting nothing but resemblance, that they do not, properly speaking,\nassert resemblance at all.\n\nBut we remarked some time ago (and the reasons of the remark will be more\nfully entered into in a subsequent Book(37)) that there is sometimes a\nconvenience in extending the boundaries of a class so as to include things\nwhich possess in a very inferior degree, if in any, some of the\ncharacteristic properties of the class\u2014provided they resemble that class\nmore than any other, insomuch that the general propositions which are true\nof the class, will be nearer to being true of those things than any other\nequally general propositions. For instance, there are substances called\nmetals which have very few of the properties by which metals are commonly\nrecognized; and almost every great family of plants or animals has a few\nanomalous genera or species on its borders, which are admitted into it by\na sort of courtesy, and concerning which it has been matter of discussion\nto what family they properly belonged. Now when the class-name is\npredicated of any object of this description, we do, by so predicating it,\naffirm resemblance and nothing more. And in order to be scrupulously\ncorrect it ought to be said, that in every case in which we predicate a\ngeneral name, we affirm, not absolutely that the object possesses the\nproperties designated by the name, but that it _either_ possesses those\nproperties, or if it does not, at any rate resembles the things which do\nso, more than it resembles any other things. In most cases, however, it is\nunnecessary to suppose any such alternative, the latter of the two grounds\nbeing very seldom that on which the assertion is made: and when it is,\nthere is generally some slight difference in the form of the expression,\nas, This species (or genus) is _considered_, or _may be ranked_, as\nbelonging to such and such a family: we should hardly say positively that\nit does belong to it, unless it possessed unequivocally the properties of\nwhich the class-name is scientifically significant.\n\nThere is still another exceptional case, in which, though the predicate is\nthe name of a class, yet in predicating it we affirm nothing but\nresemblance, the class being founded not on resemblance in any given\nparticular, but on general unanalyzable resemblance. The classes in\nquestion are those into which our simple sensations, or other simple\nfeelings, are divided. Sensations of white, for instance, are classed\ntogether, not because we can take them to pieces, and say they are alike\nin this, and not alike in that, but because we feel them to be alike\naltogether, though in different degrees. When, therefore, I say, The color\nI saw yesterday was a white color, or, The sensation I feel is one of\ntightness, in both cases the attribute I affirm of the color or of the\nother sensation is mere resemblance\u2014simple _likeness_ to sensations which\nI have had before, and which have had those names bestowed upon them. The\nnames of feelings, like other concrete general names, are connotative; but\nthey connote a mere resemblance. When predicated of any individual\nfeeling, the information they convey is that of its likeness to the other\nfeelings which we have been accustomed to call by the same name. Thus much\nmay suffice in illustration of the kind of propositions in which the\nmatter-of-fact asserted (or denied) is simple Resemblance.\n\nExistence, Co-existence, Sequence, Causation, Resemblance: one or other of\nthese is asserted (or denied) in every proposition which is not merely\nverbal. This five-fold division is an exhaustive classification of\nmatters-of-fact; of all things that can be believed, or tendered for\nbelief; of all questions that can be propounded, and all answers that can\nbe returned to them.\n\nProfessor Bain(38) distinguishes two kinds of Propositions of\nCo-existence. \u201cIn the one kind, account is taken of Place; they may be\ndescribed as propositions of Order in Place.\u201d In the other kind, the\nco-existence which is predicated is termed by Mr. Bain Co-inherence of\nAttributes. \u201cThis is a distinct variety of Propositions of Co-existence.\nInstead of an arrangement in place with numerical intervals, we have the\nconcurrence of two or more attributes or powers in the same part or\nlocality. A mass of gold contains, in every atom, the concurring\nattributes that mark the substance\u2014weight, hardness, color, lustre,\nincorrosibility, etc. An animal, besides having parts situated in place,\nhas co-inhering functions in the same parts, exerted by the very same\nmasses and molecules of its substance.... The Mind, which affords no\nPropositions of Order in Place, has co-inhering functions. We affirm mind\nto contain Feeling, Will, and Thought, not in local separation, but in\ncommingling exercise. The concurring properties of minerals, of plants,\nand of the bodily and the mental structure of animals, are united in\naffirmations of co-inherence.\u201d\n\nThe distinction is real and important. But, as has been seen, an\nAttribute, when it is any thing but a simple unanalyzable Resemblance\nbetween the subject and some other things, consists in causing impressions\nof some sort on consciousness. Consequently, the co-inherence of two\nattributes is but the co-existence of the two states of consciousness\nimplied in their meaning: with the difference, however, that this\nco-existence is sometimes potential only, the attribute being considered\nas in existence, though the fact on which it is grounded may not be\nactually, but only potentially present. Snow, for instance, is, with great\nconvenience, said to be white even in a state of total darkness, because,\nthough we are not now conscious of the color, we shall be conscious of it\nas soon as morning breaks. Co-inherence of attributes is therefore still a\ncase, though a complex one, of co-existence of states of consciousness; a\ntotally different thing, however, from Order in Place. Being a part of\nsimultaneity, it belongs not to Place but to Time.\n\nWe may therefore (and we shall sometimes find it a convenience) instead of\nCo-existence and Sequence, say, for greater particularity, Order in Place\nand Order in Time: Order in Place being a specific mode of co-existence,\nnot necessary to be more particularly analyzed here; while the mere fact\nof co-existence, whether between actual sensations, or between the\npotentialities of causing them, known by the name of attributes, may be\nclassed, together with Sequence, under the head of Order in Time.\n\n\u00a7 7. In the foregoing inquiry into the import of propositions, we have\nthought it necessary to analyze directly those alone, in which the terms\nof the proposition (or the predicate at least) are concrete terms. But, in\ndoing so, we have indirectly analyzed those in which the terms are\nabstract. The distinction between an abstract term and its corresponding\nconcrete, does not turn upon any difference in what they are appointed to\nsignify; for the real signification of a concrete general name is, as we\nhave so often said, its connotation; and what the concrete term connotes,\nforms the entire meaning of the abstract name. Since there is nothing in\nthe import of an abstract name which is not in the import of the\ncorresponding concrete, it is natural to suppose that neither can there be\nany thing in the import of a proposition of which the terms are abstract,\nbut what there is in some proposition which can be framed of concrete\nterms.\n\nAnd this presumption a closer examination will confirm. An abstract name\nis the name of an attribute, or combination of attributes. The\ncorresponding concrete is a name given to things, because of, and in order\nto express, their possessing that attribute, or that combination of\nattributes. When, therefore, we predicate of any thing a concrete name,\nthe attribute is what we in reality predicate of it. But it has now been\nshown that in all propositions of which the predicate is a concrete name,\nwhat is really predicated is one of five things: Existence, Co-existence,\nCausation, Sequence, or Resemblance. An attribute, therefore, is\nnecessarily either an existence, a co-existence, a causation, a sequence,\nor a resemblance. When a proposition consists of a subject and predicate\nwhich are abstract terms, it consists of terms which must necessarily\nsignify one or other of these things. When we predicate of any thing an\nabstract name, we affirm of the thing that it is one or other of these\nfive things; that it is a case of Existence, or of Co-existence, or of\nCausation, or of Sequence, or of Resemblance.\n\nIt is impossible to imagine any proposition expressed in abstract terms,\nwhich can not be transformed into a precisely equivalent proposition in\nwhich the terms are concrete; namely, either the concrete names which\nconnote the attributes themselves, or the names of the _fundamenta_ of\nthose attributes; the facts or phenomena on which they are grounded. To\nillustrate the latter case, let us take this proposition, of which the\nsubject only is an abstract name, \u201cThoughtlessness is dangerous.\u201d\nThoughtlessness is an attribute, grounded on the facts which we call\nthoughtless actions; and the proposition is equivalent to this,\nThoughtless actions are dangerous. In the next example the predicate as\nwell as the subject are abstract names: \u201cWhiteness is a color;\u201d or \u201cThe\ncolor of snow is a whiteness.\u201d These attributes being grounded on\nsensations, the equivalent propositions in the concrete would be, The\nsensation of white is one of the sensations called those of color\u2014The\nsensation of sight, caused by looking at snow, is one of the sensations\ncalled sensations of white. In these propositions, as we have before seen,\nthe matter-of-fact asserted is a Resemblance. In the following examples,\nthe concrete terms are those which directly correspond to the abstract\nnames; connoting the attribute which these denote. \u201cPrudence is a virtue:\u201d\nthis may be rendered, \u201cAll prudent persons, _in so far as_ prudent, are\nvirtuous:\u201d \u201cCourage is deserving of honor;\u201d thus, \u201cAll courageous persons\nare deserving of honor _in so far_ as they are courageous:\u201d which is\nequivalent to this\u2014\u201cAll courageous persons deserve an addition to the\nhonor, or a diminution of the disgrace, which would attach to them on\nother grounds.\u201d\n\nIn order to throw still further light upon the import of propositions of\nwhich the terms are abstract, we will subject one of the examples given\nabove to a minuter analysis. The proposition we shall select is the\nfollowing: \u201cPrudence is a virtue.\u201d Let us substitute for the word virtue\nan equivalent but more definite expression, such as \u201ca mental quality\nbeneficial to society,\u201d or \u201ca mental quality pleasing to God,\u201d or whatever\nelse we adopt as the definition of virtue. What the proposition asserts is\na sequence, accompanied with causation; namely, that benefit to society,\nor that the approval of God, is consequent on, and caused by, prudence.\nHere is a sequence; but between what? We understand the consequent of the\nsequence, but we have yet to analyze the antecedent. Prudence is an\nattribute; and, in connection with it, two things besides itself are to be\nconsidered; prudent persons, who are the _subjects_ of the attribute, and\nprudential conduct, which may be called the _foundation_ of it. Now is\neither of these the antecedent? and, first, is it meant, that the approval\nof God, or benefit to society, is attendant upon all prudent _persons_?\nNo; except _in so far_ as they are prudent; for prudent persons who are\nscoundrels can seldom, on the whole, be beneficial to society, nor can\nthey be acceptable to a good being. Is it upon prudential _conduct_, then,\nthat divine approbation and benefit to mankind are supposed to be\ninvariably consequent? Neither is this the assertion meant, when it is\nsaid that prudence is a virtue; except with the same reservation as\nbefore, and for the same reason, namely, that prudential conduct, although\nin _so far as_ it is prudential it is beneficial to society, may yet, by\nreason of some other of its qualities, be productive of an injury\noutweighing the benefit, and deserve a displeasure exceeding the\napprobation which would be due to the prudence. Neither the substance,\ntherefore (viz., the person), nor the phenomenon (the conduct), is an\nantecedent on which the other term of the sequence is universally\nconsequent. But the proposition, \u201cPrudence is a virtue,\u201d is a universal\nproposition. What is it, then, upon which the proposition affirms the\neffects in question to be universally consequent? Upon that in the person,\nand in the conduct, which causes them to be called prudent, and which is\nequally in them when the action, though prudent, is wicked; namely, a\ncorrect foresight of consequences, a just estimation of their importance\nto the object in view, and repression of any unreflecting impulse at\nvariance with the deliberate purpose. These, which are states of the\nperson\u2019s mind, are the real antecedent in the sequence, the real cause in\nthe causation, asserted by the proposition. But these are also the real\nground, or foundation, of the attribute Prudence; since wherever these\nstates of mind exist we may predicate prudence, even before we know\nwhether any conduct has followed. And in this manner every assertion\nrespecting an attribute, may be transformed into an assertion exactly\nequivalent respecting the fact or phenomenon which is the ground of the\nattribute. And no case can be assigned, where that which is predicated of\nthe fact or phenomenon, does not belong to one or other of the five\nspecies formerly enumerated: it is either simple Existence, or it is some\nSequence, Co-existence, Causation, or Resemblance.\n\nAnd as these five are the only things which can be affirmed, so are they\nthe only things which can be denied. \u201cNo horses are web-footed\u201d denies\nthat the attributes of a horse ever co-exist with web-feet. It is scarcely\nnecessary to apply the same analysis to Particular affirmations and\nnegations. \u201cSome birds are web-footed,\u201d affirms that, with the attributes\nconnoted by _bird_, the phenomenon web-feet is sometimes co-existent:\n\u201cSome birds are not web-footed,\u201d asserts that there are other instances in\nwhich this co-existence does not have place. Any further explanation of a\nthing which, if the previous exposition has been assented to, is so\nobvious, may here be spared.\n\n\n\n\n                               Chapter VI.\n\n\nOf Propositions Merely Verbal.\n\n\n\u00a7 1. As a preparation for the inquiry which is the proper object of Logic,\nnamely, in what manner propositions are to be proved, we have found it\nnecessary to inquire what they contain which requires, or is susceptible\nof, proof; or (which is the same thing) what they assert. In the course of\nthis preliminary investigation into the import of Propositions, we\nexamined the opinion of the Conceptualists, that a proposition is the\nexpression of a relation between two ideas; and the doctrine of the\nextreme Nominalists, that it is the expression of an agreement or\ndisagreement between the meanings of two names. We decided that, as\ngeneral theories, both of these are erroneous; and that, though\npropositions may be made both respecting names and respecting ideas,\nneither the one nor the other are the subject-matter of Propositions\nconsidered generally. We then examined the different kinds of\nPropositions, and found that, with the exception of those which are merely\nverbal, they assert five different kinds of matters of fact, namely,\nExistence, Order in Place, Order in Time, Causation, and Resemblance; that\nin every proposition one of these five is either affirmed, or denied, of\nsome fact or phenomenon, or of some object the unknown source of a fact or\nphenomenon.\n\nIn distinguishing, however, the different kinds of matters of fact\nasserted in propositions, we reserved one class of propositions, which do\nnot relate to any matter of fact, in the proper sense of the term at all,\nbut to the meaning of names. Since names and their signification are\nentirely arbitrary, such propositions are not, strictly speaking,\nsusceptible of truth or falsity, but only of conformity or disconformity\nto usage or convention; and all the proof they are capable of, is proof of\nusage; proof that the words have been employed by others in the\nacceptation in which the speaker or writer desires to use them. These\npropositions occupy, however, a conspicuous place in philosophy; and their\nnature and characteristics are of as much importance in logic, as those of\nany of the other classes of propositions previously adverted to.\n\nIf all propositions respecting the signification of words were as simple\nand unimportant as those which served us for examples when examining\nHobbes\u2019s theory of predication, viz., those of which the subject and\npredicate are proper names, and which assert only that those names have,\nor that they have not, been conventionally assigned to the same\nindividual, there would be little to attract to such propositions the\nattention of philosophers. But the class of merely verbal propositions\nembraces not only much more than these, but much more than any\npropositions which at first sight present themselves as verbal;\ncomprehending a kind of assertions which have been regarded not only as\nrelating to things, but as having actually a more intimate relation with\nthem than any other propositions whatever. The student in philosophy will\nperceive that I allude to the distinction on which so much stress was laid\nby the schoolmen, and which has been retained either under the same or\nunder other names by most metaphysicians to the present day, viz., between\nwhat were called _essential_, and what were called _accidental_,\npropositions, and between essential and accidental properties or\nattributes.\n\n\u00a7 2. Almost all metaphysicians prior to Locke, as well as many since his\ntime, have made a great mystery of Essential Predication, and of\npredicates which are said to be of the _essence_ of the subject. The\nessence of a thing, they said, was that without which the thing could\nneither be, nor be conceived to be. Thus, rationality was of the essence\nof man, because without rationality, man could not be conceived to exist.\nThe different attributes which made up the essence of the thing were\ncalled its essential properties; and a proposition in which any of these\nwere predicated of it was called an Essential Proposition, and was\nconsidered to go deeper into the nature of the thing, and to convey more\nimportant information respecting it, than any other proposition could do.\nAll properties, not of the essence of the thing, were called its\naccidents; were supposed to have nothing at all, or nothing comparatively,\nto do with its inmost nature; and the propositions in which any of these\nwere predicated of it were called Accidental Propositions. A connection\nmay be traced between this distinction, which originated with the\nschoolmen, and the well-known dogmas of _substanti\u00e6 secund\u00e6_ or general\nsubstances, and _substantial forms_, doctrines which under varieties of\nlanguage pervaded alike the Aristotelian and the Platonic schools, and of\nwhich more of the spirit has come down to modern times than might be\nconjectured from the disuse of the phraseology. The false views of the\nnature of classification and generalization which prevailed among the\nschoolmen, and of which these dogmas were the technical expression, afford\nthe only explanation which can be given of their having misunderstood the\nreal nature of those Essences which held so conspicuous a place in their\nphilosophy. They said, truly, that _man_ can not be conceived without\nrationality. But though _man_ can not, a being may be conceived exactly\nlike a man in all points except that one quality, and those others which\nare the conditions or consequences of it. All, therefore, which is really\ntrue in the assertion that man can not be conceived without rationality,\nis only, that if he had not rationality, he would not be reputed a man.\nThere is no impossibility in conceiving the _thing_, nor, for aught we\nknow, in its existing: the impossibility is in the conventions of\nlanguage, which will not allow the thing, even if it exist, to be called\nby the name which is reserved for rational beings. Rationality, in short,\nis involved in the meaning of the word man: is one of the attributes\nconnoted by the name. The essence of man, simply means the whole of the\nattributes connoted by the word; and any one of those attributes taken\nsingly, is an essential property of man.\n\nBut these reflections, so easy to us, would have been difficult to persons\nwho thought, as most of the later Aristotelians did, that objects were\nmade what they were called, that gold (for instance) was made gold, not by\nthe possession of certain properties to which mankind have chosen to\nattach that name, but by participation in the nature of a general\nsubstance, called gold in general, which substance, together with all the\nproperties that belonged to it, _inhered_ in every individual piece of\ngold.(39) As they did not consider these universal substances to be\nattached to all general names, but only to some, they thought that an\nobject borrowed only a part of its properties from a universal substance,\nand that the rest belonged to it individually: the former they called its\nessence, and the latter its accidents. The scholastic doctrine of essences\nlong survived the theory on which it rested, that of the existence of real\nentities corresponding to general terms; and it was reserved for Locke, at\nthe end of the seventeenth century, to convince philosophers that the\nsupposed essences of classes were merely the signification of their names;\nnor, among the signal services which his writings rendered to philosophy,\nwas there one more needful or more valuable.\n\nNow, as the most familiar of the general names by which an object is\ndesignated usually connotes not one only, but several attributes of the\nobject, each of which attributes separately forms also the bond of union\nof some class, and the meaning of some general name; we may predicate of a\nname which connotes a variety of attributes, another name which connotes\nonly one of these attributes, or some smaller number of them than all. In\nsuch cases, the universal affirmative proposition will be true; since\nwhatever possesses the whole of any set of attributes, must possess any\npart of that same set. A proposition of this sort, however, conveys no\ninformation to any one who previously understood the whole meaning of the\nterms. The propositions, Every man is a corporeal being, Every man is a\nliving creature, Every man is rational, convey no knowledge to any one who\nwas already aware of the entire meaning of the word _man_, for the meaning\nof the word includes all this: and that every _man_ has the attributes\nconnoted by all these predicates, is already asserted when he is called a\nman. Now, of this nature are all the propositions which have been called\nessential. They are, in fact, identical propositions.\n\nIt is true that a proposition which predicates any attribute, even though\nit be one implied in the name, is in most cases understood to involve a\ntacit assertion that there _exists_ a thing corresponding to the name, and\npossessing the attributes connoted by it; and this implied assertion may\nconvey information, even to those who understood the meaning of the name.\nBut all information of this sort, conveyed by all the essential\npropositions of which man can be made the subject, is included in the\nassertion, Men exist. And this assumption of real existence is, after all,\nthe result of an imperfection of language. It arises from the ambiguity of\nthe copula, which, in addition to its proper office of a mark to show that\nan assertion is made, is also, as formerly remarked, a concrete word\nconnoting existence. The actual existence of the subject of the\nproposition is therefore only apparently, not really, implied in the\npredication, if an essential one: we may say, A ghost is a disembodied\nspirit, without believing in ghosts. But an accidental, or non-essential,\naffirmation, does imply the real existence of the subject, because in the\ncase of a non-existent subject there is nothing for the proposition to\nassert. Such a proposition as, The ghost of a murdered person haunts the\ncouch of the murderer, can only have a meaning if understood as implying a\nbelief in ghosts; for since the signification of the word ghost implies\nnothing of the kind, the speaker either means nothing, or means to assert\na thing which he wishes to be believed to have really taken place.\n\nIt will be hereafter seen that when any important consequences seem to\nfollow, as in mathematics, from an essential proposition, or, in other\nwords, from a proposition involved in the meaning of a name, what they\nreally flow from is the tacit assumption of the real existence of the\nobjects so named. Apart from this assumption of real existence, the class\nof propositions in which the predicate is of the essence of the subject\n(that is, in which the predicate connotes the whole or part of what the\nsubject connotes, but nothing besides) answer no purpose but that of\nunfolding the whole or some part of the meaning of the name, to those who\ndid not previously know it. Accordingly, the most useful, and in\nstrictness the only useful kind of essential propositions, are\nDefinitions: which, to be complete, should unfold the whole of what is\ninvolved in the meaning of the word defined; that is (when it is a\nconnotative word), the whole of what it connotes. In defining a name,\nhowever, it is not usual to specify its entire connotation, but so much\nonly as is sufficient to mark out the objects usually denoted by it from\nall other known objects. And sometimes a merely accidental property, not\ninvolved in the meaning of the name, answers this purpose equally well.\nThe various kinds of definition which these distinctions give rise to, and\nthe purposes to which they are respectively subservient, will be minutely\nconsidered in the proper place.\n\n\u00a7 3. According to the above view of essential propositions, no proposition\ncan be reckoned such which relates to an individual by name, that is, in\nwhich the subject is a proper name. Individuals have no essences. When the\nschoolmen talked of the essence of an individual, they did not mean the\nproperties implied in its name, for the names of individuals imply no\nproperties. They regarded as of the essence of an individual, whatever was\nof the essence of the species in which they were accustomed to place that\nindividual; _i.e._, of the class to which it was most familiarly referred,\nand to which, therefore, they conceived that it by nature belonged. Thus,\nbecause the proposition Man is a rational being, was an essential\nproposition, they affirmed the same thing of the proposition, Julius C\u00e6sar\nis a rational being. This followed very naturally if genera and species\nwere to be considered as entities, distinct from, but _inhering_ in, the\nindividuals composing them. If _man_ was a substance inhering in each\nindividual man, the _essence_ of man (whatever that might mean) was\nnaturally supposed to accompany it; to inhere in John Thompson, and to\nform the _common essence_ of Thompson and Julius C\u00e6sar. It might then be\nfairly said, that rationality, being of the essence of Man, was of the\nessence also of Thompson. But if Man altogether be only the individual men\nand a name bestowed upon them in consequence of certain common properties,\nwhat becomes of John Thompson\u2019s essence?\n\nA fundamental error is seldom expelled from philosophy by a single\nvictory. It retreats slowly, defends every inch of ground, and often,\nafter it has been driven from the open country, retains a footing in some\nremote fastness. The essences of individuals were an unmeaning figment\narising from a misapprehension of the essences of classes, yet even Locke,\nwhen he extirpated the parent error, could not shake himself free from\nthat which was its fruit. He distinguished two sorts of essences, Real and\nNominal. His nominal essences were the essences of classes, explained\nnearly as we have now explained them. Nor is any thing wanting to render\nthe third book of Locke\u2019s Essay a nearly unexceptional treatise on the\nconnotation of names, except to free its language from the assumption of\nwhat are called Abstract Ideas, which unfortunately is involved in the\nphraseology, though not necessarily connected with the thoughts contained\nin that immortal Third Book.(40) But besides nominal essences, he admitted\nreal essences, or essences of individual objects, which he supposed to be\nthe causes of the sensible properties of those objects. We know not (said\nhe) what these are (and this acknowledgment rendered the fiction\ncomparatively innocuous); but if we did, we could, from them alone,\ndemonstrate the sensible properties of the object, as the properties of\nthe triangle are demonstrated from the definition of the triangle. I shall\nhave occasion to revert to this theory in treating of Demonstration, and\nof the conditions under which one property of a thing admits of being\ndemonstrated from another property. It is enough here to remark that,\naccording to this definition, the real essence of an object has, in the\nprogress of physics, come to be conceived as nearly equivalent, in the\ncase of bodies, to their corpuscular structure: what it is now supposed to\nmean in the case of any other entities, I would not take upon myself to\ndefine.\n\n\u00a7 4. An essential proposition, then, is one which is purely verbal; which\nasserts of a thing under a particular name, only what is asserted of it in\nthe fact of calling it by that name; and which, therefore, either gives no\ninformation, or gives it respecting the name, not the thing.\nNon-essential, or accidental propositions, on the contrary, may be called\nReal Propositions, in opposition to Verbal. They predicate of a thing some\nfact not involved in the signification of the name by which the\nproposition speaks of it; some attribute not connoted by that name. Such\nare all propositions concerning things individually designated, and all\ngeneral or particular propositions in which the predicate connotes any\nattribute not connoted by the subject. All these, if true, add to our\nknowledge: they convey information, not already involved in the names\nemployed. When I am told that all, or even that some objects, which have\ncertain qualities, or which stand in certain relations, have also certain\nother qualities, or stand in certain other relations, I learn from this\nproposition a new fact; a fact not included in my knowledge of the meaning\nof the words, nor even of the existence of Things answering to the\nsignification of those words. It is this class of propositions only which\nare in themselves instructive, or from which any instructive propositions\ncan be inferred.(41)\n\nNothing has probably contributed more to the opinion so long prevalent of\nthe futility of the school logic, than the circumstance that almost all\nthe examples used in the common school books to illustrate the doctrine of\npredication and that of the syllogism, consist of essential propositions.\nThey were usually taken either from the branches or from the main trunk of\nthe Predicamental Tree, which included nothing but what was of the\n_essence_ of the species: _Omne corpus est substantia_, _Omne animal est\ncorpus_, _Omnis homo est corpus_, _Omnis homo est animal_, _Omnis homo est\nrationalis_, and so forth. It is far from wonderful that the syllogistic\nart should have been thought to be of no use in assisting correct\nreasoning, when almost the only propositions which, in the hands of its\nprofessed teachers, it was employed to prove, were such as every one\nassented to without proof the moment he comprehended the meaning of the\nwords; and stood exactly on a level, in point of evidence, with the\npremises from which they were drawn. I have, therefore, throughout this\nwork, avoided the employment of essential propositions as examples, except\nwhere the nature of the principle to be illustrated specifically required\nthem.\n\n\u00a7 5. With respect to propositions which do convey information\u2014which assert\nsomething of a Thing, under a name that does not already presuppose what\nis about to be asserted; there are two different aspects in which these,\nor rather such of them as are general propositions, may be considered: we\nmay either look at them as portions of speculative truth, or as memoranda\nfor practical use. According as we consider propositions in one or the\nother of these lights, their import may be conveniently expressed in one\nor in the other of two formulas.\n\nAccording to the formula which we have hitherto employed, and which is\nbest adapted to express the import of the proposition as a portion of our\ntheoretical knowledge, All men are mortal, means that the attributes of\nman are always accompanied by the attribute mortality: No men are gods,\nmeans that the attributes of man are never accompanied by the attributes,\nor at least never by all the attributes, signified by the word god. But\nwhen the proposition is considered as a memorandum for practical use, we\nshall find a different mode of expressing the same meaning better adapted\nto indicate the office which the proposition performs. The practical use\nof a proposition is, to apprise or remind us what we have to expect, in\nany individual case which comes within the assertion contained in the\nproposition. In reference to this purpose, the proposition, All men are\nmortal, means that the attributes of man are _evidence of_, are a _mark_\nof, mortality; an indication by which the presence of that attribute is\nmade manifest. No men are gods, means that the attributes of man are a\nmark or evidence that some or all of the attributes understood to belong\nto a god are not there; that where the former are, we need not expect to\nfind the latter.\n\nThese two forms of expression are at bottom equivalent; but the one points\nthe attention more directly to what a proposition means, the latter to the\nmanner in which it is to be used.\n\nNow it is to be observed that Reasoning (the subject to which we are next\nto proceed) is a process into which propositions enter not as ultimate\nresults, but as means to the establishment of other propositions. We may\nexpect, therefore, that the mode of exhibiting the import of a general\nproposition which shows it in its application to practical use, will best\nexpress the function which propositions perform in Reasoning. And\naccordingly, in the theory of Reasoning, the mode of viewing the subject\nwhich considers a Proposition as asserting that one fact or phenomenon is\na _mark_ or _evidence_ of another fact or phenomenon, will be found almost\nindispensable. For the purposes of that Theory, the best mode of defining\nthe import of a proposition is not the mode which shows most clearly what\nit is in itself, but that which most distinctly suggests the manner in\nwhich it may be made available for advancing from it to other\npropositions.\n\n\n\n\n                               Chapter VII.\n\n\nOf The Nature Of Classification, And The Five Predicables.\n\n\n\u00a7 1. In examining into the nature of general propositions, we have\nadverted much less than is usual with logicians to the ideas of a Class,\nand Classification; ideas which, since the Realist doctrine of General\nSubstances went out of vogue, have formed the basis of almost every\nattempt at a philosophical theory of general terms and general\npropositions. We have considered general names as having a meaning, quite\nindependently of their being the names of classes. That circumstance is in\ntruth accidental, it being wholly immaterial to the signification of the\nname whether there are many objects, or only one, to which it happens to\nbe applicable, or whether there be any at all. God is as much a general\nterm to the Christian or Jew as to the Polytheist; and dragon, hippogriff,\nchimera, mermaid, ghost, are as much so as if real objects existed,\ncorresponding to those names. Every name the signification of which is\nconstituted by attributes, is potentially a name of an indefinite number\nof objects; but it needs not be actually the name of any; and if of any,\nit may be the name of only one. As soon as we employ a name to connote\nattributes, the things, be they more or fewer, which happen to possess\nthose attributes, are constituted _ipso facto_ a class. But in predicating\nthe name we predicate only the attributes; and the fact of belonging to a\nclass does not, in many cases, come into view at all.\n\nAlthough, however, Predication does not presuppose Classification, and\nthough the theory of Names and of Propositions is not cleared up, but only\nencumbered, by intruding the idea of classification into it, there is\nnevertheless a close connection between Classification and the employment\nof General Names. By every general name which we introduce, we create a\nclass, if there be any things, real or imaginary, to compose it; that is,\nany Things corresponding to the signification of the name. Classes,\ntherefore, mostly owe their existence to general language. But general\nlanguage, also, though that is not the most common case, sometimes owes\nits existence to classes. A general, which is as much as to say a\nsignificant, name, is indeed mostly introduced because we have a\nsignification to express by it; because we need a word by means of which\nto predicate the attributes which it connotes. But it is also true that a\nname is sometimes introduced because we have found it convenient to create\na class; because we have thought it useful for the regulation of our\nmental operations, that a certain group of objects should be thought of\ntogether. A naturalist, for purposes connected with his particular\nscience, sees reason to distribute the animal or vegetable creation into\ncertain groups rather than into any others, and he requires a name to\nbind, as it were, each of his groups together. It must not, however, be\nsupposed that such names, when introduced, differ in any respect, as to\ntheir mode of signification, from other connotative names. The classes\nwhich they denote are, as much as any other classes, constituted by\ncertain common attributes, and their names are significant of those\nattributes, and of nothing else. The names of Cuvier\u2019s classes and orders,\n_Plantigrades_, _Digitigrades_, etc., are as much the expression of\nattributes as if those names had preceded, instead of grown out of, his\nclassification of animals. The only peculiarity of the case is, that the\nconvenience of classification was here the primary motive for introducing\nthe names; while in other cases the name is introduced as a means of\npredication, and the formation of a class denoted by it is only an\nindirect consequence.\n\nThe principles which ought to regulate Classification, as a logical\nprocess subservient to the investigation of truth, can not be discussed to\nany purpose until a much later stage of our inquiry. But, of\nClassification as resulting from, and implied in, the fact of employing\ngeneral language, we can not forbear to treat here, without leaving the\ntheory of general names, and of their employment in predication, mutilated\nand formless.\n\n\u00a7 2. This portion of the theory of general language is the subject of what\nis termed the doctrine of the Predicables; a set of distinctions handed\ndown from Aristotle, and his follower Porphyry, many of which have taken a\nfirm root in scientific, and some of them even in popular, phraseology.\nThe predicables are a fivefold division of General Names, not grounded as\nusual on a difference in their meaning, that is, in the attribute which\nthey connote, but on a difference in the kind of class which they denote.\nWe may predicate of a thing five different varieties of class-name:\n\nA _genus_ of the thing: (\u03b3\u1f72\u03bd\u03bf\u03c2).\nA _species_: (\u03b5\u1f36\u03c3\u03bf\u03c2).\nA _differentia_: (\u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u1f70).\nA _proprium_: (\u1f30\u03b4\u03b9\u03ce\u03bd).\nAn _accidens_: (\u03c3\u03c5\u03bc\u03b2\u03b5\u03b2\u03b7\u03ba\u03cc\u03c2).\n\nIt is to be remarked of these distinctions, that they express, not what\nthe predicate is in its own meaning, but what relation it bears to the\nsubject of which it happens on the particular occasion to be predicated.\nThere are not some names which are exclusively genera, and others which\nare exclusively species, or differenti\u00e6; but the same name is referred to\none or another predicable, according to the subject of which it is\npredicated on the particular occasion. _Animal_, for instance, is a genus\nwith respect to man, or John; a species with respect to Substance, or\nBeing. _Rectangular_ is one of the Differenti\u00e6 of a geometrical square; it\nis merely one of the Accidentia of the table at which I am writing. The\nwords genus, species, etc., are therefore relative terms; they are names\napplied to certain predicates, to express the relation between them and\nsome given subject: a relation grounded, as we shall see, not on what the\npredicate connotes, but on the class which it denotes, and on the place\nwhich, in some given classification, that class occupies relatively to the\nparticular subject.\n\n\u00a7 3. Of these five names, two, Genus and Species, are not only used by\nnaturalists in a technical acceptation not precisely agreeing with their\nphilosophical meaning, but have also acquired a popular acceptation, much\nmore general than either. In this popular sense any two classes, one of\nwhich includes the whole of the other and more, may be called a Genus and\na Species. Such, for instance, are Animal and Man; Man and Mathematician.\nAnimal is a Genus; Man and Brute are its two species; or we may divide it\ninto a greater number of species, as man, horse, dog, etc. _Biped_, or\n_two-footed animal_, may also be considered a genus, of which man and bird\nare two species. _Taste_ is a genus, of which sweet taste, sour taste,\nsalt taste, etc., are species. _Virtue_ is a genus; justice, prudence,\ncourage, fortitude, generosity, etc., are its species.\n\nThe same class which is a genus with reference to the sub-classes or\nspecies included in it, may be itself a species with reference to a more\ncomprehensive, or, as it is often called, a superior genus. Man is a\nspecies with reference to animal, but a genus with reference to the\nspecies Mathematician. Animal is a genus, divided into two species, man\nand brute; but animal is also a species, which, with another species,\nvegetable, makes up the genus, organized being. Biped is a genus with\nreference to man and bird, but a species with respect to the superior\ngenus, animal. Taste is a genus divided into species, but also a species\nof the genus sensation. Virtue, a genus with reference to justice,\ntemperance, etc., is one of the species of the genus, mental quality.\n\nIn this popular sense the words Genus and Species have passed into common\ndiscourse. And it should be observed that in ordinary parlance, not the\nname of the class, but the class itself, is said to be the genus or\nspecies; not, of course, the class in the sense of each individual of the\nclass, but the individuals collectively, considered as an aggregate whole;\nthe name by which the class is designated being then called not the genus\nor species, but the generic or specific name. And this is an admissible\nform of expression; nor is it of any importance which of the two modes of\nspeaking we adopt, provided the rest of our language is consistent with\nit; but, if we call the class itself the genus, we must not talk of\npredicating the genus. We predicate of man the _name_ mortal; and by\npredicating the name, we may be said, in an intelligible sense, to\npredicate what the name expresses, the _attribute_ mortality; but in no\nallowable sense of the word predication do we predicate of man the _class_\nmortal. We predicate of him the fact of belonging to the class.\n\nBy the Aristotelian logicians, the terms genus and species were used in a\nmore restricted sense. They did not admit every class which could be\ndivided into other classes to be a genus, or every class which could be\nincluded in a larger class to be a species. Animal was by them considered\na genus; man and brute co-ordinate species under that genus: _biped_,\nhowever, would not have been admitted to be a genus with reference to man,\nbut a _proprium_ or _accidens_ only. It was requisite, according to their\ntheory, that genus and species should be of the _essence_ of the subject.\nAnimal was of the essence of man; biped was not. And in every\nclassification they considered some one class as the lowest or _infima_\nspecies. Man, for instance, was a lowest species. Any further divisions\ninto which the class might be capable of being broken down, as man into\nwhite, black, and red man, or into priest and layman, they did not admit\nto be species.\n\nIt has been seen, however, in the preceding chapter, that the distinction\nbetween the essence of a class, and the attributes or properties which are\nnot of its essence\u2014a distinction which has given occasion to so much\nabstruse speculation, and to which so mysterious a character was formerly,\nand by many writers is still, attached\u2014amounts to nothing more than the\ndifference between those attributes of the class which are, and those\nwhich are not, involved in the signification of the class-name. As applied\nto individuals, the word Essence, we found, has no meaning, except in\nconnection with the exploded tenets of the Realists; and what the\nschoolmen chose to call the essence of an individual, was simply the\nessence of the class to which that individual was most familiarly\nreferred.\n\nIs there no difference, then, save this merely verbal one, between the\nclasses which the schoolmen admitted to be genera or species, and those to\nwhich they refused the title? Is it an error to regard some of the\ndifferences which exist among objects as differences _in kind_ (_genere_\nor _specie_), and others only as differences in the accidents? Were the\nschoolmen right or wrong in giving to some of the classes into which\nthings may be divided, the name of _kinds_, and considering others as\nsecondary divisions, grounded on differences of a comparatively\nsuperficial nature? Examination will show that the Aristotelians did mean\nsomething by this distinction, and something important; but which, being\nbut indistinctly conceived, was inadequately expressed by the phraseology\nof essences, and the various other modes of speech to which they had\nrecourse.\n\n\u00a7 4. It is a fundamental principle in logic, that the power of framing\nclasses is unlimited, as long as there is any (even the smallest)\ndifference to found a distinction upon. Take any attribute whatever, and\nif some things have it, and others have not, we may ground on the\nattribute a division of all things into two classes; and we actually do\nso, the moment we create a name which connotes the attribute. The number\nof possible classes, therefore, is boundless; and there are as many actual\nclasses (either of real or of imaginary things) as there are general\nnames, positive and negative together.\n\nBut if we contemplate any one of the classes so formed, such as the class\nanimal or plant, or the class sulphur or phosphorus, or the class white or\nred, and consider in what particulars the individuals included in the\nclass differ from those which do not come within it, we find a very\nremarkable diversity in this respect between some classes and others.\nThere are some classes, the things contained in which differ from other\nthings only in certain particulars which may be numbered, while others\ndiffer in more than can be numbered, more even than we need ever expect to\nknow. Some classes have little or nothing in common to characterize them\nby, except precisely what is connoted by the name: white things, for\nexample, are not distinguished by any common properties except whiteness;\nor if they are, it is only by such as are in some way dependent on, or\nconnected with, whiteness. But a hundred generations have not exhausted\nthe common properties of animals or of plants, of sulphur or of\nphosphorus; nor do we suppose them to be exhaustible, but proceed to new\nobservations and experiments, in the full confidence of discovering new\nproperties which were by no means implied in those we previously knew.\nWhile, if any one were to propose for investigation the common properties\nof all things which are of the same color, the same shape, or the same\nspecific gravity, the absurdity would be palpable. We have no ground to\nbelieve that any such common properties exist, except such as may be shown\nto be involved in the supposition itself, or to be derivable from it by\nsome law of causation. It appears, therefore, that the properties, on\nwhich we ground our classes, sometimes exhaust all that the class has in\ncommon, or contain it all by some mode of implication; but in other\ninstances we make a selection of a few properties from among not only a\ngreater number, but a number inexhaustible by us, and to which as we know\nno bounds, they may, so far as we are concerned, be regarded as infinite.\n\nThere is no impropriety in saying that, of these two classifications, the\none answers to a much more radical distinction in the things themselves,\nthan the other does. And if any one even chooses to say that the one\nclassification is made by nature, the other by us for our convenience, he\nwill be right; provided he means no more than this: Where a certain\napparent difference between things (though perhaps in itself of little\nmoment) answers to we know not what number of other differences, pervading\nnot only their known properties, but properties yet undiscovered, it is\nnot optional but imperative to recognize this difference as the foundation\nof a specific distinction; while, on the contrary, differences that are\nmerely finite and determinate, like those designated by the words white,\nblack, or red, may be disregarded if the purpose for which the\nclassification is made does not require attention to those particular\nproperties. The differences, however, are made by nature, in both cases;\nwhile the recognition of those differences as grounds of classification\nand of naming, is, equally in both cases, the act of man: only in the one\ncase, the ends of language and of classification would be subverted if no\nnotice were taken of the difference, while in the other case, the\nnecessity of taking notice of it depends on the importance or unimportance\nof the particular qualities in which the difference happens to consist.\n\nNow, these classes, distinguished by unknown multitudes of properties, and\nnot solely by a few determinate ones\u2014which are parted off from one another\nby an unfathomable chasm, instead of a mere ordinary ditch with a visible\nbottom\u2014are the only classes which, by the Aristotelian logicians, were\nconsidered as genera or species. Differences which extended only to a\ncertain property or properties, and there terminated, they considered as\ndifferences only in the _accidents_ of things; but where any class\ndiffered from other things by an infinite series of differences, known and\nunknown, they considered the distinction as one of _kind_, and spoke of it\nas being an _essential_ difference, which is also one of the current\nmeanings of that vague expression at the present day.\n\nConceiving the schoolmen to have been justified in drawing a broad line of\nseparation between these two kinds of classes and of class-distinctions, I\nshall not only retain the division itself, but continue to express it in\ntheir language. According to that language, the proximate (or lowest) Kind\nto which any individual is referrible, is called its species. Conformably\nto this, Isaac Newton would be said to be of the species man. There are\nindeed numerous sub-classes included in the class man, to which Newton\nalso belongs; for example, Christian, and Englishman, and Mathematician.\nBut these, though distinct classes, are not, in our sense of the term,\ndistinct Kinds of men. A Christian, for example, differs from other human\nbeings; but he differs only in the attribute which the word expresses,\nnamely, belief in Christianity, and whatever else that implies, either as\ninvolved in the fact itself, or connected with it through some law of\ncause and effect. We should never think of inquiring what properties,\nunconnected with Christianity, either as cause or effect, are common to\nall Christians and peculiar to them; while in regard to all Men,\nphysiologists are perpetually carrying on such an inquiry; nor is the\nanswer ever likely to be completed. Man, therefore, we may call a species;\nChristian, or Mathematician, we can not.\n\nNote here, that it is by no means intended to imply that there may not be\ndifferent Kinds, or logical species, of man. The various races and\ntemperaments, the two sexes, and even the various ages, may be differences\nof kind, within our meaning of the term. I do not say that they are so.\nFor in the progress of physiology it may almost be said to be made out,\nthat the differences which really exist between different races, sexes,\netc., follow as consequences, under laws of nature, from a small number of\nprimary differences which can be precisely determined, and which, as the\nphrase is, _account for_ all the rest. If this be so, these are not\ndistinctions in kind; no more than Christian, Jew, Mussulman, and Pagan, a\ndifference which also carries many consequences along with it. And in this\nway classes are often mistaken for real Kinds, which are afterward proved\nnot to be so. But if it turned out that the differences were not capable\nof being thus accounted for, then Caucasian, Mongolian, Negro, etc., would\nbe really different Kinds of human beings, and entitled to be ranked as\nspecies by the logician; though not by the naturalist. For (as already\nnoticed) the word species is used in a different signification in logic\nand in natural history. By the naturalist, organized beings are not\nusually said to be of different species, if it is supposed that they have\ndescended from the same stock. That, however, is a sense artificially\ngiven to the word, for the technical purposes of a particular science. To\nthe logician, if a negro and a white man differ in the same manner\n(however less in degree) as a horse and a camel do, that is, if their\ndifferences are inexhaustible, and not referrible to any common cause,\nthey are different species, whether they are descended from common\nancestors or not. But if their differences can all be traced to climate\nand habits, or to some one or a few special differences in structure, they\nare not, in the logician\u2019s view, specifically distinct.\n\nWhen the _infima species_, or proximate Kind, to which an individual\nbelongs, has been ascertained, the properties common to that Kind include\nnecessarily the whole of the common properties of every other real Kind to\nwhich the individual can be referrible. Let the individual, for example,\nbe Socrates, and the proximate Kind, man. Animal, or living creature, is\nalso a real kind, and includes Socrates; but, since it likewise includes\nman, or in other words, since all men are animals, the properties common\nto animals form a portion of the common properties of the sub-class, man.\nAnd if there be any class which includes Socrates without including man,\nthat class is not a real Kind. Let the class, for example, be\n_flat-nosed_; that being a class which includes Socrates, without\nincluding all men. To determine whether it is a real Kind, we must ask\nourselves this question: Have all flat-nosed animals, in addition to\nwhatever is implied in their flat noses, any common properties, other than\nthose which are common to all animals whatever? If they had; if a flat\nnose were a mark or index to an indefinite number of other peculiarities,\nnot deducible from the former by an ascertainable law, then out of the\nclass man we might cut another class, flat-nosed man, which, according to\nour definition, would be a Kind. But if we could do this, man would not\nbe, as it was assumed to be, the proximate Kind. Therefore, the properties\nof the proximate Kind do comprehend those (whether known or unknown) of\nall other Kinds to which the individual belongs; which was the point we\nundertook to prove. And hence, every other Kind which is predicable of the\nindividual, will be to the proximate Kind in the relation of a genus,\naccording to even the popular acceptation of the terms genus and species;\nthat is, it will be a larger class, including it and more.\n\nWe are now able to fix the logical meaning of these terms. Every class\nwhich is a real Kind, that is, which is distinguished from all other\nclasses by an indeterminate multitude of properties not derivable from one\nanother, is either a genus or a species. A Kind which is not divisible\ninto other Kinds, can not be a genus, because it has no species under it;\nbut it is itself a species, both with reference to the individuals below\nand to the genera above (Species Pr\u00e6dicabilis and Species Subjicibilis).\nBut every Kind which admits of division into real Kinds (as animal into\nmammal, bird, fish, etc., or bird into various species of birds) is a\ngenus to all below it, a species to all genera in which it is itself\nincluded. And here we may close this part of the discussion, and pass to\nthe three remaining predicables, Differentia, Proprium, and Accidens.\n\n\u00a7 5. To begin with Differentia. This word is correlative with the words\ngenus and species, and as all admit, it signifies the attribute which\ndistinguishes a given species from every other species of the same genus.\nThis is so far clear: but we may still ask, which of the distinguishing\nattributes it signifies. For we have seen that every Kind (and a species\nmust be a Kind) is distinguished from other Kinds, not by any one\nattribute, but by an indefinite number. Man, for instance, is a species of\nthe genus animal: Rational (or rationality, for it is of no consequence\nhere whether we use the concrete or the abstract form) is generally\nassigned by logicians as the Differentia; and doubtless this attribute\nserves the purpose of distinction: but it has also been remarked of man,\nthat he is a cooking animal; the only animal that dresses its food. This,\ntherefore, is another of the attributes by which the species man is\ndistinguished from other species of the same genus: would this attribute\nserve equally well for a differentia? The Aristotelians say No; having\nlaid it down that the differentia must, like the genus and species, be of\nthe _essence_ of the subject.\n\nAnd here we lose even that vestige of a meaning grounded in the nature of\nthe things themselves, which may be supposed to be attached to the word\nessence when it is said that genus and species must be of the essence of\nthe thing. There can be no doubt that when the schoolmen talked of the\nessences of things as opposed to their accidents, they had confusedly in\nview the distinction between differences of kind, and the differences\nwhich are not of kind; they meant to intimate that genera and species must\nbe Kinds. Their notion of the essence of a thing was a vague notion of a\nsomething which makes it what it is, _i.e._, which makes it the Kind of\nthing that it is\u2014which causes it to have all that variety of properties\nwhich distinguish its Kind. But when the matter came to be looked at more\nclosely, nobody could discover what caused the thing to have all those\nproperties, nor even that there was any thing which caused it to have\nthem. Logicians, however, not liking to admit this, and being unable to\ndetect what made the thing to be what it was, satisfied themselves with\nwhat made it to be what it was called. Of the innumerable properties,\nknown and unknown, that are common to the class man, a portion only, and\nof course a very small portion, are connoted by its name; these few,\nhowever, will naturally have been thus distinguished from the rest either\nfor their greater obviousness, or for greater supposed importance. These\nproperties, then, which were connoted by the name, logicians seized upon,\nand called them the essence of the species; and not stopping there, they\naffirmed them, in the case of the _infima species_, to be the essence of\nthe individual too; for it was their maxim, that the species contained the\n\u201cwhole essence\u201d of the thing. Metaphysics, that fertile field of delusion\npropagated by language, does not afford a more signal instance of such\ndelusion. On this account it was that rationality, being connoted by the\nname man, was allowed to be a differentia of the class; but the\npeculiarity of cooking their food, not being connoted, was relegated to\nthe class of accidental properties.\n\nThe distinction, therefore, between Differentia, Proprium, and Accidens,\nis not grounded in the nature of things, but in the connotation of names;\nand we must seek it there, if we wish to find what it is.\n\nFrom the fact that the genus includes the species, in other words\n_de_notes more than the species, or is predicable of a greater number of\nindividuals, it follows that the species must connote more than the genus.\nIt must connote all the attributes which the genus connotes, or there\nwould be nothing to prevent it from denoting individuals not included in\nthe genus. And it must connote something besides, otherwise it would\ninclude the whole genus. Animal denotes all the individuals denoted by\nman, and many more. Man, therefore, must connote all that animal connotes,\notherwise there might be men who are not animals; and it must connote\nsomething more than animal connotes, otherwise all animals would be men.\nThis surplus of connotation\u2014this which the species connotes over and above\nthe connotation of the genus\u2014is the Differentia, or specific difference;\nor, to state the same proposition in other words, the Differentia is that\nwhich must be added to the connotation of the genus, to complete the\nconnotation of the species.\n\nThe word man, for instance, exclusively of what it connotes in common with\nanimal, also connotes rationality, and at least some approximation to that\nexternal form which we all know, but which as we have no name for it\nconsidered in itself, we are content to call the human. The Differentia,\nor specific difference, therefore, of man, as referred to the genus\nanimal, is that outward form and the possession of reason. The\nAristotelians said, the possession of reason, without the outward form.\nBut if they adhered to this, they would have been obliged to call the\nHouyhnhnms men. The question never arose, and they were never called upon\nto decide how such a case would have affected their notion of\nessentiality. However this may be, they were satisfied with taking such a\nportion of the differentia as sufficed to distinguish the species from all\nother _existing_ things, though by so doing they might not exhaust the\nconnotation of the name.\n\n\u00a7 6. And here, to prevent the notion of differentia from being restricted\nwithin too narrow limits, it is necessary to remark, that a species, even\nas referred to the same genus, will not always have the same differentia,\nbut a different one, according to the principle and purpose which preside\nover the particular classification. For example, a naturalist surveys the\nvarious kinds of animals, and looks out for the classification of them\nmost in accordance with the order in which, for zoological purposes, he\nconsiders it desirable that we should think of them. With this view he\nfinds it advisable that one of his fundamental divisions should be into\nwarm-blooded and cold-blooded animals; or into animals which breathe with\nlungs and those which breathe with gills; or into carnivorous, and\nfrugivorous or graminivorous; or into those which walk on the flat part\nand those which walk on the extremity of the foot, a distinction on which\ntwo of Cuvier\u2019s families are founded. In doing this, the naturalist\ncreates as many new classes; which are by no means those to which the\nindividual animal is familiarly and spontaneously referred; nor should we\never think of assigning to them so prominent a position in our arrangement\nof the animal kingdom, unless for a preconceived purpose of scientific\nconvenience. And to the liberty of doing this there is no limit. In the\nexamples we have given, most of the classes are real Kinds, since each of\nthe peculiarities is an index to a multitude of properties belonging to\nthe class which it characterizes: but even if the case were otherwise\u2014if\nthe other properties of those classes could all be derived, by any process\nknown to us, from the one peculiarity on which the class is founded\u2014even\nthen, if these derivative properties were of primary importance for the\npurposes of the naturalist, he would be warranted in founding his primary\ndivisions on them.\n\nIf, however, practical convenience is a sufficient warrant for making the\nmain demarcations in our arrangement of objects run in lines not\ncoinciding with any distinction of Kind, and so creating genera and\nspecies in the popular sense which are not genera or species in the\nrigorous sense at all; _\u00e0 fortiori_ must we be warranted, when our genera\nand species _are_ real genera and species, in marking the distinction\nbetween them by those of their properties which considerations of\npractical convenience most strongly recommend. If we cut a species out of\na given genus\u2014the species man, for instance, out of the genus animal\u2014with\nan intention on our part that the peculiarity by which we are to be guided\nin the application of the name man should be rationality, then rationality\nis the differentia of the species man. Suppose, however, that being\nnaturalists, we, for the purposes of our particular study, cut out of the\ngenus animal the same species man, but with an intention that the\ndistinction between man and all other species of animal should be, not\nrationality, but the possession of \u201cfour incisors in each jaw, tusks\nsolitary, and erect posture.\u201d It is evident that the word man, when used\nby us as naturalists, no longer connotes rationality, but connotes the\nthree other properties specified; for that which we have expressly in view\nwhen we impose a name, assuredly forms part of the meaning of that name.\nWe may, therefore, lay it down as a maxim, that wherever there is a Genus,\nand a Species marked out from that genus by an assignable differentia, the\nname of the species must be connotative, and must connote the differentia;\nbut the connotation may be special\u2014not involved in the signification of\nthe term as ordinarily used, but given to it when employed as a term of\nart or science. The word Man in common use, connotes rationality and a\ncertain form, but does not connote the number or character of the teeth;\nin the Linn\u00e6an system it connotes the number of incisor and canine teeth,\nbut does not connote rationality nor any particular form. The word _man_\nhas, therefore, two different meanings; though not commonly considered as\nambiguous, because it happens in both cases to _de_note the same\nindividual objects. But a case is conceivable in which the ambiguity would\nbecome evident: we have only to imagine that some new kind of animal were\ndiscovered, having Linn\u00e6us\u2019s three characteristics of humanity, but not\nrational, or not of the human form. In ordinary parlance, these animals\nwould not be called men; but in natural history they must still be called\nso by those, if any there should be, who adhere to the Linn\u00e6an\nclassification; and the question would arise, whether the word should\ncontinue to be used in two senses, or the classification be given up, and\nthe technical sense of the term be abandoned along with it.\n\nWords not otherwise connotative may, in the mode just adverted to, acquire\na special or technical connotation. Thus the word whiteness, as we have so\noften remarked, connotes nothing; it merely denotes the attribute\ncorresponding to a certain sensation: but if we are making a\nclassification of colors, and desire to justify, or even merely to point\nout, the particular place assigned to whiteness in our arrangement, we may\ndefine it \u201cthe color produced by the mixture of all the simple rays;\u201d and\nthis fact, though by no means implied in the meaning of the word whiteness\nas ordinarily used, but only known by subsequent scientific investigation,\nis part of its meaning in the particular essay or treatise, and becomes\nthe differentia of the species.(42)\n\nThe differentia, therefore, of a species may be defined to be, that part\nof the connotation of the specific name, whether ordinary or special and\ntechnical, which distinguishes the species in question from all other\nspecies of the genus to which on the particular occasion we are referring\nit.\n\n\u00a7 7. Having disposed of Genus, Species, and Differentia, we shall not find\nmuch difficulty in attaining a clear conception of the distinction between\nthe other two predicables, as well as between them and the first three.\n\nIn the Aristotelian phraseology, Genus and Differentia are of the\n_essence_ of the subject; by which, as we have seen, is really meant that\nthe properties signified by the genus and those signified by the\ndifferentia, form part of the connotation of the name denoting the\nspecies. Proprium and Accidens, on the other hand, form no part of the\nessence, but are predicated of the species only _accidentally_. Both are\nAccidents, in the wider sense in which the accidents of a thing are\nopposed to its essence; though, in the doctrine of the Predicables,\nAccidens is used for one sort of accident only, Proprium being another\nsort. Proprium, continue the schoolmen, is predicated _accidentally_,\nindeed, but _necessarily_; or, as they further explain it, signifies an\nattribute which is not indeed part of the essence, but which flows from,\nor is a consequence of, the essence, and is, therefore, inseparably\nattached to the species; _e.g._, the various properties of a triangle,\nwhich, though no part of its definition, must necessarily be possessed by\nwhatever comes under that definition. Accidens, on the contrary, has no\nconnection whatever with the essence, but may come and go, and the species\nstill remain what it was before. If a species could exist without its\nPropria, it must be capable of existing without that on which its Propria\nare necessarily consequent, and therefore without its essence, without\nthat which constitutes it a species. But an Accidens, whether separable or\ninseparable from the species in actual experience, may be supposed\nseparated, without the necessity of supposing any other alteration; or at\nleast, without supposing any of the essential properties of the species to\nbe altered, since with them an Accidens has no connection.\n\nA Proprium, therefore, of the species, may be defined, any attribute which\nbelongs to all the individuals included in the species, and which, though\nnot connoted by the specific name (either ordinarily if the classification\nwe are considering be for ordinary purposes, or specially if it be for a\nspecial purpose), yet follows from some attribute which the name either\nordinarily or specially connotes.\n\nOne attribute may follow from another in two ways; and there are\nconsequently two kinds of Proprium. It may follow as a conclusion follows\npremises, or it may follow as an effect follows a cause. Thus, the\nattribute of having the opposite sides equal, which is not one of those\nconnoted by the word Parallelogram, nevertheless follows from those\nconnoted by it, namely, from having the opposite sides straight lines and\nparallel, and the number of sides four. The attribute, therefore, of\nhaving the opposite sides equal, is a Proprium of the class parallelogram;\nand a Proprium of the first kind, which follows from the connoted\nattributes by way of _demonstration_. The attribute of being capable of\nunderstanding language, is a Proprium of the species man, since without\nbeing connoted by the word, it follows from an attribute which the word\ndoes connote, viz., from the attribute of rationality. But this is a\nProprium of the second kind, which follows by way of _causation_. How it\nis that one property of a thing follows, or can be inferred, from another;\nunder what conditions this is possible, and what is the exact meaning of\nthe phrase; are among the questions which will occupy us in the two\nsucceeding Books. At present it needs only be said, that whether a\nProprium follows by demonstration or by causation, it follows\n_necessarily_; that is to say, its not following would be inconsistent\nwith some law which we regard as a part of the constitution either of our\nthinking faculty or of the universe.\n\n\u00a7 8. Under the remaining predicable, Accidens, are included all attributes\nof a thing which are neither involved in the signification of the name\n(whether ordinarily or as a term of art), nor have, so far as we know, any\nnecessary connection with attributes which are so involved. They are\ncommonly divided into Separable and Inseparable Accidents. Inseparable\naccidents are those which\u2014although we know of no connection between them\nand the attributes constitutive of the species, and although, therefore,\nso far as we are aware, they might be absent without making the name\ninapplicable and the species a different species\u2014are yet never in fact\nknown to be absent. A concise mode of expressing the same meaning is, that\ninseparable accidents are properties which are universal to the species,\nbut not necessary to it. Thus, blackness is an attribute of a crow, and,\nas far as we know, a universal one. But if we were to discover a race of\nwhite birds, in other respects resembling crows, we should not say, These\nare not crows; we should say, These are white crows. Crow, therefore, does\nnot connote blackness; nor, from any of the attributes which it does\nconnote, whether as a word in popular use or as a term of art, could\nblackness be inferred. Not only, therefore, can we conceive a white crow,\nbut we know of no reason why such an animal should not exist. Since,\nhowever, none but black crows are known to exist, blackness, in the\npresent state of our knowledge, ranks as an accident, but an inseparable\naccident, of the species crow.\n\nSeparable Accidents are those which are found, in point of fact, to be\nsometimes absent from the species; which are not only not necessary, but\nnot even universal. They are such as do not belong to every individual of\nthe species, but only to some individuals; or if to all, not at all times.\nThus the color of a European is one of the separable accidents of the\nspecies man, because it is not an attribute of all human creatures. Being\nborn, is also (speaking in the logical sense) a separable accident of the\nspecies man, because, though an attribute of all human beings, it is so\nonly at one particular time. _A fortiori_ those attributes which are not\nconstant even in the same individual, as, to be in one or in another\nplace, to be hot or cold, sitting or walking, must be ranked as separable\naccidents.\n\n\n\n\n                              Chapter VIII.\n\n\nOf Definition.\n\n\n\u00a7 1. One necessary part of the theory of Names and of Propositions remains\nto be treated of in this place: the theory of Definitions. As being the\nmost important of the class of propositions which we have characterized as\npurely verbal, they have already received some notice in the chapter\npreceding the last. But their fuller treatment was at that time postponed,\nbecause definition is so closely connected with classification, that,\nuntil the nature of the latter process is in some measure understood, the\nformer can not be discussed to much purpose.\n\nThe simplest and most correct notion of a Definition is, a proposition\ndeclaratory of the meaning of a word; namely, either the meaning which it\nbears in common acceptation, or that which the speaker or writer, for the\nparticular purposes of his discourse, intends to annex to it.\n\nThe definition of a word being the proposition which enunciates its\nmeaning, words which have no meaning are unsusceptible of definition.\nProper names, therefore, can not be defined. A proper name being a mere\nmark put upon an individual, and of which it is the characteristic\nproperty to be destitute of meaning, its meaning can not of course be\ndeclared; though we may indicate by language, as we might indicate still\nmore conveniently by pointing with the finger, upon what individual that\nparticular mark has been, or is intended to be, put. It is no definition\nof \u201cJohn Thomson\u201d to say he is \u201cthe son of General Thomson;\u201d for the name\nJohn Thomson does not express this. Neither is it any definition of \u201cJohn\nThomson\u201d to say he is \u201cthe man now crossing the street.\u201d These\npropositions may serve to make known who is the particular man to whom the\nname belongs, but that may be done still more unambiguously by pointing to\nhim, which, however, has not been esteemed one of the modes of definition.\n\nIn the case of connotative names, the meaning, as has been so often\nobserved, is the connotation; and the definition of a connotative name, is\nthe proposition which declares its connotation. This might be done either\ndirectly or indirectly. The direct mode would be by a proposition in this\nform: \u201cMan\u201d (or whatsoever the word may be) \u201cis a name connoting such and\nsuch attributes,\u201d or \u201cis a name which, when predicated of any thing,\nsignifies the possession of such and such attributes by that thing.\u201d Or\nthus: Man is every thing which possesses such and such attributes: Man is\nevery thing which possesses corporeity, organization, life, rationality,\nand certain peculiarities of external form.\n\nThis form of definition is the most precise and least equivocal of any;\nbut it is not brief enough, and is besides too technical for common\ndiscourse. The more usual mode of declaring the connotation of a name, is\nto predicate of it another name or names of known signification, which\nconnote the same aggregation of attributes. This may be done either by\npredicating of the name intended to be defined, another connotative name\nexactly synonymous, as, \u201cMan is a human being,\u201d which is not commonly\naccounted a definition at all; or by predicating two or more connotative\nnames, which make up among them the whole connotation of the name to be\ndefined. In this last case, again, we may either compose our definition of\nas many connotative names as there are attributes, each attribute being\nconnoted by one, as, Man is a corporeal, organized, animated, rational\nbeing, shaped so and so; or we employ names which connote several of the\nattributes at once, as, Man is a rational _animal_, shaped so and so.\n\nThe definition of a name, according to this view of it, is the sum total\nof all the _essential_ propositions which can be framed with that name for\ntheir subject. All propositions the truth of which is implied in the name,\nall those which we are made aware of by merely hearing the name, are\nincluded in the definition, if complete, and may be evolved from it\nwithout the aid of any other premises; whether the definition expresses\nthem in two or three words, or in a larger number. It is, therefore, not\nwithout reason that Condillac and other writers have affirmed a definition\nto be an _analysis_. To resolve any complex whole into the elements of\nwhich it is compounded, is the meaning of analysis: and this we do when we\nreplace one word which connotes a set of attributes collectively, by two\nor more which connote the same attributes singly, or in smaller groups.\n\n\u00a7 2. From this, however, the question naturally arises, in what manner are\nwe to define a name which connotes only a single attribute: for instance,\n\u201cwhite,\u201d which connotes nothing but whiteness; \u201crational,\u201d which connotes\nnothing but the possession of reason. It might seem that the meaning of\nsuch names could only be declared in two ways; by a synonymous term, if\nany such can be found; or in the direct way already alluded to: \u201cWhite is\na name connoting the attribute whiteness.\u201d Let us see, however, whether\nthe analysis of the meaning of the name, that is, the breaking down of\nthat meaning into several parts, admits of being carried farther. Without\nat present deciding this question as to the word _white_, it is obvious\nthat in the case of _rational_ some further explanation may be given of\nits meaning than is contained in the proposition, \u201cRational is that which\npossesses the attribute of reason;\u201d since the attribute reason itself\nadmits of being defined. And here we must turn our attention to the\ndefinitions of attributes, or rather of the names of attributes, that is,\nof abstract names.\n\nIn regard to such names of attributes as are connotative, and express\nattributes of those attributes, there is no difficulty: like other\nconnotative names, they are defined by declaring their connotation. Thus\nthe word _fault_ may be defined, \u201ca quality productive of evil or\ninconvenience.\u201d Sometimes, again, the attribute to be defined is not one\nattribute, but a union of several: we have only, therefore, to put\ntogether the names of all the attributes taken separately, and we obtain\nthe definition of the name which belongs to them all taken together; a\ndefinition which will correspond exactly to that of the corresponding\nconcrete name. For, as we define a concrete name by enumerating the\nattributes which it connotes, and as the attributes connoted by a concrete\nname form the entire signification of the corresponding abstract name, the\nsame enumeration will serve for the definition of both. Thus, if the\ndefinition of a _human being_ be this, \u201ca being, corporeal, animated,\nrational, shaped so and so,\u201d the definition of _humanity_ will be\ncorporeity and animal life, combined with rationality, and with such and\nsuch a shape.\n\nWhen, on the other hand, the abstract name does not express a complication\nof attributes, but a single attribute, we must remember that every\nattribute is grounded on some fact or phenomenon, from which, and which\nalone, it derives its meaning. To that fact or phenomenon, called in a\nformer chapter the foundation of the attribute, we must, therefore, have\nrecourse for its definition. Now, the foundation of the attribute may be a\nphenomenon of any degree of complexity, consisting of many different\nparts, either co-existent or in succession. To obtain a definition of the\nattribute, we must analyze the phenomenon into these parts. Eloquence, for\nexample, is the name of one attribute only; but this attribute is grounded\non external effects of a complicated nature, flowing from acts of the\nperson to whom we ascribe the attribute; and by resolving this phenomenon\nof causation into its two parts, the cause and the effect, we obtain a\ndefinition of eloquence, viz. the power of influencing the feelings by\nspeech or writing.\n\nA name, therefore, whether concrete or abstract, admits of definition,\nprovided we are able to analyze, that is, to distinguish into parts, the\nattribute or set of attributes which constitute the meaning both of the\nconcrete name and of the corresponding abstract: if a set of attributes,\nby enumerating them; if a single attribute, by dissecting the fact or\nphenomenon (whether of perception or of internal consciousness) which is\nthe foundation of the attribute. But, further, even when the fact is one\nof our simple feelings or states of consciousness, and therefore\nunsusceptible of analysis, the names both of the object and of the\nattribute still admit of definition; or rather, would do so if all our\nsimple feelings had names. Whiteness may be defined, the property or power\nof exciting the sensation of white. A white object may be defined, an\nobject which excites the sensation of white. The only names which are\nunsusceptible of definition, because their meaning is unsusceptible of\nanalysis, are the names of the simple feelings themselves. These are in\nthe same condition as proper names. They are not indeed, like proper\nnames, unmeaning; for the words _sensation of white_ signify, that the\nsensation which I so denominate resembles other sensations which I\nremember to have had before, and to have called by that name. But as we\nhave no words by which to recall those former sensations, except the very\nword which we seek to define, or some other which, being exactly\nsynonymous with it, requires definition as much, words can not unfold the\nsignification of this class of names; and we are obliged to make a direct\nappeal to the personal experience of the individual whom we address.\n\n\u00a7 3. Having stated what seems to be the true idea of a Definition, I\nproceed to examine some opinions of philosophers, and some popular\nconceptions on the subject, which conflict more or less with that idea.\n\nThe only adequate definition of a name is, as already remarked, one which\ndeclares the facts, and the whole of the facts, which the name involves in\nits signification. But with most persons the object of a definition does\nnot embrace so much; they look for nothing more, in a definition, than a\nguide to the correct use of the term\u2014a protection against applying it in a\nmanner inconsistent with custom and convention. Any thing, therefore, is\nto them a sufficient definition of a term, which will serve as a correct\nindex to what the term _de_notes; though not embracing the whole, and\nsometimes, perhaps, not even any part, of what it connotes. This gives\nrise to two sorts of imperfect, or unscientific definition; Essential but\nincomplete Definitions, and Accidental Definitions, or Descriptions. In\nthe former, a connotative name is defined by a part only of its\nconnotation; in the latter, by something which forms no part of the\nconnotation at all.\n\nAn example of the first kind of imperfect definitions is the following:\nMan is a rational animal. It is impossible to consider this as a complete\ndefinition of the word Man, since (as before remarked) if we adhered to it\nwe should be obliged to call the Houyhnhnms men; but as there happen to be\nno Houyhnhnms, this imperfect definition is sufficient to mark out and\ndistinguish from all other things, the objects at present denoted by\n\u201cman;\u201d all the beings actually known to exist, of whom the name is\npredicable. Though the word is defined by some only among the attributes\nwhich it connotes, not by all, it happens that all known objects which\npossess the enumerated attributes, possess also those which are omitted;\nso that the field of predication which the word covers, and the employment\nof it which is conformable to usage, are as well indicated by the\ninadequate definition as by an adequate one. Such definitions, however,\nare always liable to be overthrown by the discovery of new objects in\nnature.\n\nDefinitions of this kind are what logicians have had in view, when they\nlaid down the rule, that the definition of a species should be _per genus\net differentiam_. Differentia being seldom taken to mean the whole of the\npeculiarities constitutive of the species, but some one of those\npeculiarities only, a complete definition would be _per genus et\ndifferentias_, rather than _differentiam_. It would include, with the name\nof the superior genus, not merely _some_ attribute which distinguishes the\nspecies intended to be defined from all other species of the same genus,\nbut _all_ the attributes implied in the name of the species, which the\nname of the superior genus has not already implied. The assertion,\nhowever, that a definition must of necessity consist of a genus and\ndifferenti\u00e6, is not tenable. It was early remarked by logicians, that the\n_summum genus_ in any classification, having no genus superior to itself,\ncould not be defined in this manner. Yet we have seen that all names,\nexcept those of our elementary feelings, are susceptible of definition in\nthe strictest sense; by setting forth in words the constituent parts of\nthe fact or phenomenon, of which the connotation of every word is\nultimately composed.\n\n\u00a7 4. Although the first kind of imperfect definition (which defines a\nconnotative term by a part only of what it connotes, but a part sufficient\nto mark out correctly the boundaries of its denotation), has been\nconsidered by the ancients, and by logicians in general, as a complete\ndefinition; it has always been deemed necessary that the attributes\nemployed should really form part of the connotation; for the rule was that\nthe definition must be drawn from the _essence_ of the class; and this\nwould not have been the case if it had been in any degree made up of\nattributes not connoted by the name. The second kind of imperfect\ndefinition, therefore, in which the name of a class is defined by any of\nits accidents\u2014that is, by attributes which are not included in its\nconnotation\u2014has been rejected from the rank of genuine Definition by all\nlogicians, and has been termed Description.\n\nThis kind of imperfect definition, however, takes its rise from the same\ncause as the other, namely, the willingness to accept as a definition any\nthing which, whether it expounds the meaning of the name or not, enables\nus to discriminate the things denoted by the name from all other things,\nand consequently to employ the term in predication without deviating from\nestablished usage. This purpose is duly answered by stating any (no matter\nwhat) of the attributes which are common to the whole of the class, and\npeculiar to it; or any combination of attributes which happens to be\npeculiar to it, though separately each of those attributes may be common\nto it with some other things. It is only necessary that the definition (or\ndescription) thus formed, should be _convertible_ with the name which it\nprofesses to define; that is, should be exactly co-extensive with it,\nbeing predicable of every thing of which it is predicable, and of nothing\nof which it is not predicable; though the attributes specified may have no\nconnection with those which mankind had in view when they formed or\nrecognized the class, and gave it a name. The following are correct\ndefinitions of Man, according to this test: Man is a mammiferous animal,\nhaving (by nature) two hands (for the human species answers to this\ndescription, and no other animal does): Man is an animal who cooks his\nfood: Man is a featherless biped.\n\nWhat would otherwise be a mere description, may be raised to the rank of a\nreal definition by the peculiar purpose which the speaker or writer has in\nview. As was seen in the preceding chapter, it may, for the ends of a\nparticular art or science, or for the more convenient statement of an\nauthor\u2019s particular doctrines, be advisable to give to some general name,\nwithout altering its denotation, a special connotation, different from its\nordinary one. When this is done, a definition of the name by means of the\nattributes which make up the special connotation, though in general a mere\naccidental definition or description, becomes on the particular occasion\nand for the particular purpose a complete and genuine definition. This\nactually occurs with respect to one of the preceding examples, \u201cMan is a\nmammiferous animal having two hands,\u201d which is the scientific definition\nof man, considered as one of the species in Cuvier\u2019s distribution of the\nanimal kingdom.\n\nIn cases of this sort, though the definition is still a declaration of the\nmeaning which in the particular instance the name is appointed to convey,\nit can not be said that to state the meaning of the word is the purpose of\nthe definition. The purpose is not to expound a name, but a\nclassification. The special meaning which Cuvier assigned to the word Man\n(quite foreign to its ordinary meaning, though involving no change in the\ndenotation of the word), was incidental to a plan of arranging animals\ninto classes on a certain principle, that is, according to a certain set\nof distinctions. And since the definition of Man according to the ordinary\nconnotation of the word, though it would have answered every other purpose\nof a definition, would not have pointed out the place which the species\nought to occupy in that particular classification; he gave the word a\nspecial connotation, that he might be able to define it by the kind of\nattributes on which, for reasons of scientific convenience, he had\nresolved to found his division of animated nature.\n\nScientific definitions, whether they are definitions of scientific terms,\nor of common terms used in a scientific sense, are almost always of the\nkind last spoken of: their main purpose is to serve as the landmarks of\nscientific classification. And since the classifications in any science\nare continually modified as scientific knowledge advances, the definitions\nin the sciences are also constantly varying. A striking instance is\nafforded by the words Acid and Alkali, especially the former. As\nexperimental discovery advanced, the substances classed with acids have\nbeen constantly multiplying, and by a natural consequence the attributes\nconnoted by the word have receded and become fewer. At first it connoted\nthe attributes, of combining with an alkali to form a neutral substance\n(called a salt); being compounded of a base and oxygen; causticity to the\ntaste and touch; fluidity, etc. The true analysis of muriatic acid, into\nchlorine and hydrogen, caused the second property, composition from a base\nand oxygen, to be excluded from the connotation. The same discovery fixed\nthe attention of chemists upon hydrogen as an important element in acids;\nand more recent discoveries having led to the recognition of its presence\nin sulphuric, nitric, and many other acids, where its existence was not\npreviously suspected, there is now a tendency to include the presence of\nthis element in the connotation of the word. But carbonic acid, silica,\nsulphurous acid, have no hydrogen in their composition; that property can\nnot, therefore, be connoted by the term, unless those substances are no\nlonger to be considered acids. Causticity and fluidity have long since\nbeen excluded from the characteristics of the class, by the inclusion of\nsilica and many other substances in it; and the formation of neutral\nbodies by combination with alkalis, together with such electro-chemical\npeculiarities as this is supposed to imply, are now the only _differenti\u00e6_\nwhich form the fixed connotation of the word Acid, as a term of chemical\nscience.\n\nWhat is true of the definition of any term of science, is of course true\nof the definition of a science itself; and accordingly (as observed in the\nIntroductory Chapter of this work), the definition of a science must\nnecessarily be progressive and provisional. Any extension of knowledge or\nalteration in the current opinions respecting the subject-matter, may lead\nto a change more or less extensive in the particulars included in the\nscience; and its composition being thus altered, it may easily happen that\na different set of characteristics will be found better adapted as\ndifferenti\u00e6 for defining its name.\n\nIn the same manner in which a special or technical definition has for its\nobject to expound the artificial classification out of which it grows; the\nAristotelian logicians seem to have imagined that it was also the business\nof ordinary definition to expound the ordinary, and what they deemed the\nnatural, classification of things, namely, the division of them into\nKinds; and to show the place which each Kind occupies, as superior,\ncollateral, or subordinate, among other Kinds. This notion would account\nfor the rule that all definition must necessarily be _per genus et\ndifferentiam_, and would also explain why a single differentia was deemed\nsufficient. But to expound, or express in words, a distinction of Kind,\nhas already been shown to be an impossibility: the very meaning of a Kind\nis, that the properties which distinguish it do not grow out of one\nanother, and can not therefore be set forth in words, even by implication,\notherwise than by enumerating them all: and all are not known, nor are\never likely to be so. It is idle, therefore, to look to this as one of the\npurposes of a definition: while, if it be only required that the\ndefinition of a Kind should indicate what kinds include it or are included\nby it, any definitions which expound the connotation of the names will do\nthis: for the name of each class must necessarily connote enough of its\nproperties to fix the boundaries of the class. If the definition,\ntherefore, be a full statement of the connotation, it is all that a\ndefinition can be required to be.(43)\n\n\u00a7 5. Of the two incomplete and popular modes of definition, and in what\nthey differ from the complete or philosophical mode, enough has now been\nsaid. We shall next examine an ancient doctrine, once generally prevalent\nand still by no means exploded, which I regard as the source of a great\npart of the obscurity hanging over some of the most important processes of\nthe understanding in the pursuit of truth. According to this, the\ndefinitions of which we have now treated are only one of two sorts into\nwhich definitions may be divided, viz., definitions of names, and\ndefinitions of things. The former are intended to explain the meaning of a\nterm; the latter, the nature of a thing; the last being incomparably the\nmost important.\n\nThis opinion was held by the ancient philosophers, and by their followers,\nwith the exception of the Nominalists; but as the spirit of modern\nmetaphysics, until a recent period, has been on the whole a Nominalist\nspirit, the notion of definitions of things has been to a certain extent\nin abeyance, still continuing, however, to breed confusion in logic, by\nits consequences indeed rather than by itself. Yet the doctrine in its own\nproper form now and then breaks out, and has appeared (among other places)\nwhere it was scarcely to be expected, in a justly admired word, Archbishop\nWhately\u2019s _Logic_.(44) In a review of that work published by me in the\n_Westminster __ Review_ for January, 1828, and containing some opinions\nwhich I no longer entertain, I find the following observations on the\nquestion now before us; observations with which my present view of that\nquestion is still sufficiently in accordance.\n\n\u201cThe distinction between nominal and real definitions, between definitions\nof words and what are called definitions of things, though conformable to\nthe ideas of most of the Aristotelian logicians, can not, as it appears to\nus, be maintained. We apprehend that no definition is ever intended to\n\u2018explain and unfold the nature of a thing.\u2019 It is some confirmation of our\nopinion, that none of those writers who have thought that there were\ndefinitions of things, have ever succeeded in discovering any criterion by\nwhich the definition of a thing can be distinguished from any other\nproposition relating to the thing. The definition, they say, unfolds the\nnature of the thing: but no definition can unfold its whole nature; and\nevery proposition in which any quality whatever is predicated of the\nthing, unfolds some part of its nature. The true state of the case we take\nto be this. All definitions are of names, and of names only; but, in some\ndefinitions, it is clearly apparent, that nothing is intended except to\nexplain the meaning of the word; while in others, besides explaining the\nmeaning of the word, it is intended to be implied that there exists a\nthing, corresponding to the word. Whether this be or be not implied in any\ngiven case, can not be collected from the mere form of the expression. \u2018A\ncentaur is an animal with the upper parts of a man and the lower parts of\na horse,\u2019 and \u2018A triangle is a rectilineal figure with three sides,\u2019 are,\nin form, expressions precisely similar; although in the former it is not\nimplied that any _thing_, conformable to the term, really exists, while in\nthe latter it is; as may be seen by substituting in both definitions, the\nword _means_ for _is_. In the first expression, \u2018A centaur means an\nanimal,\u2019 etc., the sense would remain unchanged: in the second, \u2018A\ntriangle means,\u2019 etc., the meaning would be altered, since it would be\nobviously impossible to deduce any of the truths of geometry from a\nproposition expressive only of the manner in which we intend to employ a\nparticular sign.\n\n\u201cThere are, therefore, expressions, commonly passing for definitions,\nwhich include in themselves more than the mere explanation of the meaning\nof a term. But it is not correct to call an expression of this sort a\npeculiar kind of definition. Its difference from the other kind consists\nin this, that it is not a definition, but a definition and something more.\nThe definition above given of a triangle, obviously comprises not one, but\ntwo propositions, perfectly distinguishable. The one is, \u2018There may exist\na figure, bounded by three straight lines;\u2019 the other, \u2018And this figure\nmay be termed a triangle.\u2019 The former of these propositions is not a\ndefinition at all: the latter is a mere nominal definition, or explanation\nof the use and application of a term. The first is susceptible of truth or\nfalsehood, and may therefore be made the foundation of a train of\nreasoning. The latter can neither be true nor false; the only character it\nis susceptible of is that of conformity or disconformity to the ordinary\nusage of language.\u201d\n\nThere is a real distinction, then, between definitions of names, and what\nare erroneously called definitions of things; but it is, that the latter,\nalong with the meaning of a name, covertly asserts a matter of fact. This\ncovert assertion is not a definition, but a postulate. The definition is a\nmere identical proposition, which gives information only about the use of\nlanguage, and from which no conclusions affecting matters of fact can\npossibly be drawn. The accompanying postulate, on the other hand, affirms\na fact, which may lead to consequences of every degree of importance. It\naffirms the actual or possible existence of Things possessing the\ncombination of attributes set forth in the definition; and this, if true,\nmay be foundation sufficient on which to build a whole fabric of\nscientific truth.\n\nWe have already made, and shall often have to repeat, the remark, that the\nphilosophers who overthrew Realism by no means got rid of the consequences\nof Realism, but retained long afterward, in their own philosophy, numerous\npropositions which could only have a rational meaning as part of a\nRealistic system. It had been handed down from Aristotle, and probably\nfrom earlier times, as an obvious truth, that the science of Geometry is\ndeduced from definitions. This, so long as a definition was considered to\nbe a proposition \u201cunfolding the nature of the thing,\u201d did well enough. But\nHobbes followed, and rejected utterly the notion that a definition\ndeclares the nature of the thing, or does any thing but state the meaning\nof a name; yet he continued to affirm as broadly as any of his\npredecessors, that the \u1f00\u03c1\u03c7\u03b1\u1f76, _principia_, or original premises of\nmathematics, and even of all science, are definitions; producing the\nsingular paradox, that systems of scientific truth, nay, all truths\nwhatever at which we arrive by reasoning, are deduced from the arbitrary\nconventions of mankind concerning the signification of words.\n\nTo save the credit of the doctrine that definitions are the premises of\nscientific knowledge, the proviso is sometimes added, that they are so\nonly under a certain condition, namely, that they be framed conformably to\nthe phenomena of nature; that is, that they ascribe such meanings to terms\nas shall suit objects actually existing. But this is only an instance of\nthe attempt so often made, to escape from the necessity of abandoning old\nlanguage after the ideas which it expresses have been exchanged for\ncontrary ones. From the meaning of a name (we are told) it is possible to\ninfer physical facts, provided the name has corresponding to it an\nexisting thing. But if this proviso be necessary, from which of the two is\nthe inference really drawn? From the existence of a thing having the\nproperties, or from the existence of a name meaning them?\n\nTake, for instance, any of the definitions laid down as premises in\nEuclid\u2019s Elements; the definition, let us say, of a circle. This, being\nanalyzed, consists of two propositions; the one an assumption with respect\nto a matter of fact, the other a genuine definition. \u201cA figure may exist,\nhaving all the points in the line which bounds it equally distant from a\nsingle point within it:\u201d \u201cAny figure possessing this property is called a\ncircle.\u201d Let us look at one of the demonstrations which are said to depend\non this definition, and observe to which of the two propositions contained\nin it the demonstration really appeals. \u201cAbout the centre A, describe the\ncircle B C D.\u201d\n\nHere is an assumption that a figure, such as the definition expresses,\n_may_ be described; which is no other than the postulate, or covert\nassumption, involved in the so-called definition. But whether that figure\nbe called a circle or not is quite immaterial. The purpose would be as\nwell answered, in all respects except brevity, were we to say, \u201cThrough\nthe point B, draw a line returning into itself, of which every point shall\nbe at an equal distance from the point A.\u201d By this the definition of a\ncircle would be got rid of, and rendered needless; but not the postulate\nimplied in it; without that the demonstration could not stand. The circle\nbeing now described, let us proceed to the consequence. \u201cSince B C D is a\ncircle, the radius B A is equal to the radius C A.\u201d B A is equal to C A,\nnot because B C D is a circle, but because B C D is a figure with the\nradii equal. Our warrant for assuming that such a figure about the centre\nA, with the radius B A, may be made to exist, is the postulate. Whether\nthe admissibility of these postulates rests on intuition, or on proof, may\nbe a matter of dispute; but in either case they are the premises on which\nthe theorems depend; and while these are retained it would make no\ndifference in the certainty of geometrical truths, though every definition\nin Euclid, and every technical term therein defined, were laid aside.\n\nIt is, perhaps, superfluous to dwell at so much length on what is so\nnearly self-evident; but when a distinction, obvious as it may appear, has\nbeen confounded, and by powerful intellects, it is better to say too much\nthan too little for the purpose of rendering such mistakes impossible in\nfuture. I will, therefore detain the reader while I point out one of the\nabsurd consequences flowing from the supposition that definitions, as\nsuch, are the premises in any of our reasonings, except such as relate to\nwords only. If this supposition were true, we might argue correctly from\ntrue premises, and arrive at a false conclusion. We should only have to\nassume as a premise the definition of a nonentity; or rather of a name\nwhich has no entity corresponding to it. Let this, for instance, be our\ndefinition:\n\n\n    A dragon is a serpent breathing flame.\n\n\nThis proposition, considered only as a definition, is indisputably\ncorrect. A dragon _is_ a serpent breathing flame: the word _means_ that.\nThe tacit assumption, indeed (if there were any such understood\nassertion), of the existence of an object with properties corresponding to\nthe definition, would, in the present instance, be false. Out of this\ndefinition we may carve the premises of the following syllogism:\n\n\n    A dragon is a thing which breathes flame:\n    A dragon is a serpent:\n\n\nFrom which the conclusion is,\n\n\n    Therefore some serpent or serpents breathe flame:\n\n\nan unexceptionable syllogism in the first mode of the third figure, in\nwhich both premises are true and yet the conclusion false; which every\nlogician knows to be an absurdity. The conclusion being false and the\nsyllogism correct, the premises can not be true. But the premises,\nconsidered as parts of a definition, are true. Therefore, the premises\nconsidered as parts of a definition can not be the real ones. The real\npremises must be\u2014\n\n\n    A dragon is a _really existing_ thing which breathes flame:\n    A dragon is a _really existing_ serpent:\n\n\nwhich implied premises being false, the falsity of the conclusion presents\nno absurdity.\n\nIf we would determine what conclusion follows from the same ostensible\npremises when the tacit assumption of real existence is left out, let us,\naccording to the recommendation in a previous page, substitute _means_ for\n_is_. We then have\u2014\n\n\n    Dragon is _a word meaning_ a thing which breathes flame:\n    Dragon is _a word meaning_ a serpent:\n\n\nFrom which the conclusion is,\n\n\n    Some _word or words which mean_ a serpent, also mean a thing which\n    breathes flame:\n\n\nwhere the conclusion (as well as the premises) is true, and is the only\nkind of conclusion which can ever follow from a definition, namely, a\nproposition relating to the meaning of words.\n\nThere is still another shape into which we may transform this syllogism.\nWe may suppose the middle term to be the designation neither of a thing\nnor of a name, but of an idea. We then have\u2014\n\n\n    The _idea of_ a dragon is _an idea of_ a thing which breathes\n                flame:\n    The _idea of_ a dragon is _an idea of_ a serpent:\n    Therefore, there is _an idea of_ a serpent, which is _an idea of_\n                a thing breathing flame.\n\n\nHere the conclusion is true, and also the premises; but the premises are\nnot definitions. They are propositions affirming that an idea existing in\nthe mind, includes certain ideal elements. The truth of the conclusion\nfollows from the existence of the psychological phenomenon called the idea\nof a dragon; and therefore still from the tacit assumption of a matter of\nfact.(45)\n\nWhen, as in this last syllogism, the conclusion is a proposition\nrespecting an idea, the assumption on which it depends may be merely that\nof the existence of an idea. But when the conclusion is a proposition\nconcerning a Thing, the postulate involved in the definition which stands\nas the apparent premise, is the existence of a thing conformable to the\ndefinition, and not merely of an idea conformable to it. This assumption\nof real existence we always convey the impression that we intend to make,\nwhen we profess to define any name which is already known to be a name of\nreally existing objects. On this account it is, that the assumption was\nnot necessarily implied in the definition of a dragon, while there was no\ndoubt of its being included in the definition of a circle.\n\n\u00a7 6. One of the circumstances which have contributed to keep up the\nnotion, that demonstrative truths follow from definitions rather than from\nthe postulates implied in those definitions, is, that the postulates, even\nin those sciences which are considered to surpass all others in\ndemonstrative certainty, are not always exactly true. It is not true that\na circle exists, or can be described, which has all its radii _exactly_\nequal. Such accuracy is ideal only; it is not found in nature, still less\ncan it be realized by art. People had a difficulty, therefore, in\nconceiving that the most certain of all conclusions could rest on premises\nwhich, instead of being certainly true, are certainly not true to the full\nextent asserted. This apparent paradox will be examined when we come to\ntreat of Demonstration; where we shall be able to show that as much of the\npostulate is true, as is required to support as much as is true of the\nconclusion. Philosophers, however, to whom this view had not occurred, or\nwhom it did not satisfy, have thought it indispensable that there should\nbe found in definitions something _more_ certain, or at least more\naccurately true, than the implied postulate of the real existence of a\ncorresponding object. And this something they flattered themselves they\nhad found, when they laid it down that a definition is a statement and\nanalysis not of the mere meaning of a word, nor yet of the nature of a\nthing, but of an idea. Thus, the proposition, \u201cA circle is a plane figure\nbounded by a line all the points of which are at an equal distance from a\ngiven point within it,\u201d was considered by them, not as an assertion that\nany real circle has that property (which would not be exactly true), but\nthat we _conceive_ a circle as having it; that our abstract idea of a\ncircle is an idea of a figure with its radii exactly equal.\n\nConformably to this it is said, that the subject-matter of mathematics,\nand of every other demonstrative science, is not things as they really\nexist, but abstractions of the mind. A geometrical line is a line without\nbreadth; but no such line exists in nature; it is a notion merely\nsuggested to the mind by its experience of nature. The definition (it is\nsaid) is a definition of this mental line, not of any actual line: and it\nis only of the mental line, not of any line existing in nature, that the\ntheorems of geometry are accurately true.\n\nAllowing this doctrine respecting the nature of demonstrative truth to be\ncorrect (which, in a subsequent place, I shall endeavor to prove that it\nis not); even on that supposition, the conclusions which seem to follow\nfrom a definition, do not follow from the definition as such, but from an\nimplied postulate. Even if it be true that there is no object in nature\nanswering to the definition of a line, and that the geometrical properties\nof lines are not true of any lines in nature, but only of the idea of a\nline; the definition, at all events, postulates the real existence of such\nan idea: it assumes that the mind can frame, or rather has framed, the\nnotion of length without breadth, and without any other sensible property\nwhatever. To me, indeed, it appears that the mind can not form any such\nnotion; it can not conceive length without breadth; it can only, in\ncontemplating objects, attend to their length, exclusively of their other\nsensible qualities, and so determine what properties may be predicated of\nthem in virtue of their length alone. If this be true, the postulate\ninvolved in the geometrical definition of a line, is the real existence,\nnot of length without breadth, but merely of length, that is, of long\nobjects. This is quite enough to support all the truths of geometry, since\nevery property of a geometrical line is really a property of all physical\nobjects in so far as possessing length. But even what I hold to be the\nfalse doctrine on the subject, leaves the conclusion that our reasonings\nare grounded on the matters of fact postulated in definitions, and not on\nthe definitions themselves, entirely unaffected; and accordingly this\nconclusion is one which I have in common with Dr. Whewell, in his\n_Philosophy of the Inductive Sciences_: though, on the nature of\ndemonstrative truth, Dr. Whewell\u2019s opinions are greatly at variance with\nmine. And here, as in many other instances, I gladly acknowledge that his\nwritings are eminently serviceable in clearing from confusion the initial\nsteps in the analysis of the mental processes, even where his views\nrespecting the ultimate analysis are such as (though with unfeigned\nrespect) I can not but regard as fundamentally erroneous.\n\n\u00a7 7. Although, according to the opinion here presented, Definitions are\nproperly of names only, and not of things, it does not follow from this\nthat definitions are arbitrary. How to define a name, may not only be an\ninquiry of considerable difficulty and intricacy, but may involve\nconsiderations going deep into the nature of the things which are denoted\nby the name. Such, for instance, are the inquiries which form the subjects\nof the most important of Plato\u2019s Dialogues; as, \u201cWhat is rhetoric?\u201d the\ntopic of the Gorgias, or, \u201cWhat is justice?\u201d that of the Republic. Such,\nalso, is the question scornfully asked by Pilate, \u201cWhat is truth?\u201d and the\nfundamental question with speculative moralists in all ages, \u201cWhat is\nvirtue?\u201d\n\nIt would be a mistake to represent these difficult and noble inquiries as\nhaving nothing in view beyond ascertaining the conventional meaning of a\nname. They are inquiries not so much to determine what is, as what should\nbe, the meaning of a name; which, like other practical questions of\nterminology, requires for its solution that we should enter, and sometimes\nenter very deeply, into the properties not merely of names but of the\nthings named.\n\nAlthough the meaning of every concrete general name resides in the\nattributes which it connotes, the objects were named before the\nattributes; as appears from the fact that in all languages, abstract names\nare mostly compounds or other derivatives of the concrete names which\ncorrespond to them. Connotative names, therefore, were, after proper\nnames, the first which were used: and in the simpler cases, no doubt, a\ndistinct connotation was present to the minds of those who first used the\nname, and was distinctly intended by them to be conveyed by it. The first\nperson who used the word white, as applied to snow or to any other object,\nknew, no doubt, very well what quality he intended to predicate, and had a\nperfectly distinct conception in his mind of the attribute signified by\nthe name.\n\nBut where the resemblances and differences on which our classifications\nare founded are not of this palpable and easily determinable kind;\nespecially where they consist not in any one quality but in a number of\nqualities, the effects of which, being blended together, are not very\neasily discriminated, and referred each to its true source; it often\nhappens that names are applied to namable objects, with no distinct\nconnotation present to the minds of those who apply them. They are only\ninfluenced by a general resemblance between the new object and all or some\nof the old familiar objects which they have been accustomed to call by\nthat name. This, as we have seen, is the law which even the mind of the\nphilosopher must follow, in giving names to the simple elementary feelings\nof our nature: but, where the things to be named are complex wholes, a\nphilosopher is not content with noticing a general resemblance; he\nexamines what the resemblance consists in: and he only gives the same name\nto things which resemble one another in the same definite particulars. The\nphilosopher, therefore, habitually employs his general names with a\ndefinite connotation. But language was not made, and can only in some\nsmall degree be mended, by philosophers. In the minds of the real arbiters\nof language, general names, especially where the classes they denote can\nnot be brought before the tribunal of the outward senses to be identified\nand discriminated, connote little more than a vague gross resemblance to\nthe things which they were earliest, or have been most, accustomed to call\nby those names. When, for instance, ordinary persons predicate the words\n_just_ or _unjust_ of any action, _noble_ or _mean_ of any sentiment,\nexpression, or demeanor, _statesman_ or _charlatan_ of any personage\nfiguring in politics, do they mean to affirm of those various subjects any\ndeterminate attributes, of whatever kind? No: they merely recognize, as\nthey think, some likeness, more or less vague and loose, between these and\nsome other things which they have been accustomed to denominate or to hear\ndenominated by those appellations.\n\nLanguage, as Sir James Mackintosh used to say of governments, \u201cis not\nmade, but grows.\u201d A name is not imposed at once and by previous purpose\nupon a _class_ of objects, but is first applied to one thing, and then\nextended by a series of transitions to another and another. By this\nprocess (as has been remarked by several writers, and illustrated with\ngreat force and clearness by Dugald Stewart in his Philosophical Essays) a\nname not unfrequently passes by successive links of resemblance from one\nobject to another, until it becomes applied to things having nothing in\ncommon with the first things to which the name was given; which, however,\ndo not, for that reason, drop the name; so that it at last denotes a\nconfused huddle of objects, having nothing whatever in common; and\nconnotes nothing, not even a vague and general resemblance. When a name\nhas fallen into this state, in which by predicating it of any object we\nassert literally nothing about the object, it has become unfit for the\npurposes either of thought or of the communication of thought; and can\nonly be made serviceable by stripping it of some part of its multifarious\ndenotation, and confining it to objects possessed of some attributes in\ncommon, which it may be made to connote. Such are the inconveniences of a\nlanguage which \u201cis not made, but grows.\u201d Like the governments which are in\na similar case, it may be compared to a road which is not made but has\nmade itself: it requires continual mending in order to be passable.\n\nFrom this it is already evident, why the question respecting the\ndefinition of an abstract name is often one of so much difficulty. The\nquestion, What is justice? is, in other words, What is the attribute which\nmankind mean to predicate when they call an action just? To which the\nfirst answer is, that having come to no precise agreement on the point,\nthey do not mean to predicate distinctly any attribute at all.\nNevertheless, all believe that there is some common attribute belonging to\nall the actions which they are in the habit of calling just. The question\nthen must be, whether there is any such common attribute? and, in the\nfirst place, whether mankind agree sufficiently with one another as to the\nparticular actions which they do or do not call just, to render the\ninquiry, what quality those actions have in common, a possible one: if so,\nwhether the actions really have any quality in common; and if they have,\nwhat it is. Of these three, the first alone is an inquiry into usage and\nconvention; the other two are inquiries into matters of fact. And if the\nsecond question (whether the actions form a class at all) has been\nanswered negatively, there remains a fourth, often more arduous than all\nthe rest, namely, how best to form a class artificially, which the name\nmay denote.\n\nAnd here it is fitting to remark, that the study of the spontaneous growth\nof languages is of the utmost importance to those who would logically\nremodel them. The classifications rudely made by established language,\nwhen retouched, as they almost all require to be, by the hands of the\nlogician, are often themselves excellently suited to his purposes. As\ncompared with the classifications of a philosopher, they are like the\ncustomary law of a country, which has grown up as it were spontaneously,\ncompared with laws methodized and digested into a code: the former are a\nfar less perfect instrument than the latter; but being the result of a\nlong, though unscientific, course of experience, they contain a mass of\nmaterials which may be made very usefully available in the formation of\nthe systematic body of written law. In like manner, the established\ngrouping of objects under a common name, even when founded only on a gross\nand general resemblance, is evidence, in the first place, that the\nresemblance is obvious, and therefore considerable; and, in the next\nplace, that it is a resemblance which has struck great numbers of persons\nduring a series of years and ages. Even when a name, by successive\nextensions, has come to be applied to things among which there does not\nexist this gross resemblance common to them all, still at every step in\nits progress we shall find such a resemblance. And these transitions of\nthe meaning of words are often an index to real connections between the\nthings denoted by them, which might otherwise escape the notice of\nthinkers; of those at least who, from using a different language, or from\nany difference in their habitual associations, have fixed their attention\nin preference on some other aspect of the things. The history of\nphilosophy abounds in examples of such oversights, committed for want of\nperceiving the hidden link that connected together the seemingly disparate\nmeanings of some ambiguous word.(46)\n\nWhenever the inquiry into the definition of the name of any real object\nconsists of any thing else than a mere comparison of authorities, we\ntacitly assume that a meaning must be found for the name, compatible with\nits continuing to denote, if possible all, but at any rate the greater or\nthe more important part, of the things of which it is commonly predicated.\nThe inquiry, therefore, into the definition, is an inquiry into the\nresemblances and differences among those things: whether there be any\nresemblance running through them all; if not, through what portion of them\nsuch a general resemblance can be traced: and finally, what are the common\nattributes, the possession of which gives to them all, or to that portion\nof them, the character of resemblance which has led to their being classed\ntogether. When these common attributes have been ascertained and\nspecified, the name which belongs in common to the resembling objects\nacquires a distinct instead of a vague connotation; and by possessing this\ndistinct connotation, becomes susceptible of definition.\n\nIn giving a distinct connotation to the general name, the philosopher will\nendeavor to fix upon such attributes as, while they are common to all the\nthings usually denoted by the name, are also of greatest importance in\nthemselves; either directly, or from the number, the conspicuousness, or\nthe interesting character, of the consequences to which they lead. He will\nselect, as far as possible, such _differenti\u00e6_ as lead to the greatest\nnumber of interesting _propria_. For these, rather than the more obscure\nand recondite qualities on which they often depend, give that general\ncharacter and aspect to a set of objects, which determine the groups into\nwhich they naturally fall. But to penetrate to the more hidden agreement\non which these obvious and superficial agreements depend, is often one of\nthe most difficult of scientific problems. As it is among the most\ndifficult, so it seldom fails to be among the most important. And since\nupon the result of this inquiry respecting the causes of the properties of\na class of things, there incidentally depends the question what shall be\nthe meaning of a word; some of the most profound and most valuable\ninvestigations which philosophy presents to us, have been introduced by,\nand have offered themselves under the guise of, inquiries into the\ndefinition of a name.\n\n\n\n\n                                 Book II.\n\n\nOF REASONING.\n\n\n    \u0394\u03b9\u03c9\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u03b4\u03b5 \u03c4\u03bf\u03cd\u03c4\u03c9\u03bd \u03bb\u03ad\u03b3\u03c9\u03bc\u03b5\u03bd \u1f24\u03b4\u03b7, \u03b4\u03b9\u03ac \u03c4\u03af\u03bd\u03c9\u03bd, \u03ba\u03b1\u1f76 \u03c0\u03cc\u03c4\u03b5, \u03ba\u03b1\u1f76 \u03c0\u1ff6\u03c2\n    \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u1fb6\u03c2 \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u1f55\u03c3\u03c4\u03b5\u03c1\u03bf\u03bd \u03b4\u1f72 \u03bb\u03b5\u03ba\u03c4\u03ad\u03bf\u03bd \u03c0\u03b5\u03c1\u1f76 \u1f00\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c9\u03c2.\n    \u03a0\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03bd \u03b3\u1f70\u03c1 \u03c0\u03b5\u03c1\u1f76 \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u1fe6 \u03bb\u03b5\u03ba\u03c4\u03ad\u03bf\u03bd, \u1f25 \u03c0\u03b5\u03c1\u1f76 \u1f00\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c9\u03c2, \u03b4\u03b9\u1f70 \u03c4\u1f78\n    \u03ba\u03b1\u03b8\u03cc\u03bb\u03bf\u03c5 \u03bc\u1fb6\u03bb\u03bb\u03bf\u03bd \u03b5\u1f30\u03bd\u03b1\u1f76 \u03c4\u1f78\u03bd \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03bd. \u1f29 \u03bc\u03ad\u03bd \u03b3\u1f70\u03c1 \u1f00\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b9\u03c2,\n    \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c4\u03b9\u03c2; \u1f41 \u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b4\u1f72 \u03bf\u03cd \u03c0\u1fb6\u03c2, \u1f00\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b9\u03c2.\u2014ARIST.,\n    _Analyt. Prior._, l. i., cap. 4.\n\n\n\n\n                                Chapter I.\n\n\nOf Inference, Or Reasoning, In General.\n\n\n\u00a7 1. In the preceding Book, we have been occupied not with the nature of\nProof, but with the nature of Assertion: the import conveyed by a\nProposition, whether that Proposition be true or false; not the means by\nwhich to discriminate true from false Propositions. The proper subject,\nhowever, of Logic is Proof. Before we could understand what Proof is, it\nwas necessary to understand what that is to which proof is applicable;\nwhat that is which can be a subject of belief or disbelief, of affirmation\nor denial; what, in short, the different kinds of Propositions assert.\n\nThis preliminary inquiry we have prosecuted to a definite result.\nAssertion, in the first place, relates either to the meaning of words, or\nto some property of the things which words signify. Assertions respecting\nthe meaning of words, among which definitions are the most important, hold\na place, and an indispensable one, in philosophy; but as the meaning of\nwords is essentially arbitrary, this class of assertions are not\nsusceptible of truth or falsity, nor therefore of proof or disproof.\nAssertions respecting Things, or what may be called Real Propositions, in\ncontradistinction to verbal ones, are of various sorts. We have analyzed\nthe import of each sort, and have ascertained the nature of the things\nthey relate to, and the nature of what they severally assert respecting\nthose things. We found that whatever be the form of the proposition, and\nwhatever its nominal subject or predicate, the real subject of every\nproposition is some one or more facts or phenomena of consciousness, or\nsome one or more of the hidden causes or powers to which we ascribe those\nfacts; and that what is predicated or asserted, either in the affirmative\nor negative, of those phenomena or those powers, is always either\nExistence, Order in Place, Order in Time, Causation, or Resemblance. This,\nthen, is the theory of the Import of Propositions, reduced to its ultimate\nelements: but there is another and a less abstruse expression for it,\nwhich, though stopping short in an earlier stage of the analysis, is\nsufficiently scientific for many of the purposes for which such a general\nexpression is required. This expression recognizes the commonly received\ndistinction between Subject and Attribute, and gives the following as the\nanalysis of the meaning of propositions:\u2014Every Proposition asserts, that\nsome given subject does or does not possess some attribute; or that some\nattribute is or is not (either in all or in some portion of the subjects\nin which it is met with) conjoined with some other attribute.\n\nWe shall now for the present take our leave of this portion of our\ninquiry, and proceed to the peculiar problem of the Science of Logic,\nnamely, how the assertions, of which we have analyzed the import, are\nproved or disproved; such of them, at least, as, not being amenable to\ndirect consciousness or intuition, are appropriate subjects of proof.\n\nWe say of a fact or statement, that it is proved, when we believe its\ntruth by reason of some other fact or statement from which it is said to\n_follow_. Most of the propositions, whether affirmative or negative,\nuniversal, particular, or singular, which we believe, are not believed on\ntheir own evidence, but on the ground of something previously assented to,\nfrom which they are said to be _inferred_. To infer a proposition from a\nprevious proposition or propositions; to give credence to it, or claim\ncredence for it, as a conclusion from something else; is to _reason_, in\nthe most extensive sense of the term. There is a narrower sense, in which\nthe name reasoning is confined to the form of inference which is termed\nratiocination, and of which the syllogism is the general type. The reasons\nfor not conforming to this restricted use of the term were stated in an\nearlier stage of our inquiry, and additional motives will be suggested by\nthe considerations on which we are now about to enter.\n\n\u00a7 2. In proceeding to take into consideration the cases in which\ninferences can legitimately be drawn, we shall first mention some cases in\nwhich the inference is apparent, not real; and which require notice\nchiefly that they may not be confounded with cases of inference properly\nso called. This occurs when the proposition ostensibly inferred from\nanother, appears on analysis to be merely a repetition of the same, or\npart of the same, assertion, which was contained in the first. All the\ncases mentioned in books of Logic as examples of equipollency or\nequivalence of propositions, are of this nature. Thus, if we were to\nargue, No man is incapable of reason, for every man is rational; or, All\nmen are mortal, for no man is exempt from death; it would be plain that we\nwere not proving the proposition, but only appealing to another mode of\nwording it, which may or may not be more readily comprehensible by the\nhearer, or better adapted to suggest the real proof, but which contains in\nitself no shadow of proof.\n\nAnother case is where, from a universal proposition, we affect to infer\nanother which differs from it only in being particular: as All A is B,\ntherefore Some A is B: No A is B, therefore Some A is not B. This, too, is\nnot to conclude one proposition from another, but to repeat a second time\nsomething which had been asserted at first; with the difference, that we\ndo not here repeat the whole of the previous assertion, but only an\nindefinite part of it.\n\nA third case is where, the antecedent having affirmed a predicate of a\ngiven subject, the consequent affirms of the same subject something\nalready connoted by the former predicate: as, Socrates is a man, therefore\nSocrates is a living creature; where all that is connoted by living\ncreature was affirmed of Socrates when he was asserted to be a man. If the\npropositions are negative, we must invert their order, thus: Socrates is\nnot a living creature, therefore he is not a man; for if we deny the less,\nthe greater, which includes it, is already denied by implication. These,\ntherefore, are not really cases of inference; and yet the trivial examples\nby which, in manuals of Logic, the rules of the syllogism are illustrated,\nare often of this ill-chosen kind; formal demonstrations of conclusions to\nwhich whoever understands the terms used in the statement of the data, has\nalready, and consciously, assented.(47)\n\nThe most complex case of this sort of apparent inference is what is called\nthe Conversion of propositions; which consists in turning the predicate\ninto a subject, and the subject into a predicate, and framing out of the\nsame terms thus reversed, another proposition, which must be true if the\nformer is true. Thus, from the particular affirmative proposition, Some A\nis B, we may infer that Some B is A. From the universal negative, No A is\nB, we may conclude that No B is A. From the universal affirmative\nproposition, All A is B, it can not be inferred that all B is A; though\nall water is liquid, it is not implied that all liquid is water; but it is\nimplied that some liquid is so; and hence the proposition, All A is B, is\nlegitimately convertible into Some B is A. This process, which converts a\nuniversal proposition into a particular, is termed conversion _per\naccidens_. From the proposition, Some A is not B, we can not even infer\nthat some B is not A; though some men are not Englishmen, it does not\nfollow that some Englishmen are not men. The only mode usually recognized\nof converting a particular negative proposition, is in the form, Some A is\nnot B, therefore something which is not B is A; and this is termed\nconversion by contraposition. In this case, however, the predicate and\nsubject are not merely reversed, but one of them is changed. Instead of\n[A] and [B], the terms of the new proposition are [a thing which is not\nB], and [A]. The original proposition, Some A _is not_ B, is first changed\ninto a proposition equipollent with it, Some A _is_ \u201ca thing which is not\nB;\u201d and the proposition, being now no longer a particular negative, but a\nparticular affirmative, admits of conversion in the first mode, or as it\nis called, _simple_ conversion.(48)\n\nIn all these cases there is not really any inference; there is in the\nconclusion no new truth, nothing but what was already asserted in the\npremises, and obvious to whoever apprehends them. The fact asserted in the\nconclusion is either the very same fact, or part of the fact, asserted in\nthe original proposition. This follows from our previous analysis of the\nImport of Propositions. When we say, for example, that some lawful\nsovereigns are tyrants, what is the meaning of the assertion? That the\nattributes connoted by the term \u201clawful sovereign,\u201d and the attributes\nconnoted by the term \u201ctyrant,\u201d sometimes co-exist in the same individual.\nNow this is also precisely what we mean, when we say that some tyrants are\nlawful sovereigns; which, therefore, is not a second proposition inferred\nfrom the first, any more than the English translation of Euclid\u2019s Elements\nis a collection of theorems different from and consequences of, those\ncontained in the Greek original. Again, if we assert that no great general\nis a rash man, we mean that the attributes connoted by \u201cgreat general,\u201d\nand those connoted by \u201crash,\u201d never co-exist in the same subject; which is\nalso the exact meaning which would be expressed by saying, that no rash\nman is a great general. When we say that all quadrupeds are warm-blooded,\nwe assert, not only that the attributes connoted by \u201cquadruped\u201d and those\nconnoted by \u201cwarm-blooded\u201d sometimes co-exist, but that the former never\nexist without the latter: now the proposition, Some warm-blooded creatures\nare quadrupeds, expresses the first half of this meaning, dropping the\nlatter half; and therefore has been already affirmed in the antecedent\nproposition, All quadrupeds are warm-blooded. But that _all_ warm-blooded\ncreatures are quadrupeds, or, in other words, that the attributes connoted\nby \u201cwarm-blooded\u201d never exist without those connoted by \u201cquadruped,\u201d has\nnot been asserted, and can not be inferred. In order to re-assert, in an\ninverted form, the whole of what was affirmed in the proposition, All\nquadrupeds are warm-blooded, we must convert it by contraposition, thus,\nNothing which is not warm-blooded is a quadruped. This proposition, and\nthe one from which it is derived, are exactly equivalent, and either of\nthem may be substituted for the other; for, to say that when the\nattributes of a quadruped are present, those of a warm-blooded creature\nare present, is to say that when the latter are absent the former are\nabsent.\n\nIn a manual for young students, it would be proper to dwell at greater\nlength on the conversion and equipollency of propositions. For though that\ncan not be called reasoning or inference which is a mere re-assertion in\ndifferent words of what had been asserted before, there is no more\nimportant intellectual habit, nor any the cultivation of which falls more\nstrictly within the province of the art of logic, than that of discerning\nrapidly and surely the identity of an assertion when disguised under\ndiversity of language. That important chapter in logical treatises which\nrelates to the Opposition of Propositions, and the excellent technical\nlanguage which logic provides for distinguishing the different kinds or\nmodes of opposition, are of use chiefly for this purpose. Such\nconsiderations as these, that contrary propositions may both be false, but\ncan not both be true; that subcontrary propositions may both be true, but\ncan not both be false; that of two contradictory propositions one must be\ntrue and the other false; that of two subalternate propositions the truth\nof the universal proves the truth of the particular, and the falsity of\nthe particular proves the falsity of the universal, but not _vic\u00e8\nversa_;(49) are apt to appear, at first sight, very technical and\nmysterious, but when explained, seem almost too obvious to require so\nformal a statement, since the same amount of explanation which is\nnecessary to make the principles intelligible, would enable the truths\nwhich they convey to be apprehended in any particular case which can\noccur. In this respect, however, these axioms of logic are on a level with\nthose of mathematics. That things which are equal to the same thing are\nequal to one another, is as obvious in any particular case as it is in the\ngeneral statement: and if no such general maxim had ever been laid down,\nthe demonstrations in Euclid would never have halted for any difficulty in\nstepping across the gap which this axiom at present serves to bridge over.\nYet no one has ever censured writers on geometry, for placing a list of\nthese elementary generalizations at the head of their treatises, as a\nfirst exercise to the learner of the faculty which will be required in him\nat every step, that of apprehending a _general_ truth. And the student of\nlogic, in the discussion even of such truths as we have cited above,\nacquires habits of circumspect interpretation of words, and of exactly\nmeasuring the length and breadth of his assertions, which are among the\nmost indispensable conditions of any considerable mental attainment, and\nwhich it is one of the primary objects of logical discipline to cultivate.\n\n\u00a7 3. Having noticed, in order to exclude from the province of Reasoning or\nInference properly so called, the cases in which the progression from one\ntruth to another is only apparent, the logical consequent being a mere\nrepetition of the logical antecedent; we now pass to those which are cases\nof inference in the proper acceptation of the term, those in which we set\nout from known truths, to arrive at others really distinct from them.\n\nReasoning, in the extended sense in which I use the term, and in which it\nis synonymous with Inference, is popularly said to be of two kinds:\nreasoning from particulars to generals, and reasoning from generals to\nparticulars; the former being called Induction, the latter Ratiocination\nor Syllogism. It will presently be shown that there is a third species of\nreasoning, which falls under neither of these descriptions, and which,\nnevertheless, is not only valid, but is the foundation of both the others.\n\nIt is necessary to observe, that the expressions, reasoning from\nparticulars to generals, and reasoning from generals to particulars, are\nrecommended by brevity rather than by precision, and do not adequately\nmark, without the aid of a commentary, the distinction between Induction\n(in the sense now adverted to) and Ratiocination. The meaning intended by\nthese expressions is, that Induction is inferring a proposition from\npropositions _less general_ than itself, and Ratiocination is inferring a\nproposition from propositions _equally_ or _more_ general. When, from the\nobservation of a number of individual instances, we ascend to a general\nproposition, or when, by combining a number of general propositions, we\nconclude from them another proposition still more general, the process,\nwhich is substantially the same in both instances, is called Induction.\nWhen from a general proposition, not alone (for from a single proposition\nnothing can be concluded which is not involved in the terms), but by\ncombining it with other propositions, we infer a proposition of the same\ndegree of generality with itself, or a less general proposition, or a\nproposition merely individual, the process is Ratiocination. When, in\nshort, the conclusion is more general than the largest of the premises,\nthe argument is commonly called Induction; when less general, or equally\ngeneral, it is Ratiocination.\n\nAs all experience begins with individual cases, and proceeds from them to\ngenerals, it might seem most conformable to the natural order of thought\nthat Induction should be treated of before we touch upon Ratiocination. It\nwill, however, be advantageous, in a science which aims at tracing our\nacquired knowledge to its sources, that the inquirer should commence with\nthe latter rather than with the earlier stages of the process of\nconstructing our knowledge; and should trace derivative truths backward to\nthe truths from which they are deduced, and on which they depend for their\nevidence, before attempting to point out the original spring from which\nboth ultimately take their rise. The advantages of this order of\nproceeding in the present instance will manifest themselves as we advance,\nin a manner superseding the necessity of any further justification or\nexplanation.\n\nOf Induction, therefore, we shall say no more at present, than that it at\nleast is, without doubt, a process of real inference. The conclusion in an\ninduction embraces more than is contained in the premises. The principle\nor law collected from particular instances, the general proposition in\nwhich we embody the result of our experience, covers a much larger extent\nof ground than the individual experiments which form its basis. A\nprinciple ascertained by experience, is more than a mere summing up of\nwhat has been specifically observed in the individual cases which have\nbeen examined; it is a generalization grounded on those cases, and\nexpressive of our belief, that what we there found true is true in an\nindefinite number of cases which we have not examined, and are never\nlikely to examine. The nature and grounds of this inference, and the\nconditions necessary to make it legitimate, will be the subject of\ndiscussion in the Third Book: but that such inference really takes place\nis not susceptible of question. In every induction we proceed from truths\nwhich we knew, to truths which we did not know; from facts certified by\nobservation, to facts which we have not observed, and even to facts not\ncapable of being now observed; future facts, for example; but which we do\nnot hesitate to believe on the sole evidence of the induction itself.\n\nInduction, then, is a real process of Reasoning or Inference. Whether, and\nin what sense, as much can be said of the Syllogism, remains to be\ndetermined by the examination into which we are about to enter.\n\n\n\n\n                               Chapter II.\n\n\nOf Ratiocination, Or Syllogism.\n\n\n\u00a7 1. The analysis of the Syllogism has been so accurately and fully\nperformed in the common manuals of Logic, that in the present work, which\nis not designed as a manual, it is sufficient to recapitulate, _memori\u00e6\ncaus\u00e2_, the leading results of that analysis, as a foundation for the\nremarks to be afterward made on the functions of the Syllogism, and the\nplace which it holds in science.\n\nTo a legitimate syllogism it is essential that there should be three, and\nno more than three, propositions, namely, the conclusion, or proposition\nto be proved, and two other propositions which together prove it, and\nwhich are called the premises. It is essential that there should be three,\nand no more than three, terms, namely, the subject and predicate of the\nconclusion, and another called the middle term, which must be found in\nboth premises, since it is by means of it that the other two terms are to\nbe connected together. The predicate of the conclusion is called the major\nterm of the syllogism; the subject of the conclusion is called the minor\nterm. As there can be but three terms, the major and minor terms must each\nbe found in one, and only one, of the premises, together with the middle\nterm which is in them both. The premise which contains the middle term and\nthe major term is called the major premise; that which contains the middle\nterm and the minor term is called the minor premise.\n\nSyllogisms are divided by some logicians into three _figures_, by others\ninto four, according to the position of the middle term, which may either\nbe the subject in both premises, the predicate in both, or the subject in\none and the predicate in the other. The most common case is that in which\nthe middle term is the subject of the major premise and the predicate of\nthe minor. This is reckoned as the first figure. When the middle term is\nthe predicate in both premises, the syllogism belongs to the second\nfigure; when it is the subject in both, to the third. In the fourth figure\nthe middle term is the subject of the minor premise and the predicate of\nthe major. Those writers who reckon no more than three figures, include\nthis case in the first.\n\nEach figure is divided into _moods_, according to what are called the\n_quantity_ and _quality_ of the propositions, that is, according as they\nare universal or particular, affirmative or negative. The following are\nexamples of all the legitimate moods, that is, all those in which the\nconclusion correctly follows from the premises. A is the minor term, C the\nmajor, B the middle term.\n\nFIRST FIGURE.\n\nAll B is C   No B is C    All B is C    No B is C\nAll A is B   All A is B   Some A is B   Some A is B\ntherefore    therefore    therefore     therefore\nAll A is C   No A is C    Some A is C   Some A is not C\n\nSECOND FIGURE.\n\nNo C is B    All C is B   No C is B         All C is B\nAll A is B   No A is B    Some A is B       Some A is not B\ntherefore    therefore    therefore         therefore\nNo A is C    No A is C    Some A is not C   Some A is not C\n\nTHIRD FIGURE.\n\nAll B is    No B is C   Some B is   All B is    Some B is   No B is C\nC                       C           C           not C\nAll B is    All B is    All B is    Some B is   All B is    Some B is\nA           A           A           A           A           A\ntherefore   therefore   therefore   therefore   therefore   therefore\nSome A is   Some A is   Some A is   Some A is   Some A is   Some A is\nC           not C       C           C           not C       not C\n\nFOURTH FIGURE.\n\nAll C is B    All C is B   Some C is B   No C is B    No C is B\nAll B is A    No B is A    All B is A    All B is A   Some B is A\ntherefore     therefore    therefore     therefore    therefore\nSome A is C   Some A is    Some A is C   Some A is    Some A is\n              not C                      not C        not C\n\nIn these exemplars, or blank forms for making syllogisms, no place is\nassigned to _singular_ propositions; not, of course, because such\npropositions are not used in ratiocination, but because, their predicate\nbeing affirmed or denied of the whole of the subject, they are ranked, for\nthe purposes of the syllogism, with universal propositions. Thus, these\ntwo syllogisms\u2014\n\nAll men are mortal,     All men are mortal,\nAll kings are men,      Socrates is a man,\ntherefore               therefore\nAll kings are mortal,   Socrates is mortal,\n\nare arguments precisely similar, and are both ranked in the first mood of\nthe first figure.(50)\n\nThe reasons why syllogisms in any of the above forms are legitimate, that\nis, why, if the premises are true, the conclusion must inevitably be so,\nand why this is not the case in any other possible mood (that is, in any\nother combination of universal and particular, affirmative and negative\npropositions), any person taking interest in these inquiries may be\npresumed to have either learned from the common-school books of the\nsyllogistic logic, or to be capable of discovering for himself. The reader\nmay, however, be referred, for every needful explanation, to Archbishop\nWhately\u2019s _Elements of Logic_, where he will find stated with\nphilosophical precision, and explained with remarkable perspicuity, the\nwhole of the common doctrine of the syllogism.\n\nAll valid ratiocination; all reasoning by which, from general propositions\npreviously admitted, other propositions equally or less general are\ninferred; may be exhibited in some of the above forms. The whole of\nEuclid, for example, might be thrown without difficulty into a series of\nsyllogisms, regular in mood and figure.\n\nThough a syllogism framed according to any of these formul\u00e6 is a valid\nargument, all correct ratiocination admits of being stated in syllogisms\nof the first figure alone. The rules for throwing an argument in any of\nthe other figures into the first figure, are called rules for the\n_reduction_ of syllogisms. It is done by the _conversion_ of one or other,\nor both, of the premises. Thus an argument in the first mood of the second\nfigure, as\u2014\n\nNo C is B\nAll A is B\ntherefore\nNo A is C,\n\nmay be reduced as follows. The proposition, No C is B, being a universal\nnegative, admits of simple conversion, and may be changed into No B is C,\nwhich, as we showed, is the very same assertion in other words\u2014the same\nfact differently expressed. This transformation having been effected, the\nargument assumes the following form:\n\nNo B is C\nAll A is B\ntherefore\nNo A is C,\n\nwhich is a good syllogism in the second mood of the first figure. Again,\nan argument in the first mood of the third figure must resemble the\nfollowing:\n\nAll B is C\nAll B is A\ntherefore\nSome A is C,\n\nwhere the minor premise, All B is A, conformably to what was laid down in\nthe last chapter respecting universal affirmatives, does not admit of\nsimple conversion, but may be converted _per accidens_, thus, Some A is B;\nwhich, though it does not express the whole of what is asserted in the\nproposition All B is A, expresses, as was formerly shown, part of it, and\nmust therefore be true if the whole is true. We have, then, as the result\nof the reduction, the following syllogism in the third mood of the first\nfigure:\n\nAll B is C\nSome A is B,\n\nfrom which it obviously follows, that\n\nSome A is C.\n\nIn the same manner, or in a manner on which after these examples it is not\nnecessary to enlarge, every mood of the second, third, and fourth figures\nmay be reduced to some one of the four moods of the first. In other words,\nevery conclusion which can be proved in any of the last three figures, may\nbe proved in the first figure from the same premises, with a slight\nalteration in the mere manner of expressing them. Every valid\nratiocination, therefore, may be stated in the first figure, that is, in\none of the following forms:\n\nEvery B is C   No B is C\nAll A is B,    All A is B,\nSome A is B,   Some A is B,\ntherefore      therefore\nAll A is C.    No A is C.\nSome A is C.   Some A is not C.\n\nOr, if more significant symbols are preferred:\n\nTo prove an affirmative, the argument must admit of being stated in this\nform:\n\nAll animals are mortal;\nAll men/Some men/Socrates are animals;\ntherefore\nAll men/Some men/Socrates are mortal.\n\nTo prove a negative, the argument must be capable of being expressed in\nthis form:\n\nNo one who is capable of self-control is necessarily vicious;\n\nNo one who is capable of self-control is necessarily vicious;\nAll negroes/Some negroes/Mr. A\u2019s negro are capable of self-control;\ntherefore\nNo negroes are/Some negroes are not/Mr. A\u2019s negro is not necessarily\nvicious.\n\nThough all ratiocination admits of being thrown into one or the other of\nthese forms, and sometimes gains considerably by the transformation, both\nin clearness and in the obviousness of its consequence; there are, no\ndoubt, cases in which the argument falls more naturally into one of the\nother three figures, and in which its conclusiveness is more apparent at\nthe first glance in those figures, than when reduced to the first. Thus,\nif the proposition were that pagans may be virtuous, and the evidence to\nprove it were the example of Aristides; a syllogism in the third figure,\n\nAristides was virtuous,\nAristides was a pagan,\ntherefore\nSome pagan was virtuous,\n\nwould be a more natural mode of stating the argument, and would carry\nconviction more instantly home, than the same ratiocination strained into\nthe first figure, thus\u2014\n\nAristides was virtuous,\nSome pagan was Aristides,\ntherefore\nSome pagan was virtuous.\n\nA German philosopher, Lambert, whose _Neues Organon_ (published in the\nyear 1764) contains among other things one of the most elaborate and\ncomplete expositions which had ever been made of the syllogistic doctrine,\nhas expressly examined what sort of arguments fall most naturally and\nsuitably into each of the four figures; and his investigation is\ncharacterized by great ingenuity and clearness of thought.(51) The\nargument, however, is one and the same, in whichever figure it is\nexpressed; since, as we have already seen, the premises of a syllogism in\nthe second, third, or fourth figure, and those of the syllogism in the\nfirst figure to which it may be reduced, are the same premises in every\nthing except language, or, at least, as much of them as contributes to the\nproof of the conclusion is the same. We are therefore at liberty, in\nconformity with the general opinion of logicians, to consider the two\nelementary forms of the first figure as the universal types of all correct\nratiocination; the one, when the conclusion to be proved is affirmative,\nthe other, when it is negative; even though certain arguments may have a\ntendency to clothe themselves in the forms of the second, third, and\nfourth figures; which, however, can not possibly happen with the only\nclass of arguments which are of first-rate scientific importance, those in\nwhich the conclusion is a universal affirmative, such conclusions being\nsusceptible of proof in the first figure alone.(52)\n\n\u00a7 2. On examining, then, these two general formul\u00e6, we find that in both\nof them, one premise, the major, is a universal proposition; and according\nas this is affirmative or negative, the conclusion is so too. All\nratiocination, therefore, starts from a _general_ proposition, principle,\nor assumption: a proposition in which a predicate is affirmed or denied of\nan entire class; that is, in which some attribute, or the negation of some\nattribute, is asserted of an indefinite number of objects distinguished by\na common characteristic, and designated, in consequence, by a common name.\n\nThe other premise is always affirmative, and asserts that something (which\nmay be either an individual, a class, or part of a class) belongs to, or\nis included in, the class respecting which something was affirmed or\ndenied in the major premise. It follows that the attribute affirmed or\ndenied of the entire class may (if that affirmation or denial was correct)\nbe affirmed or denied of the object or objects alleged to be included in\nthe class: and this is precisely the assertion made in the conclusion.\n\nWhether or not the foregoing is an adequate account of the constituent\nparts of the syllogism, will be presently considered; but as far as it\ngoes it is a true account. It has accordingly been generalized, and\nerected into a logical maxim, on which all ratiocination is said to be\nfounded, insomuch that to reason, and to apply the maxim, are supposed to\nbe one and the same thing. The maxim is, That whatever can be affirmed (or\ndenied) of a class, may be affirmed (or denied) of every thing included in\nthe class. This axiom, supposed to be the basis of the syllogistic theory,\nis termed by logicians the _dictum de omni et nullo_.\n\nThis maxim, however, when considered as a principle of reasoning, appears\nsuited to a system of metaphysics once indeed generally received, but\nwhich for the last two centuries has been considered as finally abandoned,\nthough there have not been wanting in our own day attempts at its revival.\nSo long as what are termed Universals were regarded as a peculiar kind of\nsubstances, having an objective existence distinct from the individual\nobjects classed under them, the _dictum de omni_ conveyed an important\nmeaning; because it expressed the intercommunity of nature, which it was\nnecessary on that theory that we should suppose to exist between those\ngeneral substances and the particular substances which were subordinated\nto them. That every thing predicable of the universal was predicable of\nthe various individuals contained under it, was then no identical\nproposition, but a statement of what was conceived as a fundamental law of\nthe universe. The assertion that the entire nature and properties of the\n_substantia secunda_ formed part of the nature and properties of each of\nthe individual substances called by the same name; that the properties of\nMan, for example, were properties of all men; was a proposition of real\nsignificance when man did not _mean_ all men, but something inherent in\nmen, and vastly superior to them in dignity. Now, however, when it is\nknown that a class, a universal, a genus or species, is not an entity _per\nse_, but neither more nor less than the individual substances themselves\nwhich are placed in the class, and that there is nothing real in the\nmatter except those objects, a common name given to them, and common\nattributes indicated by the name; what, I should be glad to know, do we\nlearn by being told, that whatever can be affirmed of a class, may be\naffirmed of every object contained in the class? The class _is_ nothing\nbut the objects contained in it: and the _dictum de omni_ merely amounts\nto the identical proposition, that whatever is true of certain objects, is\ntrue of each of those objects. If all ratiocination were no more than the\napplication of this maxim to particular cases, the syllogism would indeed\nbe, what it has so often been declared to be, solemn trifling. The _dictum\nde omni_ is on a par with another truth, which in its time was also\nreckoned of great importance, \u201cWhatever is, is.\u201d To give any real meaning\nto the _dictum de omni_, we must consider it not as an axiom, but as a\ndefinition; we must look upon it as intended to explain, in a circuitous\nand paraphrastic manner, the meaning of the word _class_.\n\nAn error which seemed finally refuted and dislodged from thought, often\nneeds only put on a new suit of phrases, to be welcomed back to its old\nquarters, and allowed to repose unquestioned for another cycle of ages.\nModern philosophers have not been sparing in their contempt for the\nscholastic dogma that genera and species are a peculiar kind of\nsubstances, which general substances being the only permanent things,\nwhile the individual substances comprehended under them are in a perpetual\nflux, knowledge, which necessarily imports stability, can only have\nrelation to those general substances or universals, and not to the facts\nor particulars included under them. Yet, though nominally rejected, this\nvery doctrine, whether disguised under the Abstract Ideas of Locke (whose\nspeculations, however, it has less vitiated than those of perhaps any\nother writer who has been infected with it), under the ultra-nominalism of\nHobbes and Condillac, or the ontology of the later German schools, has\nnever ceased to poison philosophy. Once accustomed to consider scientific\ninvestigation as essentially consisting in the study of universals, men\ndid not drop this habit of thought when they ceased to regard universals\nas possessing an independent existence: and even those who went the length\nof considering them as mere names, could not free themselves from the\nnotion that the investigation of truth consisted entirely or partly in\nsome kind of conjuration or juggle with those names. When a philosopher\nadopted fully the Nominalist view of the signification of general\nlanguage, retaining along with it the _dictum de omni_ as the foundation\nof all reasoning, two such premises fairly put together were likely, if he\nwas a consistent thinker, to land him in rather startling conclusions.\nAccordingly it has been seriously held, by writers of deserved celebrity,\nthat the process of arriving at new truths by reasoning consists in the\nmere substitution of one set of arbitrary signs for another; a doctrine\nwhich they suppose to derive irresistible confirmation from the example of\nalgebra. If there were any process in sorcery or necromancy more\npreternatural than this, I should be much surprised. The culminating point\nof this philosophy is the noted aphorism of Condillac, that a science is\nnothing, or scarcely any thing, but _une langue bien faite_; in other\nwords, that the one sufficient rule for discovering the nature and\nproperties of objects is to name them properly: as if the reverse were not\nthe truth, that it is impossible to name them properly except in\nproportion as we are already acquainted with their nature and properties.\nCan it be necessary to say, that none, not even the most trivial knowledge\nwith respect to Things, ever was or could be originally got at by any\nconceivable manipulation of mere names, as such; and that what can be\nlearned from names, is only what somebody who used the names knew before?\nPhilosophical analysis confirms the indication of common sense, that the\nfunction of names is but that of enabling us to _remember_ and to\n_communicate_ our thoughts. That they also strengthen, even to an\nincalculable extent, the power of thought itself, is most true: but they\ndo this by no intrinsic and peculiar virtue; they do it by the power\ninherent in an artificial memory, an instrument of which few have\nadequately considered the immense potency. As an artificial memory,\nlanguage truly is, what it has so often been called, an instrument of\nthought; but it is one thing to be the instrument, and another to be the\nexclusive subject upon which the instrument is exercised. We think,\nindeed, to a considerable extent, by means of names, but what we think of,\nare the things called by those names; and there can not be a greater error\nthan to imagine that thought can be carried on with nothing in our mind\nbut names, or that we can make the names think for us.\n\n\u00a7 3. Those who considered the _dictum de omni_ as the foundation of the\nsyllogism, looked upon arguments in a manner corresponding to the\nerroneous view which Hobbes took of propositions. Because there are some\npropositions which are merely verbal, Hobbes, in order apparently that his\ndefinition might be rigorously universal, defined a proposition as if no\npropositions declared any thing except the meaning of words. If Hobbes was\nright; if no further account than this could be given of the import of\npropositions; no theory could be given but the commonly received one, of\nthe combination of propositions in a syllogism. If the minor premise\nasserted nothing more than that something belongs to a class, and if the\nmajor premise asserted nothing of that class except that it is included in\nanother class, the conclusion would only be that what was included in the\nlower class is included in the higher, and the result, therefore, nothing\nexcept that the classification is consistent with itself. But we have seen\nthat it is no sufficient account of the meaning of a proposition, to say\nthat it refers something to, or excludes something from, a class. Every\nproposition which conveys real information asserts a matter of fact,\ndependent on the laws of nature, and not on classification. It asserts\nthat a given object does or does not possess a given attribute; or it\nasserts that two attributes, or sets of attributes, do or do not\n(constantly or occasionally) co-exist. Since such is the purport of all\npropositions which convey any real knowledge, and since ratiocination is a\nmode of acquiring real knowledge, any theory of ratiocination which does\nnot recognize this import of propositions, can not, we may be sure, be the\ntrue one.\n\nApplying this view of propositions to the two premises of a syllogism, we\nobtain the following results. The major premise, which, as already\nremarked, is always universal, asserts, that all things which have a\ncertain attribute (or attributes) have or have not along with it, a\ncertain other attribute (or attributes). The minor premise asserts that\nthe thing or set of things which are the subject of that premise, have the\nfirst-mentioned attribute; and the conclusion is, that they have (or that\nthey have not), the second. Thus in our former example,\n\nAll men are mortal,\nSocrates is a man,\ntherefore\nSocrates is mortal,\n\nthe subject and predicate of the major premise are connotative terms,\ndenoting objects and connoting attributes. The assertion in the major\npremise is, that along with one of the two sets of attributes, we always\nfind the other: that the attributes connoted by \u201cman\u201d never exist unless\nconjoined with the attribute called mortality. The assertion in the minor\npremise is that the individual named Socrates possesses the former\nattributes; and it is concluded that he possesses also the attribute\nmortality. Or, if both the premises are general propositions, as\n\nAll men are mortal,\nAll kings are men,\ntherefore\nAll kings are mortal,\n\nthe minor premise asserts that the attributes denoted by kingship only\nexist in conjunction with those signified by the word man. The major\nasserts as before, that the last-mentioned attributes are never found\nwithout the attribute of mortality. The conclusion is, that wherever the\nattributes of kingship are found, that of mortality is found also.\n\nIf the major premise were negative, as, No men are omnipotent, it would\nassert, not that the attributes connoted by \u201cman\u201d never exist without, but\nthat they never exist with, those connoted by \u201comnipotent:\u201d from which,\ntogether with the minor premise, it is concluded, that the same\nincompatibility exists between the attribute omnipotence and those\nconstituting a king. In a similar manner we might analyze any other\nexample of the syllogism.\n\nIf we generalize this process, and look out for the principle or law\ninvolved in every such inference, and presupposed in every syllogism, the\npropositions of which are any thing more than merely verbal; we find, not\nthe unmeaning _dictum de omni et nullo_, but a fundamental principle, or\nrather two principles, strikingly resembling the axioms of mathematics.\nThe first, which is the principle of affirmative syllogisms, is, that\nthings which co-exist with the same thing, co-exist with one another: or\n(still more precisely) a thing which co-exists with another thing, which\nother co-exists with a third thing, also co-exists with that third thing.\nThe second is the principle of negative syllogisms, and is to this effect:\nthat a thing which co-exists with another thing, with which other a third\nthing does not co-exist, is not co-existent with that third thing. These\naxioms manifestly relate to facts, and not to conventions; and one or\nother of them is the ground of the legitimacy of every argument in which\nfacts and not conventions are the matter treated of.(53)\n\n\u00a7 4. It remains to translate this exposition of the syllogism from the one\ninto the other of the two languages in which we formerly remarked(54) that\nall propositions, and of course therefore all combinations of\npropositions, might be expressed. We observed that a proposition might be\nconsidered in two different lights; as a portion of our knowledge of\nnature, or as a memorandum for our guidance. Under the former, or\nspeculative aspect, an affirmative general proposition is an assertion of\na speculative truth, viz., that whatever has a certain attribute has a\ncertain other attribute. Under the other aspect, it is to be regarded not\nas a part of our knowledge, but as an aid for our practical exigencies, by\nenabling us, when we see or learn that an object possesses one of the two\nattributes, to infer that it possesses the other; thus employing the first\nattribute as a mark or evidence of the second. Thus regarded, every\nsyllogism comes within the following general formula:\n\nAttribute A is a mark of attribute B,\nThe given object has the mark A,\ntherefore\nThe given object has the attribute B.\n\nReferred to this type, the arguments which we have lately cited as\nspecimens of the syllogism, will express themselves in the following\nmanner:\n\nThe attributes of man are a mark of the attribute mortality,\nSocrates has the attributes of man,\ntherefore\nSocrates has the attribute mortality.\n\nAnd again,\n\nThe attributes of man are a mark of the attribute mortality,\nThe attributes of a king are a mark of the attributes of man,\ntherefore\nThe attributes of a king are a mark of the attribute mortality.\n\nAnd, lastly,\n\nThe attributes of man are a mark of the absence of the attribute\nomnipotence,\nThe attributes of a king are a mark of the attributes of man,\ntherefore\nThe attributes of a king are a mark of the absence of the attribute\nsignified by the word omnipotent (or, are evidence of the absence of that\nattribute).\n\nTo correspond with this alteration in the form of the syllogisms, the\naxioms on which the syllogistic process is founded must undergo a\ncorresponding transformation. In this altered phraseology, both those\naxioms may be brought under one general expression; namely, that whatever\nhas any mark, has that which it is a mark of. Or, when the minor premise\nas well as the major is universal, we may state it thus: Whatever is a\nmark of any mark, is a mark of that which this last is a mark of. To trace\nthe identity of these axioms with those previously laid down, may be left\nto the intelligent reader. We shall find, as we proceed, the great\nconvenience of the phraseology into which we have last thrown them, and\nwhich is better adapted than any I am acquainted with, to express with\nprecision and force what is aimed at, and actually accomplished, in every\ncase of the ascertainment of a truth by ratiocination.(55)\n\n\n\n\n                               Chapter III.\n\n\nOf The Functions And Logical Value Of The Syllogism.\n\n\n\u00a7 1. We have shown what is the real nature of the truths with which the\nSyllogism is conversant, in contradistinction to the more superficial\nmanner in which their import is conceived in the common theory; and what\nare the fundamental axioms on which its probative force or conclusiveness\ndepends. We have now to inquire, whether the syllogistic process, that of\nreasoning from generals to particulars, is, or is not, a process of\ninference; a progress from the known to the unknown: a means of coming to\na knowledge of something which we did not know before.\n\nLogicians have been remarkably unanimous in their mode of answering this\nquestion. It is universally allowed that a syllogism is vicious if there\nbe any thing more in the conclusion than was assumed in the premises. But\nthis is, in fact, to say, that nothing ever was, or can be, proved by\nsyllogism, which was not known, or assumed to be known, before. Is\nratiocination, then, not a process of inference? And is the syllogism, to\nwhich the word reasoning has so often been represented to be exclusively\nappropriate, not really entitled to be called reasoning at all? This seems\nan inevitable consequence of the doctrine, admitted by all writers on the\nsubject, that a syllogism can prove no more than is involved in the\npremises. Yet the acknowledgment so explicitly made, has not prevented one\nset of writers from continuing to represent the syllogism as the correct\nanalysis of what the mind actually performs in discovering and proving the\nlarger half of the truths, whether of science or of daily life, which we\nbelieve; while those who have avoided this inconsistency, and followed out\nthe general theorem respecting the logical value of the syllogism to its\nlegitimate corollary, have been led to impute uselessness and frivolity to\nthe syllogistic theory itself, on the ground of the _petitio principii_\nwhich they allege to be inherent in every syllogism. As I believe both\nthese opinions to be fundamentally erroneous, I must request the attention\nof the reader to certain considerations, without which any just\nappreciation of the true character of the syllogism, and the functions it\nperforms in philosophy, appears to me impossible; but which seem to have\nbeen either overlooked, or insufficiently adverted to, both by the\ndefenders of the syllogistic theory and by its assailants.\n\n\u00a7 2. It must be granted that in every syllogism, considered as an argument\nto prove the conclusion, there is a _petitio principii_. When we say,\n\nAll men are mortal,\nSocrates is a man,\ntherefore\nSocrates is mortal;\n\nit is unanswerably urged by the adversaries of the syllogistic theory,\nthat the proposition, Socrates is mortal, is presupposed in the more\ngeneral assumption, All men are mortal: that we can not be assured of the\nmortality of all men, unless we are already certain of the mortality of\nevery individual man: that if it be still doubtful whether Socrates, or\nany other individual we choose to name, be mortal or not, the same degree\nof uncertainty must hang over the assertion, All men are mortal: that the\ngeneral principle, instead of being given as evidence of the particular\ncase, can not itself be taken for true without exception, until every\nshadow of doubt which could affect any case comprised with it, is\ndispelled by evidence _aliund\u00e8_; and then what remains for the syllogism\nto prove? That, in short, no reasoning from generals to particulars can,\nas such, prove any thing: since from a general principle we can not infer\nany particulars, but those which the principle itself assumes as known.\n\nThis doctrine appears to me irrefragable; and if logicians, though unable\nto dispute it, have usually exhibited a strong disposition to explain it\naway, this was not because they could discover any flaw in the argument\nitself, but because the contrary opinion seemed to rest on arguments\nequally indisputable. In the syllogism last referred to, for example, or\nin any of those which we previously constructed, is it not evident that\nthe conclusion may, to the person to whom the syllogism is presented, be\nactually and _bona fide_ a new truth? Is it not matter of daily experience\nthat truths previously unthought of, facts which have not been, and can\nnot be, directly observed, are arrived at by way of general reasoning? We\nbelieve that the Duke of Wellington is mortal. We do not know this by\ndirect observation, so long as he is not yet dead. If we were asked how,\nthis being the case, we know the duke to be mortal, we should probably\nanswer, Because all men are so. Here, therefore, we arrive at the\nknowledge of a truth not (as yet) susceptible of observation, by a\nreasoning which admits of being exhibited in the following syllogism:\n\nAll men are mortal,\nThe Duke of Wellington is a man,\ntherefore\nThe Duke of Wellington is mortal.\n\nAnd since a large portion of our knowledge is thus acquired, logicians\nhave persisted in representing the syllogism as a process of inference or\nproof; though none of them has cleared up the difficulty which arises from\nthe inconsistency between that assertion, and the principle, that if there\nbe any thing in the conclusion which was not already asserted in the\npremises, the argument is vicious. For it is impossible to attach any\nserious scientific value to such a mere salvo, as the distinction drawn\nbetween being involved _by implication_ in the premises, and being\ndirectly asserted in them. When Archbishop Whately says(56) that the\nobject of reasoning is \u201cmerely to expand and unfold the assertions wrapped\nup, as it were, and implied in those with which we set out, and to bring a\nperson to perceive and acknowledge the full force of that which he has\nadmitted,\u201d he does not, I think, meet the real difficulty requiring to be\nexplained, namely, how it happens that a science, like geometry, _can_ be\nall \u201cwrapped up\u201d in a few definitions and axioms. Nor does this defense of\nthe syllogism differ much from what its assailants urge against it as an\naccusation, when they charge it with being of no use except to those who\nseek to press the consequences of an admission into which a person has\nbeen entrapped without having considered and understood its full force.\nWhen you admitted the major premise, you asserted the conclusion; but,\nsays Archbishop Whately, you asserted it by implication merely: this,\nhowever, can here only mean that you asserted it unconsciously; that you\ndid not know you were asserting it; but, if so, the difficulty revives in\nthis shape\u2014Ought you not to have known? Were you warranted in asserting\nthe general proposition without having satisfied yourself of the truth of\nevery thing which it fairly includes? And if not, is not the syllogistic\nart _prima facie_ what its assailants affirm it to be, a contrivance for\ncatching you in a trap, and holding you fast in it?(57)\n\n\u00a7 3. From this difficulty there appears to be but one issue. The\nproposition that the Duke of Wellington is mortal, is evidently an\ninference; it is got at as a conclusion from something else; but do we, in\nreality, conclude it from the proposition, All men are mortal? I answer,\nno.\n\nThe error committed is, I conceive, that of overlooking the distinction\nbetween two parts of the process of philosophizing, the inferring part,\nand the registering part; and ascribing to the latter the functions of the\nformer. The mistake is that of referring a person to his own notes for the\norigin of his knowledge. If a person is asked a question, and is at the\nmoment unable to answer it, he may refresh his memory by turning to a\nmemorandum which he carries about with him. But if he were asked, how the\nfact came to his knowledge, he would scarcely answer, because it was set\ndown in his note-book: unless the book was written, like the Koran, with a\nquill from the wing of the angel Gabriel.\n\nAssuming that the proposition, The Duke of Wellington is mortal, is\nimmediately an inference from the proposition, All men are mortal; whence\ndo we derive our knowledge of that general truth? Of course from\nobservation. Now, all which man can observe are individual cases. From\nthese all general truths must be drawn, and into these they may be again\nresolved; for a general truth is but an aggregate of particular truths; a\ncomprehensive expression, by which an indefinite number of individual\nfacts are affirmed or denied at once. But a general proposition is not\nmerely a compendious form for recording and preserving in the memory a\nnumber of particular facts, all of which have been observed.\nGeneralization is not a process of mere naming, it is also a process of\ninference. From instances which we have observed, we feel warranted in\nconcluding, that what we found true in those instances, holds in all\nsimilar ones, past, present, and future, however numerous they may be. We\nthen, by that valuable contrivance of language which enables us to speak\nof many as if they were one, record all that we have observed, together\nwith all that we infer from our observations, in one concise expression;\nand have thus only one proposition, instead of an endless number, to\nremember or to communicate. The results of many observations and\ninferences, and instructions for making innumerable inferences in\nunforeseen cases, are compressed into one short sentence.\n\nWhen, therefore, we conclude from the death of John and Thomas, and every\nother person we ever heard of in whose case the experiment had been fairly\ntried, that the Duke of Wellington is mortal like the rest; we may,\nindeed, pass through the generalization, All men are mortal, as an\nintermediate stage; but it is not in the latter half of the process, the\ndescent from all men to the Duke of Wellington, that the _inference_\nresides. The inference is finished when we have asserted that all men are\nmortal. What remains to be performed afterward is merely deciphering our\nown notes.\n\nArchbishop Whately has contended that syllogizing, or reasoning from\ngenerals to particulars, is not, agreeably to the vulgar idea, a peculiar\n_mode_ of reasoning, but the philosophical analysis of _the_ mode in which\nall men reason, and must do so if they reason at all. With the deference\ndue to so high an authority, I can not help thinking that the vulgar\nnotion is, in this case, the more correct. If, from our experience of\nJohn, Thomas, etc., who once were living, but are now dead, we are\nentitled to conclude that all human beings are mortal, we might surely\nwithout any logical inconsequence have concluded at once from those\ninstances, that the Duke of Wellington is mortal. The mortality of John,\nThomas, and others is, after all, the whole evidence we have for the\nmortality of the Duke of Wellington. Not one iota is added to the proof by\ninterpolating a general proposition. Since the individual cases are all\nthe evidence we can possess, evidence which no logical form into which we\nchoose to throw it can make greater than it is; and since that evidence is\neither sufficient in itself, or, if insufficient for the one purpose, can\nnot be sufficient for the other; I am unable to see why we should be\nforbidden to take the shortest cut from these sufficient premises to the\nconclusion, and constrained to travel the \u201chigh priori road,\u201d by the\narbitrary fiat of logicians. I can not perceive why it should be\nimpossible to journey from one place to another unless we \u201cmarch up a\nhill, and then march down again.\u201d It may be the safest road, and there may\nbe a resting-place at the top of the hill, affording a commanding view of\nthe surrounding country; but for the mere purpose of arriving at our\njourney\u2019s end, our taking that road is perfectly optional; it is a\nquestion of time, trouble, and danger.\n\nNot only _may_ we reason from particulars to particulars without passing\nthrough generals, but we perpetually do so reason. All our earliest\ninferences are of this nature. From the first dawn of intelligence we draw\ninferences, but years elapse before we learn the use of general language.\nThe child, who, having burned his fingers, avoids to thrust them again\ninto the fire, has reasoned or inferred, though he has never thought of\nthe general maxim, Fire burns. He knows from memory that he has been\nburned, and on this evidence believes, when he sees a candle, that if he\nputs his finger into the flame of it, he will be burned again. He believes\nthis in every case which happens to arise; but without looking, in each\ninstance, beyond the present case. He is not generalizing; he is inferring\na particular from particulars. In the same way, also, brutes reason. There\nis no ground for attributing to any of the lower animals the use of signs,\nof such a nature as to render general propositions possible. But those\nanimals profit by experience, and avoid what they have found to cause them\npain, in the same manner, though not always with the same skill, as a\nhuman creature. Not only the burned child, but the burned dog, dreads the\nfire.\n\nI believe that, in point of fact, when drawing inferences from our\npersonal experience, and not from maxims handed down to us by books or\ntradition, we much oftener conclude from particulars to particulars\ndirectly, than through the intermediate agency of any general proposition.\nWe are constantly reasoning from ourselves to other people, or from one\nperson to another, without giving ourselves the trouble to erect our\nobservations into general maxims of human or external nature. When we\nconclude that some person will, on some given occasion, feel or act so and\nso, we sometimes judge from an enlarged consideration of the manner in\nwhich human beings in general, or persons of some particular character,\nare accustomed to feel and act; but much oftener from merely recollecting\nthe feelings and conduct of the same person in some previous instance, or\nfrom considering how we should feel or act ourselves. It is not only the\nvillage matron, who, when called to a consultation upon the case of a\nneighbor\u2019s child, pronounces on the evil and its remedy simply on the\nrecollection and authority of what she accounts the similar case of her\nLucy. We all, where we have no definite maxims to steer by, guide\nourselves in the same way: and if we have an extensive experience, and\nretain its impressions strongly, we may acquire in this manner a very\nconsiderable power of accurate judgment, which we may be utterly incapable\nof justifying or of communicating to others. Among the higher order of\npractical intellects there have been many of whom it was remarked how\nadmirably they suited their means to their ends, without being able to\ngive any sufficient reasons for what they did; and applied, or seemed to\napply, recondite principles which they were wholly unable to state. This\nis a natural consequence of having a mind stored with appropriate\nparticulars, and having been long accustomed to reason at once from these\nto fresh particulars, without practicing the habit of stating to one\u2019s\nself or to others the corresponding general propositions. An old warrior,\non a rapid glance at the outlines of the ground, is able at once to give\nthe necessary orders for a skillful arrangement of his troops; though if\nhe has received little theoretical instruction, and has seldom been called\nupon to answer to other people for his conduct, he may never have had in\nhis mind a single general theorem respecting the relation between ground\nand array. But his experience of encampments, in circumstances more or\nless similar, has left a number of vivid, unexpressed, ungeneralized\nanalogies in his mind, the most appropriate of which, instantly suggesting\nitself, determines him to a judicious arrangement.\n\nThe skill of an uneducated person in the use of weapons, or of tools, is\nof a precisely similar nature. The savage who executes unerringly the\nexact throw which brings down his game, or his enemy, in the manner most\nsuited to his purpose, under the operation of all the conditions\nnecessarily involved, the weight and form of the weapon, the direction and\ndistance of the object, the action of the wind, etc., owes this power to a\nlong series of previous experiments, the results of which he certainly\nnever framed into any verbal theorems or rules. The same thing may\ngenerally be said of any other extraordinary manual dexterity. Not long\nago a Scotch manufacturer procured from England, at a high rate of wages,\na working dyer, famous for producing very fine colors, with the view of\nteaching to his other workmen the same skill. The workman came; but his\nmode of proportioning the ingredients, in which lay the secret of the\neffects he produced, was by taking them up in handfuls, while the common\nmethod was to weigh them. The manufacturer sought to make him turn his\nhandling system into an equivalent weighing system, that the general\nprinciple of his peculiar mode of proceeding might be ascertained. This,\nhowever, the man found himself quite unable to do, and therefore could\nimpart his skill to nobody. He had, from the individual cases of his own\nexperience, established a connection in his mind between fine effects of\ncolor, and tactual perceptions in handling his dyeing materials; and from\nthese perceptions he could, in any particular case, infer the means to be\nemployed, and the effects which would be produced, but could not put\nothers in possession of the grounds on which he proceeded, from having\nnever generalized them in his own mind, or expressed them in language.\n\nAlmost every one knows Lord Mansfield\u2019s advice to a man of practical good\nsense, who, being appointed governor of a colony, had to preside in its\ncourts of justice, without previous judicial practice or legal education.\nThe advice was to give his decision boldly, for it would probably be\nright; but never to venture on assigning reasons, for they would almost\ninfallibly be wrong. In cases like this, which are of no uncommon\noccurrence, it would be absurd to suppose that the bad reason was the\nsource of the good decision. Lord Mansfield knew that if any reason were\nassigned it would be necessarily an afterthought, the judge being _in\nfact_ guided by impressions from past experience, without the circuitous\nprocess of framing general principles from them, and that if he attempted\nto frame any such he would assuredly fail. Lord Mansfield, however, would\nnot have doubted that a man of equal experience who had also a mind stored\nwith general propositions derived by legitimate induction from that\nexperience, would have been greatly preferable as a judge, to one, however\nsagacious, who could not be trusted with the explanation and justification\nof his own judgments. The cases of men of talent performing wonderful\nthings they know not how, are examples of the rudest and most spontaneous\nform of the operations of superior minds. It is a defect in them, and\noften a source of errors, not to have generalized as they went on; but\ngeneralization, though a help, the most important indeed of all helps, is\nnot an essential.\n\nEven the scientifically instructed, who possess, in the form of general\npropositions, a systematic record of the results of the experience of\nmankind, need not always revert to those general propositions in order to\napply that experience to a new case. It is justly remarked by Dugald\nStewart, that though the reasonings in mathematics depend entirely on the\naxioms, it is by no means necessary to our seeing the conclusiveness of\nthe proof, that the axioms should be expressly adverted to. When it is\ninferred that AB is equal to CD because each of them is equal to EF, the\nmost uncultivated understanding, as soon as the propositions were\nunderstood, would assent to the inference, without having ever heard of\nthe general truth that \u201cthings which are equal to the same thing are equal\nto one another.\u201d This remark of Stewart, consistently followed out, goes\nto the root, as I conceive, of the philosophy of ratiocination; and it is\nto be regretted that he himself stopped short at a much more limited\napplication of it. He saw that the general propositions on which a\nreasoning is said to depend, may, in certain cases, be altogether omitted,\nwithout impairing its probative force. But he imagined this to be a\npeculiarity belonging to axioms; and argued from it, that axioms are not\nthe foundations or first principles of geometry, from which all the other\ntruths of the science are synthetically deduced (as the laws of motion and\nof the composition of forces in dynamics, the equal mobility of fluids in\nhydrostatics, the laws of reflection and refraction in optics, are the\nfirst principles of those sciences); but are merely necessary assumptions,\nself-evident indeed, and the denial of which would annihilate all\ndemonstration, but from which, as premises, nothing can be demonstrated.\nIn the present, as in many other instances, this thoughtful and elegant\nwriter has perceived an important truth, but only by halves. Finding, in\nthe case of geometrical axioms, that general names have not any talismanic\nvirtue for conjuring new truths out of the well where they lie hid, and\nnot seeing that this is equally true in every other case of\ngeneralization, he contended that axioms are in their nature barren of\nconsequences, and that the really fruitful truths, the real first\nprinciples of geometry, are the definitions; that the definition, for\nexample, of the circle is to the properties of the circle, what the laws\nof equilibrium and of the pressure of the atmosphere are to the rise of\nthe mercury in the Torricellian tube. Yet all that he had asserted\nrespecting the function to which the axioms are confined in the\ndemonstrations of geometry, holds equally true of the definitions. Every\ndemonstration in Euclid might be carried on without them. This is apparent\nfrom the ordinary process of proving a proposition of geometry by means of\na diagram. What assumption, in fact, do we set out from, to demonstrate by\na diagram any of the properties of the circle? Not that in all circles the\nradii are equal, but only that they are so in the circle ABC. As our\nwarrant for assuming this, we appeal, it is true, to the definition of a\ncircle in general; but it is only necessary that the assumption be granted\nin the case of the particular circle supposed. From this, which is not a\ngeneral but a singular proposition, combined with other propositions of a\nsimilar kind, some of which _when generalized_ are called definitions, and\nother axioms, we prove that a certain conclusion is true, not of all\ncircles, but of the particular circle ABC; or at least would be so, if the\nfacts precisely accorded with our assumptions. The enunciation, as it is\ncalled, that is, the general theorem which stands at the head of the\ndemonstration, is not the proposition actually demonstrated. One instance\nonly is demonstrated: but the process by which this is done, is a process\nwhich, when we consider its nature, we perceive might be exactly copied in\nan indefinite number of other instances; in every instance which conforms\nto certain conditions. The contrivance of general language furnishing us\nwith terms which connote these conditions, we are able to assert this\nindefinite multitude of truths in a single expression, and this expression\nis the general theorem. By dropping the use of diagrams, and substituting,\nin the demonstrations, general phrases for the letters of the alphabet, we\nmight prove the general theorem directly, that is, we might demonstrate\nall the cases at once; and to do this we must, of course, employ as our\npremises, the axioms and definitions in their general form. But this only\nmeans, that if we can prove an individual conclusion by assuming an\nindividual fact, then in whatever case we are warranted in making an\nexactly similar assumption, we may draw an exactly similar conclusion. The\ndefinition is a sort of notice to ourselves and others, what assumptions\nwe think ourselves entitled to make. And so in all cases, the general\npropositions, whether called definitions, axioms, or laws of nature, which\nwe lay down at the beginning of our reasonings, are merely abridged\nstatements, in a kind of short-hand, of the particular facts, which, as\noccasion arises, we either think we may proceed on as proved, or intend to\nassume. In any one demonstration it is enough if we assume for a\nparticular case suitably selected, what by the statement of the definition\nor principle we announce that we intend to assume in all cases which may\narise. The definition of the circle, therefore, is to one of Euclid\u2019s\ndemonstrations, exactly what, according to Stewart, the axioms are; that\nis, the demonstration does not depend on it, but yet if we deny it the\ndemonstration fails. The proof does not rest on the general assumption,\nbut on a similar assumption confined to the particular case: that case,\nhowever, being chosen as a specimen or paradigm of the whole class of\ncases included in the theorem, there can be no ground for making the\nassumption in that case which does not exist in every other; and to deny\nthe assumption as a general truth, is to deny the right of making it in\nthe particular instance.\n\nThere are, undoubtedly, the most ample reasons for stating both the\nprinciples and the theorems in their general form, and these will be\nexplained presently, so far as explanation is requisite. But, that\nunpracticed learners, even in making use of one theorem to demonstrate\nanother, reason rather from particular to particular than from the general\nproposition, is manifest from the difficulty they find in applying a\ntheorem to a case in which the configuration of the diagram is extremely\nunlike that of the diagram by which the original theorem was demonstrated.\nA difficulty which, except in cases of unusual mental power, long practice\ncan alone remove, and removes chiefly by rendering us familiar with all\nthe configurations consistent with the general conditions of the theorem.\n\n\u00a7 4. From the considerations now adduced, the following conclusions seem\nto be established. All inference is from particulars to particulars:\nGeneral propositions are merely registers of such inferences already made,\nand short formul\u00e6 for making more: The major premise of a syllogism,\nconsequently, is a formula of this description: and the conclusion is not\nan inference drawn _from_ the formula, but an inference drawn _according_\nto the formula: the real logical antecedent, or premise, being the\nparticular facts from which the general proposition was collected by\ninduction. Those facts, and the individual instances which supplied them,\nmay have been forgotten: but a record remains, not indeed descriptive of\nthe facts themselves, but showing how those cases may be distinguished,\nrespecting which, the facts, when known, were considered to warrant a\ngiven inference. According to the indications of this record we draw our\nconclusion: which is, to all intents and purposes, a conclusion from the\nforgotten facts. For this it is essential that we should read the record\ncorrectly: and the rules of the syllogism are a set of precautions to\ninsure our doing so.\n\nThis view of the functions of the syllogism is confirmed by the\nconsideration of precisely those cases which might be expected to be least\nfavorable to it, namely, those in which ratiocination is independent of\nany previous induction. We have already observed that the syllogism, in\nthe ordinary course of our reasoning, is only the latter half of the\nprocess of traveling from premises to a conclusion. There are, however,\nsome peculiar cases in which it is the whole process. Particulars alone\nare capable of being subjected to observation; and all knowledge which is\nderived from observation, begins, therefore, of necessity, in particulars;\nbut our knowledge may, in cases of certain descriptions, be conceived as\ncoming to us from other sources than observation. It may present itself as\ncoming from testimony, which, on the occasion and for the purpose in hand,\nis accepted as of an authoritative character: and the information thus\ncommunicated, may be conceived to comprise not only particular facts but\ngeneral propositions, as when a scientific doctrine is accepted without\nexamination on the authority of writers, or a theological doctrine on that\nof Scripture. Or the generalization may not be, in the ordinary sense, an\nassertion at all, but a command; a law, not in the philosophical, but in\nthe moral and political sense of the term: an expression of the desire of\na superior, that we, or any number of other persons, shall conform our\nconduct to certain general instructions. So far as this asserts a fact,\nnamely, a volition of the legislator, that fact is an individual fact, and\nthe proposition, therefore, is not a general proposition. But the\ndescription therein contained of the conduct which it is the will of the\nlegislator that his subjects should observe, is general. The proposition\nasserts, not that all men _are_ any thing, but that all men _shall_ do\nsomething.\n\nIn both these cases the generalities are the original data, and the\nparticulars are elicited from them by a process which correctly resolves\nitself into a series of syllogisms. The real nature, however, of the\nsupposed deductive process, is evident enough. The only point to be\ndetermined is, whether the authority which declared the general\nproposition, intended to include this case in it; and whether the\nlegislator intended his command to apply to the present case among others,\nor not. This is ascertained by examining whether the case possesses the\nmarks by which, as those authorities have signified, the cases which they\nmeant to certify or to influence may be known. The object of the inquiry\nis to make out the witness\u2019s or the legislator\u2019s intention, through the\nindication given by their words. This is a question, as the Germans\nexpress it, of hermeneutics. The operation is not a process of inference,\nbut a process of interpretation.\n\nIn this last phrase we have obtained an expression which appears to me to\ncharacterize, more aptly than any other, the functions of the syllogism in\nall cases. When the premises are given by authority, the function of\nReasoning is to ascertain the testimony of a witness, or the will of a\nlegislator, by interpreting the signs in which the one has intimated his\nassertion and the other his command. In like manner, when the premises are\nderived from observation, the function of Reasoning is to ascertain what\nwe (or our predecessors) formerly thought might be inferred from the\nobserved facts, and to do this by interpreting a memorandum of ours, or of\ntheirs. The memorandum reminds us, that from evidence, more or less\ncarefully weighed, it formerly appeared that a certain attribute might be\ninferred wherever we perceive a certain mark. The proposition, All men are\nmortal (for instance) shows that we have had experience from which we\nthought it followed that the attributes connoted by the term man, are a\nmark of mortality. But when we conclude that the Duke of Wellington is\nmortal, we do not infer this from the memorandum, but from the former\nexperience. All that we infer from the memorandum is our own previous\nbelief, (or that of those who transmitted to us the proposition),\nconcerning the inferences which that former experience would warrant.\n\nThis view of the nature of the syllogism renders consistent and\nintelligible what otherwise remains obscure and confused in the theory of\nArchbishop Whately and other enlightened defenders of the syllogistic\ndoctrine, respecting the limits to which its functions are confined. They\naffirm in as explicit terms as can be used, that the sole office of\ngeneral reasoning is to prevent inconsistency in our opinions; to prevent\nus from assenting to any thing, the truth of which would contradict\nsomething to which we had previously on good grounds given our assent. And\nthey tell us, that the sole ground which a syllogism affords for assenting\nto the conclusion, is that the supposition of its being false, combined\nwith the supposition that the premises are true, would lead to a\ncontradiction in terms. Now this would be but a lame account of the real\ngrounds which we have for believing the facts which we learn from\nreasoning, in contradistinction to observation. The true reason why we\nbelieve that the Duke of Wellington will die, is that his fathers, and our\nfathers, and all other persons who were contemporary with them, have died.\nThose facts are the real premises of the reasoning. But we are not led to\ninfer the conclusion from those premises, by the necessity of avoiding any\nverbal inconsistency. There is no contradiction in supposing that all\nthose persons have died, and that the Duke of Wellington may,\nnotwithstanding, live forever. But there would be a contradiction if we\nfirst, on the ground of those same premises, made a general assertion\nincluding and covering the case of the Duke of Wellington, and then\nrefused to stand to it in the individual case. There is an inconsistency\nto be avoided between the memorandum we make of the inferences which may\nbe justly drawn in future cases, and the inferences we actually draw in\nthose cases when they arise. With this view we interpret our own formula,\nprecisely as a judge interprets a law: in order that we may avoid drawing\nany inferences not conformable to our former intention, as a judge avoids\ngiving any decision not conformable to the legislator\u2019s intention. The\nrules for this interpretation are the rules of the syllogism: and its sole\npurpose is to maintain consistency between the conclusions we draw in\nevery particular case, and the previous general directions for drawing\nthem; whether those general directions were framed by ourselves as the\nresult of induction, or were received by us from an authority competent to\ngive them.\n\n\u00a7 5. In the above observations it has, I think, been shown, that, though\nthere is always a process of reasoning or inference where a syllogism is\nused, the syllogism is not a correct analysis of that process of reasoning\nor inference; which is, on the contrary (when not a mere inference from\ntestimony), an inference from particulars to particulars; authorized by a\nprevious inference from particulars to generals, and substantially the\nsame with it; of the nature, therefore, of Induction. But while these\nconclusions appear to me undeniable, I must yet enter a protest, as strong\nas that of Archbishop Whately himself, against the doctrine that the\nsyllogistic art is useless for the purposes of reasoning. The reasoning\nlies in the act of generalization, not in interpreting the record of that\nact; but the syllogistic form is an indispensable collateral security for\nthe correctness of the generalization itself.\n\nIt has already been seen, that if we have a collection of particulars\nsufficient for grounding an induction, we need not frame a general\nproposition; we may reason at once from those particulars to other\nparticulars. But it is to be remarked withal, that whenever, from a set of\nparticular cases, we can legitimately draw any inference, we may\nlegitimately make our inference a general one. If, from observation and\nexperiment, we can conclude to one new case, so may we to an indefinite\nnumber. If that which has held true in our past experience will therefore\nhold in time to come, it will hold not merely in some individual case, but\nin all cases of some given description. Every induction, therefore, which\nsuffices to prove one fact, proves an indefinite multitude of facts: the\nexperience which justifies a single prediction must be such as will\nsuffice to bear out a general theorem. This theorem it is extremely\nimportant to ascertain and declare, in its broadest form of generality;\nand thus to place before our minds, in its full extent, the whole of what\nour evidence must prove if it proves any thing.\n\nThis throwing of the whole body of possible inferences from a given set of\nparticulars, into one general expression, operates as a security for their\nbeing just inferences, in more ways than one. First, the general principle\npresents a larger object to the imagination than any of the singular\npropositions which it contains. A process of thought which leads to a\ncomprehensive generality, is felt as of greater importance than one which\nterminates in an insulated fact; and the mind is, even unconsciously, led\nto bestow greater attention upon the process, and to weigh more carefully\nthe sufficiency of the experience appealed to, for supporting the\ninference grounded upon it. There is another, and a more important,\nadvantage. In reasoning from a course of individual observations to some\nnew and unobserved case, which we are but imperfectly acquainted with (or\nwe should not be inquiring into it), and in which, since we are inquiring\ninto it, we probably feel a peculiar interest; there is very little to\nprevent us from giving way to negligence, or to any bias which may affect\nour wishes or our imagination, and, under that influence, accepting\ninsufficient evidence as sufficient. But if, instead of concluding\nstraight to the particular case, we place before ourselves an entire class\nof facts\u2014the whole contents of a general proposition, every tittle of\nwhich is legitimately inferable from our premises, if that one particular\nconclusion is so; there is then a considerable likelihood that if the\npremises are insufficient, and the general inference therefore,\ngroundless, it will comprise within it some fact or facts the reverse of\nwhich we already know to be true; and we shall thus discover the error in\nour generalization by a _reductio ad impossibile_.\n\nThus if, during the reign of Marcus Aurelius, a subject of the Roman\nempire, under the bias naturally given to the imagination and expectations\nby the lives and characters of the Antonines, had been disposed to expect\nthat Commodus would be a just ruler; supposing him to stop there, he might\nonly have been undeceived by sad experience. But if he reflected that this\nexpectation could not be justifiable unless from the same evidence he was\nwarranted in concluding some general proposition, as, for instance, that\nall Roman emperors are just rulers; he would immediately have thought of\nNero, Domitian, and other instances, which, showing the falsity of the\ngeneral conclusion, and therefore the insufficiency of the premises, would\nhave warned him that those premises could not prove in the instance of\nCommodus, what they were inadequate to prove in any collection of cases in\nwhich his was included.\n\nThe advantage, in judging whether any controverted inference is\nlegitimate, of referring to a parallel case, is universally acknowledged.\nBut by ascending to the general proposition, we bring under our view not\none parallel case only, but all possible parallel cases at once; all cases\nto which the same set of evidentiary considerations are applicable.\n\nWhen, therefore, we argue from a number of known cases to another case\nsupposed to be analogous, it is always possible, and generally\nadvantageous, to divert our argument into the circuitous channel of an\ninduction from those known cases to a general proposition, and a\nsubsequent application of that general proposition to the unknown case.\nThis second part of the operation, which, as before observed, is\nessentially a process of interpretation, will be resolvable into a\nsyllogism or a series of syllogisms, the majors of which will be general\npropositions embracing whole classes of cases; every one of which\npropositions must be true in all its extent, if the argument is\nmaintainable. If, therefore, any fact fairly coming within the range of\none of these general propositions, and consequently asserted by it, is\nknown or suspected to be other than the proposition asserts it to be, this\nmode of stating the argument causes us to know or to suspect that the\noriginal observations, which are the real grounds of our conclusion, are\nnot sufficient to support it. And in proportion to the greater chance of\nour detecting the inconclusiveness of our evidence, will be the increased\nreliance we are entitled to place in it if no such evidence of defect\nshall appear.\n\nThe value, therefore, of the syllogistic form, and of the rules for using\nit correctly, does not consist in their being the form and the rules\naccording to which our reasonings are necessarily, or even usually, made;\nbut in their furnishing us with a mode in which those reasonings may\nalways be represented, and which is admirably calculated, if they are\ninconclusive, to bring their inconclusiveness to light. An induction from\nparticulars to generals, followed by a syllogistic process from those\ngenerals to other particulars, is a form in which we may always state our\nreasonings if we please. It is not a form in which we _must_ reason, but\nit is a form in which we _may_ reason, and into which it is indispensable\nto throw our reasoning, when there is any doubt of its validity: though\nwhen the case is familiar and little complicated, and there is no\nsuspicion of error, we may, and do, reason at once from the known\nparticular cases to unknown ones.(58)\n\nThese are the uses of syllogism, as a mode of verifying any given\nargument. Its ulterior uses, as respects the general course of our\nintellectual operations, hardly require illustration, being in fact the\nacknowledged uses of general language. They amount substantially to this,\nthat the inductions may be made once for all: a single careful\ninterrogation of experience may suffice, and the result may be registered\nin the form of a general proposition, which is committed to memory or to\nwriting, and from which afterward we have only to syllogize. The\nparticulars of our experiments may then be dismissed from the memory, in\nwhich it would be impossible to retain so great a multitude of details;\nwhile the knowledge which those details afforded for future use, and which\nwould otherwise be lost as soon as the observations were forgotten, or as\ntheir record became too bulky for reference, is retained in a commodious\nand immediately available shape by means of general language.\n\nAgainst this advantage is to be set the countervailing inconvenience, that\ninferences originally made on insufficient evidence become consecrated,\nand, as it were, hardened into general maxims; and the mind cleaves to\nthem from habit, after it has outgrown any liability to be misled by\nsimilar fallacious appearances if they were now for the first time\npresented; but having forgotten the particulars, it does not think of\nrevising its own former decision. An inevitable drawback, which, however\nconsiderable in itself, forms evidently but a small set-off against the\nimmense benefits of general language.\n\nThe use of the syllogism is in truth no other than the use of general\npropositions in reasoning. We _can_ reason without them; in simple and\nobvious cases we habitually do so; minds of great sagacity can do it in\ncases not simple and obvious, provided their experience supplies them with\ninstances essentially similar to every combination of circumstances likely\nto arise. But other minds, and the same minds where they have not the same\npre-eminent advantages of personal experience, are quite helpless without\nthe aid of general propositions, wherever the case presents the smallest\ncomplication; and if we made no general propositions, few persons would\nget much beyond those simple inferences which are drawn by the more\nintelligent of the brutes. Though not necessary to reasoning, general\npropositions are necessary to any considerable progress in reasoning. It\nis, therefore, natural and indispensable to separate the process of\ninvestigation into two parts; and obtain general formul\u00e6 for determining\nwhat inferences may be drawn, before the occasion arises for drawing the\ninferences. The work of drawing them is then that of applying the formul\u00e6;\nand the rules of syllogism are a system of securities for the correctness\nof the application.\n\n\u00a7 6. To complete the series of considerations connected with the\nphilosophical character of the syllogism, it is requisite to consider,\nsince the syllogism is not the universal type of the reasoning process,\nwhat is the real type. This resolves itself into the question, what is the\nnature of the minor premise, and in what manner it contributes to\nestablish the conclusion: for as to the major, we now fully understand,\nthat the place which it nominally occupies in our reasonings, properly\nbelongs to the individual facts or observations of which it expresses the\ngeneral result; the major itself being no real part of the argument, but\nan intermediate halting-place for the mind, interposed by an artifice of\nlanguage between the real premises and the conclusion, by way of a\nsecurity, which it is in a most material degree, for the correctness of\nthe process. The minor, however, being an indispensable part of the\nsyllogistic expression of an argument, without doubt either is, or\ncorresponds to, an equally indispensable part of the argument itself, and\nwe have only to inquire what part.\n\nIt is perhaps worth while to notice here a speculation of a philosopher to\nwhom mental science is much indebted, but who, though a very penetrating,\nwas a very hasty thinker, and whose want of due circumspection rendered\nhim fully as remarkable for what he did not see, as for what he saw. I\nallude to Dr. Thomas Brown, whose theory of ratiocination is peculiar. He\nsaw the _petitio principii_ which is inherent in every syllogism, if we\nconsider the major to be itself the evidence by which the conclusion is\nproved, instead of being, what in fact it is, an assertion of the\nexistence of evidence sufficient to prove any conclusion of a given\ndescription. Seeing this, Dr. Brown not only failed to see the immense\nadvantage, in point of security for correctness, which is gained by\ninterposing this step between the real evidence and the conclusion; but he\nthought it incumbent on him to strike out the major altogether from the\nreasoning process, without substituting any thing else, and maintained\nthat our reasonings consist only of the minor premise and the conclusion,\nSocrates is a man, therefore Socrates is mortal: thus actually\nsuppressing, as an unnecessary step in the argument, the appeal to former\nexperience. The absurdity of this was disguised from him by the opinion he\nadopted, that reasoning is merely analyzing our own general notions, or\nabstract ideas; and that the proposition, Socrates is mortal, is evolved\nfrom the proposition, Socrates is a man, simply by recognizing the notion\nof mortality as already contained in the notion we form of a man.\n\nAfter the explanations so fully entered into on the subject of\npropositions, much further discussion can not be necessary to make the\nradical error of this view of ratiocination apparent. If the word man\nconnoted mortality; if the meaning of \u201cmortal\u201d were involved in the\nmeaning of \u201cman;\u201d we might, undoubtedly, evolve the conclusion from the\nminor alone, because the minor would have already asserted it. But if, as\nis in fact the case, the word man does not connote mortality, how does it\nappear that in the mind of every person who admits Socrates to be a man,\nthe idea of man must include the idea of mortality? Dr. Brown could not\nhelp seeing this difficulty, and in order to avoid it, was led, contrary\nto his intention, to re-establish, under another name, that step in the\nargument which corresponds to the major, by affirming the necessity of\n_previously perceiving_ the relation between the idea of man and the idea\nof mortal. If the reasoner has not previously perceived this relation, he\nwill not, says Dr. Brown, infer because Socrates is a man, that Socrates\nis mortal. But even this admission, though amounting to a surrender of the\ndoctrine that an argument consists of the minor and the conclusion alone,\nwill not save the remainder of Dr. Brown\u2019s theory. The failure of assent\nto the argument does not take place merely because the reasoner, for want\nof due analysis, does not perceive that his idea of man includes the idea\nof mortality; it takes place, much more commonly, because in his mind that\nrelation between the two ideas has never existed. And in truth it never\ndoes exist, except as the result of experience. Consenting, for the sake\nof the argument, to discuss the question on a supposition of which we have\nrecognized the radical incorrectness, namely, that the meaning of a\nproposition relates to the ideas of the things spoken of, and not to the\nthings themselves; I must yet observe, that the idea of man, as a\nuniversal idea, the common property of all rational creatures, can not\ninvolve any thing but what is strictly implied in the name. If any one\nincludes in his own private idea of man, as no doubt is always the case,\nsome other attributes, such for instance as mortality, he does so only as\nthe consequence of experience, after having satisfied himself that all men\npossess that attribute: so that whatever the idea contains, in any\nperson\u2019s mind, beyond what is included in the conventional signification\nof the word, has been added to it as the result of assent to a\nproposition; while Dr. Brown\u2019s theory requires us to suppose, on the\ncontrary, that assent to the proposition is produced by evolving, through\nan analytic process, this very element out of the idea. This theory,\ntherefore, may be considered as sufficiently refuted; and the minor\npremise must be regarded as totally insufficient to prove the conclusion,\nexcept with the assistance of the major, or of that which the major\nrepresents, namely, the various singular propositions expressive of the\nseries of observations, of which the generalization called the major\npremise is the result.\n\nIn the argument, then, which proves that Socrates is mortal, one\nindispensable part of the premises will be as follows: \u201cMy father, and my\nfather\u2019s father, A, B, C, and an indefinite number of other persons, were\nmortal;\u201d which is only an expression in different words of the observed\nfact that they have died. This is the major premise divested of the\n_petitio principii_, and cut down to as much as is really known by direct\nevidence.\n\nIn order to connect this proposition with the conclusion Socrates is\nmortal, the additional link necessary is such a proposition as the\nfollowing: \u201cSocrates resembles my father, and my father\u2019s father, and the\nother individuals specified.\u201d This proposition we assert when we say that\nSocrates is a man. By saying so we likewise assert in what respect he\nresembles them, namely, in the attributes connoted by the word man. And we\nconclude that he further resembles them in the attribute mortality.\n\n\u00a7 7. We have thus obtained what we were seeking, a universal type of the\nreasoning process. We find it resolvable in all cases into the following\nelements: Certain individuals have a given attribute; an individual or\nindividuals resemble the former in certain other attributes; therefore\nthey resemble them also in the given attribute. This type of ratiocination\ndoes not claim, like the syllogism, to be conclusive from the mere form of\nthe expression; nor can it possibly be so. That one proposition does or\ndoes not assert the very fact which was already asserted in another, may\nappear from the form of the expression, that is, from a comparison of the\nlanguage; but when the two propositions assert facts which are _bona fide_\ndifferent, whether the one fact proves the other or not can never appear\nfrom the language, but must depend on other considerations. Whether, from\nthe attributes in which Socrates resembles those men who have heretofore\ndied, it is allowable to infer that he resembles them also in being\nmortal, is a question of Induction; and is to be decided by the principles\nor canons which we shall hereafter recognize as tests of the correct\nperformance of that great mental operation.\n\nMeanwhile, however, it is certain, as before remarked, that if this\ninference can be drawn as to Socrates, it can be drawn as to all others\nwho resemble the observed individuals in the same attributes in which he\nresembles them; that is (to express the thing concisely) of all mankind.\nIf, therefore, the argument be admissible in the case of Socrates, we are\nat liberty, once for all, to treat the possession of the attributes of man\nas a mark, or satisfactory evidence, of the attribute of mortality. This\nwe do by laying down the universal proposition, All men are mortal, and\ninterpreting this, as occasion arises, in its application to Socrates and\nothers. By this means we establish a very convenient division of the\nentire logical operation into two steps; first, that of ascertaining what\nattributes are marks of mortality; and, secondly, whether any given\nindividuals possess those marks. And it will generally be advisable, in\nour speculations on the reasoning process, to consider this double\noperation as in fact taking place, and all reasoning as carried on in the\nform into which it must necessarily be thrown to enable us to apply to it\nany test of its correct performance.\n\nAlthough, therefore, all processes of thought in which the ultimate\npremises are particulars, whether we conclude from particulars to a\ngeneral formula, or from particulars to other particulars according to\nthat formula, are equally Induction; we shall yet, conformably to usage,\nconsider the name Induction as more peculiarly belonging to the process of\nestablishing the general proposition, and the remaining operation, which\nis substantially that of interpreting the general proposition, we shall\ncall by its usual name, Deduction. And we shall consider every process by\nwhich any thing is inferred respecting an unobserved case, as consisting\nof an Induction followed by a Deduction; because, although the process\nneeds not necessarily be carried on in this form, it is always susceptible\nof the form, and must be thrown into it when assurance of scientific\naccuracy is needed and desired.\n\n\u00a7 8. The theory of the syllogism laid down in the preceding pages, has\nobtained, among other important adhesions, three of peculiar value: those\nof Sir John Herschel,(59) Dr. Whewell,(60) and Mr. Bailey;(61) Sir John\nHerschel considering the doctrine, though not strictly \u201ca discovery,\u201d\nhaving been anticipated by Berkeley,(62) to be \u201cone of the greatest steps\nwhich have yet been made in the philosophy of Logic.\u201d \u201cWhen we consider\u201d\n(to quote the further words of the same authority) \u201cthe inveteracy of the\nhabits and prejudices which it has cast to the winds,\u201d there is no cause\nfor misgiving in the fact that other thinkers, no less entitled to\nconsideration, have formed a very different estimate of it. Their\nprincipal objection can not be better or more succinctly stated than by\nborrowing a sentence from Archbishop Whately.(63) \u201cIn every case where an\ninference is drawn from Induction (unless that name is to be given to a\nmere random guess without any grounds at all) we must form a judgment that\nthe instance or instances adduced are _sufficient_ to authorize the\nconclusion; that it is _allowable_ to take these instances as a sample\nwarranting an inference respecting the whole class;\u201d and the expression of\nthis judgment in words (it has been said by several of my critics) _is_\nthe major premise.\n\nI quite admit that the major is an affirmation of the sufficiency of the\nevidence on which the conclusion rests. That it is so, is the very essence\nof my own theory. And whoever admits that the major premise is _only_\nthis, adopts the theory in its essentials.\n\nBut I can not concede that this recognition of the sufficiency of the\nevidence\u2014that is, of the correctness of the induction\u2014is a part of the\ninduction itself; unless we ought to say that it is a part of every thing\nwe do, to satisfy ourselves that it has been done rightly. We conclude\nfrom known instances to unknown by the impulse of the generalizing\npropensity; and (until after a considerable amount of practice and mental\ndiscipline) the question of the sufficiency of the evidence is only raised\nby a retrospective act, turning back upon our own footsteps, and examining\nwhether we were warranted in doing what we have provisionally done. To\nspeak of this reflex operation as part of the original one, requiring to\nbe expressed in words in order that the verbal formula may correctly\nrepresent the psychological process, appears to me false psychology.(64)\nWe review our syllogistic as well as our inductive processes, and\nrecognize that they have been correctly performed; but logicians do not\nadd a third premise to the syllogism, to express this act of recognition.\nA careful copyist verifies his transcript by collating it with the\noriginal; and if no error appears, he recognizes that the transcript has\nbeen correctly made. But we do not call the examination of the copy a part\nof the act of copying.\n\nThe conclusion in an induction is inferred from the evidence itself, and\nnot from a recognition of the sufficiency of the evidence; as I infer that\nmy friend is walking toward me because I see him, and not because I\nrecognize that my eyes are open, and that eyesight is a means of\nknowledge. In all operations which require care, it is good to assure\nourselves that the process has been performed accurately; but the testing\nof the process is not the process itself; and, besides, may have been\nomitted altogether, and yet the process be correct. It is precisely\nbecause that operation is omitted in ordinary unscientific reasoning, that\nthere is any thing gained in certainty by throwing reasoning into the\nsyllogistic form. To make sure, as far as possible, that it shall not be\nomitted, we make the testing operation a part of the reasoning process\nitself. We insist that the inference from particulars to particulars shall\npass through a general proposition. But this is a security for good\nreasoning, not a condition of all reasoning; and in some cases not even a\nsecurity. Our most familiar inferences are all made before we learn the\nuse of general propositions; and a person of untutored sagacity will\nskillfully apply his acquired experience to adjacent cases, though he\nwould bungle grievously in fixing the limits of the appropriate general\ntheorem. But though he may conclude rightly, he never, properly speaking,\nknows whether he has done so or not; he has not tested his reasoning. Now,\nthis is precisely what forms of reasoning do for us. We do not need them\nto enable us to reason, but to enable us to know whether we reason\ncorrectly.\n\nIn still further answer to the objection, it may be added that\u2014even when\nthe test has been applied, and the sufficiency of the evidence\nrecognized\u2014if it is sufficient to support the general proposition, it is\nsufficient also to support an inference from particulars to particulars\nwithout passing through the general proposition. The inquirer who has\nlogically satisfied himself that the conditions of legitimate induction\nwere realized in the cases A, B, C, would be as much justified in\nconcluding directly to the Duke of Wellington as in concluding to all men.\nThe general conclusion is never legitimate, unless the particular one\nwould be so too; and in no sense, intelligible to me, can the particular\nconclusion be said to be drawn from the general one. Whenever there is\nground for drawing any conclusion at all from particular instances, there\nis ground for a general conclusion; but that this general conclusion\nshould be actually drawn, however useful, can not be an indispensable\ncondition of the validity of the inference in the particular case. A man\ngives away sixpence by the same power by which he disposes of his whole\nfortune; but it is not necessary to the legality of the smaller act, that\nhe should make a formal assertion of his right to the greater one.\n\nSome additional remarks, in reply to minor objections, are appended.(65)\n\n\u00a7 9. The preceding considerations enable us to understand the true nature\nof what is termed, by recent writers, Formal Logic, and the relation\nbetween it and Logic in the widest sense. Logic, as I conceive it, is the\nentire theory of the ascertainment of reasoned or inferred truth. Formal\nLogic, therefore, which Sir William Hamilton from his own point of view,\nand Archbishop Whately from his, have represented as the whole of Logic\nproperly so called, is really a very subordinate part of it, not being\ndirectly concerned with the process of Reasoning or Inference in the sense\nin which that process is a part of the Investigation of Truth. What, then,\nis Formal Logic? The name seems to be properly applied to all that portion\nof doctrine which relates to the equivalence of different modes of\nexpression; the rules for determining when assertions in a given form\nimply or suppose the truth or falsity of other assertions. This includes\nthe theory of the Import of Propositions, and of their Conversion,\n\u00c6quipollence, and Opposition; of those falsely called Inductions (to be\nhereafter spoken of)(66), in which the apparent generalization is a mere\nabridged statement of cases known individually; and finally, of the\nsyllogism: while the theory of Naming, and of (what is inseparably\nconnected with it) Definition, though belonging still more to the other\nand larger kind of logic than to this, is a necessary preliminary to this.\nThe end aimed at by Formal Logic, and attained by the observance of its\nprecepts, is not truth, but consistency. It has been seen that this is the\nonly direct purpose of the rules of the syllogism; the intention and\neffect of which is simply to keep our inferences or conclusions in\ncomplete consistency with our general formul\u00e6 or directions for drawing\nthem. The Logic of Consistency is a necessary auxiliary to the logic of\ntruth, not only because what is inconsistent with itself or with other\ntruths can not be true, but also because truth can only be successfully\npursued by drawing inferences from experience, which, if warrantable at\nall, admit of being generalized, and, to test their warrantableness,\nrequire to be exhibited in a generalized form; after which the correctness\nof their application to particular cases is a question which specially\nconcerns the Logic of Consistency. This Logic, not requiring any\npreliminary knowledge of the processes or conclusions of the various\nsciences, may be studied with benefit in a much earlier stage of education\nthan the Logic of Truth: and the practice which has empirically obtained\nof teaching it apart, through elementary treatises which do not attempt to\ninclude any thing else, though the reasons assigned for the practice are\nin general very far from philosophical, admits of philosophical\njustification.\n\n\n\n\n                               Chapter IV.\n\n\nOf Trains Of Reasoning, And Deductive Sciences.\n\n\n\u00a7 1. In our analysis of the syllogism, it appeared that the minor premise\nalways affirms a resemblance between a new case and some cases previously\nknown; while the major premise asserts something which, having been found\ntrue of those known cases, we consider ourselves warranted in holding true\nof any other case resembling the former in certain given particulars.\n\nIf all ratiocinations resembled, as to the minor premise, the examples\nwhich were exclusively employed in the preceding chapter; if the\nresemblance, which that premise asserts, were obvious to the senses, as in\nthe proposition \u201cSocrates is a man,\u201d or were at once ascertainable by\ndirect observation; there would be no necessity for trains of reasoning,\nand Deductive or Ratiocinative Sciences would not exist. Trains of\nreasoning exist only for the sake of extending an induction founded, as\nall inductions must be, on observed cases, to other cases in which we not\nonly can not directly observe the fact which is to be proved, but can not\ndirectly observe even the mark which is to prove it.\n\n\u00a7 2. Suppose the syllogism to be, All cows ruminate, the animal which is\nbefore me is a cow, therefore it ruminates. The minor, if true at all, is\nobviously so: the only premise the establishment of which requires any\nanterior process of inquiry, is the major; and provided the induction of\nwhich that premise is the expression was correctly performed, the\nconclusion respecting the animal now present will be instantly drawn;\nbecause, as soon as she is compared with the formula, she will be\nidentified as being included in it. But suppose the syllogism to be the\nfollowing: All arsenic is poisonous, the substance which is before me is\narsenic, therefore it is poisonous. The truth of the minor may not here be\nobvious at first sight; it may not be intuitively evident, but may itself\nbe known only by inference. It may be the conclusion of another argument,\nwhich, thrown into the syllogistic form, would stand thus: Whatever when\nlighted produces a dark spot on a piece of white porcelain held in the\nflame, which spot is soluble in hypochloride of calcium, is arsenic; the\nsubstance before me conforms to this condition; therefore it is arsenic.\nTo establish, therefore, the ultimate conclusion, The substance before me\nis poisonous, requires a process, which, in order to be syllogistically\nexpressed, stands in need of two syllogisms; and we have a Train of\nReasoning.\n\nWhen, however, we thus add syllogism to syllogism, we are really adding\ninduction to induction. Two separate inductions must have taken place to\nrender this chain of inference possible; inductions founded, probably, on\ndifferent sets of individual instances, but which converge in their\nresults, so that the instance which is the subject of inquiry comes within\nthe range of them both. The record of these inductions is contained in the\nmajors of the two syllogisms. First, we, or others for us, have examined\nvarious objects which yielded under the given circumstances a dark spot\nwith the given property, and found that they possessed the properties\nconnoted by the word arsenic; they were metallic, volatile, their vapor\nhad a smell of garlic, and so forth. Next, we, or others for us, have\nexamined various specimens which possessed this metallic and volatile\ncharacter, whose vapor had this smell, etc., and have invariably found\nthat they were poisonous. The first observation we judge that we may\nextend to all substances whatever which yield that particular kind of dark\nspot; the second, to all metallic and volatile substances resembling those\nwe examined; and consequently, not to those only which are seen to be\nsuch, but to those which are concluded to be such by the prior induction.\nThe substance before us is only seen to come within one of these\ninductions; but by means of this one, it is brought within the other. We\nare still, as before, concluding from particulars to particulars; but we\nare now concluding from particulars observed, to other particulars which\nare not, as in the simple case, _seen_ to resemble them in material\npoints, but _inferred_ to do so, because resembling them in something\nelse, which we have been led by quite a different set of instances to\nconsider as a mark of the former resemblance.\n\nThis first example of a train of reasoning is still extremely simple, the\nseries consisting of only two syllogisms. The following is somewhat more\ncomplicated: No government, which earnestly seeks the good of its\nsubjects, is likely to be overthrown; some particular government earnestly\nseeks the good of its subjects, therefore it is not likely to be\noverthrown. The major premise in this argument we shall suppose not to be\nderived from considerations _a priori_, but to be a generalization from\nhistory, which, whether correct or erroneous, must have been founded on\nobservation of governments concerning whose desire of the good of their\nsubjects there was no doubt. It has been found, or thought to be found,\nthat these were not easily overthrown, and it has been deemed that those\ninstances warranted an extension of the same predicate to any and every\ngovernment which resembles them in the attribute of desiring earnestly the\ngood of its subjects. But _does_ the government in question thus resemble\nthem? This may be debated _pro_ and _con_ by many arguments, and must, in\nany case, be proved by another induction; for we can not directly observe\nthe sentiments and desires of the persons who carry on the government. To\nprove the minor, therefore, we require an argument in this form: Every\ngovernment which acts in a certain manner, desires the good of its\nsubjects; the supposed government acts in that particular manner,\ntherefore it desires the good of its subjects. But is it true that the\ngovernment acts in the manner supposed? This minor also may require proof;\nstill another induction, as thus: What is asserted by intelligent and\ndisinterested witnesses, may be believed to be true; that the government\nacts in this manner, is asserted by such witnesses, therefore it may be\nbelieved to be true. The argument hence consists of three steps. Having\nthe evidence of our senses that the case of the government under\nconsideration resembles a number of former cases, in the circumstance of\nhaving something asserted respecting it by intelligent and disinterested\nwitnesses, we infer, first, that, as in those former instances, so in this\ninstance, the assertion is true. Secondly, what was asserted of the\ngovernment being that it acts in a particular manner, and other\ngovernments or persons having been observed to act in the same manner, the\ngovernment in question is brought into known resemblance with those other\ngovernments or persons; and since they were known to desire the good of\nthe people, it is thereupon, by a second induction, inferred that the\nparticular government spoken of, desires the good of the people. This\nbrings that government into known resemblance with the other governments\nwhich were thought likely to escape revolution, and thence, by a third\ninduction, it is concluded that this particular government is also likely\nto escape. This is still reasoning from particulars to particulars, but we\nnow reason to the new instance from three distinct sets of former\ninstances: to one only of those sets of instances do we directly perceive\nthe new one to be similar; but from that similarity we inductively infer\nthat it has the attribute by which it is assimilated to the next set, and\nbrought within the corresponding induction; after which by a repetition of\nthe same operation we infer it to be similar to the third set, and hence a\nthird induction conducts us to the ultimate conclusion.\n\n\u00a7 3. Notwithstanding the superior complication of these examples, compared\nwith those by which in the preceding chapter we illustrated the general\ntheory of reasoning, every doctrine which we then laid down holds equally\ntrue in these more intricate cases. The successive general propositions\nare not steps in the reasoning, are not intermediate links in the chain of\ninference, between the particulars observed and those to which we apply\nthe observation. If we had sufficiently capacious memories, and a\nsufficient power of maintaining order among a huge mass of details, the\nreasoning could go on without any general propositions; they are mere\nformul\u00e6 for inferring particulars from particulars. The principle of\ngeneral reasoning is (as before explained), that if, from observation of\ncertain known particulars, what was seen to be true of them can be\ninferred to be true of any others, it may be inferred of all others which\nare of a certain description. And in order that we may never fail to draw\nthis conclusion in a new case when it can be drawn correctly, and may\navoid drawing it when it can not, we determine once for all what are the\ndistinguishing marks by which such cases may be recognized. The subsequent\nprocess is merely that of identifying an object, and ascertaining it to\nhave those marks; whether we identify it by the very marks themselves, or\nby others which we have ascertained (through another and a similar\nprocess) to be marks of those marks. The real inference is always from\nparticulars to particulars, from the observed instances to an unobserved\none: but in drawing this inference, we conform to a formula which we have\nadopted for our guidance in such operations, and which is a record of the\ncriteria by which we thought we had ascertained that we might distinguish\nwhen the inference could, and when it could not, be drawn. The real\npremises are the individual observations, even though they may have been\nforgotten, or, being the observations of others and not of ourselves, may,\nto us, never have been known: but we have before us proof that we or\nothers once thought them sufficient for an induction, and we have marks to\nshow whether any new case is one of those to which, if then known, the\ninduction would have been deemed to extend. These marks we either\nrecognize at once, or by the aid of other marks, which by another previous\ninduction we collected to be marks of the first. Even these marks of marks\nmay only be recognized through a third set of marks; and we may have a\ntrain of reasoning, of any length, to bring a new case within the scope of\nan induction grounded on particulars its similarity to which is only\nascertained in this indirect manner.\n\nThus, in the preceding example, the ultimate inductive inference was, that\na certain government was not likely to be overthrown; this inference was\ndrawn according to a formula in which desire of the public good was set\ndown as a mark of not being likely to be overthrown; a mark of this mark\nwas, acting in a particular manner; and a mark of acting in that manner\nwas, being asserted to do so by intelligent and disinterested witnesses:\nthis mark, the government under discussion was recognized by the senses as\npossessing. Hence that government fell within the last induction, and by\nit was brought within all the others. The perceived resemblance of the\ncase to one set of observed particular cases, brought it into known\nresemblance with another set, and that with a third.\n\nIn the more complex branches of knowledge, the deductions seldom consist,\nas in the examples hitherto exhibited, of a single chain, _a_ a mark of\n_b, b_ of _c, c_ of _d_, therefore _a_ a mark of _d_. They consist (to\ncarry on the same metaphor) of several chains united at the extremity, as\nthus: _a_ a mark of _d, b_ of _e, c_ of _f, d e f_ of _n_, therefore _a b\nc_ a mark of _n_. Suppose, for example, the following combination of\ncircumstances: 1st, rays of light impinging on a reflecting surface; 2d,\nthat surface parabolic; 3d, those rays parallel to each other and to the\naxis of the surface. It is to be proved that the concourse of these three\ncircumstances is a mark that the reflected rays will pass through the\nfocus of the parabolic surface. Now, each of the three circumstances is\nsingly a mark of something material to the case. Rays of light impinging\non a reflecting surface are a mark that those rays will be reflected at an\nangle equal to the angle of incidence. The parabolic form of the surface,\nis a mark that, from any point of it, a line drawn to the focus and a line\nparallel to the axis will make equal angles with the surface. And finally,\nthe parallelism of the rays to the axis is a mark that their angle of\nincidence coincides with one of these equal angles. The three marks taken\ntogether are therefore a mark of all these three things united. But the\nthree united are evidently a mark that the angle of reflection must\ncoincide with the other of the two equal angles, that formed by a line\ndrawn to the focus; and this again, by the fundamental axiom concerning\nstraight lines, is a mark that the reflected rays pass through the focus.\nMost chains of physical deduction are of this more complicated type; and\neven in mathematics such are abundant, as in all propositions where the\nhypothesis includes numerous conditions: \u201c_If_ a circle be taken, and _if_\nwithin that circle a point be taken, not the centre, and _if_ straight\nlines be drawn from that point to the circumference, then,\u201d etc.\n\n\u00a7 4. The considerations now stated remove a serious difficulty from the\nview we have taken of reasoning; which view might otherwise have seemed\nnot easily reconcilable with the fact that there are Deductive or\nRatiocinative Sciences. It might seem to follow, if all reasoning be\ninduction, that the difficulties of philosophical investigation must lie\nin the inductions exclusively, and that when these were easy, and\nsusceptible of no doubt or hesitation, there could be no science, or, at\nleast, no difficulties in science. The existence, for example, of an\nextensive Science of Mathematics, requiring the highest scientific genius\nin those who contributed to its creation, and calling for a most continued\nand vigorous exertion of intellect in order to appropriate it when\ncreated, may seem hard to be accounted for on the foregoing theory. But\nthe considerations more recently adduced remove the mystery, by showing,\nthat even when the inductions themselves are obvious, there may be much\ndifficulty in finding whether the particular case which is the subject of\ninquiry comes within them; and ample room for scientific ingenuity in so\ncombining various inductions, as, by means of one within which the case\nevidently falls, to bring it within others in which it can not be directly\nseen to be included.\n\nWhen the more obvious of the inductions which can be made in any science\nfrom direct observations, have been made, and general formulas have been\nframed, determining the limits within which these inductions are\napplicable; as often as a new case can be at once seen to come within one\nof the formulas, the induction is applied to the new case, and the\nbusiness is ended. But new cases are continually arising, which do not\nobviously come within any formula whereby the question we want solved in\nrespect of them could be answered. Let us take an instance from geometry:\nand as it is taken only for illustration, let the reader concede to us for\nthe present, what we shall endeavor to prove in the next chapter, that the\nfirst principles of geometry are results of induction. Our example shall\nbe the fifth proposition of the first book of Euclid. The inquiry is, Are\nthe angles at the base of an isosceles triangle equal or unequal? The\nfirst thing to be considered is, what inductions we have, from which we\ncan infer equality or inequality. For inferring equality we have the\nfollowing formul\u00e6: Things which being applied to each other coincide, are\nequals. Things which are equal to the same thing are equals. A whole and\nthe sum of its parts are equals. The sums of equal things are equals. The\ndifferences of equal things are equals. There are no other original\nformul\u00e6 to prove equality. For inferring inequality we have the following:\nA whole and its parts are unequals. The sums of equal things and unequal\nthings are unequals. The differences of equal things and unequal things\nare unequals. In all, eight formul\u00e6. The angles at the base of an\nisosceles triangle do not obviously come within any of these. The formul\u00e6\nspecify certain marks of equality and of inequality, but the angles can\nnot be perceived intuitively to have any of those marks. On examination it\nappears that they have; and we ultimately succeed in bringing them within\nthe formula, \u201cThe differences of equal things are equal.\u201d Whence comes the\ndifficulty of recognizing these angles as the differences of equal things?\nBecause each of them is the difference not of one pair only, but of\ninnumerable pairs of angles; and out of these we had to imagine and select\ntwo, which could either be intuitively perceived to be equals, or\npossessed some of the marks of equality set down in the various formul\u00e6.\nBy an exercise of ingenuity, which, on the part of the first inventor,\ndeserves to be regarded as considerable, two pairs of angles were hit\nupon, which united these requisites. First, it could be perceived\nintuitively that their differences were the angles at the base; and,\nsecondly, they possessed one of the marks of equality, namely, coincidence\nwhen applied to one another. This coincidence, however, was not perceived\nintuitively, but inferred, in conformity to another formula.\n\nFor greater clearness, I subjoin an analysis of the demonstration. Euclid,\nit will be remembered, demonstrates his fifth proposition by means of the\nfourth. This it is not allowable for us to do, because we are undertaking\nto trace deductive truths not to prior deductions, but to their original\ninductive foundation. We must, therefore, use the premises of the fourth\nproposition instead of its conclusion, and prove the fifth directly from\nfirst principles. To do so requires six formulas. (We presuppose an\nequilateral triangle, whose vertices are A, D, E, with point B on the side\nAD, and point C on the side AE, such that BC is parallel to DE. We must\nbegin, as in Euclid, by prolonging the equal sides AB, AC, to equal\ndistances, and joining the extremities BE, DC.)\n\nFIRST FORMULA.\u2014_The sums of equals are equal._\n\nAD and AE are sums of equals by the supposition. Having that mark of\nequality, they are concluded by this formula to be equal.\n\nSECOND FORMULA.\u2014_Equal straight lines or angles, being applied to one\nanother, coincide._\n\nAC, AB, are within this formula by supposition; AD, AE, have been brought\nwithin it by the preceding step. The angle at A considered as an angle of\nthe triangle ABE, and the same angle considered as an angle of the\ntriangle ACD, are of course within the formula. All these pairs,\ntherefore, possess the property which, according to the second formula, is\na mark that when applied to one another they will coincide. Conceive them,\nthen, applied to one another, by turning over the triangle ABE, and laying\nit on the triangle ACD in such a manner that AB of the one shall lie upon\nAC of the other. Then, by the equality of the angles, AE will lie on AD.\nBut AB and AC, AE and AD are equals; therefore they will coincide\naltogether, and of course at their extremities, D, E, and B, C.\n\nTHIRD FORMULA.\u2014_Straight lines, having their extremities coincident,\ncoincide._\n\nBE and CD have been brought within this formula by the preceding\ninduction; they will, therefore, coincide.\n\nFOURTH FORMULA.\u2014_Angles, having their sides coincident, coincide._\n\nThe third induction having shown that BE and CD coincide, and the second\nthat AB, AC, coincide, the angles ABE and ACD are thereby brought within\nthe fourth formula, and accordingly coincide.\n\nFIFTH FORMULA.\u2014_Things which coincide are equal._\n\nThe angles ABE and ACD are brought within this formula by the induction\nimmediately preceding. This train of reasoning being also applicable,\n_mutatis mutandis_, to the angles EBC, DCB, these also are brought within\nthe fifth formula. And, finally,\n\nSIXTH FORMULA.\u2014_The differences of equals are equal._\n\nThe angle ABC being the difference of ABE, CBE, and the angle ACB being\nthe difference of ACD, DCB; which have been proved to be equals; ABC and\nACB are brought within the last formula by the whole of the previous\nprocess.\n\nThe difficulty here encountered is chiefly that of figuring to ourselves\nthe two angles at the base of the triangle ABC as remainders made by\ncutting one pair of angles out of another, while each pair shall be\ncorresponding angles of triangles which have two sides and the intervening\nangle equal. It is by this happy contrivance that so many different\ninductions are brought to bear upon the same particular case. And this not\nbeing at all an obvious thought, it may be seen from an example so near\nthe threshold of mathematics, how much scope there may well be for\nscientific dexterity in the higher branches of that and other sciences, in\norder so to combine a few simple inductions, as to bring within each of\nthem innumerable cases which are not obviously included in it; and how\nlong, and numerous, and complicated may be the processes necessary for\nbringing the inductions together, even when each induction may itself be\nvery easy and simple. All the inductions involved in all geometry are\ncomprised in those simple ones, the formul\u00e6 of which are the Axioms, and a\nfew of the so-called Definitions. The remainder of the science is made up\nof the processes employed for bringing unforeseen cases within these\ninductions; or (in syllogistic language) for proving the minors necessary\nto complete the syllogisms; the majors being the definitions and axioms.\nIn those definitions and axioms are laid down the whole of the marks, by\nan artful combination of which it has been found possible to discover and\nprove all that is proved in geometry. The marks being so few, and the\ninductions which furnish them being so obvious and familiar; the\nconnecting of several of them together, which constitutes Deductions, or\nTrains of Reasoning, forms the whole difficulty of the science, and, with\na trifling exception, its whole bulk; and hence Geometry is a Deductive\nScience.\n\n\u00a7 5. It will be seen hereafter(67) that there are weighty scientific\nreasons for giving to every science as much of the character of a\nDeductive Science as possible; for endeavoring to construct the science\nfrom the fewest and the simplest possible inductions, and to make these,\nby any combinations however complicated, suffice for proving even such\ntruths, relating to complex cases, as could be proved, if we chose, by\ninductions from specific experience. Every branch of natural philosophy\nwas originally experimental; each generalization rested on a special\ninduction, and was derived from its own distinct set of observations and\nexperiments. From being sciences of pure experiment, as the phrase is, or,\nto speak more correctly, sciences in which the reasonings mostly consist\nof no more than one step, and are expressed by single syllogisms, all\nthese sciences have become to some extent, and some of them in nearly the\nwhole of their extent, sciences of pure reasoning; whereby multitudes of\ntruths, already known by induction from as many different sets of\nexperiments, have come to be exhibited as deductions or corollaries from\ninductive propositions of a simpler and more universal character. Thus\nmechanics, hydrostatics, optics, acoustics, thermology, have successively\nbeen rendered mathematical; and astronomy was brought by Newton within the\nlaws of general mechanics. Why it is that the substitution of this\ncircuitous mode of proceeding for a process apparently much easier and\nmore natural, is held, and justly, to be the greatest triumph of the\ninvestigation of nature, we are not, in this stage of our inquiry,\nprepared to examine. But it is necessary to remark, that although, by this\nprogressive transformation, all sciences tend to become more and more\nDeductive, they are not, therefore, the less Inductive; every step in the\nDeduction is still an Induction. The opposition is not between the terms\nDeductive and Inductive, but between Deductive and Experimental. A science\nis experimental, in proportion as every new case, which presents any\npeculiar features, stands in need of a new set of observations and\nexperiments\u2014a fresh induction. It is deductive, in proportion as it can\ndraw conclusions, respecting cases of a new kind, by processes which bring\nthose cases under old inductions; by ascertaining that cases which can not\nbe observed to have the requisite marks, have, however, marks of those\nmarks.\n\nWe can now, therefore, perceive what is the generic distinction between\nsciences which can be made Deductive, and those which must as yet remain\nExperimental. The difference consists in our having been able, or not yet\nable, to discover marks of marks. If by our various inductions we have\nbeen able to proceed no further than to such propositions as these, _a_ a\nmark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of _d_, or c\nand _d_ marks of one another, without any thing to connect _a_ or _b_ with\n_c_ or _d_; we have a science of detached and mutually independent\ngeneralizations, such as these, that acids redden vegetable blues, and\nthat alkalies color them green; from neither of which propositions could\nwe, directly or indirectly, infer the other: and a science, so far as it\nis composed of such propositions, is purely experimental. Chemistry, in\nthe present state of our knowledge, has not yet thrown off this character.\nThere are other sciences, however, of which the propositions are of this\nkind: _a_ a mark of _b, b_ a mark of _c, c_ of _d, d_ of _e_, etc. In\nthese sciences we can mount the ladder from _a_ to _e_ by a process of\nratiocination; we can conclude that _a_ is a mark of _e_, and that every\nobject which has the mark _a_ has the property _e_, although, perhaps, we\nnever were able to observe _a_ and _e_ together, and although even _d_,\nour only direct mark of _e_, may not be perceptible in those objects, but\nonly inferable. Or, varying the first metaphor, we may be said to get from\n_a_ to _e_ underground: the marks _b_, _c_, _d_, which indicate the route,\nmust all be possessed somewhere by the objects concerning which we are\ninquiring; but they are below the surface: _a_ is the only mark that is\nvisible, and by it we are able to trace in succession all the rest.\n\n\u00a7 6. We can now understand how an experimental may transform itself into a\ndeductive science by the mere progress of experiment. In an experimental\nscience, the inductions, as we have said, lie detached, as, _a_ a mark of\n_b, c_ a mark of _d_, _e_ a mark of _f_, and so on: now, a new set of\ninstances, and a consequent new induction, may at any time bridge over the\ninterval between two of these unconnected arches; _b_, for example, may be\nascertained to be a mark of _c_, which enables us thenceforth to prove\ndeductively that _a_ is a mark of _c_. Or, as sometimes happens, some\ncomprehensive induction may raise an arch high in the air, which bridges\nover hosts of them at once; _b_, _d_, _f_, and all the rest, turning out\nto be marks of some one thing, or of things between which a connection has\nalready been traced. As when Newton discovered that the motions, whether\nregular or apparently anomalous, of all the bodies of the solar system\n(each of which motions had been inferred by a separate logical operation,\nfrom separate marks), were all marks of moving round a common centre, with\na centripetal force varying directly as the mass, and inversely as the\nsquare of the distance from that centre. This is the greatest example\nwhich has yet occurred of the transformation, at one stroke, of a science\nwhich was still to a great degree merely experimental, into a deductive\nscience.\n\nTransformations of the same nature, but on a smaller scale, continually\ntake place in the less advanced branches of physical knowledge, without\nenabling them to throw off the character of experimental sciences. Thus\nwith regard to the two unconnected propositions before cited, namely,\nAcids redden vegetable blues, Alkalies make them green; it is remarked by\nLiebig, that all blue coloring matters which are reddened by acids (as\nwell as, reciprocally, all red coloring matters which are rendered blue by\nalkalies) contain nitrogen: and it is quite possible that this\ncircumstance may one day furnish a bond of connection between the two\npropositions in question, by showing that the antagonistic action of acids\nand alkalies in producing or destroying the color blue, is the result of\nsome one, more general, law. Although this connecting of detached\ngeneralizations is so much gain, it tends but little to give a deductive\ncharacter to any science as a whole; because the new courses of\nobservation and experiment, which thus enable us to connect together a few\ngeneral truths, usually make known to us a still greater number of\nunconnected new ones. Hence chemistry, though similar extensions and\nsimplifications of its generalizations are continually taking place, is\nstill in the main an experimental science; and is likely so to continue\nunless some comprehensive induction should be hereafter arrived at, which,\nlike Newton\u2019s, shall connect a vast number of the smaller known inductions\ntogether, and change the whole method of the science at once. Chemistry\nhas already one great generalization, which, though relating to one of the\nsubordinate aspects of chemical phenomena, possesses within its limited\nsphere this comprehensive character; the principle of Dalton, called the\natomic theory, or the doctrine of chemical equivalents: which by enabling\nus to a certain extent to foresee the proportions in which two substances\nwill combine, before the experiment has been tried, constitutes\nundoubtedly a source of new chemical truths obtainable by deduction, as\nwell as a connecting principle for all truths of the same description\npreviously obtained by experiment.\n\n\u00a7 7. The discoveries which change the method of a science from\nexperimental to deductive, mostly consist in establishing, either by\ndeduction or by direct experiment, that the varieties of a particular\nphenomenon uniformly accompany the varieties of some other phenomenon\nbetter known. Thus the science of sound, which previously stood in the\nlowest rank of merely experimental science, became deductive when it was\nproved by experiment that every variety of sound was consequent on, and\ntherefore a mark of, a distinct and definable variety of oscillatory\nmotion among the particles of the transmitting medium. When this was\nascertained, it followed that every relation of succession or co-existence\nwhich obtained between phenomena of the more known class, obtained also\nbetween the phenomena which correspond to them in the other class. Every\nsound, being a mark of a particular oscillatory motion, became a mark of\nevery thing which, by the laws of dynamics, was known to be inferable from\nthat motion; and every thing which by those same laws was a mark of any\noscillatory motion among the particles of an elastic medium, became a mark\nof the corresponding sound. And thus many truths, not before suspected,\nconcerning sound, become deducible from the known laws of the propagation\nof motion through an elastic medium; while facts already empirically known\nrespecting sound, become an indication of corresponding properties of\nvibrating bodies, previously undiscovered.\n\nBut the grand agent for transforming experimental into deductive sciences,\nis the science of number. The properties of number, alone among all known\nphenomena, are, in the most rigorous sense, properties of all things\nwhatever. All things are not colored, or ponderable, or even extended; but\nall things are numerable. And if we consider this science in its whole\nextent, from common arithmetic up to the calculus of variations, the\ntruths already ascertained seem all but infinite, and admit of indefinite\nextension.\n\nThese truths, though affirmable of all things whatever, of course apply to\nthem only in respect of their quantity. But if it comes to be discovered\nthat variations of quality in any class of phenomena, correspond regularly\nto variations of quantity either in those same or in some other phenomena;\nevery formula of mathematics applicable to quantities which vary in that\nparticular manner, becomes a mark of a corresponding general truth,\nrespecting the variations in quality which accompany them: and the science\nof quantity being (as far as any science can be) altogether deductive, the\ntheory of that particular kind of qualities becomes, to this extent,\ndeductive likewise.\n\nThe most striking instance in point which history affords (though not an\nexample of an experimental science rendered deductive, but of an\nunparalleled extension given to the deductive process in a science which\nwas deductive already), is the revolution in geometry which originated\nwith Descartes, and was completed by Clairaut. These great mathematicians\npointed out the importance of the fact, that to every variety of position\nin points, direction in lines, or form in curves or surfaces (all of which\nare Qualities), there corresponds a peculiar relation of quantity between\neither two or three rectilineal co-ordinates; insomuch that if the law\nwere known according to which those co-ordinates vary relatively to one\nanother, every other geometrical property of the line or surface in\nquestion, whether relating to quantity or quality, would be capable of\nbeing inferred. Hence it followed that every geometrical question could be\nsolved, if the corresponding algebraical one could; and geometry received\nan accession (actual or potential) of new truths, corresponding to every\nproperty of numbers which the progress of the calculus had brought, or\nmight in future bring, to light. In the same general manner, mechanics,\nastronomy, and in a less degree, every branch of natural philosophy\ncommonly so called, have been made algebraical. The varieties of physical\nphenomena with which those sciences are conversant, have been found to\nanswer to determinable varieties in the quantity of some circumstance or\nother; or at least to varieties of form or position, for which\ncorresponding equations of quantity had already been, or were susceptible\nof being, discovered by geometers.\n\nIn these various transformations, the propositions of the science of\nnumber do but fulfill the function proper to all propositions forming a\ntrain of reasoning, viz., that of enabling us to arrive in an indirect\nmethod, by marks of marks, at such of the properties of objects as we can\nnot directly ascertain (or not so conveniently) by experiment. We travel\nfrom a given visible or tangible fact, through the truths of numbers, to\nthe facts sought. The given fact is a mark that a certain relation\nsubsists between the quantities of some of the elements concerned; while\nthe fact sought presupposes a certain relation between the quantities of\nsome other elements: now, if these last quantities are dependent in some\nknown manner upon the former, or _vic\u00e8 versa_, we can argue from the\nnumerical relation between the one set of quantities, to determine that\nwhich subsists between the other set; the theorems of the calculus\naffording the intermediate links. And thus one of the two physical facts\nbecomes a mark of the other, by being a mark of a mark of a mark of it.\n\n\n\n\n                                Chapter V.\n\n\nOf Demonstration, And Necessary Truths.\n\n\n\u00a7 1. If, as laid down in the two preceding chapters, the foundation of all\nsciences, even deductive or demonstrative sciences, is Induction; if every\nstep in the ratiocinations even of geometry is an act of induction; and if\na train of reasoning is but bringing many inductions to bear upon the same\nsubject of inquiry, and drawing a case within one induction by means of\nanother; wherein lies the peculiar certainty always ascribed to the\nsciences which are entirely, or almost entirely, deductive? Why are they\ncalled the Exact Sciences? Why are mathematical certainty, and the\nevidence of demonstration, common phrases to express the very highest\ndegree of assurance attainable by reason? Why are mathematics by almost\nall philosophers, and (by some) even those branches of natural philosophy\nwhich, through the medium of mathematics, have been converted into\ndeductive sciences, considered to be independent of the evidence of\nexperience and observation, and characterized as systems of Necessary\nTruth?\n\nThe answer I conceive to be, that this character of necessity, ascribed to\nthe truths of mathematics, and (even with some reservations to be\nhereafter made) the peculiar certainty attributed to them, is an illusion;\nin order to sustain which, it is necessary to suppose that those truths\nrelate to, and express the properties of, purely imaginary objects. It is\nacknowledged that the conclusions of geometry are deduced, partly at\nleast, from the so-called Definitions, and that those definitions are\nassumed to be correct representations, as far as they go, of the objects\nwith which geometry is conversant. Now we have pointed out that, from a\ndefinition as such, no proposition, unless it be one concerning the\nmeaning of a word, can ever follow; and that what apparently follows from\na definition, follows in reality from an implied assumption that there\nexists a real thing conformable thereto. This assumption, in the case of\nthe definitions of geometry, is not strictly true: there exist no real\nthings exactly conformable to the definitions. There exist no points\nwithout magnitude; no lines without breadth, nor perfectly straight; no\ncircles with all their radii exactly equal, nor squares with all their\nangles perfectly right. It will perhaps be said that the assumption does\nnot extend to the actual, but only to the possible, existence of such\nthings. I answer that, according to any test we have of possibility, they\nare not even possible. Their existence, so far as we can form any\njudgment, would seem to be inconsistent with the physical constitution of\nour planet at least, if not of the universe. To get rid of this\ndifficulty, and at the same time to save the credit of the supposed system\nof necessary truth, it is customary to say that the points, lines,\ncircles, and squares which are the subject of geometry, exist in our\nconceptions merely, and are part of our minds; which minds, by working on\ntheir own materials, construct an _a priori_ science, the evidence of\nwhich is purely mental, and has nothing whatever to do with outward\nexperience. By howsoever high authorities this doctrine may have been\nsanctioned, it appears to me psychologically incorrect. The points, lines,\ncircles, and squares which any one has in his mind, are (I apprehend)\nsimply copies of the points, lines, circles, and squares which he has\nknown in his experience. Our idea of a point, I apprehend to be simply our\nidea of the _minimum visibile_, the smallest portion of surface which we\ncan see. A line, as defined by geometers, is wholly inconceivable. We can\nreason about a line as if it had no breadth; because we have a power,\nwhich is the foundation of all the control we can exercise over the\noperations of our minds; the power, when a perception is present to our\nsenses, or a conception to our intellects, of _attending_ to a part only\nof that perception or conception, instead of the whole. But we can not\n_conceive_ a line without breadth; we can form no mental picture of such a\nline: all the lines which we have in our minds are lines possessing\nbreadth. If any one doubts this, we may refer him to his own experience. I\nmuch question if any one who fancies that he can conceive what is called a\nmathematical line, thinks so from the evidence of his consciousness: I\nsuspect it is rather because he supposes that unless such a conception\nwere possible, mathematics could not exist as a science: a supposition\nwhich there will be no difficulty in showing to be entirely groundless.\n\nSince, then, neither in nature, nor in the human mind, do there exist any\nobjects exactly corresponding to the definitions of geometry, while yet\nthat science can not be supposed to be conversant about nonentities;\nnothing remains but to consider geometry as conversant with such lines,\nangles, and figures, as really exist; and the definitions, as they are\ncalled, must be regarded as some of our first and most obvious\ngeneralizations concerning those natural objects. The correctness of those\ngeneralizations, as generalizations, is without a flaw: the equality of\nall the radii of a circle is true of all circles, so far as it is true of\nany one: but it is not exactly true of any circle; it is only nearly true;\nso nearly that no error of any importance in practice will be incurred by\nfeigning it to be exactly true. When we have occasion to extend these\ninductions, or their consequences, to cases in which the error would be\nappreciable\u2014to lines of perceptible breadth or thickness, parallels which\ndeviate sensibly from equidistance, and the like\u2014we correct our\nconclusions, by combining with them a fresh set of propositions relating\nto the aberration; just as we also take in propositions relating to the\nphysical or chemical properties of the material, if those properties\nhappen to introduce any modification into the result; which they easily\nmay, even with respect to figure and magnitude, as in the case, for\ninstance, of expansion by heat. So long, however, as there exists no\npractical necessity for attending to any of the properties of the object\nexcept its geometrical properties, or to any of the natural irregularities\nin those, it is convenient to neglect the consideration of the other\nproperties and of the irregularities, and to reason as if these did not\nexist: accordingly, we formally announce in the definitions, that we\nintend to proceed on this plan. But it is an error to suppose, because we\nresolve to confine our attention to a certain number of the properties of\nan object, that we therefore conceive, or have an idea of, the object,\ndenuded of its other properties. We are thinking, all the time, of\nprecisely such objects as we have seen and touched, and with all the\nproperties which naturally belong to them; but, for scientific\nconvenience, we feign them to be divested of all properties, except those\nwhich are material to our purpose, and in regard to which we design to\nconsider them.\n\nThe peculiar accuracy, supposed to be characteristic of the first\nprinciples of geometry, thus appears to be fictitious. The assertions on\nwhich the reasonings of the science are founded, do not, any more than in\nother sciences, exactly correspond with the fact; but we suppose that they\ndo so, for the sake of tracing the consequences which follow from the\nsupposition. The opinion of Dugald Stewart respecting the foundations of\ngeometry, is, I conceive, substantially correct; that it is built on\nhypotheses; that it owes to this alone the peculiar certainty supposed to\ndistinguish it; and that in any science whatever, by reasoning from a set\nof hypotheses, we may obtain a body of conclusions as certain as those of\ngeometry, that is, as strictly in accordance with the hypotheses, and as\nirresistibly compelling assent, _on condition_ that those hypotheses are\ntrue.(68)\n\nWhen, therefore, it is affirmed that the conclusions of geometry are\nnecessary truths, the necessity consists in reality only in this, that\nthey correctly follow from the suppositions from which they are deduced.\nThose suppositions are so far from being necessary, that they are not even\ntrue; they purposely depart, more or less widely, from the truth. The only\nsense in which necessity can be ascribed to the conclusions of any\nscientific investigation, is that of legitimately following from some\nassumption, which, by the conditions of the inquiry, is not to be\nquestioned. In this relation, of course, the derivative truths of every\ndeductive science must stand to the inductions, or assumptions, on which\nthe science is founded, and which, whether true or untrue, certain or\ndoubtful in themselves, are always supposed certain for the purposes of\nthe particular science. And therefore the conclusions of all deductive\nsciences were said by the ancients to be necessary propositions. We have\nobserved already that to be predicated necessarily was characteristic of\nthe predicable Proprium, and that a proprium was any property of a thing\nwhich could be deduced from its essence, that is, from the properties\nincluded in its definition.\n\n\u00a7 2. The important doctrine of Dugald Stewart, which I have endeavored to\nenforce, has been contested by Dr. Whewell, both in the dissertation\nappended to his excellent _Mechanical Euclid_, and in his elaborate work\non the _Philosophy of the Inductive Sciences_; in which last he also\nreplies to an article in the Edinburgh Review (ascribed to a writer of\ngreat scientific eminence), in which Stewart\u2019s opinion was defended\nagainst his former strictures. The supposed refutation of Stewart consists\nin proving against him (as has also been done in this work) that the\npremises of geometry are not definitions, but assumptions of the real\nexistence of things corresponding to those definitions. This, however, is\ndoing little for Dr. Whewell\u2019s purpose; for it is these very assumptions\nwhich are asserted to be hypotheses, and which he, if he denies that\ngeometry is founded on hypotheses, must show to be absolute truths. All he\ndoes, however, is to observe, that they, at any rate, are not _arbitrary_\nhypotheses; that we should not be at liberty to substitute other\nhypotheses for them; that not only \u201ca definition, to be admissible, must\nnecessarily refer to and agree with some conception which we can\ndistinctly frame in our thoughts,\u201d but that the straight lines, for\ninstance, which we define, must be \u201cthose by which angles are contained,\nthose by which triangles are bounded, those of which parallelism may be\npredicated, and the like.\u201d(69) And this is true; but this has never been\ncontradicted. Those who say that the premises of geometry are hypotheses,\nare not bound to maintain them to be hypotheses which have no relation\nwhatever to fact. Since an hypothesis framed for the purpose of scientific\ninquiry must relate to something which has real existence (for there can\nbe no science respecting nonentities), it follows that any hypothesis we\nmake respecting an object, to facilitate our study of it, must not involve\nany thing which is distinctly false, and repugnant to its real nature: we\nmust not ascribe to the thing any property which it has not; our liberty\nextends only to slightly exaggerating some of those which it has (by\nassuming it to be completely what it really is very nearly), and\nsuppressing others, under the indispensable obligation of restoring them\nwhenever, and in as far as, their presence or absence would make any\nmaterial difference in the truth of our conclusions. Of this nature,\naccordingly, are the first principles involved in the definitions of\ngeometry. That the hypotheses should be of this particular character, is,\nhowever, no further necessary, than inasmuch as no others could enable us\nto deduce conclusions which, with due corrections, would be true of real\nobjects: and in fact, when our aim is only to illustrate truths, and not\nto investigate them, we are not under any such restriction. We might\nsuppose an imaginary animal, and work out by deduction, from the known\nlaws of physiology, its natural history; or an imaginary commonwealth, and\nfrom the elements composing it, might argue what would be its fate. And\nthe conclusions which we might thus draw from purely arbitrary hypotheses,\nmight form a highly useful intellectual exercise: but as they could only\nteach us what _would_ be the properties of objects which do not really\nexist, they would not constitute any addition to our knowledge of nature:\nwhile, on the contrary, if the hypothesis merely divests a real object of\nsome portion of its properties, without clothing it in false ones, the\nconclusions will always express, under known liability to correction,\nactual truth.\n\n\u00a7 3. But though Dr. Whewell has not shaken Stewart\u2019s doctrine as to the\nhypothetical character of that portion of the first principles of geometry\nwhich are involved in the so-called definitions, he has, I conceive,\ngreatly the advantage of Stewart on another important point in the theory\nof geometrical reasoning; the necessity of admitting, among those first\nprinciples, axioms as well as definitions. Some of the axioms of Euclid\nmight, no doubt, be exhibited in the form of definitions, or might be\ndeduced, by reasoning, from propositions similar to what are so called.\nThus, if instead of the axiom, Magnitudes which can be made to coincide\nare equal, we introduce a definition, \u201cEqual magnitudes are those which\nmay be so applied to one another as to coincide;\u201d the three axioms which\nfollow (Magnitudes which are equal to the same are equal to one another\u2014If\nequals are added to equals, the sums are equal\u2014If equals are taken from\nequals, the remainders are equal), may be proved by an imaginary\nsuperposition, resembling that by which the fourth proposition of the\nfirst book of Euclid is demonstrated. But though these and several others\nmay be struck out of the list of first principles, because, though not\nrequiring demonstration, they are susceptible of it; there will be found\nin the list of axioms two or three fundamental truths, not capable of\nbeing demonstrated: among which must be reckoned the proposition that two\nstraight lines can not inclose a space (or its equivalent, Straight lines\nwhich coincide in two points coincide altogether), and some property of\nparallel lines, other than that which constitutes their definition: one of\nthe most suitable for the purpose being that selected by Professor\nPlayfair: \u201cTwo straight lines which intersect each other can not both of\nthem be parallel to a third straight line.\u201d(70)\n\nThe axioms, as well those which are indemonstrable as those which admit of\nbeing demonstrated, differ from that other class of fundamental principles\nwhich are involved in the definitions, in this, that they are true without\nany mixture of hypothesis. That things which are equal to the same thing\nare equal to one another, is as true of the lines and figures in nature,\nas it would be of the imaginary ones assumed in the definitions. In this\nrespect, however, mathematics are only on a par with most other sciences.\nIn almost all sciences there are some general propositions which are\nexactly true, while the greater part are only more or less distant\napproximations to the truth. Thus in mechanics, the first law of motion\n(the continuance of a movement once impressed, until stopped or slackened\nby some resisting force) is true without qualification or error. The\nrotation of the earth in twenty-four hours, of the same length as in our\ntime, has gone on since the first accurate observations, without the\nincrease or diminution of one second in all that period. These are\ninductions which require no fiction to make them be received as accurately\ntrue: but along with them there are others, as for instance the\npropositions respecting the figure of the earth, which are but\napproximations to the truth; and in order to use them for the further\nadvancement of our knowledge, we must feign that they are exactly true,\nthough they really want something of being so.\n\n\u00a7 4. It remains to inquire, what is the ground of our belief in\naxioms\u2014what is the evidence on which they rest? I answer, they are\nexperimental truths; generalizations from observation. The proposition,\nTwo straight lines can not inclose a space\u2014or, in other words, Two\nstraight lines which have once met, do not meet again, but continue to\ndiverge\u2014is an induction from the evidence of our senses.\n\nThis opinion runs counter to a scientific prejudice of long standing and\ngreat strength, and there is probably no proposition enunciated in this\nwork for which a more unfavorable reception is to be expected. It is,\nhowever, no new opinion; and even if it were so, would be entitled to be\njudged, not by its novelty, but by the strength of the arguments by which\nit can be supported. I consider it very fortunate that so eminent a\nchampion of the contrary opinion as Dr. Whewell has found occasion for a\nmost elaborate treatment of the whole theory of axioms, in attempting to\nconstruct the philosophy of the mathematical and physical sciences on the\nbasis of the doctrine against which I now contend. Whoever is anxious that\na discussion should go to the bottom of the subject, must rejoice to see\nthe opposite side of the question worthily represented. If what is said by\nDr. Whewell, in support of an opinion which he has made the foundation of\na systematic work, can be shown not to be conclusive, enough will have\nbeen done, without going elsewhere in quest of stronger arguments and a\nmore powerful adversary.\n\nIt is not necessary to show that the truths which we call axioms are\noriginally _suggested_ by observation, and that we should never have known\nthat two straight lines can not inclose a space if we had never seen a\nstraight line: thus much being admitted by Dr. Whewell, and by all, in\nrecent times, who have taken his view of the subject. But they contend,\nthat it is not experience which _proves_ the axiom; but that its truth is\nperceived _a priori_, by the constitution of the mind itself, from the\nfirst moment when the meaning of the proposition is apprehended; and\nwithout any necessity for verifying it by repeated trials, as is requisite\nin the case of truths really ascertained by observation.\n\nThey can not, however, but allow that the truth of the axiom, Two straight\nlines can not inclose a space, even if evident independently of\nexperience, is also evident from experience. Whether the axiom needs\nconfirmation or not, it receives confirmation in almost every instant of\nour lives; since we can not look at any two straight lines which intersect\none another, without seeing that from that point they continue to diverge\nmore and more. Experimental proof crowds in upon us in such endless\nprofusion, and without one instance in which there can be even a suspicion\nof an exception to the rule, that we should soon have stronger ground for\nbelieving the axiom, even as an experimental truth, than we have for\nalmost any of the general truths which we confessedly learn from the\nevidence of our senses. Independently of _a priori_ evidence, we should\ncertainly believe it with an intensity of conviction far greater than we\naccord to any ordinary physical truth: and this too at a time of life much\nearlier than that from which we date almost any part of our acquired\nknowledge, and much too early to admit of our retaining any recollection\nof the history of our intellectual operations at that period. Where then\nis the necessity for assuming that our recognition of these truths has a\ndifferent origin from the rest of our knowledge, when its existence is\nperfectly accounted for by supposing its origin to be the same? when the\ncauses which produce belief in all other instances, exist in this\ninstance, and in a degree of strength as much superior to what exists in\nother cases, as the intensity of the belief itself is superior? The burden\nof proof lies on the advocates of the contrary opinion: it is for them to\npoint out some fact, inconsistent with the supposition that this part of\nour knowledge of nature is derived from the same sources as every other\npart.(71)\n\nThis, for instance, they would be able to do, if they could prove\nchronologically that we had the conviction (at least practically) so early\nin infancy as to be anterior to those impressions on the senses, upon\nwhich, on the other theory, the conviction is founded. This, however, can\nnot be proved: the point being too far back to be within the reach of\nmemory, and too obscure for external observation. The advocates of the _a\npriori_ theory are obliged to have recourse to other arguments. These are\nreducible to two, which I shall endeavor to state as clearly and as\nforcibly as possible.\n\n\u00a7 5. In the first place it is said, that if our assent to the proposition\nthat two straight lines can not inclose a space, were derived from the\nsenses, we could only be convinced of its truth by actual trial, that is,\nby seeing or feeling the straight lines; whereas, in fact, it is seen to\nbe true by merely thinking of them. That a stone thrown into water goes to\nthe bottom, may be perceived by our senses, but mere thinking of a stone\nthrown into the water would never have led us to that conclusion: not so,\nhowever, with the axioms relating to straight lines: if I could be made to\nconceive what a straight line is, without having seen one, I should at\nonce recognize that two such lines can not inclose a space. Intuition is\n\u201cimaginary looking;\u201d(72) but experience must be real looking: if we see a\nproperty of straight lines to be true by merely fancying ourselves to be\nlooking at them, the ground of our belief can not be the senses, or\nexperience; it must be something mental.\n\nTo this argument it might be added in the case of this particular axiom\n(for the assertion would not be true of all axioms), that the evidence of\nit from actual ocular inspection is not only unnecessary, but\nunattainable. What says the axiom? That two straight lines _can not_\ninclose a space; that after having once intersected, if they are prolonged\nto infinity they do not meet, but continue to diverge from one another.\nHow can this, in any single case, be proved by actual observation? We may\nfollow the lines to any distance we please; but we can not follow them to\ninfinity: for aught our senses can testify, they may, immediately beyond\nthe farthest point to which we have traced them, begin to approach, and at\nlast meet. Unless, therefore, we had some other proof of the impossibility\nthan observation affords us, we should have no ground for believing the\naxiom at all.\n\nTo these arguments, which I trust I can not be accused of understating, a\nsatisfactory answer will, I conceive, be found, if we advert to one of the\ncharacteristic properties of geometrical forms\u2014their capacity of being\npainted in the imagination with a distinctness equal to reality: in other\nwords, the exact resemblance of our ideas of form to the sensations which\nsuggest them. This, in the first place, enables us to make (at least with\na little practice) mental pictures of all possible combinations of lines\nand angles, which resemble the realities quite as well as any which we\ncould make on paper; and in the next place, make those pictures just as\nfit subjects of geometrical experimentation as the realities themselves;\ninasmuch as pictures, if sufficiently accurate, exhibit of course all the\nproperties which would be manifested by the realities at one given\ninstant, and on simple inspection: and in geometry we are concerned only\nwith such properties, and not with that which pictures could not exhibit,\nthe mutual action of bodies one upon another. The foundations of geometry\nwould therefore be laid in direct experience, even if the experiments\n(which in this case consist merely in attentive contemplation) were\npracticed solely upon what we call our ideas, that is, upon the diagrams\nin our minds, and not upon outward objects. For in all systems of\nexperimentation we take some objects to serve as representatives of all\nwhich resemble them; and in the present case the conditions which qualify\na real object to be the representative of its class, are completely\nfulfilled by an object existing only in our fancy. Without denying,\ntherefore, the possibility of satisfying ourselves that two straight lines\ncan not inclose a space, by merely thinking of straight lines without\nactually looking at them; I contend, that we do not believe this truth on\nthe ground of the imaginary intuition simply, but because we know that the\nimaginary lines exactly resemble real ones, and that we may conclude from\nthem to real ones with quite as much certainty as we could conclude from\none real line to another. The conclusion, therefore, is still an induction\nfrom observation. And we should not be authorized to substitute\nobservation of the image in our mind, for observation of the reality, if\nwe had not learned by long-continued experience that the properties of the\nreality are faithfully represented in the image; just as we should be\nscientifically warranted in describing an animal which we have never seen,\nfrom a picture made of it with a daguerreotype; but not until we had\nlearned by ample experience, that observation of such a picture is\nprecisely equivalent to observation of the original.\n\nThese considerations also remove the objection arising from the\nimpossibility of ocularly following the lines in their prolongation to\ninfinity. For though, in order actually to see that two given lines never\nmeet, it would be necessary to follow them to infinity; yet without doing\nso we may know that if they ever do meet, or if, after diverging from one\nanother, they begin again to approach, this must take place not at an\ninfinite, but at a finite distance. Supposing, therefore, such to be the\ncase, we can transport ourselves thither in imagination, and can frame a\nmental image of the appearance which one or both of the lines must present\nat that point, which we may rely on as being precisely similar to the\nreality. Now, whether we fix our contemplation upon this imaginary\npicture, or call to mind the generalizations we have had occasion to make\nfrom former ocular observation, we learn by the evidence of experience,\nthat a line which, after diverging from another straight line, begins to\napproach to it, produces the impression on our senses which we describe by\nthe expression, \u201ca bent line,\u201d not by the expression, \u201ca straight\nline.\u201d(73)\n\nThe preceding argument, which is, to my mind unanswerable, merges,\nhowever, in a still more comprehensive one, which is stated most clearly\nand conclusively by Professor Bain. The psychological reason why axioms,\nand indeed many propositions not ordinarily classed as such, may be\nlearned from the idea only without referring to the fact, is that in the\nprocess of acquiring the idea we have learned the fact. The proposition is\nassented to as soon as the terms are understood, because in learning to\nunderstand the terms we have acquired the experience which proves the\nproposition to be true. \u201cWe required,\u201d says Mr. Bain,(74) \u201cconcrete\nexperience in the first instance, to attain to the notion of whole and\npart; but the notion, once arrived at, implies that the whole is greater.\nIn fact, we could not have the notion without an experience tantamount to\nthis conclusion.... When we have mastered the notion of straightness, we\nhave also mastered that aspect of it expressed by the affirmation that two\nstraight lines can not inclose a space. No intuitive or innate powers or\nperceptions are needed in such case.... We can not have the full meaning\nof Straightness, without going through a comparison of straight objects\namong themselves, and with their opposites, bent or crooked objects. The\nresult of this comparison is, _inter alia_, that straightness in two lines\nis seen to be incompatible with inclosing a space; the inclosure of space\ninvolves crookedness in at least one of the lines.\u201d And similarly, in the\ncase of every first principle,(75) \u201cthe same knowledge that makes it\nunderstood, suffices to verify it.\u201d The more this observation is\nconsidered the more (I am convinced) it will be felt to go to the very\nroot of the controversy.\n\n\u00a7 6. The first of the two arguments in support of the theory that axioms\nare _a priori_ truths, having, I think, been sufficiently answered; I\nproceed to the second, which is usually the most relied on. Axioms (it is\nasserted) are conceived by us not only as true, but as universally and\nnecessarily true. Now, experience can not possibly give to any proposition\nthis character. I may have seen snow a hundred times, and may have seen\nthat it was white, but this can not give me entire assurance even that all\nsnow is white; much less that snow _must_ be white. \u201cHowever many\ninstances we may have observed of the truth of a proposition, there is\nnothing to assure us that the next case shall not be an exception to the\nrule. If it be strictly true that every ruminant animal yet known has\ncloven hoofs, we still can not be sure that some creature will not\nhereafter be discovered which has the first of these attributes, without\nhaving the other.... Experience must always consist of a limited number of\nobservations; and, however numerous these may be, they can show nothing\nwith regard to the infinite number of cases in which the experiment has\nnot been made.\u201d Besides, Axioms are not only universal, they are also\nnecessary. Now \u201cexperience can not offer the smallest ground for the\nnecessity of a proposition. She can observe and record what has happened;\nbut she can not find, in any case, or in any accumulation of cases, any\nreason for what _must_ happen. She may see objects side by side; but she\ncan not see a reason why they must ever be side by side. She finds certain\nevents to occur in succession; but the succession supplies, in its\noccurrence, no reason for its recurrence. She contemplates external\nobjects; but she can not detect any internal bond, which indissolubly\nconnects the future with the past, the possible with the real. To learn a\nproposition by experience, and to see it to be necessarily true, are two\naltogether different processes of thought.\u201d(76) And Dr. Whewell adds, \u201cIf\nany one does not clearly comprehend this distinction of necessary and\ncontingent truths, he will not be able to go along with us in our\nresearches into the foundations of human knowledge; nor, indeed, to pursue\nwith success any speculation on the subject.\u201d(77)\n\nIn the following passage, we are told what the distinction is, the\nnon-recognition of which incurs this denunciation. \u201cNecessary truths are\nthose in which we not only learn that the proposition _is_ true, but see\nthat it _must be_ true; in which the negation of the truth is not only\nfalse, but impossible; in which we can not, even by an effort of\nimagination, or in a supposition, conceive the reverse of that which is\nasserted. That there are such truths can not be doubted. We may take, for\nexample, all relations of number. Three and Two added together make Five.\nWe can not conceive it to be otherwise. We can not, by any freak of\nthought, imagine Three and Two to make Seven.\u201d(78)\n\nAlthough Dr. Whewell has naturally and properly employed a variety of\nphrases to bring his meaning more forcibly home, he would, I presume,\nallow that they are all equivalent; and that what he means by a necessary\ntruth, would be sufficiently defined, a proposition the negation of which\nis not only false but inconceivable. I am unable to find in any of his\nexpressions, turn them what way you will, a meaning beyond this, and I do\nnot believe he would contend that they mean any thing more.\n\nThis, therefore, is the principle asserted: that propositions, the\nnegation of which is inconceivable, or in other words, which we can not\nfigure to ourselves as being false, must rest on evidence of a higher and\nmore cogent description than any which experience can afford.\n\nNow I can not but wonder that so much stress should be laid on the\ncircumstance of inconceivableness, when there is such ample experience to\nshow, that our capacity or incapacity of conceiving a thing has very\nlittle to do with the possibility of the thing in itself; but is in truth\nvery much an affair of accident, and depends on the past history and\nhabits of our own minds. There is no more generally acknowledged fact in\nhuman nature, than the extreme difficulty at first felt in conceiving any\nthing as possible, which is in contradiction to long established and\nfamiliar experience; or even to old familiar habits of thought. And this\ndifficulty is a necessary result of the fundamental laws of the human\nmind. When we have often seen and thought of two things together, and have\nnever in any one instance either seen or thought of them separately, there\nis by the primary law of association an increasing difficulty, which may\nin the end become insuperable, of conceiving the two things apart. This is\nmost of all conspicuous in uneducated persons, who are in general utterly\nunable to separate any two ideas which have once become firmly associated\nin their minds; and if persons of cultivated intellect have any advantage\non the point, it is only because, having seen and heard and read more, and\nbeing more accustomed to exercise their imagination, they have experienced\ntheir sensations and thoughts in more varied combinations, and have been\nprevented from forming many of these inseparable associations. But this\nadvantage has necessarily its limits. The most practiced intellect is not\nexempt from the universal laws of our conceptive faculty. If daily habit\npresents to any one for a long period two facts in combination, and if he\nis not led during that period either by accident or by his voluntary\nmental operations to think of them apart, he will probably in time become\nincapable of doing so even by the strongest effort; and the supposition\nthat the two facts can be separated in nature, will at last present itself\nto his mind with all the characters of an inconceivable phenomenon.(79)\nThere are remarkable instances of this in the history of science:\ninstances in which the most instructed men rejected as impossible, because\ninconceivable, things which their posterity, by earlier practice and\nlonger perseverance in the attempt, found it quite easy to conceive, and\nwhich every body now knows to be true. There was a time when men of the\nmost cultivated intellects, and the most emancipated from the dominion of\nearly prejudice, could not credit the existence of antipodes; were unable\nto conceive, in opposition to old association, the force of gravity acting\nupward instead of downward. The Cartesians long rejected the Newtonian\ndoctrine of the gravitation of all bodies toward one another, on the faith\nof a general proposition, the reverse of which seemed to them to be\ninconceivable\u2014the proposition that a body can not act where it is not. All\nthe cumbrous machinery of imaginary vortices, assumed without the smallest\nparticle of evidence, appeared to these philosophers a more rational mode\nof explaining the heavenly motions, than one which involved what seemed to\nthem so great an absurdity.(80)\n\nAnd they no doubt found it as impossible to conceive that a body should\nact upon the earth from the distance of the sun or moon, as we find it to\nconceive an end to space or time, or two straight lines inclosing a space.\nNewton himself had not been able to realize the conception, or we should\nnot have had his hypothesis of a subtle ether, the occult cause of\ngravitation; and his writings prove, that though he deemed the particular\nnature of the intermediate agency a matter of conjecture, the necessity of\n_some_ such agency appeared to him indubitable.\n\nIf, then, it be so natural to the human mind, even in a high state of\nculture, to be incapable of conceiving, and on that ground to believe\nimpossible, what is afterward not only found to be conceivable but proved\nto be true; what wonder if in cases where the association is still older,\nmore confirmed, and more familiar, and in which nothing ever occurs to\nshake our conviction, or even suggest to us any conception at variance\nwith the association, the acquired incapacity should continue, and be\nmistaken for a natural incapacity? It is true, our experience of the\nvarieties in nature enables us, within certain limits, to conceive other\nvarieties analogous to them. We can conceive the sun or moon falling; for\nthough we never saw them fall, nor ever, perhaps, imagined them falling,\nwe have seen so many other things fall, that we have innumerable familiar\nanalogies to assist the conception; which, after all, we should probably\nhave some difficulty in framing, were we not well accustomed to see the\nsun and moon move (or appear to move), so that we are only called upon to\nconceive a slight change in the direction of motion, a circumstance\nfamiliar to our experience. But when experience affords no model on which\nto shape the new conception, how is it possible for us to form it? How,\nfor example, can we imagine an end to space or time? We never saw any\nobject without something beyond it, nor experienced any feeling without\nsomething following it. When, therefore, we attempt to conceive the last\npoint of space, we have the idea irresistibly raised of other points\nbeyond it. When we try to imagine the last instant of time, we can not\nhelp conceiving another instant after it. Nor is there any necessity to\nassume, as is done by a modern school of metaphysicians, a peculiar\nfundamental law of the mind to account for the feeling of infinity\ninherent in our conceptions of space and time; that apparent infinity is\nsufficiently accounted for by simpler and universally acknowledged laws.\n\nNow, in the case of a geometrical axiom, such, for example, as that two\nstraight lines can not inclose a space\u2014a truth which is testified to us by\nour very earliest impressions of the external world\u2014how is it possible\n(whether those external impressions be or be not the ground of our belief)\nthat the reverse of the proposition _could_ be otherwise than\ninconceivable to us? What analogy have we, what similar order of facts in\nany other branch of our experience, to facilitate to us the conception of\ntwo straight lines inclosing a space? Nor is even this all. I have already\ncalled attention to the peculiar property of our impressions of form, that\nthe ideas or mental images exactly resemble their prototypes, and\nadequately represent them for the purposes of scientific observation. From\nthis, and from the intuitive character of the observation, which in this\ncase reduces itself to simple inspection, we can not so much as call up in\nour imagination two straight lines, in order to attempt to conceive them\ninclosing a space, without by that very act repeating the scientific\nexperiment which establishes the contrary. Will it really be contended\nthat the inconceivableness of the thing, in such circumstances, proves any\nthing against the experimental origin of the conviction? Is it not clear\nthat in whichever mode our belief in the proposition may have originated,\nthe impossibility of our conceiving the negative of it must, on either\nhypothesis, be the same? As, then, Dr. Whewell exhorts those who have any\ndifficulty in recognizing the distinction held by him between necessary\nand contingent truths, to study geometry\u2014a condition which I can assure\nhim I have conscientiously fulfilled\u2014I, in return, with equal confidence,\nexhort those who agree with him, to study the general laws of association;\nbeing convinced that nothing more is requisite than a moderate familiarity\nwith those laws, to dispel the illusion which ascribes a peculiar\nnecessity to our earliest inductions from experience, and measures the\npossibility of things in themselves, by the human capacity of conceiving\nthem.\n\nI hope to be pardoned for adding, that Dr. Whewell himself has both\nconfirmed by his testimony the effect of habitual association in giving to\nan experimental truth the appearance of a necessary one, and afforded a\nstriking instance of that remarkable law in his own person. In his\n_Philosophy of the Inductive Sciences_ he continually asserts, that\npropositions which not only are not self-evident, but which we know to\nhave been discovered gradually, and by great efforts of genius and\npatience, have, when once established, appeared so self-evident that, but\nfor historical proof, it would have been impossible to conceive that they\nhad not been recognized from the first by all persons in a sound state of\ntheir faculties. \u201cWe now despise those who, in the Copernican controversy,\ncould not conceive the apparent motion of the sun on the heliocentric\nhypothesis; or those who, in opposition to Galileo, thought that a uniform\nforce might be that which generated a velocity proportional to the space;\nor those who held there was something absurd in Newton\u2019s doctrine of the\ndifferent refrangibility of differently colored rays; or those who\nimagined that when elements combine, their sensible qualities must be\nmanifest in the compound; or those who were reluctant to give up the\ndistinction of vegetables into herbs, shrubs, and trees. We can not help\nthinking that men must have been singularly dull of comprehension, to find\na difficulty in admitting what is to us so plain and simple. We have a\nlatent persuasion that we in their place should have been wiser and more\nclear-sighted; that we should have taken the right side, and given our\nassent at once to the truth. Yet in reality such a persuasion is a mere\ndelusion. The persons who, in such instances as the above, were on the\nlosing side, were very far, in most cases, from being persons more\nprejudiced, or stupid, or narrow-minded, than the greater part of mankind\nnow are; and the cause for which they fought was far from being a\nmanifestly bad one, till it had been so decided by the result of the\nwar.... So complete has been the victory of truth in most of these\ninstances, that at present we can hardly imagine the struggle to have been\nnecessary. _The very essence of these triumphs is, that they lead us to\nregard the views we reject as not only false but inconceivable._\u201d(81)\n\nThis last proposition is precisely what I contend for; and I ask no more,\nin order to overthrow the whole theory of its author on the nature of the\nevidence of axioms. For what is that theory? That the truth of axioms can\nnot have been learned from experience, because their falsity is\ninconceivable. But Dr. Whewell himself says, that we are continually led,\nby the natural progress of thought, to regard as inconceivable what our\nforefathers not only conceived but believed, nay even (he might have\nadded) were unable to conceive the reverse of. He can not intend to\njustify this mode of thought: he can not mean to say, that we can be right\nin regarding as inconceivable what others have conceived, and as\nself-evident what to others did not appear evident at all. After so\ncomplete an admission that inconceivableness is an accidental thing, not\ninherent in the phenomenon itself, but dependent on the mental history of\nthe person who tries to conceive it, how can he ever call upon us to\nreject a proposition as impossible on no other ground than its\ninconceivableness? Yet he not only does so, but has unintentionally\nafforded some of the most remarkable examples which can be cited of the\nvery illusion which he has himself so clearly pointed out. I select as\nspecimens, his remarks on the evidence of the three laws of motion, and of\nthe atomic theory.\n\nWith respect to the laws of motion, Dr. Whewell says: \u201cNo one can doubt\nthat, in historical fact, these laws were collected from experience. That\nsuch is the case, is no matter of conjecture. We know the time, the\npersons, the circumstances, belonging to each step of each discovery.\u201d(82)\nAfter this testimony, to adduce evidence of the fact would be superfluous.\nAnd not only were these laws by no means intuitively evident, but some of\nthem were originally paradoxes. The first law was especially so. That a\nbody, once in motion, would continue forever to move in the same direction\nwith undiminished velocity unless acted upon by some new force, was a\nproposition which mankind found for a long time the greatest difficulty in\ncrediting. It stood opposed to apparent experience of the most familiar\nkind, which taught that it was the nature of motion to abate gradually,\nand at last terminate of itself. Yet when once the contrary doctrine was\nfirmly established, mathematicians, as Dr. Whewell observes, speedily\nbegan to believe that laws, thus contradictory to first appearances, and\nwhich, even after full proof had been obtained, it had required\ngenerations to render familiar to the minds of the scientific world, were\nunder \u201ca demonstrable necessity, compelling them to be such as they are\nand no other;\u201d and he himself, though not venturing \u201cabsolutely to\npronounce\u201d that _all_ these laws \u201ccan be rigorously traced to an absolute\nnecessity in the nature of things,\u201d(83) does actually so think of the law\njust mentioned; of which he says: \u201cThough the discovery of the first law\nof motion was made, historically speaking, by means of experiment, we have\nnow attained a point of view in which we see that it might have been\ncertainly known to be true, independently of experience.\u201d(84) Can there be\na more striking exemplification than is here afforded, of the effect of\nassociation which we have described? Philosophers, for generations, have\nthe most extraordinary difficulty in putting certain ideas together; they\nat last succeed in doing so; and after a sufficient repetition of the\nprocess, they first fancy a natural bond between the ideas, then\nexperience a growing difficulty, which at last, by the continuation of the\nsame progress, becomes an impossibility, of severing them from one\nanother. If such be the progress of an experimental conviction of which\nthe date is of yesterday, and which is in opposition to first appearances,\nhow must it fare with those which are conformable to appearances familiar\nfrom the first dawn of intelligence, and of the conclusiveness of which,\nfrom the earliest records of human thought, no skeptic has suggested even\na momentary doubt?\n\nThe other instance which I shall quote is a truly astonishing one, and may\nbe called the _reductio ad absurdum_ of the theory of inconceivableness.\nSpeaking of the laws of chemical composition, Dr. Whewell says:(85) \u201cThat\nthey could never have been clearly understood, and therefore never firmly\nestablished, without laborious and exact experiments, is certain; but yet\nwe may venture to say, that being once known, they possess an evidence\nbeyond that of mere experiment. _For how in fact can we conceive\ncombinations, otherwise than as definite in kind and quality?_ If we were\nto suppose each element ready to combine with any other indifferently, and\nindifferently in any quantity, we should have a world in which all would\nbe confusion and indefiniteness. There would be no fixed kinds of bodies.\nSalts, and stones, and ores, would approach to and graduate into each\nother by insensible degrees. Instead of this, we know that the world\nconsists of bodies distinguishable from each other by definite\ndifferences, capable of being classified and named, and of having general\npropositions asserted concerning them. And as _we can not conceive a world\nin which this should not be the case_, it would appear that we can not\nconceive a state of things in which the laws of the combination of\nelements should not be of that definite and measured kind which we have\nabove asserted.\u201d\n\nThat a philosopher of Dr. Whewell\u2019s eminence should gravely assert that we\ncan not conceive a world in which the simple elements should combine in\nother than definite proportions; that by dint of meditating on a\nscientific truth, the original discoverer of which was still living, he\nshould have rendered the association in his own mind between the idea of\ncombination and that of constant proportions so familiar and intimate as\nto be unable to conceive the one fact without the other; is so signal an\ninstance of the mental law for which I am contending, that one word more\nin illustration must be superfluous.\n\nIn the latest and most complete elaboration of his metaphysical system\n(the _Philosophy of Discovery_), as well as in the earlier discourse on\nthe _Fundamental Antithesis of Philosophy_, reprinted as an appendix to\nthat work, Dr. Whewell, while very candidly admitting that his language\nwas open to misconception, disclaims having intended to say that mankind\nin general can _now_ perceive the law of definite proportions in chemical\ncombination to be a necessary truth. All he meant was that philosophical\nchemists in a future generation may possibly see this. \u201cSome truths may be\nseen by intuition, but yet the intuition of them may be a rare and a\ndifficult attainment.\u201d(86) And he explains that the inconceivableness\nwhich, according to his theory, is the test of axioms, \u201cdepends entirely\nupon the clearness of the Ideas which the axioms involve. So long as those\nideas are vague and indistinct, the contrary of an axiom may be assented\nto, though it can not be distinctly conceived. It may be assented to, not\nbecause it is possible, but because we do not see clearly what is\npossible. To a person who is only beginning to think geometrically, there\nmay appear nothing absurd in the assertion that two straight lines may\ninclose a space. And in the same manner, to a person who is only beginning\nto think of mechanical truths, it may not appear to be absurd, that in\nmechanical processes, Reaction should be greater or less than Action; and\nso, again, to a person who has not thought steadily about Substance, it\nmay not appear inconceivable, that by chemical operations, we should\ngenerate new matter, or destroy matter which already exists.\u201d(87)\nNecessary truths, therefore, are not those of which we can not conceive,\nbut \u201cthose of which we can not _distinctly_ conceive, the contrary.\u201d(88)\nSo long as our ideas are indistinct altogether, we do not know what is or\nis not capable of being distinctly conceived; but, by the ever increasing\ndistinctness with which scientific men apprehend the general conceptions\nof science, they in time come to perceive that there are certain laws of\nnature, which, though historically and as a matter of fact they were\nlearned from experience, we can not, now that we know them, distinctly\nconceive to be other than they are.\n\nThe account which I should give of this progress of the scientific mind is\nsomewhat different. After a general law of nature has been ascertained,\nmen\u2019s minds do not at first acquire a complete facility of familiarly\nrepresenting to themselves the phenomena of nature in the character which\nthat law assigns to them. The habit which constitutes the scientific cast\nof mind, that of conceiving facts of all descriptions conformably to the\nlaws which regulate them\u2014phenomena of all descriptions according to the\nrelations which have been ascertained really to exist between them; this\nhabit, in the case of newly-discovered relations, comes only by degrees.\nSo long as it is not thoroughly formed, no necessary character is ascribed\nto the new truth. But in time, the philosopher attains a state of mind in\nwhich his mental picture of nature spontaneously represents to him all the\nphenomena with which the new theory is concerned, in the exact light in\nwhich the theory regards them: all images or conceptions derived from any\nother theory, or from the confused view of the facts which is anterior to\nany theory, having entirely disappeared from his mind. The mode of\nrepresenting facts which results from the theory, has now become, to his\nfaculties, the only natural mode of conceiving them. It is a known truth,\nthat a prolonged habit of arranging phenomena in certain groups, and\nexplaining them by means of certain principles, makes any other\narrangement or explanation of these facts be felt as unnatural: and it may\nat last become as difficult to him to represent the facts to himself in\nany other mode, as it often was, originally, to represent them in that\nmode.\n\nBut, further (if the theory is true, as we are supposing it to be), any\nother mode in which he tries, or in which he was formerly accustomed, to\nrepresent the phenomena, will be seen by him to be inconsistent with the\nfacts that suggested the new theory\u2014facts which now form a part of his\nmental picture of nature. And since a contradiction is always\ninconceivable, his imagination rejects these false theories, and declares\nitself incapable of conceiving them. Their inconceivableness to him does\nnot, however, result from any thing in the theories themselves,\nintrinsically and _a priori_ repugnant to the human faculties; it results\nfrom the repugnance between them and a portion of the facts; which facts\nas long as he did not know, or did not distinctly realize in his mental\nrepresentations, the false theory did not appear other than conceivable;\nit becomes inconceivable, merely from the fact that contradictory elements\ncan not be combined in the same conception. Although, then, his real\nreason for rejecting theories at variance with the true one, is no other\nthan that they clash with his experience, he easily falls into the belief,\nthat he rejects them because they are inconceivable, and that he adopts\nthe true theory because it is self-evident, and does not need the evidence\nof experience at all.\n\nThis I take to be the real and sufficient explanation of the paradoxical\ntruth, on which so much stress is laid by Dr. Whewell, that a\nscientifically cultivated mind is actually, in virtue of that cultivation,\nunable to conceive suppositions which a common man conceives without the\nsmallest difficulty. For there is nothing inconceivable in the\nsuppositions themselves; the impossibility is in combining them with facts\ninconsistent with them, as part of the same mental picture; an obstacle of\ncourse only felt by those who know the facts, and are able to perceive the\ninconsistency. As far as the suppositions themselves are concerned, in the\ncase of many of Dr. Whewell\u2019s necessary truths the negative of the axiom\nis, and probably will be as long as the human race lasts, as easily\nconceivable as the affirmative. There is no axiom (for example) to which\nDr. Whewell ascribes a more thorough character of necessity and\nself-evidence, than that of the indestructibility of matter. That this is\na true law of nature I fully admit; but I imagine there is no human being\nto whom the opposite supposition is inconceivable\u2014who has any difficulty\nin imagining a portion of matter annihilated: inasmuch as its apparent\nannihilation, in no respect distinguishable from real by our unassisted\nsenses, takes place every time that water dries up, or fuel is consumed.\nAgain, the law that bodies combine chemically in definite proportions is\nundeniably true; but few besides Dr. Whewell have reached the point which\nhe seems personally to have arrived at (though he only dares prophesy\nsimilar success to the multitude after the lapse of generations), that of\nbeing unable to conceive a world in which the elements are ready to\ncombine with one another \u201cindifferently in any quantity;\u201d nor is it likely\nthat we shall ever rise to this sublime height of inability, so long as\nall the mechanical mixtures in our planet, whether solid, liquid, or\na\u00ebriform, exhibit to our daily observation the very phenomenon declared to\nbe inconceivable.\n\nAccording to Dr. Whewell, these and similar laws of nature can not be\ndrawn from experience, inasmuch as they are, on the contrary, assumed in\nthe interpretation of experience. Our inability to \u201cadd to or diminish the\nquantity of matter in the world,\u201d is a truth which \u201cneither is nor can be\nderived from experience; for the experiments which we make to verify it\npresuppose its truth.... When men began to use the balance in chemical\nanalysis, they did not prove by trial, but took for granted, as\nself-evident, that the weight of the whole must be found in the aggregate\nweight of the elements.\u201d(89) True, it is assumed; but, I apprehend, no\notherwise than as all experimental inquiry assumes provisionally some\ntheory or hypothesis, which is to be finally held true or not, according\nas the experiments decide. The hypothesis chosen for this purpose will\nnaturally be one which groups together some considerable number of facts\nalready known. The proposition that the material of the world, as\nestimated by weight, is neither increased nor diminished by any of the\nprocesses of nature or art, had many appearances in its favor to begin\nwith. It expressed truly a great number of familiar facts. There were\nother facts which it had the appearance of conflicting with, and which\nmade its truth, as a universal law of nature, at first doubtful. Because\nit was doubtful, experiments were devised to verify it. Men assumed its\ntruth hypothetically, and proceeded to try whether, on more careful\nexamination, the phenomena which apparently pointed to a different\nconclusion, would not be found to be consistent with it. This turned out\nto be the case; and from that time the doctrine took its place as a\nuniversal truth, but as one proved to be such by experience. That the\ntheory itself preceded the proof of its truth\u2014that it had to be conceived\nbefore it could be proved, and in order that it might be proved\u2014does not\nimply that it was self-evident, and did not need proof. Otherwise all the\ntrue theories in the sciences are necessary and self-evident; for no one\nknows better than Dr. Whewell that they all began by being assumed, for\nthe purpose of connecting them by deductions with those facts of\nexperience on which, as evidence, they now confessedly rest.(90)\n\n\n\n\n                               Chapter VI.\n\n\nThe Same Subject Continued.\n\n\n\u00a7 1. In the examination which formed the subject of the last chapter, into\nthe nature of the evidence of those deductive sciences which are commonly\nrepresented to be systems of necessary truth, we have been led to the\nfollowing conclusions. The results of those sciences are indeed necessary,\nin the sense of necessarily following from certain first principles,\ncommonly called axioms and definitions; that is, of being certainly true\nif those axioms and definitions are so; for the word necessity, even in\nthis acceptation of it, means no more than certainty. But their claim to\nthe character of necessity in any sense beyond this, as implying an\nevidence independent of and superior to observation and experience, must\ndepend on the previous establishment of such a claim in favor of the\ndefinitions and axioms themselves. With regard to axioms, we found that,\nconsidered as experimental truths, they rest on superabundant and obvious\nevidence. We inquired, whether, since this is the case, it be imperative\nto suppose any other evidence of those truths than experimental evidence,\nany other origin for our belief of them than an experimental origin. We\ndecided, that the burden of proof lies with those who maintain the\naffirmative, and we examined, at considerable length, such arguments as\nthey have produced. The examination having led to the rejection of those\narguments, we have thought ourselves warranted in concluding that axioms\nare but a class, the most universal class, of inductions from experience;\nthe simplest and easiest cases of generalization from the facts furnished\nto us by our senses or by our internal consciousness.\n\nWhile the axioms of demonstrative sciences thus appeared to be\nexperimental truths, the definitions, as they are incorrectly called, in\nthose sciences, were found by us to be generalizations from experience\nwhich are not even, accurately speaking, truths; being propositions in\nwhich, while we assert of some kind of object, some property or properties\nwhich observation shows to belong to it, we at the same time deny that it\npossesses any other properties, though in truth other properties do in\nevery individual instance accompany, and in almost all instances modify,\nthe property thus exclusively predicated. The denial, therefore, is a mere\nfiction, or supposition, made for the purpose of excluding the\nconsideration of those modifying circumstances, when their influence is of\ntoo trifling amount to be worth considering, or adjourning it, when\nimportant to a more convenient moment.\n\nFrom these considerations it would appear that Deductive or Demonstrative\nSciences are all, without exception, Inductive Sciences; that their\nevidence is that of experience; but that they are also, in virtue of the\npeculiar character of one indispensable portion of the general formul\u00e6\naccording to which their inductions are made, Hypothetical Sciences. Their\nconclusions are only true on certain suppositions, which are, or ought to\nbe, approximations to the truth, but are seldom, if ever, exactly true;\nand to this hypothetical character is to be ascribed the peculiar\ncertainty, which is supposed to be inherent in demonstration.\n\nWhat we have now asserted, however, cannot be received as universally true\nof Deductive or Demonstrative Sciences, until verified by being applied to\nthe most remarkable of all those sciences, that of Numbers; the theory of\nthe Calculus; Arithmetic and Algebra. It is harder to believe of the\ndoctrines of this science than of any other, either that they are not\ntruths _a priori_, but experimental truths, or that their peculiar\ncertainty is owing to their being not absolute but only conditional\ntruths. This, therefore, is a case which merits examination apart; and the\nmore so, because on this subject we have a double set of doctrines to\ncontend with; that of the _a priori_ philosophers on one side; and on the\nother, a theory the most opposite to theirs, which was at one time very\ngenerally received, and is still far from being altogether exploded, among\nmetaphysicians.\n\n\u00a7 2. This theory attempts to solve the difficulty apparently inherent in\nthe case, by representing the propositions of the science of numbers as\nmerely verbal, and its processes as simple transformations of language,\nsubstitutions of one expression for another. The proposition, Two and one\nis equal to three, according to these writers, is not a truth, is not the\nassertion of a really existing fact, but a definition of the word three; a\nstatement that mankind have agreed to use the name three as a sign exactly\nequivalent to two and one; to call by the former name whatever is called\nby the other more clumsy phrase. According to this doctrine, the longest\nprocess in algebra is but a succession of changes in terminology, by which\nequivalent expressions are substituted one for another; a series of\ntranslations of the same fact, from one into another language; though how,\nafter such a series of translations, the fact itself comes out changed (as\nwhen we demonstrate a new geometrical theorem by algebra), they have not\nexplained; and it is a difficulty which is fatal to their theory.\n\nIt must be acknowledged that there are peculiarities in the processes of\narithmetic and algebra which render the theory in question very plausible,\nand have not unnaturally made those sciences the stronghold of Nominalism.\nThe doctrine that we can discover facts, detect the hidden processes of\nnature, by an artful manipulation of language, is so contrary to common\nsense, that a person must have made some advances in philosophy to believe\nit: men fly to so paradoxical a belief to avoid, as they think, some even\ngreater difficulty, which the vulgar do not see. What has led many to\nbelieve that reasoning is a mere verbal process, is, that no other theory\nseemed reconcilable with the nature of the Science of Numbers. For we do\nnot carry any ideas along with us when we use the symbols of arithmetic or\nof algebra. In a geometrical demonstration we have a mental diagram, if\nnot one on paper; AB, AC, are present to our imagination as lines,\nintersecting other lines, forming an angle with one another, and the like;\nbut not so _a_ and _b_. These may represent lines or any other magnitudes,\nbut those magnitudes are never thought of; nothing is realized in our\nimagination but _a_ and _b_. The ideas which, on the particular occasion,\nthey happen to represent, are banished from the mind during every\nintermediate part of the process, between the beginning, when the premises\nare translated from things into signs, and the end, when the conclusion is\ntranslated back from signs into things. Nothing, then, being in the\nreasoner\u2019s mind but the symbols, what can seem more inadmissible than to\ncontend that the reasoning process has to do with any thing more? We seem\nto have come to one of Bacon\u2019s Prerogative Instances; an _experimentum\ncrucis_ on the nature of reasoning itself.\n\nNevertheless, it will appear on consideration, that this apparently so\ndecisive instance is no instance at all; that there is in every step of an\narithmetical or algebraical calculation a real induction, a real inference\nof facts from facts; and that what disguises the induction is simply its\ncomprehensive nature, and the consequent extreme generality of the\nlanguage. All numbers must be numbers of something: there are no such\nthings as numbers in the abstract. _Ten_ must mean ten bodies, or ten\nsounds, or ten beatings of the pulse. But though numbers must be numbers\nof something, they may be numbers of any thing. Propositions, therefore,\nconcerning numbers, have the remarkable peculiarity that they are\npropositions concerning all things whatever; all objects, all existences\nof every kind, known to our experience. All things possess quantity;\nconsist of parts which can be numbered; and in that character possess all\nthe properties which are called properties of numbers. That half of four\nis two, must be true whatever the word four represents, whether four\nhours, four miles, or four pounds weight. We need only conceive a thing\ndivided into four equal parts (and all things may be conceived as so\ndivided), to be able to predicate of it every property of the number four,\nthat is, every arithmetical proposition in which the number four stands on\none side of the equation. Algebra extends the generalization still\nfarther: every number represents that particular number of all things\nwithout distinction, but every algebraical symbol does more, it represents\nall numbers without distinction. As soon as we conceive a thing divided\ninto equal parts, without knowing into what number of parts, we may call\nit _a_ or _x_, and apply to it, without danger of error, every algebraical\nformula in the books. The proposition, 2 (_a_ + _b_)= 2 _a_ + 2 _b_, is a\ntruth co-extensive with all nature. Since then algebraical truths are true\nof all things whatever, and not, like those of geometry, true of lines\nonly or of angles only, it is no wonder that the symbols should not excite\nin our minds ideas of any things in particular. When we demonstrate the\nforty-seventh proposition of Euclid, it is not necessary that the words\nshould raise in us an image of all right-angled triangles, but only of\nsome one right-angled triangle: so in algebra we need not, under the\nsymbol _a_, picture to ourselves all things whatever, but only some one\nthing; why not, then, the letter itself? The mere written characters, _a_,\n_b_, _x_, _y_, _z_, serve as well for representatives of Things in\ngeneral, as any more complex and apparently more concrete conception. That\nwe are conscious of them, however, in their character of things, and not\nof mere signs, is evident from the fact that our whole process of\nreasoning is carried on by predicating of them the properties of things.\nIn resolving an algebraic equation, by what rules do we proceed? By\napplying at each step to _a_, _b_, and _x_, the proposition that equals\nadded to equals make equals; that equals taken from equals leave equals;\nand other propositions founded on these two. These are not properties of\nlanguage, or of signs as such, but of magnitudes, which is as much as to\nsay, of all things. The inferences, therefore, which are successively\ndrawn, are inferences concerning things, not symbols; though as any Things\nwhatever will serve the turn, there is no necessity for keeping the idea\nof the Thing at all distinct, and consequently the process of thought may,\nin this case, be allowed without danger to do what all processes of\nthought, when they have been performed often, will do if permitted,\nnamely, to become entirely mechanical. Hence the general language of\nalgebra comes to be used familiarly without exciting ideas, as all other\ngeneral language is prone to do from mere habit, though in no other case\nthan this can it be done with complete safety. But when we look back to\nsee from whence the probative force of the process is derived, we find\nthat at every single step, unless we suppose ourselves to be thinking and\ntalking of the things, and not the mere symbols, the evidence fails.\n\nThere is another circumstance, which, still more than that which we have\nnow mentioned, gives plausibility to the notion that the propositions of\narithmetic and algebra are merely verbal. That is, that when considered as\npropositions respecting Things, they all have the appearance of being\nidentical propositions. The assertion, Two and one is equal to three,\nconsidered as an assertion respecting objects, as for instance, \u201cTwo\npebbles and one pebble are equal to three pebbles,\u201d does not affirm\nequality between two collections of pebbles, but absolute identity. It\naffirms that if we put one pebble to two pebbles, those very pebbles are\nthree. The objects, therefore, being the very same, and the mere assertion\nthat \u201cobjects are themselves\u201d being insignificant, it seems but natural to\nconsider the proposition, Two and one is equal to three, as asserting mere\nidentity of signification between the two names.\n\nThis, however, though it looks so plausible, will not bear examination.\nThe expression \u201ctwo pebbles and one pebble,\u201d and the expression \u201cthree\npebbles,\u201d stand indeed for the same aggregation of objects, but they by no\nmeans stand for the same physical fact. They are names of the same\nobjects, but of those objects in two different states: though they\n_de_note the same things, their _con_notation is different. Three pebbles\nin two separate parcels, and three pebbles in one parcel, do not make the\nsame impression on our senses; and the assertion that the very same\npebbles may by an alteration of place and arrangement be made to produce\neither the one set of sensations or the other, though a very familiar\nproposition, is not an identical one. It is a truth known to us by early\nand constant experience: an inductive truth; and such truths are the\nfoundation of the science of Number. The fundamental truths of that\nscience all rest on the evidence of sense; they are proved by showing to\nour eyes and our fingers that any given number of objects\u2014ten balls, for\nexample\u2014may by separation and re-arrangement exhibit to our senses all the\ndifferent sets of numbers the sums of which is equal to ten. All the\nimproved methods of teaching arithmetic to children proceed on a knowledge\nof this fact. All who wish to carry the child\u2019s _mind_ along with them in\nlearning arithmetic; all who wish to teach numbers, and not mere\nciphers\u2014now teach it through the evidence of the senses, in the manner we\nhave described.\n\nWe may, if we please, call the proposition, \u201cThree is two and one,\u201d a\ndefinition of the number three, and assert that arithmetic, as it has been\nasserted that geometry, is a science founded on definitions. But they are\ndefinitions in the geometrical sense, not the logical; asserting not the\nmeaning of a term only, but along with it an observed matter of fact. The\nproposition, \u201cA circle is a figure bounded by a line which has all its\npoints equally distant from a point within it,\u201d is called the definition\nof a circle; but the proposition from which so many consequences follow,\nand which is really a first principle in geometry, is, that figures\nanswering to this description exist. And thus we may call \u201cThree is two\nand one\u201d a definition of three; but the calculations which depend on that\nproposition do not follow from the definition itself, but from an\narithmetical theorem presupposed in it, namely, that collections of\nobjects exist, which while they impress the senses thus, [Symbol: three\ncircles, two above one], may be separated into two parts, thus, [Symbol:\ntwo circles, a space, and a third circle]. This proposition being granted,\nwe term all such parcels Threes, after which the enunciation of the\nabove-mentioned physical fact will serve also for a definition of the word\nThree.\n\nThe Science of Number is thus no exception to the conclusion we previously\narrived at, that the processes even of deductive sciences are altogether\ninductive, and that their first principles are generalizations from\nexperience. It remains to be examined whether this science resembles\ngeometry in the further circumstance, that some of its inductions are not\nexactly true; and that the peculiar certainty ascribed to it, on account\nof which its propositions are called Necessary Truths, is fictitious and\nhypothetical, being true in no other sense than that those propositions\nlegitimately follow from the hypothesis of the truth of premises which are\navowedly mere approximations to truth.\n\n\u00a7 3. The inductions of arithmetic are of two sorts: first, those which we\nhave just expounded, such as One and one are two, Two and one are three,\netc., which may be called the definitions of the various numbers, in the\nimproper or geometrical sense of the word Definition; and secondly, the\ntwo following axioms: The sums of equals are equal, The differences of\nequals are equal. These two are sufficient; for the corresponding\npropositions respecting unequals may be proved from these by a _reductio\nad absurdum_.\n\nThese axioms, and likewise the so-called definitions, are, as has already\nbeen said, results of induction; true of all objects whatever, and, as it\nmay seem, exactly true, without the hypothetical assumption of unqualified\ntruth where an approximation to it is all that exists. The conclusions,\ntherefore, it will naturally be inferred, are exactly true, and the\nscience of number is an exception to other demonstrative sciences in this,\nthat the categorical certainty which is predicable of its demonstrations\nis independent of all hypothesis.\n\nOn more accurate investigation, however, it will be found that, even in\nthis case, there is one hypothetical element in the ratiocination. In all\npropositions concerning numbers, a condition is implied, without which\nnone of them would be true; and that condition is an assumption which may\nbe false. The condition is, that 1=1; that all the numbers are numbers of\nthe same or of equal units. Let this be doubtful, and not one of the\npropositions of arithmetic will hold true. How can we know that one pound\nand one pound make two pounds, if one of the pounds may be troy, and the\nother avoirdupois? They may not make two pounds of either, or of any\nweight. How can we know that a forty-horse power is always equal to\nitself, unless we assume that all horses are of equal strength? It is\ncertain that 1 is always equal in _number_ to 1; and where the mere number\nof objects, or of the parts of an object, without supposing them to be\nequivalent in any other respect, is all that is material, the conclusions\nof arithmetic, so far as they go to that alone, are true without mixture\nof hypothesis. There are such cases in statistics; as, for instance, an\ninquiry into the amount of the population of any country. It is\nindifferent to that inquiry whether they are grown people or children,\nstrong or weak, tall or short; the only thing we want to ascertain is\ntheir number. But whenever, from equality or inequality of number,\nequality or inequality in any other respect is to be inferred, arithmetic\ncarried into such inquiries becomes as hypothetical a science as geometry.\nAll units must be assumed to be equal in that other respect; and this is\nnever accurately true, for one actual pound weight is not exactly equal to\nanother, nor one measured mile\u2019s length to another; a nicer balance, or\nmore accurate measuring instruments, would always detect some difference.\n\n\n    What is commonly called mathematical certainty, therefore, which\n    comprises the twofold conception of unconditional truth and\n    perfect accuracy, is not an attribute of all mathematical truths,\n    but of those only which relate to pure Number, as distinguished\n    from Quantity in the more enlarged sense; and only so long as we\n    abstain from supposing that the numbers are a precise index to\n    actual quantities. The certainty usually ascribed to the\n    conclusions of geometry, and even to those of mechanics, is\n    nothing whatever but certainty of inference. We can have full\n    assurance of particular results under particular suppositions, but\n    we can not have the same assurance that these suppositions are\n    accurately true, nor that they include all the data which may\n    exercise an influence over the result in any given instance.\n\n\n\u00a7 4. It appears, therefore, that the method of all Deductive Sciences is\nhypothetical. They proceed by tracing the consequences of certain\nassumptions; leaving for separate consideration whether the assumptions\nare true or not, and if not exactly true, whether they are a sufficiently\nnear approximation to the truth. The reason is obvious. Since it is only\nin questions of pure number that the assumptions are exactly true, and\neven there only so long as no conclusions except purely numerical ones are\nto be founded on them; it must, in all other cases of deductive\ninvestigation, form a part of the inquiry, to determine how much the\nassumptions want of being exactly true in the case in hand. This is\ngenerally a matter of observation, to be repeated in every fresh case; or\nif it has to be settled by argument instead of observation, may require in\nevery different case different evidence, and present every degree of\ndifficulty, from the lowest to the highest. But the other part of the\nprocess\u2014namely, to determine what else may be concluded if we find, and in\nproportion as we find, the assumptions to be true\u2014may be performed once\nfor all, and the results held ready to be employed as the occasions turn\nup for use. We thus do all beforehand that can be so done, and leave the\nleast possible work to be performed when cases arise and press for a\ndecision. This inquiry into the inferences which can be drawn from\nassumptions, is what properly constitutes Demonstrative Science.\n\nIt is of course quite as practicable to arrive at new conclusions from\nfacts assumed, as from facts observed; from fictitious, as from real,\ninductions. Deduction, as we have seen, consists of a series of inferences\nin this form\u2014_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_\nis a mark of _d_, which last may be a truth inaccessible to direct\nobservation. In like manner it is allowable to say, _suppose_ that a were\na mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a mark of _d_,\nwhich last conclusion was not thought of by those who laid down the\npremises. A system of propositions as complicated as geometry might be\ndeduced from assumptions which are false; as was done by Ptolemy,\nDescartes, and others, in their attempts to explain synthetically the\nphenomena of the solar system on the supposition that the apparent motions\nof the heavenly bodies were the real motions, or were produced in some way\nmore or less different from the true one. Sometimes the same thing is\nknowingly done, for the purpose of showing the falsity of the assumption;\nwhich is called a _reductio ad absurdum_. In such cases, the reasoning is\nas follows: _a_ is a mark of _b_, and _b_ of _c_; now if c were also a\nmark of _d, a_ would be a mark of _d_; but _d_ is known to be a mark of\nthe absence of _a_; consequently _a_ would be a mark of its own absence,\nwhich is a contradiction; therefore _c_ is not a mark of _d_.\n\n\u00a7 5. It has even been held by some writers, that all ratiocination rests\nin the last resort on a _reductio ad absurdum_; since the way to enforce\nassent to it, in case of obscurity, would be to show that if the\nconclusion be denied we must deny some one at least of the premises,\nwhich, as they are all supposed true, would be a contradiction. And in\naccordance with this, many have thought that the peculiar nature of the\nevidence of ratiocination consisted in the impossibility of admitting the\npremises and rejecting the conclusion without a contradiction in terms.\nThis theory, however, is inadmissible as an explanation of the grounds on\nwhich ratiocination itself rests. If any one denies the conclusion\nnotwithstanding his admission of the premises, he is not involved in any\ndirect and express contradiction until he is compelled to deny some\npremise; and he can only be forced to do this by a _reductio ad absurdum_,\nthat is, by another ratiocination: now, if he denies the validity of the\nreasoning process itself, he can no more be forced to assent to the second\nsyllogism than to the first. In truth, therefore, no one is ever forced to\na contradiction in terms: he can only be forced to a contradiction (or\nrather an infringement) of the fundamental maxim of ratiocination, namely,\nthat whatever has a mark, has what it is a mark of; or (in the case of\nuniversal propositions), that whatever is a mark of any thing, is a mark\nof whatever else that thing is a mark of. For in the case of every correct\nargument, as soon as thrown into the syllogistic form, it is evident\nwithout the aid of any other syllogism, that he who, admitting the\npremises, fails to draw the conclusion, does not conform to the above\naxiom.\n\nWe have now proceeded as far in the theory of Deduction as we can advance\nin the present stage of our inquiry. Any further insight into the subject\nrequires that the foundation shall have been laid of the philosophic\ntheory of Induction itself; in which theory that of Deduction, as a mode\nof Induction, which we have now shown it to be, will assume spontaneously\nthe place which belongs to it, and will receive its share of whatever\nlight may be thrown upon the great intellectual operation of which it\nforms so important a part.\n\n\n\n\n                               Chapter VII.\n\n\nExamination Of Some Opinions Opposed To The Preceding Doctrines.\n\n\n\u00a7 1. Polemical discussion is foreign to the plan of this work. But an\nopinion which stands in need of much illustration, can often receive it\nmost effectually, and least tediously, in the form of a defense against\nobjections. And on subjects concerning which speculative minds are still\ndivided, a writer does but half his duty by stating his own doctrine, if\nhe does not also examine, and to the best of his ability judge, those of\nother thinkers.\n\nIn the dissertation which Mr. Herbert Spencer has prefixed to his, in many\nrespects, highly philosophical treatise on the Mind,(91) he criticises\nsome of the doctrines of the two preceding chapters, and propounds a\ntheory of his own on the subject of first principles. Mr. Spencer agrees\nwith me in considering axioms to be \u201csimply our earliest inductions from\nexperience.\u201d But he differs from me \u201cwidely as to the worth of the test of\ninconceivableness.\u201d He thinks that it is the ultimate test of all beliefs.\nHe arrives at this conclusion by two steps. First, we never can have any\nstronger ground for believing any thing, than that the belief of it\n\u201cinvariably exists.\u201d Whenever any fact or proposition is invariably\nbelieved; that is, if I understand Mr. Spencer rightly, believed by all\npersons, and by one\u2019s self at all times; it is entitled to be received as\none of the primitive truths, or original premises of our knowledge.\nSecondly, the criterion by which we decide whether any thing is invariably\nbelieved to be true, is our inability to conceive it as false. \u201cThe\ninconceivability of its negation is the test by which we ascertain whether\na given belief invariably exists or not.\u201d \u201cFor our primary beliefs, the\nfact of invariable existence, tested by an abortive effort to cause their\nnon-existence, is the only reason assignable.\u201d He thinks this the sole\nground of our belief in our own sensations. If I believe that I feel cold,\nI only receive this as true because I can not conceive that I am not\nfeeling cold. \u201cWhile the proposition remains true, the negation of it\nremains inconceivable.\u201d There are numerous other beliefs which Mr. Spencer\nconsiders to rest on the same basis; being chiefly those, or a part of\nthose, which the metaphysicians of the Reid and Stewart school consider as\ntruths of immediate intuition. That there exists a material world; that\nthis is the very world which we directly and immediately perceive, and not\nmerely the hidden cause of our perceptions; that Space, Time, Force,\nExtension, Figure, are not modes of our consciousness, but objective\nrealities; are regarded by Mr. Spencer as truths known by the\ninconceivableness of their negatives. We can not, he says, by any effort,\nconceive these objects of thought as mere states of our mind; as not\nhaving an existence external to us. Their real existence is, therefore, as\ncertain as our sensations themselves. The truths which are the subject of\ndirect knowledge, being, according to this doctrine, known to be truths\nonly by the inconceivability of their negation; and the truths which are\nnot the object of direct knowledge, being known as inferences from those\nwhich are; and those inferences being believed to follow from the\npremises, only because we can not conceive them not to follow;\ninconceivability is thus the ultimate ground of all assured beliefs.\n\nThus far, there is no very wide difference between Mr. Spencer\u2019s doctrine\nand the ordinary one of philosophers of the intuitive school, from\nDescartes to Dr. Whewell; but at this point Mr. Spencer diverges from\nthem. For he does not, like them, set up the test of inconceivability as\ninfallible. On the contrary, he holds that it may be fallacious, not from\nany fault in the test itself, but because \u201cmen have mistaken for\ninconceivable things, some things which were not inconceivable.\u201d And he\nhimself, in this very book, denies not a few propositions usually regarded\nas among the most marked examples of truths whose negations are\ninconceivable. But occasional failure, he says, is incident to all tests.\nIf such failure vitiates \u201cthe test of inconceivableness,\u201d it \u201cmust\nsimilarly vitiate all tests whatever. We consider an inference logically\ndrawn from established premises to be true. Yet in millions of cases men\nhave been wrong in the inferences they have thought thus drawn. Do we\ntherefore argue that it is absurd to consider an inference true on no\nother ground than that it is logically drawn from established premises?\nNo: we say that though men may have taken for logical inferences,\ninferences that were not logical, there nevertheless _are_ logical\ninferences, and that we are justified in assuming the truth of what seem\nto us such, until better instructed. Similarly, though men may have\nthought some things inconceivable which were not so, there may still be\ninconceivable things; and the inability to conceive the negation of a\nthing, may still be our best warrant for believing it.... Though\noccasionally it may prove an imperfect test, yet, as our most certain\nbeliefs are capable of no better, to doubt any one belief because we have\nno higher guarantee for it, is really to doubt all beliefs.\u201d Mr. Spencer\u2019s\ndoctrine, therefore, does not erect the curable, but only the incurable\nlimitations of the human conceptive faculty, into laws of the outward\nuniverse.\n\n\u00a7 2. The doctrine, that \u201ca belief which is proved by the inconceivableness\nof its negation to invariably exist, is true,\u201d Mr. Spencer enforces by two\narguments, one of which may be distinguished as positive, and the other as\nnegative.\n\nThe positive argument is, that every such belief represents the aggregate\nof all past experience. \u201cConceding the entire truth of\u201d the \u201cposition,\nthat during any phase of human progress, the ability or inability to form\na specific conception wholly depends on the experiences men have had; and\nthat, by a widening of their experiences, they may, by and by, be enabled\nto conceive things before inconceivable to them, it may still be argued\nthat as, at any time, the best warrant men can have for a belief is the\nperfect agreement of all pre-existing experience in support of it, it\nfollows that, at any time, the inconceivableness of its negation is the\ndeepest test any belief admits of.... Objective facts are ever impressing\nthemselves upon us; our experience is a register of these objective facts;\nand the inconceivableness of a thing implies that it is wholly at variance\nwith the register. Even were this all, it is not clear how, if every truth\nis primarily inductive, any better test of truth could exist. But it must\nbe remembered that while many of these facts, impressing themselves upon\nus, are occasional; while others again are very general; some are\nuniversal and unchanging. These universal and unchanging facts are, by the\nhypothesis, certain to establish beliefs of which the negations are\ninconceivable; while the others are not certain to do this; and if they\ndo, subsequent facts will reverse their action. Hence if, after an immense\naccumulation of experiences, there remain beliefs of which the negations\nare still inconceivable, most, if not all of them, must correspond to\nuniversal objective facts. If there be ... certain absolute uniformities\nin nature; if these uniformities produce, as they must, absolute\nuniformities in our experience; and if ... these absolute uniformities in\nour experience disable us from conceiving the negations of them; then\nanswering to each absolute uniformity in nature which we can cognize,\nthere must exist in us a belief of which the negation is inconceivable,\nand which is absolutely true. In this wide range of cases subjective\ninconceivableness must correspond to objective impossibility. Further\nexperience will produce correspondence where it may not yet exist; and we\nmay expect the correspondence to become ultimately complete. In nearly all\ncases this test of inconceivableness must be valid now\u201d (I wish I could\nthink we were so nearly arrived at omniscience); \u201cand where it is not, it\nstill expresses the net result of our experience up to the present time;\nwhich is the most that any test can do.\u201d\n\nTo this I answer, first, that it is by no means true that the\ninconceivability, by us, of the negative of a proposition proves all, or\neven any, \u201cpre-existing experience\u201d to be in favor of the affirmative.\nThere may have been no such pre-existing experiences, but only a mistaken\nsupposition of experience. How did the inconceivability of antipodes prove\nthat experience had given any testimony against their possibility? How did\nthe incapacity men felt of conceiving sunset otherwise than as a motion of\nthe sun, represent any \u201cnet result\u201d of experience in support of its being\nthe sun and not the earth that moves? It is not experience that is\nrepresented, it is only a superficial semblance of experience. The only\nthing proved with regard to real experience, is the negative fact, that\nmen have _not had_ it of the kind which would have made the inconceivable\nproposition conceivable.\n\nNext: Even if it were true that inconceivableness represents the net\nresult of all past experience, why should we stop at the representative\nwhen we can get at the thing represented? If our incapacity to conceive\nthe negation of a given supposition is proof of its truth, because proving\nthat our experience has hitherto been uniform in its favor, the real\nevidence for the supposition is not the inconceivableness, but the\nuniformity of experience. Now this, which is the substantial and only\nproof, is directly accessible. We are not obliged to presume it from an\nincidental consequence. If all past experience is in favor of a belief,\nlet this be stated, and the belief openly rested on that ground: after\nwhich the question arises, what that fact may be worth as evidence of its\ntruth? For uniformity of experience is evidence in very different degrees:\nin some cases it is strong evidence, in others weak, in others it scarcely\namounts to evidence at all. That all metals sink in water, was a uniform\nexperience, from the origin of the human race to the discovery of\npotassium in the present century by Sir Humphry Davy. That all swans are\nwhite, was a uniform experience down to the discovery of Australia. In the\nfew cases in which uniformity of experience does amount to the strongest\npossible proof, as with such propositions as these, Two straight lines can\nnot inclose a space, Every event has a cause, it is not because their\nnegations are inconceivable, which is not always the fact; but because the\nexperience, which has been thus uniform, pervades all nature. It will be\nshown in the following Book that none of the conclusions either of\ninduction or of deduction can be considered certain, except as far as\ntheir truth is shown to be inseparably bound up with truths of this class.\n\nI maintain then, first, that uniformity of past experience is very far\nfrom being universally a criterion of truth. But secondly,\ninconceivableness is still further from being a test even of that test.\nUniformity of contrary experience is only one of many causes of\ninconceivability. Tradition handed down from a period of more limited\nknowledge, is one of the commonest. The mere familiarity of one mode of\nproduction of a phenomenon often suffices to make every other mode appear\ninconceivable. Whatever connects two ideas by a strong association may,\nand continually does, render their separation in thought impossible; as\nMr. Spencer, in other parts of his speculations, frequently recognizes. It\nwas not for want of experience that the Cartesians were unable to conceive\nthat one body could produce motion in another without contact. They had as\nmuch experience of other modes of producing motion as they had of that\nmode. The planets had revolved, and heavy bodies had fallen, every hour of\ntheir lives. But they fancied these phenomena to be produced by a hidden\nmachinery which they did not see, because without it they were unable to\nconceive what they did see. The inconceivableness, instead of representing\ntheir experience, dominated and overrode their experience. Without\ndwelling further on what I have termed the positive argument of Mr.\nSpencer in support of his criterion of truth, I pass to his negative\nargument, on which he lays more stress.\n\n\u00a7 3. The negative argument is, that, whether inconceivability be good\nevidence or bad, no stronger evidence is to be obtained. That what is\ninconceivable can not be true, is postulated in every act of thought. It\nis the foundation of all our original premises. Still more it is assumed\nin all conclusions from those premises. The invariability of belief,\ntested by the inconceivableness of its negation, \u201cis our sole warrant for\nevery demonstration. Logic is simply a systematization of the process by\nwhich we indirectly obtain this warrant for beliefs that do not directly\npossess it. To gain the strongest conviction possible respecting any\ncomplex fact, we either analytically descend from it by successive steps,\neach of which we unconsciously test by the inconceivableness of its\nnegation, until we reach some axiom or truth which we have similarly\ntested; or we synthetically ascend from such axiom or truth by such steps.\nIn either case we connect some isolated belief, with a belief which\ninvariably exists, by a series of intermediate beliefs which invariably\nexist.\u201d The following passage sums up the theory: \u201cWhen we perceive that\nthe negation of the belief is inconceivable, we have all possible warrant\nfor asserting the invariability of its existence: and in asserting this,\nwe express alike our logical justification of it, and the inexorable\nnecessity we are under of holding it.... We have seen that this is the\nassumption on which every conclusion whatever ultimately rests. We have no\nother guarantee for the reality of consciousness, of sensations, of\npersonal existence; we have no other guarantee for any axiom; we have no\nother guarantee for any step in a demonstration. Hence, as being taken for\ngranted in every act of the understanding, it must be regarded as the\nUniversal Postulate.\u201d But as this postulate, which we are under an\n\u201cinexorable necessity\u201d of holding true, is sometimes false; as \u201cbeliefs\nthat once were shown by the inconceivableness of their negations to\ninvariably exist, have since been found untrue,\u201d and as \u201cbeliefs that now\npossess this character may some day share the same fate;\u201d the canon of\nbelief laid down by Mr. Spencer is, that \u201cthe most certain conclusion\u201d is\nthat \u201cwhich involves the postulate the fewest times.\u201d Reasoning,\ntherefore, never ought to prevail against one of the immediate beliefs\n(the belief in Matter, in the outward reality of Extension, Space, and the\nlike), because each of these involves the postulate only once; while an\nargument, besides involving it in the premises, involves it again in every\nstep of the ratiocination, no one of the successive acts of inference\nbeing recognized as valid except because we can not conceive the\nconclusion not to follow from the premises.\n\nIt will be convenient to take the last part of this argument first. In\nevery reasoning, according to Mr. Spencer, the assumption of the postulate\nis renewed at every step. At each inference we judge that the conclusion\nfollows from the premises, our sole warrant for that judgment being that\nwe can not conceive it not to follow. Consequently if the postulate is\nfallible, the conclusions of reasoning are more vitiated by that\nuncertainty than direct intuitions; and the disproportion is greater, the\nmore numerous the steps of the argument.\n\nTo test this doctrine, let us first suppose an argument consisting only of\na single step, which would be represented by one syllogism. This argument\ndoes rest on an assumption, and we have seen in the preceding chapters\nwhat the assumption is. It is, that whatever has a mark, has what it is a\nmark of. The evidence of this axiom I shall not consider at present;(92)\nlet us suppose it (with Mr. Spencer) to be the inconceivableness of its\nreverse.\n\nLet us now add a second step to the argument: we require, what? Another\nassumption? No: the same assumption a second time; and so on to a third,\nand a fourth. I confess I do not see how, on Mr. Spencer\u2019s own principles,\nthe repetition of the assumption at all weakens the force of the argument.\nIf it were necessary the second time to assume some other axiom, the\nargument would no doubt be weakened, since it would be necessary to its\nvalidity that both axioms should be true, and it might happen that one was\ntrue and not the other: making two chances of error instead of one. But\nsince it is the _same_ axiom, if it is true once it is true every time;\nand if the argument, being of a hundred links, assumed the axiom a hundred\ntimes, these hundred assumptions would make but one chance of error among\nthem all. It is satisfactory that we are not obliged to suppose the\ndeductions of pure mathematics to be among the most uncertain of\nargumentative processes, which on Mr. Spencer\u2019s theory they could hardly\nfail to be, since they are the longest. But the number of steps in an\nargument does not subtract from its reliableness, if no new _premises_, of\nan uncertain character, are taken up by the way.(93)\n\nTo speak next of the premises. Our assurance of their truth, whether they\nbe generalities or individual facts, is grounded, in Mr. Spencer\u2019s\nopinion, on the inconceivableness of their being false. It is necessary to\nadvert to a double meaning of the word inconceivable, which Mr. Spencer is\naware of, and would sincerely disclaim founding an argument upon, but from\nwhich his case derives no little advantage notwithstanding. By\ninconceivableness is sometimes meant, inability to form or get rid of an\n_idea_; sometimes, inability to form or get rid of a _belief_. The former\nmeaning is the most conformable to the analogy of language; for a\nconception always means an idea, and never a belief. The wrong meaning of\n\u201cinconceivable\u201d is, however, fully as frequent in philosophical discussion\nas the right meaning, and the intuitive school of metaphysicians could not\nwell do without either. To illustrate the difference, we will take two\ncontrasted examples. The early physical speculators considered antipodes\nincredible, because inconceivable. But antipodes were not inconceivable in\nthe primitive sense of the word. An idea of them could be formed without\ndifficulty: they could be completely pictured to the mental eye. What was\ndifficult, and, as it then seemed, impossible, was to apprehend them as\nbelievable. The idea could be put together, of men sticking on by their\nfeet to the under side of the earth; but the belief _would_ follow, that\nthey must fall off. Antipodes were not unimaginable, but they were\nunbelievable.\n\nOn the other hand, when I endeavor to conceive an end to extension, the\ntwo ideas refuse to come together. When I attempt to form a conception of\nthe last point of space, I can not help figuring to myself a vast space\nbeyond that last point. The combination is, under the conditions of our\nexperience, unimaginable. This double meaning of inconceivable it is very\nimportant to bear in mind, for the argument from inconceivableness almost\nalways turns on the alternate substitution of each of those meanings for\nthe other.\n\nIn which of these two senses does Mr. Spencer employ the term, when he\nmakes it a test of the truth of a proposition that its negation is\ninconceivable? Until Mr. Spencer expressly stated the contrary, I inferred\nfrom the course of his argument, that he meant unbelievable. He has,\nhowever, in a paper published in the fifth number of the _Fortnightly\nReview_, disclaimed this meaning, and declared that by an inconceivable\nproposition he means, now and always, \u201cone of which the terms can not, by\nany effort, be brought before consciousness in that relation which the\nproposition asserts between them\u2014a proposition of which the subject and\npredicate offer an insurmountable resistance to union in thought.\u201d We now,\ntherefore, know positively that Mr. Spencer always endeavors to use the\nword inconceivable in this, its proper, sense: but it may yet be\nquestioned whether his endeavor is always successful; whether the other,\nand popular use of the word, does not sometimes creep in with its\nassociations, and prevent him from maintaining a clear separation between\nthe two. When, for example, he says, that when I feel cold, I can not\nconceive that I am not feeling cold, this expression can not be translated\ninto \u201cI can not conceive myself not feeling cold,\u201d for it is evident that\nI can: the word conceive, therefore, is here used to express the\nrecognition of a matter of fact\u2014the perception of truth or falsehood;\nwhich I apprehend to be exactly the meaning of an act of belief, as\ndistinguished from simple conception. Again, Mr. Spencer calls the attempt\nto conceive something which is inconceivable \u201can abortive effort to cause\nthe non-existence,\u201d not of a conception or mental representation, but of a\nbelief. There is need, therefore, to revise a considerable part of Mr.\nSpencer\u2019s language, if it is to be kept always consistent with his\ndefinition of inconceivability. But in truth the point is of little\nimportance; since inconceivability, in Mr. Spencer\u2019s theory, is only a\ntest of truth, inasmuch as it is a test of believability. The\ninconceivableness of a supposition is the extreme case of its\nunbelievability. This is the very foundation of Mr. Spencer\u2019s doctrine.\nThe invariability of the belief is with him the real guarantee. The\nattempt to conceive the negative is made in order to test the\ninevitableness of the belief. It should be called, an attempt to _believe_\nthe negative. When Mr. Spencer says that while looking at the sun a man\ncan not conceive that he is looking into darkness, he should have said\nthat a man can not _believe_ that he is doing so. For it is surely\npossible, in broad daylight, to _imagine_ one\u2019s self looking into\ndarkness.(94) As Mr. Spencer himself says, speaking of the belief of our\nown existence, \u201cThat he _might_ not exist, he can conceive well enough;\nbut that he _does_ not exist, he finds it impossible to conceive,\u201d _i.e._,\nto believe. So that the statement resolves itself into this: That I exist,\nand that I have sensations, I believe, because I can not believe\notherwise. And in this case every one will admit that the impossibility is\nreal. Any one\u2019s present sensations, or other states of subjective\nconsciousness, that one person inevitably believes. They are facts known\n_per se_: it is impossible to ascend beyond them. Their negative is really\nunbelievable, and therefore there is never any question about believing\nit. Mr. Spencer\u2019s theory is not needed for these truths.\n\nBut according to Mr. Spencer there are other beliefs, relating to other\nthings than our own subjective feelings, for which we have the same\nguarantee\u2014which are, in a similar manner, invariable and necessary. With\nregard to these other beliefs, they can not be necessary, since they do\nnot always exist. There have been, and are, many persons who do not\nbelieve the reality of an external world, still less the reality of\nextension and figure as the forms of that external world; who do not\nbelieve that space and time have an existence independent of the mind\u2014nor\nany other of Mr. Spencer\u2019s objective intuitions. The negations of these\nalleged invariable beliefs are not unbelievable, for they are believed. It\nmay be maintained, without obvious error, that we can not _imagine_\ntangible objects as mere states of our own and other people\u2019s\nconsciousness; that the perception of them irresistibly suggests to us the\n_idea_ of something external to ourselves: and I am not in a condition to\nsay that this is not the fact (though I do not think any one is entitled\nto affirm it of any person besides himself). But many thinkers have\nbelieved, whether they could conceive it or not, that what we represent to\nourselves as material objects, are mere modifications of consciousness;\ncomplex feelings of touch and of muscular action. Mr. Spencer may think\nthe inference correct from the unimaginable to the unbelievable, because\nhe holds that belief itself is but the persistence of an idea, and that\nwhat we can succeed in imagining we can not at the moment help\napprehending as believable. But of what consequence is it what we\napprehend at the moment, if the moment is in contradiction to the\npermanent state of our mind? A person who has been frightened when an\ninfant by stories of ghosts, though he disbelieves them in after years\n(and perhaps never believed them), may be unable all his life to be in a\ndark place, in circumstances stimulating to the imagination, without\nmental discomposure. The idea of ghosts, with all its attendant terrors,\nis irresistibly called up in his mind by the outward circumstances. Mr.\nSpencer may say, that while he is under the influence of this terror he\ndoes not disbelieve in ghosts, but has a temporary and uncontrollable\nbelief in them. Be it so; but allowing it to be so, which would it be\ntruest to say of this man on the whole\u2014that he believes in ghosts, or that\nhe does not believe in them? Assuredly that he does not believe in them.\nThe case is similar with those who disbelieve a material world. Though\nthey can not get rid of the idea; though while looking at a solid object\nthey can not help having the conception, and therefore, according to Mr.\nSpencer\u2019s metaphysics, the momentary belief, of its externality; even at\nthat moment they would sincerely deny holding that belief: and it would be\nincorrect to call them other than disbelievers of the doctrine. The belief\ntherefore is not invariable; and the test of inconceivableness fails in\nthe only cases to which there could ever be any occasion to apply it.\n\nThat a thing may be perfectly believable, and yet may not have become\nconceivable, and that we may habitually believe one side of an\nalternative, and conceive only in the other, is familiarly exemplified in\nthe state of mind of educated persons respecting sunrise and sunset. All\neducated persons either know by investigation, or believe on the authority\nof science, that it is the earth and not the sun which moves: but there\nare probably few who habitually _conceive_ the phenomenon otherwise than\nas the ascent or descent of the sun. Assuredly no one can do so without a\nprolonged trial; and it is probably not easier now than in the first\ngeneration after Copernicus. Mr. Spencer does not say, \u201cIn looking at\nsunrise it is impossible not to conceive that it is the sun which moves,\ntherefore this is what every body believes, and we have all the evidence\nfor it that we can have for any truth.\u201d Yet this would be an exact\nparallel to his doctrine about the belief in matter.\n\nThe existence of matter, and other Noumena, as distinguished from the\nphenomenal world, remains a question of argument, as it was before; and\nthe very general, but neither necessary nor universal, belief in them,\nstands as a psychological phenomenon to be explained, either on the\nhypothesis of its truth, or on some other. The belief is not a conclusive\nproof of its own truth, unless there are no such things as _idola trib\u00fbs_;\nbut being a fact, it calls on antagonists to show, from what except the\nreal existence of the thing believed, so general and apparently\nspontaneous a belief can have originated. And its opponents have never\nhesitated to accept this challenge.(95) The amount of their success in\nmeeting it will probably determine the ultimate verdict of philosophers on\nthe question.\n\n\u00a7 4. In the revision, or rather reconstruction, of his \u201cPrinciples of\nPsychology,\u201d as one of the stages or platforms in the imposing structure\nof his System of Philosophy, Mr. Spencer has resumed what he justly\nterms(96) the \u201camicable controversy that has been long pending between\nus;\u201d expressing at the same time a regret, which I cordially share, that\n\u201cthis lengthened exposition of a single point of difference, unaccompanied\nby an exposition of the numerous points of concurrence, unavoidably\nproduces an appearance of dissent very far greater than that which\nexists.\u201d I believe, with Mr. Spencer, that the difference between us, if\nmeasured by our conclusions, is \u201csuperficial rather than substantial;\u201d and\nthe value I attach to so great an amount of agreement, in the field of\nanalytic psychology, with a thinker of his force and depth, is such as I\ncan hardly overstate. But I also agree with him that the difference which\nexists in our premises is one of \u201cprofound importance, philosophically\nconsidered;\u201d and not to be dismissed while any part of the case of either\nof us has not been fully examined and discussed.\n\nIn his present statement of the Universal Postulate, Mr. Spencer has\nexchanged his former expression, \u201cbeliefs which invariably exist,\u201d for the\nfollowing: \u201ccognitions of which the predicates invariably exist along with\ntheir subjects.\u201d And he says that \u201can abortive effort to conceive the\nnegation of a proposition, shows that the cognition expressed is one of\nwhich the predicate invariably exists along with its subject; and the\ndiscovery that the predicate invariably exists along with its subject, is\nthe discovery that this cognition is one we are compelled to accept.\u201d Both\nthese premises of Mr. Spencer\u2019s syllogism I am able to assent to, but in\ndifferent senses of the middle term. If the invariable existence of the\npredicate along with its subject, is to be understood in the most obvious\nmeaning, as an existence in actual Nature, or in other words, in our\nobjective, or sensational, experience, I of course admit that this, once\nascertained, compels us to accept the proposition: but then I do not admit\nthat the failure of an attempt to conceive the negative, proves the\npredicate to be always co-existent with the subject in actual Nature. If,\non the other hand (which I believe to be Mr. Spencer\u2019s meaning) the\ninvariable existence of the predicate along with the subject is to be\nunderstood only of our conceptive faculty, _i.e._, that the one is\ninseparable from the other in our thoughts; then, indeed, the inability to\nseparate the two ideas proves their inseparable conjunction, here and now,\nin the mind which has failed in the attempt; but this inseparability in\nthought does not prove a corresponding inseparability in fact; nor even in\nthe thoughts of other people, or of the same person in a possible future.\n\n\u201cThat some propositions have been wrongly accepted as true, because their\nnegations were supposed inconceivable when they were not,\u201d does not, in\nMr. Spencer\u2019s opinion, \u201cdisprove the validity of the test;\u201d not only\nbecause any test whatever \u201cis liable to yield untrue results, either from\nincapacity or from carelessness in those who use it,\u201d but because the\npropositions in question \u201cwere complex propositions, not to be established\nby a test applicable to propositions no further decomposable.\u201d \u201cA test\nlegitimately applicable to a simple proposition, the subject and predicate\nof which are in direct relation, can not be legitimately applied to a\ncomplex proposition, the subject and predicate of which are indirectly\nrelated through the many simple propositions implied.\u201d \u201cThat things which\nare equal to the same thing are equal to one another, is a fact which can\nbe known by direct comparison of actual or ideal relations.... But that\nthe square of the hypothenuse of a right-angled triangle equals the sum of\nthe squares of the other two sides, can not be known immediately by\ncomparison of two states of consciousness: here the truth can be reached\nonly mediately, through a series of simple judgments respecting the\nlikenesses or unlikenesses of certain relations.\u201d Moreover, even when the\nproposition admits of being tested by immediate consciousness, people\noften neglect to do it. A school-boy, in adding up a column of figures,\nwill say \u201c35 and 9 are 46,\u201d though this is contrary to the verdict which\nconsciousness gives when 35 and 9 are really called up before it; but this\nis not done. And not only school-boys, but men and thinkers, do not always\n\u201cdistinctly translate into their equivalent states of consciousness the\nwords they use.\u201d\n\nIt is but just to give Mr. Spencer\u2019s doctrine the benefit of the\nlimitation he claims\u2014viz., that it is only applicable to propositions\nwhich are assented to on simple inspection, without any intervening media\nof proof. But this limitation does not exclude some of the most marked\ninstances of propositions now known to be false or groundless, but whose\nnegative was once found inconceivable: such as, that in sunrise and sunset\nit is the sun which moves; that gravitation may exist without an\nintervening medium; and even the case of antipodes. The distinction drawn\nby Mr. Spencer is real; but, in the case of the propositions classed by\nhim as complex, consciousness, until the media of proof are supplied,\ngives no verdict at all: it neither declares the equality of the square of\nthe hypothenuse with the sum of the squares of the sides to be\ninconceivable, nor their inequality to be inconceivable. But in all the\nthree cases which I have just cited, the inconceivability seems to be\napprehended directly; no train of argument was needed, as in the case of\nthe square of the hypothenuse, to obtain the verdict of consciousness on\nthe point. Neither is any of the three a case like that of the\nschool-boy\u2019s mistake, in which the mind was never really brought into\ncontact with the proposition. They are cases in which one of two opposite\npredicates, _mero adspectu_, seemed to be incompatible with the subject,\nand the other, therefore, to be proved always to exist with it.(97)\n\nAs now limited by Mr. Spencer, the ultimate cognitions fit to be submitted\nto his test are only those of so universal and elementary a character as\nto be represented in the earliest and most unvarying experience, or\napparent experience, of all mankind. In such cases the inconceivability of\nthe negative, if real, is accounted for by the experience: and why (I have\nasked) should the truth be tested by the inconceivability, when we can go\nfurther back for proof\u2014namely, to the experience itself? To this Mr.\nSpencer answers, that the experiences can not be all recalled to mind, and\nif recalled, would be of unmanageable multitude. To test a proposition by\nexperience seems to him to mean that \u201cbefore accepting as certain the\nproposition that any rectilineal figure must have as many angles as it has\nsides,\u201d I have \u201cto think of every triangle, square, pentagon, hexagon,\netc., which I have ever seen, and to verify the asserted relation in each\ncase.\u201d I can only say, with surprise, that I do not understand this to be\nthe meaning of an appeal to experience. It is enough to know that one has\nbeen seeing the fact all one\u2019s life, and has never remarked any instance\nto the contrary, and that other people, with every opportunity of\nobservation, unanimously declare the same thing. It is true, even this\nexperience may be insufficient, and so it might be even if I could recall\nto mind every instance of it; but its insufficiency, instead of being\nbrought to light, is disguised, if instead of sifting the experience\nitself, I appeal to a test which bears no relation to the sufficiency of\nthe experience, but, at the most, only to its familiarity. These remarks\ndo not lose their force even if we believe, with Mr. Spencer, that mental\ntendencies originally derived from experience impress themselves\npermanently on the cerebral structure and are transmitted by inheritance,\nso that modes of thinking which are acquired by the race become innate and\n_a priori_ in the individual, thus representing, in Mr. Spencer\u2019s opinion,\nthe experience of his progenitors, in addition to his own. All that would\nfollow from this is, that a conviction might be really innate, _i.e._,\nprior to individual experience, and yet not be true, since the inherited\ntendency to accept it may have been originally the result of other causes\nthan its truth.\n\nMr. Spencer would have a much stronger case, if he could really show that\nthe evidence of Reasoning rests on the Postulate, or, in other words, that\nwe believe that a conclusion follows from premises only because we can not\nconceive it not to follow. But this statement seems to me to be of the\nsame kind as one I have previously commented on, viz., that I believe I\nsee light, because I can not, while the sensation remains, conceive that I\nam looking into darkness. Both these statements seem to me incompatible\nwith the meaning (as very rightly limited by Mr. Spencer) of the verb to\nconceive. To say that when I apprehend that A is B and that B is C, I can\nnot conceive that A is not C, is to my mind merely to say that I am\ncompelled to _believe_ that A is C. If to conceive be taken in its proper\nmeaning, viz., to form a mental representation, I _may_ be able to\nconceive A as not being C. After assenting, with full understanding, to\nthe Copernican proof that it is the earth and not the sun that moves, I\nnot only can conceive, or represent to myself, sunset as a motion of the\nsun, but almost every one finds this conception of sunset easier to form,\nthan that which they nevertheless know to be the true one.\n\n\u00a7 5. Sir William Hamilton holds as I do, that inconceivability is no\ncriterion of impossibility. \u201cThere is no ground for inferring a certain\nfact to be impossible, merely from our inability to conceive its\npossibility.\u201d \u201cThings there are which _may_, nay _must_, be true, of which\nthe understanding is wholly unable to construe to itself the\npossibility.\u201d(98) Sir William Hamilton is, however, a firm believer in the\n_a priori_ character of many axioms, and of the sciences deduced from\nthem; and is so far from considering those axioms to rest on the evidence\nof experience, that he declares certain of them to be true even of\nNoumena\u2014of the Unconditioned\u2014of which it is one of the principal aims of\nhis philosophy to prove that the nature of our faculties debars us from\nhaving any knowledge. The axioms to which he attributes this exceptional\nemancipation from the limits which confine all our other possibilities of\nknowledge; the chinks through which, as he represents, one ray of light\nfinds its way to us from behind the curtain which veils from us the\nmysterious world of Things in themselves\u2014are the two principles, which he\nterms, after the school-men, the Principle of Contradiction, and the\nPrinciple of Excluded Middle: the first, that two contradictory\npropositions can not both be true; the second, that they can not both be\nfalse. Armed with these logical weapons, we may boldly face Things in\nthemselves, and tender to them the double alternative, sure that they must\nabsolutely elect one or the other side, though we may be forever precluded\nfrom discovering which. To take his favorite example, we can not conceive\nthe infinite divisibility of matter, and we can not conceive a minimum, or\nend to divisibility: yet one or the other must be true.\n\nAs I have hitherto said nothing of the two axioms in question, those of\nContradiction and of Excluded Middle, it is not unseasonable to consider\nthem here. The former asserts that an affirmative proposition and the\ncorresponding negative proposition can not both be true; which has\ngenerally been held to be intuitively evident. Sir William Hamilton and\nthe Germans consider it to be the statement in words of a form or law of\nour thinking faculty. Other philosophers, not less deserving of\nconsideration, deem it to be an identical proposition; an assertion\ninvolved in the meaning of terms; a mode of defining Negation, and the\nword Not.\n\nI am able to go one step with these last. An affirmative assertion and its\nnegative are not two independent assertions, connected with each other\nonly as mutually incompatible. That if the negative be true, the\naffirmative must be false, really is a mere identical proposition; for the\nnegative proposition asserts nothing but the falsity of the affirmative,\nand has no other sense or meaning whatever. The Principium Contradictionis\nshould therefore put off the ambitious phraseology which gives it the air\nof a fundamental antithesis pervading nature, and should be enunciated in\nthe simpler form, that the same proposition can not at the same time be\nfalse and true. But I can go no further with the Nominalists; for I can\nnot look upon this last as a merely verbal proposition. I consider it to\nbe, like other axioms, one of our first and most familiar generalizations\nfrom experience. The original foundation of it I take to be, that Belief\nand Disbelief are two different mental states, excluding one another. This\nwe know by the simplest observation of our own minds. And if we carry our\nobservation outward, we also find that light and darkness, sound and\nsilence, motion and quiescence, equality and inequality, preceding and\nfollowing, succession and simultaneousness, any positive phenomenon\nwhatever and its negative, are distinct phenomena, pointedly contrasted,\nand the one always absent where the other is present. I consider the maxim\nin question to be a generalization from all these facts.\n\nIn like manner as the Principle of Contradiction (that one of two\ncontradictories must be false) means that an assertion can not be _both_\ntrue and false, so the Principle of Excluded Middle, or that one of two\ncontradictories must be true, means that an assertion must be _either_\ntrue or false: either the affirmative is true, or otherwise the negative\nis true, which means that the affirmative is false. I can not help\nthinking this principle a surprising specimen of a so-called necessity of\nThought, since it is not even true, unless with a large qualification. A\nproposition must be either true or false, _provided_ that the predicate be\none which can in any intelligible sense be attributed to the subject; (and\nas this is always assumed to be the case in treatises on logic, the axiom\nis always laid down there as of absolute truth). \u201cAbracadabra is a second\nintention\u201d is neither true nor false. Between the true and the false there\nis a third possibility, the Unmeaning: and this alternative is fatal to\nSir William Hamilton\u2019s extension of the maxim to Noumena. That Matter must\neither have a minimum of divisibility or be infinitely divisible, is more\nthan we can ever know. For in the first place, Matter, in any other than\nthe phenomenal sense of the term, may not exist: and it will scarcely be\nsaid that a nonentity must be either infinitely or finitely divisible. In\nthe second place, though matter, considered as the occult cause of our\nsensations, do really exist, yet what we call divisibility may be an\nattribute only of our sensations of sight and touch, and not of their\nuncognizable cause. Divisibility may not be predicable at all, in any\nintelligible sense, of Things in themselves, nor therefore of Matter in\nitself; and the assumed necessity of being either infinitely or finitely\ndivisible, may be an inapplicable alternative.\n\nOn this question I am happy to have the full concurrence of Mr. Herbert\nSpencer, from whose paper in the _Fortnightly Review_ I extract the\nfollowing passage. The germ of an idea identical with that of Mr. Spencer\nmay be found in the present chapter, on a preceding page; but in Mr.\nSpencer it is not an undeveloped thought, but a philosophical theory.\n\n\u201cWhen remembering a certain thing as in a certain place, the place and the\nthing are mentally represented together; while to think of the\nnon-existence of the thing in that place implies a consciousness in which\nthe place is represented, but not the thing. Similarly, if instead of\nthinking of an object as colorless, we think of its having color, the\nchange consists in the addition to the concept of an element that was\nbefore absent from it\u2014the object can not be thought of first as red and\nthen as not red, without one component of the thought being totally\nexpelled from the mind by another. The law of the Excluded Middle, then,\nis simply a generalization of the universal experience that some mental\nstates are directly destructive of other states. It formulates a certain\nabsolutely constant law, that the appearance of any positive mode of\nconsciousness can not occur without excluding a correlative negative mode;\nand that the negative mode can not occur without excluding the correlative\npositive mode: the antithesis of positive and negative being, indeed,\nmerely an expression of this experience. Hence it follows that if\nconsciousness is not in one of the two modes it must be in the other.\u201d(99)\n\nI must here close this supplementary chapter, and with it the Second Book.\nThe theory of Induction, in the most comprehensive sense of the term, will\nform the subject of the Third.\n\n\n\n\n                                Book III.\n\n\nOF INDUCTION.\n\n\n    \u201cAccording to the doctrine now stated, the highest, or rather the\n    only proper object of physics, is to ascertain those established\n    conjunctions of successive events, which constitute the order of\n    the universe; to record the phenomena which it exhibits to our\n    observations, or which it discloses to our experiments; and to\n    refer these phenomena to their general laws.\u201d\u2014D. STEWART,\n    _Elements of the Philosophy of the Human Mind_, vol. ii., chap.\n    iv., sect. 1.\n\n    \u201cIn such cases the inductive and deductive methods of inquiry may\n    be said to go hand in hand, the one verifying the conclusions\n    deduced by the other; and the combination of experiment and\n    theory, which may thus be brought to bear in such cases, forms an\n    engine of discovery infinitely more powerful than either taken\n    separately. This state of any department of science is perhaps of\n    all others the most interesting, and that which promises the most\n    to research.\u201d\u2014SIR J. HERSCHEL, _Discourse on the Study of Natural\n    Philosophy_.\n\n\n\n\n                                Chapter I.\n\n\nPreliminary Observations On Induction In General.\n\n\n\u00a7 1. The portion of the present inquiry upon which we are now about to\nenter, may be considered as the principal, both from its surpassing in\nintricacy all the other branches, and because it relates to a process\nwhich has been shown in the preceding Book to be that in which the\ninvestigation of nature essentially consists. We have found that all\nInference, consequently all Proof, and all discovery of truths not\nself-evident, consists of inductions, and the interpretation of\ninductions: that all our knowledge, not intuitive, comes to us exclusively\nfrom that source. What Induction is, therefore, and what conditions render\nit legitimate, can not but be deemed the main question of the science of\nlogic\u2014the question which includes all others. It is, however, one which\nprofessed writers on logic have almost entirely passed over. The\ngeneralities of the subject have not been altogether neglected by\nmetaphysicians; but, for want of sufficient acquaintance with the\nprocesses by which science has actually succeeded in establishing general\ntruths, their analysis of the inductive operation, even when\nunexceptionable as to correctness, has not been specific enough to be made\nthe foundation of practical rules, which might be for induction itself\nwhat the rules of the syllogism are for the interpretation of induction:\nwhile those by whom physical science has been carried to its present state\nof improvement\u2014and who, to arrive at a complete theory of the process,\nneeded only to generalize, and adapt to all varieties of problems, the\nmethods which they themselves employed in their habitual pursuits\u2014never\nuntil very lately made any serious attempt to philosophize on the subject,\nnor regarded the mode in which they arrived at their conclusions as\ndeserving of study, independently of the conclusions themselves.\n\n\u00a7 2. For the purposes of the present inquiry, Induction may be defined,\nthe operation of discovering and proving general propositions. It is true\nthat (as already shown) the process of indirectly ascertaining individual\nfacts, is as truly inductive as that by which we establish general truths.\nBut it is not a different kind of induction; it is a form of the very same\nprocess: since, on the one hand, generals are but collections of\nparticulars, definite in kind but indefinite in number; and on the other\nhand, whenever the evidence which we derive from observation of known\ncases justifies us in drawing an inference respecting even one unknown\ncase, we should on the same evidence be justified in drawing a similar\ninference with respect to a whole class of cases. The inference either\ndoes not hold at all, or it holds in all cases of a certain description;\nin all cases which, in certain definable respects, resemble those we have\nobserved.\n\nIf these remarks are just; if the principles and rules of inference are\nthe same whether we infer general propositions or individual facts; it\nfollows that a complete logic of the sciences would be also a complete\nlogic of practical business and common life. Since there is no case of\nlegitimate inference from experience, in which the conclusion may not\nlegitimately be a general proposition; an analysis of the process by which\ngeneral truths are arrived at, is virtually an analysis of all induction\nwhatever. Whether we are inquiring into a scientific principle or into an\nindividual fact, and whether we proceed by experiment or by ratiocination,\nevery step in the train of inferences is essentially inductive, and the\nlegitimacy of the induction depends in both cases on the same conditions.\n\nTrue it is that in the case of the practical inquirer, who is endeavoring\nto ascertain facts not for the purposes of science but for those of\nbusiness, such, for instance, as the advocate or the judge, the chief\ndifficulty is one in which the principles of induction will afford him no\nassistance. It lies not in making his inductions, but in the selection of\nthem; in choosing from among all general propositions ascertained to be\ntrue, those which furnish marks by which he may trace whether the given\nsubject possesses or not the predicate in question. In arguing a doubtful\nquestion of fact before a jury, the general propositions or principles to\nwhich the advocate appeals are mostly, in themselves, sufficiently trite,\nand assented to as soon as stated: his skill lies in bringing his case\nunder those propositions or principles; in calling to mind such of the\nknown or received maxims of probability as admit of application to the\ncase in hand, and selecting from among them those best adapted to his\nobject. Success is here dependent on natural or acquired sagacity, aided\nby knowledge of the particular subject, and of subjects allied with it.\nInvention, though it can be cultivated, can not be reduced to rule; there\nis no science which will enable a man to bethink himself of that which\nwill suit his purpose.\n\nBut when he _has_ thought of something, science can tell him whether that\nwhich he has thought of will suit his purpose or not. The inquirer or\narguer must be guided by his own knowledge and sagacity in the choice of\nthe inductions out of which he will construct his argument. But the\nvalidity of the argument when constructed, depends on principles, and must\nbe tried by tests which are the same for all descriptions of inquiries,\nwhether the result be to give A an estate, or to enrich science with a new\ngeneral truth. In the one case and in the other, the senses, or testimony,\nmust decide on the individual facts; the rules of the syllogism will\ndetermine whether, those facts being supposed correct, the case really\nfalls within the formul\u00e6 of the different inductions under which it has\nbeen successively brought; and finally, the legitimacy of the inductions\nthemselves must be decided by other rules, and these it is now our purpose\nto investigate. If this third part of the operation be, in many of the\nquestions of practical life, not the most, but the least arduous portion\nof it, we have seen that this is also the case in some great departments\nof the field of science; in all those which are principally deductive, and\nmost of all in mathematics; where the inductions themselves are few in\nnumber, and so obvious and elementary that they seem to stand in no need\nof the evidence of experience, while to combine them so as to prove a\ngiven theorem or solve a problem, may call for the utmost powers of\ninvention and contrivance with which our species is gifted.\n\nIf the identity of the logical processes which prove particular facts and\nthose which establish general scientific truths, required any additional\nconfirmation, it would be sufficient to consider that in many branches of\nscience, single facts have to be proved, as well as principles; facts as\ncompletely individual as any that are debated in a court of justice; but\nwhich are proved in the same manner as the other truths of the science,\nand without disturbing in any degree the homogeneity of its method. A\nremarkable example of this is afforded by astronomy. The individual facts\non which that science grounds its most important deductions, such facts as\nthe magnitudes of the bodies of the solar system, their distances from one\nanother, the figure of the earth, and its rotation, are scarcely any of\nthem accessible to our means of direct observation: they are proved\nindirectly, by the aid of inductions founded on other facts which we can\nmore easily reach. For example, the distance of the moon from the earth\nwas determined by a very circuitous process. The share which direct\nobservation had in the work consisted in ascertaining, at one and the same\ninstant, the zenith distances of the moon, as seen from two points very\nremote from one another on the earth\u2019s surface. The ascertainment of these\nangular distances ascertained their supplements; and since the angle at\nthe earth\u2019s centre subtended by the distance between the two places of\nobservation was deducible by spherical trigonometry from the latitude and\nlongitude of those places, the angle at the moon subtended by the same\nline became the fourth angle of a quadrilateral of which the other three\nangles were known. The four angles being thus ascertained, and two sides\nof the quadrilateral being radii of the earth; the two remaining sides and\nthe diagonal, or, in other words, the moon\u2019s distance from the two places\nof observation and from the centre of the earth, could be ascertained, at\nleast in terms of the earth\u2019s radius, from elementary theorems of\ngeometry. At each step in this demonstration a new induction is taken in,\nrepresented in the aggregate of its results by a general proposition.\n\nNot only is the process by which an individual astronomical fact was thus\nascertained, exactly similar to those by which the same science\nestablishes its general truths, but also (as we have shown to be the case\nin all legitimate reasoning) a general proposition might have been\nconcluded instead of a single fact. In strictness, indeed, the result of\nthe reasoning _is_ a general proposition; a theorem respecting the\ndistance, not of the moon in particular, but of any inaccessible object;\nshowing in what relation that distance stands to certain other quantities.\nAnd although the moon is almost the only heavenly body the distance of\nwhich from the earth can really be thus ascertained, this is merely owing\nto the accidental circumstances of the other heavenly bodies, which render\nthem incapable of affording such data as the application of the theorem\nrequires; for the theorem itself is as true of them as it is of the\nmoon.(100)\n\nWe shall fall into no error, then, if in treating of Induction, we limit\nour attention to the establishment of general propositions. The principles\nand rules of Induction as directed to this end, are the principles and\nrules of all Induction; and the logic of Science is the universal Logic,\napplicable to all inquiries in which man can engage.\n\n\n\n\n                               Chapter II.\n\n\nOf Inductions Improperly So Called.\n\n\n\u00a7 1. Induction, then, is that operation of the mind, by which we infer\nthat what we know to be true in a particular case or cases, will be true\nin all cases which resemble the former in certain assignable respects. In\nother words, Induction is the process by which we conclude that what is\ntrue of certain individuals of a class is true of the whole class, or that\nwhat is true at certain times will be true in similar circumstances at all\ntimes.\n\nThis definition excludes from the meaning of the term Induction, various\nlogical operations, to which it is not unusual to apply that name.\n\nInduction, as above defined, is a process of inference; it proceeds from\nthe known to the unknown; and any operation involving no inference, any\nprocess in which what seems the conclusion is no wider than the premises\nfrom which it is drawn, does not fall within the meaning of the term. Yet\nin the common books of Logic we find this laid down as the most perfect,\nindeed the only quite perfect, form of induction. In those books, every\nprocess which sets out from a less general and terminates in a more\ngeneral expression\u2014which admits of being stated in the form, \u201cThis and\nthat A are B, therefore every A is B\u201d\u2014is called an induction, whether any\nthing be really concluded or not: and the induction is asserted not to be\nperfect, unless every single individual of the class A is included in the\nantecedent, or premise: that is, unless what we affirm of the class has\nalready been ascertained to be true of every individual in it, so that the\nnominal conclusion is not really a conclusion, but a mere re-assertion of\nthe premises. If we were to say, All the planets shine by the sun\u2019s light,\nfrom observation of each separate planet, or All the Apostles were Jews,\nbecause this is true of Peter, Paul, John, and every other apostle\u2014these,\nand such as these, would, in the phraseology in question, be called\nperfect, and the only perfect, Inductions. This, however, is a totally\ndifferent kind of induction from ours; it is not an inference from facts\nknown to facts unknown, but a mere short-hand registration of facts known.\nThe two simulated arguments which we have quoted, are not generalizations;\nthe propositions purporting to be conclusions from them, are not really\ngeneral propositions. A general proposition is one in which the predicate\nis affirmed or denied of an unlimited number of individuals; namely, all,\nwhether few or many, existing or capable of existing, which possess the\nproperties connoted by the subject of the proposition. \u201cAll men are\nmortal\u201d does not mean all now living, but all men past, present, and to\ncome. When the signification of the term is limited so as to render it a\nname not for any and every individual falling under a certain general\ndescription, but only for each of a number of individuals, designated as\nsuch, and as it were counted off individually, the proposition, though it\nmay be general in its language, is no general proposition, but merely that\nnumber of singular propositions, written in an abridged character. The\noperation may be very useful, as most forms of abridged notation are; but\nit is no part of the investigation of truth, though often bearing an\nimportant part in the preparation of the materials for that investigation.\n\nAs we may sum up a definite number of singular propositions in one\nproposition, which will be apparently, but not really, general, so we may\nsum up a definite number of general propositions in one proposition, which\nwill be apparently, but not really, more general. If by a separate\ninduction applied to every distinct species of animals, it has been\nestablished that each possesses a nervous system, and we affirm thereupon\nthat all animals have a nervous system; this looks like a generalization,\nthough as the conclusion merely affirms of all what has already been\naffirmed of each, it seems to tell us nothing but what we knew before. A\ndistinction, however, must be made. If in concluding that all animals have\na nervous system, we mean the same thing and no more as if we had said\n\u201call known animals,\u201d the proposition is not general, and the process by\nwhich it is arrived at is not induction. But if our meaning is that the\nobservations made of the various species of animals have discovered to us\na law of animal nature, and that we are in a condition to say that a\nnervous system will be found even in animals yet undiscovered, this indeed\nis an induction; but in this case the general proposition contains more\nthan the sum of the special propositions from which it is inferred. The\ndistinction is still more forcibly brought out when we consider, that if\nthis real generalization be legitimate at all, its legitimacy probably\ndoes not require that we should have examined without exception every\nknown species. It is the number and nature of the instances, and not their\nbeing the whole of those which happen to be known, that makes them\nsufficient evidence to prove a general law: while the more limited\nassertion, which stops at all known animals, can not be made unless we\nhave rigorously verified it in every species. In like manner (to return to\na former example) we might have inferred, not that all _the_ planets, but\nthat all _planets_, shine by reflected light: the former is no induction;\nthe latter is an induction, and a bad one, being disproved by the case of\ndouble stars\u2014self-luminous bodies which are properly planets, since they\nrevolve round a centre.\n\n\u00a7 2. There are several processes used in mathematics which require to be\ndistinguished from Induction, being not unfrequently called by that name,\nand being so far similar to Induction properly so called, that the\npropositions they lead to are really general propositions. For example,\nwhen we have proved with respect to the circle, that a straight line can\nnot meet it in more than two points, and when the same thing has been\nsuccessively proved of the ellipse, the parabola, and the hyperbola, it\nmay be laid down as a universal property of the sections of the cone. The\ndistinction drawn in the two previous examples can have no place here,\nthere being no difference between all _known_ sections of the cone and\n_all_ sections, since a cone demonstrably can not be intersected by a\nplane except in one of these four lines. It would be difficult, therefore,\nto refuse to the proposition arrived at, the name of a generalization,\nsince there is no room for any generalization beyond it. But there is no\ninduction, because there is no inference: the conclusion is a mere summing\nup of what was asserted in the various propositions from which it is\ndrawn. A case somewhat, though not altogether, similar, is the proof of a\ngeometrical theorem by means of a diagram. Whether the diagram be on paper\nor only in the imagination, the demonstration (as formerly observed(101))\ndoes not prove directly the general theorem; it proves only that the\nconclusion, which the theorem asserts generally, is true of the particular\ntriangle or circle exhibited in the diagram; but since we perceive that in\nthe same way in which we have proved it of that circle, it might also be\nproved of any other circle, we gather up into one general expression all\nthe singular propositions susceptible of being thus proved, and embody\nthem in a universal proposition. Having shown that the three angles of the\ntriangle ABC are together equal to two right angles, we conclude that this\nis true of every other triangle, not because it is true of ABC, but for\nthe same reason which proved it to be true of ABC. If this were to be\ncalled Induction, an appropriate name for it would be, induction by parity\nof reasoning. But the term can not properly belong to it; the\ncharacteristic quality of Induction is wanting, since the truth obtained,\nthough really general, is not believed on the evidence of particular\ninstances. We do not conclude that all triangles have the property because\nsome triangles have, but from the ulterior demonstrative evidence which\nwas the ground of our conviction in the particular instances.\n\nThere are nevertheless, in mathematics, some examples of so-called\nInduction, in which the conclusion does bear the appearance of a\ngeneralization grounded on some of the particular cases included in it. A\nmathematician, when he has calculated a sufficient number of the terms of\nan algebraical or arithmetical series to have ascertained what is called\nthe _law_ of the series, does not hesitate to fill up any number of the\nsucceeding terms without repeating the calculations. But I apprehend he\nonly does so when it is apparent from _a priori_ considerations (which\nmight be exhibited in the form of demonstration) that the mode of\nformation of the subsequent terms, each from that which preceded it, must\nbe similar to the formation of the terms which have been already\ncalculated. And when the attempt has been hazarded without the sanction of\nsuch general considerations, there are instances on record in which it has\nled to false results.\n\nIt is said that Newton discovered the binomial theorem by induction; by\nraising a binomial successively to a certain number of powers, and\ncomparing those powers with one another until he detected the relation in\nwhich the algebraic formula of each power stands to the exponent of that\npower, and to the two terms of the binomial. The fact is not improbable:\nbut a mathematician like Newton, who seemed to arrive _per saltum_ at\nprinciples and conclusions that ordinary mathematicians only reached by a\nsuccession of steps, certainly could not have performed the comparison in\nquestion without being led by it to the _a priori_ ground of the law;\nsince any one who understands sufficiently the nature of multiplication to\nventure upon multiplying several lines of symbols at one operation, can\nnot but perceive that in raising a binomial to a power, the co-efficients\nmust depend on the laws of permutation and combination: and as soon as\nthis is recognized, the theorem is demonstrated. Indeed, when once it was\nseen that the law prevailed in a few of the lower powers, its identity\nwith the law of permutation would at once suggest the considerations which\nprove it to obtain universally. Even, therefore, such cases as these, are\nbut examples of what I have called Induction by parity of reasoning, that\nis, not really Induction, because not involving inference of a general\nproposition from particular instances.\n\n\u00a7 3. There remains a third improper use of the term Induction, which it is\nof real importance to clear up, because the theory of Induction has been,\nin no ordinary degree, confused by it, and because the confusion is\nexemplified in the most recent and elaborate treatise on the inductive\nphilosophy which exists in our language. The error in question is that of\nconfounding a mere description, by general terms, of a set of observed\nphenomena, with an induction from them.\n\nSuppose that a phenomenon consists of parts, and that these parts are only\ncapable of being observed separately, and as it were piecemeal. When the\nobservations have been made, there is a convenience (amounting for many\npurposes to a necessity) in obtaining a representation of the phenomenon\nas a whole, by combining, or as we may say, piecing these detached\nfragments together. A navigator sailing in the midst of the ocean\ndiscovers land: he can not at first, or by any one observation, determine\nwhether it is a continent or an island; but he coasts along it, and after\na few days finds himself to have sailed completely round it: he then\npronounces it an island. Now there was no particular time or place of\nobservation at which he could perceive that this land was entirely\nsurrounded by water: he ascertained the fact by a succession of partial\nobservations, and then selected a general expression which summed up in\ntwo or three words the whole of what he so observed. But is there any\nthing of the nature of an induction in this process? Did he infer any\nthing that had not been observed, from something else which had? Certainly\nnot. He had observed the whole of what the proposition asserts. That the\nland in question is an island, is not an inference from the partial facts\nwhich the navigator saw in the course of his circumnavigation; it is the\nfacts themselves; it is a summary of those facts; the description of a\ncomplex fact, to which those simpler ones are as the parts of a whole.\n\nNow there is, I conceive, no difference in kind between this simple\noperation, and that by which Kepler ascertained the nature of the\nplanetary orbits: and Kepler\u2019s operation, all at least that was\ncharacteristic in it, was not more an inductive act than that of our\nsupposed navigator.\n\nThe object of Kepler was to determine the real path described by each of\nthe planets, or let us say by the planet Mars (since it was of that body\nthat he first established the two of his three laws which did not require\na comparison of planets). To do this there was no other mode than that of\ndirect observation: and all which observation could do was to ascertain a\ngreat number of the successive places of the planet; or rather, of its\napparent places. That the planet occupied successively all these\npositions, or at all events, positions which produced the same impressions\non the eye, and that it passed from one of these to another insensibly,\nand without any apparent breach of continuity; thus much the senses, with\nthe aid of the proper instruments, could ascertain. What Kepler did more\nthan this, was to find what sort of a curve these different points would\nmake, supposing them to be all joined together. He expressed the whole\nseries of the observed places of Mars by what Dr. Whewell calls the\ngeneral conception of an ellipse. This operation was far from being as\neasy as that of the navigator who expressed the series of his observations\non successive points of the coast by the general conception of an island.\nBut it is the very same sort of operation; and if the one is not an\ninduction but a description, this must also be true of the other.\n\nThe only real induction concerned in the case, consisted in inferring that\nbecause the observed places of Mars were correctly represented by points\nin an imaginary ellipse, therefore Mars would continue to revolve in that\nsame ellipse; and in concluding (before the gap had been filled up by\nfurther observations) that the positions of the planet during the time\nwhich intervened between two observations, must have coincided with the\nintermediate points of the curve. For these were facts which had not been\ndirectly observed. They were inferences from the observations; facts\ninferred, as distinguished from facts seen. But these inferences were so\nfar from being a part of Kepler\u2019s philosophical operation, that they had\nbeen drawn long before he was born. Astronomers had long known that the\nplanets periodically returned to the same places. When this had been\nascertained, there was no induction left for Kepler to make, nor did he\nmake any further induction. He merely applied his new conception to the\nfacts inferred, as he did to the facts observed. Knowing already that the\nplanets continued to move in the same paths; when he found that an ellipse\ncorrectly represented the past path, he knew that it would represent the\nfuture path. In finding a compendious expression for the one set of facts,\nhe found one for the other: but he found the expression only, not the\ninference; nor did he (which is the true test of a general truth) add any\nthing to the power of prediction already possessed.\n\n\u00a7 4. The descriptive operation which enables a number of details to be\nsummed up in a single proposition, Dr. Whewell, by an aptly chosen\nexpression, has termed the Colligation of Facts. In most of his\nobservations concerning that mental process I fully agree, and would\ngladly transfer all that portion of his book into my own pages. I only\nthink him mistaken in setting up this kind of operation, which according\nto the old and received meaning of the term, is not induction at all, as\nthe type of induction generally; and laying down, throughout his work, as\nprinciples of induction, the principles of mere colligation.\n\nDr. Whewell maintains that the general proposition which binds together\nthe particular facts, and makes them, as it were, one fact, is not the\nmere sum of those facts, but something more, since there is introduced a\nconception of the mind, which did not exist in the facts themselves. \u201cThe\nparticular facts,\u201d says he,(102) \u201care not merely brought together, but\nthere is a new element added to the combination by the very act of thought\nby which they are combined.... When the Greeks, after long observing the\nmotions of the planets, saw that these motions might be rightly considered\nas produced by the motion of one wheel revolving in the inside of another\nwheel, these wheels were creations of their minds, added to the facts\nwhich they perceived by sense. And even if the wheels were no longer\nsupposed to be material, but were reduced to mere geometrical spheres or\ncircles, they were not the less products of the mind alone\u2014something\nadditional to the facts observed. The same is the case in all other\ndiscoveries. The facts are known, but they are insulated and unconnected,\ntill the discoverer supplies from his own store a principle of connection.\nThe pearls are there, but they will not hang together till some one\nprovides the string.\u201d\n\nLet me first remark that Dr. Whewell, in this passage, blends together,\nindiscriminately, examples of both the processes which I am endeavoring to\ndistinguish from one another. When the Greeks abandoned the supposition\nthat the planetary motions were produced by the revolution of material\nwheels, and fell back upon the idea of \u201cmere geometrical spheres or\ncircles,\u201d there was more in this change of opinion than the mere\nsubstitution of an ideal curve for a physical one. There was the\nabandonment of a theory, and the replacement of it by a mere description.\nNo one would think of calling the doctrine of material wheels a mere\ndescription. That doctrine was an attempt to point out the force by which\nthe planets were acted upon, and compelled to move in their orbits. But\nwhen, by a great step in philosophy, the materiality of the wheels was\ndiscarded, and the geometrical forms alone retained, the attempt to\naccount for the motions was given up, and what was left of the theory was\na mere description of the orbits. The assertion that the planets were\ncarried round by wheels revolving in the inside of other wheels, gave\nplace to the proposition, that they moved in the same lines which would be\ntraced by bodies so carried: which was a mere mode of representing the sum\nof the observed facts; as Kepler\u2019s was another and a better mode of\nrepresenting the same observations.\n\nIt is true that for these simply descriptive operations, as well as for\nthe erroneous inductive one, a conception of the mind was required. The\nconception of an ellipse must have presented itself to Kepler\u2019s mind,\nbefore he could identify the planetary orbits with it. According to Dr.\nWhewell, the conception was something added to the facts. He expresses\nhimself as if Kepler had put something into the facts by his mode of\nconceiving them. But Kepler did no such thing. The ellipse was in the\nfacts before Kepler recognized it; just as the island was an island before\nit had been sailed round. Kepler did not _put_ what he had conceived into\nthe facts, but _saw_ it in them. A conception implies, and corresponds to,\nsomething conceived: and though the conception itself is not in the facts,\nbut in our mind, yet if it is to convey any knowledge relating to them, it\nmust be a conception _of_ something which really is in the facts, some\nproperty which they actually possess, and which they would manifest to our\nsenses, if our senses were able to take cognizance of it. If, for\ninstance, the planet left behind it in space a visible track, and if the\nobserver were in a fixed position at such a distance from the plane of the\norbit as would enable him to see the whole of it at once, he would see it\nto be an ellipse; and if gifted with appropriate instruments and powers of\nlocomotion, he could prove it to be such by measuring its different\ndimensions. Nay, further: if the track were visible, and he were so placed\nthat he could see all parts of it in succession, but not all of them at\nonce, he might be able, by piecing together his successive observations,\nto discover both that it was an ellipse and that the planet moved in it.\nThe case would then exactly resemble that of the navigator who discovers\nthe land to be an island by sailing round it. If the path was visible, no\none I think would dispute that to identify it with an ellipse is to\ndescribe it: and I can not see why any difference should be made by its\nnot being directly an object of sense, when every point in it is as\nexactly ascertained as if it were so.\n\nSubject to the indispensable condition which has just been stated, I do\nnot conceive that the part which conceptions have in the operation of\nstudying facts, has ever been overlooked or undervalued. No one ever\ndisputed that in order to reason about any thing we must have a conception\nof it; or that when we include a multitude of things under a general\nexpression, there is implied in the expression a conception of something\ncommon to those things. But it by no means follows that the conception is\nnecessarily pre-existent, or constructed by the mind out of its own\nmaterials. If the facts are rightly classed under the conception, it is\nbecause there is in the facts themselves something of which the conception\nis itself a copy; and which if we can not directly perceive, it is because\nof the limited power of our organs, and not because the thing itself is\nnot there. The conception itself is often obtained by abstraction from the\nvery facts which, in Dr. Whewell\u2019s language, it is afterward called in to\nconnect. This he himself admits, when he observes (which he does on\nseveral occasions), how great a service would be rendered to the science\nof physiology by the philosopher \u201cwho should establish a precise, tenable,\nand consistent conception of life.\u201d(103) Such a conception can only be\nabstracted from the phenomena of life itself; from the very facts which it\nis put in requisition to connect. In other cases, no doubt, instead of\ncollecting the conception from the very phenomena which we are attempting\nto colligate, we select it from among those which have been previously\ncollected by abstraction from other facts. In the instance of Kepler\u2019s\nlaws, the latter was the case. The facts being out of the reach of being\nobserved, in any such manner as would have enabled the senses to identify\ndirectly the path of the planet, the conception requisite for framing a\ngeneral description of that path could not be collected by abstraction\nfrom the observations themselves; the mind had to supply hypothetically,\nfrom among the conceptions it had obtained from other portions of its\nexperience, some one which would correctly represent the series of the\nobserved facts. It had to frame a supposition respecting the general\ncourse of the phenomenon, and ask itself, If this be the general\ndescription, what will the details be? and then compare these with the\ndetails actually observed. If they agreed, the hypothesis would serve for\na description of the phenomenon: if not, it was necessarily abandoned, and\nanother tried. It is such a case as this which gives rise to the doctrine\nthat the mind, in framing the descriptions, adds something of its own\nwhich it does not find in the facts.\n\nYet it is a fact surely, that the planet does describe an ellipse; and a\nfact which we could see, if we had adequate visual organs and a suitable\nposition. Not having these advantages, but possessing the conception of an\nellipse, or (to express the meaning in less technical language) knowing\nwhat an ellipse was, Kepler tried whether the observed places of the\nplanet were consistent with such a path. He found they were so; and he,\nconsequently, asserted as a fact that the planet moved in an ellipse. But\nthis fact, which Kepler did not add to, but found in, the motions of the\nplanet, namely, that it occupied in succession the various points in the\ncircumference of a given ellipse, was the very fact, the separate parts of\nwhich had been separately observed; it was the sum of the different\nobservations.\n\nHaving stated this fundamental difference between my opinion and that of\nDr. Whewell, I must add, that his account of the manner in which a\nconception is selected, suitable to express the facts, appears to me\nperfectly just. The experience of all thinkers will, I believe, testify\nthat the process is tentative; that it consists of a succession of\nguesses; many being rejected, until one at last occurs fit to be chosen.\nWe know from Kepler himself that before hitting upon the \u201cconception\u201d of\nan ellipse, he tried nineteen other imaginary paths, which, finding them\ninconsistent with the observations, he was obliged to reject. But as Dr.\nWhewell truly says, the successful hypothesis, though a guess, ought\ngenerally to be called, not a lucky, but a skillful guess. The guesses\nwhich serve to give mental unity and wholeness to a chaos of scattered\nparticulars, are accidents which rarely occur to any minds but those\nabounding in knowledge and disciplined in intellectual combinations.\n\nHow far this tentative method, so indispensable as a means to the\ncolligation of facts for purposes of description, admits of application to\nInduction itself, and what functions belong to it in that department, will\nbe considered in the chapter of the present Book which relates to\nHypotheses. On the present occasion we have chiefly to distinguish this\nprocess of Colligation from Induction properly so called; and that the\ndistinction may be made clearer, it is well to advert to a curious and\ninteresting remark, which is as strikingly true of the former operation,\nas it appears to me unequivocally false of the latter.\n\nIn different stages of the progress of knowledge, philosophers have\nemployed, for the colligation of the same order of facts, different\nconceptions. The early rude observations of the heavenly bodies, in which\nminute precision was neither attained nor sought, presented nothing\ninconsistent with the representation of the path of a planet as an exact\ncircle, having the earth for its centre. As observations increased in\naccuracy, facts were disclosed which were not reconcilable with this\nsimple supposition: for the colligation of those additional facts, the\nsupposition was varied; and varied again and again as facts became more\nnumerous and precise. The earth was removed from the centre to some other\npoint within the circle; the planet was supposed to revolve in a smaller\ncircle called an epicycle, round an imaginary point which revolved in a\ncircle round the earth: in proportion as observation elicited fresh facts\ncontradictory to these representations, other epicycles and other\neccentrics were added, producing additional complication; until at last\nKepler swept all these circles away, and substituted the conception of an\nexact ellipse. Even this is found not to represent with complete\ncorrectness the accurate observations of the present day, which disclose\nmany slight deviations from an orbit exactly elliptical. Now Dr. Whewell\nhas remarked that these successive general expressions, though apparently\nso conflicting, were all correct: they all answered the purpose of\ncolligation; they all enabled the mind to represent to itself with\nfacility, and by a simultaneous glance, the whole body of facts at the\ntime ascertained: each in its turn served as a correct description of the\nphenomena, so far as the senses had up to that time taken cognizance of\nthem. If a necessity afterward arose for discarding one of these general\ndescriptions of the planet\u2019s orbit, and framing a different imaginary\nline, by which to express the series of observed positions, it was because\na number of new facts had now been added, which it was necessary to\ncombine with the old facts into one general description. But this did not\naffect the correctness of the former expression, considered as a general\nstatement of the only facts which it was intended to represent. And so\ntrue is this, that, as is well remarked by M. Comte, these ancient\ngeneralizations, even the rudest and most imperfect of them, that of\nuniform movement in a circle, are so far from being entirely false, that\nthey are even now habitually employed by astronomers when only a rough\napproximation to correctness is required. \u201cL\u2019astronomie moderne, en\nd\u00e9truisant sans retour les hypoth\u00e8ses primitives, envisag\u00e9es comme lois\nr\u00e9elles du monde, a soigneusement maintenu leur valeur positive et\npermanente, la propri\u00e9t\u00e9 de repr\u00e9senter commod\u00e9ment les ph\u00e9nom\u00e8nes quand\nil s\u2019agit d\u2019une premi\u00e8re \u00e9bauche. Nos ressources \u00e0 cet \u00e9gard sont m\u00eame\nbien plus \u00e9tendues, pr\u00e9cis\u00e9ment \u00e0 cause que nous ne nous faisons aucune\nillusion sur la r\u00e9alit\u00e9 des hypoth\u00e8ses; ce qui nous permet d\u2019employer sans\nscrupule, en chaque cas, celle que nous jugeons la plus avantageuse.\u201d(104)\n\nDr. Whewell\u2019s remark, therefore, is philosophically correct. Successive\nexpressions for the colligation of observed facts, or, in other words,\nsuccessive descriptions of a phenomenon as a whole, which has been\nobserved only in parts, may, though conflicting, be all correct as far as\nthey go. But it would surely be absurd to assert this of conflicting\ninductions.\n\nThe scientific study of facts may be undertaken for three different\npurposes: the simple description of the facts; their explanation; or their\nprediction: meaning by prediction, the determination of the conditions\nunder which similar facts may be expected again to occur. To the first of\nthese three operations the name of Induction does not properly belong: to\nthe other two it does. Now, Dr. Whewell\u2019s observation is true of the first\nalone. Considered as a mere description, the circular theory of the\nheavenly motions represents perfectly well their general features: and by\nadding epicycles without limit, those motions, even as now known to us,\nmight be expressed with any degree of accuracy that might be required. The\nelliptical theory, as a mere description, would have a great advantage in\npoint of simplicity, and in the consequent facility of conceiving it and\nreasoning about it; but it would not really be more true than the other.\nDifferent descriptions, therefore, may be all true: but not, surely,\ndifferent explanations. The doctrine that the heavenly bodies moved by a\nvirtue inherent in their celestial nature; the doctrine that they were\nmoved by impact (which led to the hypothesis of vortices as the only\nimpelling force capable of whirling bodies in circles), and the Newtonian\ndoctrine, that they are moved by the composition of a centripetal with an\noriginal projectile force; all these are explanations, collected by real\ninduction from supposed parallel cases; and they were all successively\nreceived by philosophers, as scientific truths on the subject of the\nheavenly bodies. Can it be said of these, as was said of the different\ndescriptions, that they are all true as far as they go? Is it not clear\nthat only one can be true in any degree, and the other two must be\naltogether false? So much for explanations: let us now compare different\npredictions: the first, that eclipses will occur when one planet or\nsatellite is so situated as to cast its shadow upon another; the second,\nthat they will occur when some great calamity is impending over mankind.\nDo these two doctrines only differ in the degree of their truth, as\nexpressing real facts with unequal degrees of accuracy? Assuredly the one\nis true, and the other absolutely false.(105)\n\nIn every way, therefore, it is evident that to explain induction as the\ncolligation of facts by means of appropriate conceptions, that is,\nconceptions which will really express them, is to confound mere\ndescription of the observed facts with inference from those facts, and\nascribe to the latter what is a characteristic property of the former.\n\nThere is, however, between Colligation and Induction, a real correlation,\nwhich it is important to conceive correctly. Colligation is not always\ninduction; but induction is always colligation. The assertion that the\nplanets move in ellipses, was but a mode of representing observed facts;\nit was but a colligation; while the assertion that they are drawn, or\ntend, toward the sun, was the statement of a new fact, inferred by\ninduction. But the induction, once made, accomplishes the purposes of\ncolligation likewise. It brings the same facts, which Kepler had connected\nby his conception of an ellipse, under the additional conception of bodies\nacted upon by a central force, and serves, therefore, as a new bond of\nconnection for those facts; a new principle for their classification.\n\nFurther, the descriptions which are improperly confounded with induction,\nare nevertheless a necessary preparation for induction; no less necessary\nthan correct observation of the facts themselves. Without the previous\ncolligation of detached observations by means of one general conception,\nwe could never have obtained any basis for an induction, except in the\ncase of phenomena of very limited compass. We should not be able to affirm\nany predicates at all, of a subject incapable of being observed otherwise\nthan piecemeal: much less could we extend those predicates by induction to\nother similar subjects. Induction, therefore, always presupposes, not only\nthat the necessary observations are made with the necessary accuracy, but\nalso that the results of these observations are, so far as practicable,\nconnected together by general descriptions, enabling the mind to represent\nto itself as wholes whatever phenomena are capable of being so\nrepresented.\n\n\u00a7 5. Dr. Whewell has replied at some length to the preceding observations,\nrestating his opinions, but without (as far as I can perceive) adding any\nthing material to his former arguments. Since, however, mine have not had\nthe good fortune to make any impression upon him, I will subjoin a few\nremarks, tending to show more clearly in what our difference of opinion\nconsists, as well as, in some measure, to account for it.\n\nNearly all the definitions of induction, by writers of authority, make it\nconsist in drawing inferences from known cases to unknown; affirming of a\nclass, a predicate which has been found true of some cases belonging to\nthe class; concluding because some things have a certain property, that\nother things which resemble them have the same property\u2014or because a thing\nhas manifested a property at a certain time, that it has and will have\nthat property at other times.\n\nIt will scarcely be contended that Kepler\u2019s operation was an Induction in\nthis sense of the term. The statement, that Mars moves in an elliptical\norbit, was no generalization from individual cases to a class of cases.\nNeither was it an extension to all time, of what had been found true at\nsome particular time. The whole amount of generalization which the case\nadmitted of, was already completed, or might have been so. Long before the\nelliptic theory was thought of, it had been ascertained that the planets\nreturned periodically to the same apparent places; the series of these\nplaces was, or might have been, completely determined, and the apparent\ncourse of each planet marked out on the celestial globe in an\nuninterrupted line. Kepler did not extend an observed truth to other cases\nthan those in which it had been observed: he did not widen the _subject_\nof the proposition which expressed the observed facts. The alteration he\nmade was in the predicate. Instead of saying, the successive places of\nMars are so and so, he summed them up in the statement, that the\nsuccessive places of Mars are points in an ellipse. It is true, this\nstatement, as Dr. Whewell says, was not the sum of the observations\n_merely_; it was the sum of the observations _seen under a new point of\nview_.(106) But it was not the sum of _more_ than the observations, as a\nreal induction is. It took in no cases but those which had been actually\nobserved, or which could have been inferred from the observations before\nthe new point of view presented itself. There was not that transition from\nknown cases to unknown, which constitutes Induction in the original and\nacknowledged meaning of the term.\n\nOld definitions, it is true, can not prevail against new knowledge: and if\nthe Keplerian operation, as a logical process, be really identical with\nwhat takes place in acknowledged induction, the definition of induction\nought to be so widened as to take it in; since scientific language ought\nto adapt itself to the true relations which subsist between the things it\nis employed to designate. Here then it is that I am at issue with Dr.\nWhewell. He does think the operations identical. He allows of no logical\nprocess in any case of induction, other than what there was in Kepler\u2019s\ncase, namely, guessing until a guess is found which tallies with the\nfacts; and accordingly, as we shall see hereafter, he rejects all canons\nof induction, because it is not by means of them that we guess. Dr.\nWhewell\u2019s theory of the logic of science would be very perfect if it did\nnot pass over altogether the question of Proof. But in my apprehension\nthere is such a thing as proof, and inductions differ altogether from\ndescriptions in their relation to that element. Induction is proof; it is\ninferring something unobserved from something observed: it requires,\ntherefore, an appropriate test of proof; and to provide that test, is the\nspecial purpose of inductive logic. When, on the contrary, we merely\ncollate known observations, and, in Dr. Whewell\u2019s phraseology, connect\nthem by means of a new conception; if the conception does serve to connect\nthe observations, we have all we want. As the proposition in which it is\nembodied pretends to no other truth than what it may share with many other\nmodes of representing the same facts, to be consistent with the facts is\nall it requires: it neither needs nor admits of proof; though it may serve\nto prove other things, inasmuch as, by placing the facts in mental\nconnection with other facts, not previously seen to resemble them, it\nassimilates the case to another class of phenomena, concerning which real\nInductions have already been made. Thus Kepler\u2019s so-called law brought the\norbit of Mars into the class ellipse, and by doing so, proved all the\nproperties of an ellipse to be true of the orbit: but in this proof\nKepler\u2019s law supplied the minor premise, and not (as is the case with real\nInductions) the major.\n\nDr. Whewell calls nothing Induction where there is not a new mental\nconception introduced, and every thing induction where there is. But this\nis to confound two very different things, Invention and Proof. The\nintroduction of a new conception belongs to Invention: and invention may\nbe required in any operation, but is the essence of none. A new conception\nmay be introduced for descriptive purposes, and so it may for inductive\npurposes. But it is so far from constituting induction, that induction\ndoes not necessarily stand in need of it. Most inductions require no\nconception but what was present in every one of the particular instances\non which the induction is grounded. That all men are mortal is surely an\ninductive conclusion; yet no new conception is introduced by it. Whoever\nknows that any man has died, has all the conceptions involved in the\ninductive generalization. But Dr. Whewell considers the process of\ninvention which consists in framing a new conception consistent with the\nfacts, to be not merely a necessary part of all induction, but the whole\nof it.\n\nThe mental operation which extracts from a number of detached observations\ncertain general characters in which the observed phenomena resemble one\nanother, or resemble other known facts, is what Bacon, Locke, and most\nsubsequent metaphysicians, have understood by the word Abstraction. A\ngeneral expression obtained by abstraction, connecting known facts by\nmeans of common characters, but without concluding from them to unknown,\nmay, I think, with strict logical correctness, be termed a Description;\nnor do I know in what other way things can ever be described. My position,\nhowever, does not depend on the employment of that particular word; I am\nquite content to use Dr. Whewell\u2019s term Colligation, or the more general\nphrases, \u201cmode of representing, or of expressing, phenomena:\u201d provided it\nbe clearly seen that the process is not Induction, but something radically\ndifferent.\n\nWhat more may usefully be said on the subject of Colligation, or of the\ncorrelative expression invented by Dr. Whewell, the Explication of\nConceptions, and generally on the subject of ideas and mental\nrepresentations as connected with the study of facts, will find a more\nappropriate place in the Fourth Book, on the Operations Subsidiary to\nInduction: to which I must refer the reader for the removal of any\ndifficulty which the present discussion may have left.\n\n\n\n\n                               Chapter III.\n\n\nOf The Ground Of Induction.\n\n\n\u00a7 1. Induction properly so called, as distinguished from those mental\noperations, sometimes, though improperly, designated by the name, which I\nhave attempted in the preceding chapter to characterize, may, then, be\nsummarily defined as Generalization from Experience. It consists in\ninferring from some individual instances in which a phenomenon is observed\nto occur, that it occurs in all instances of a certain class; namely, in\nall which _resemble_ the former, in what are regarded as the material\ncircumstances.\n\nIn what way the material circumstances are to be distinguished from those\nwhich are immaterial, or why some of the circumstances are material and\nothers not so, we are not yet ready to point out. We must first observe,\nthat there is a principle implied in the very statement of what Induction\nis; an assumption with regard to the course of nature and the order of the\nuniverse; namely, that there are such things in nature as parallel cases;\nthat what happens once, will, under a sufficient degree of similarity of\ncircumstances, happen again, and not only again, but as often as the same\ncircumstances recur. This, I say, is an assumption, involved in every case\nof induction. And, if we consult the actual course of nature, we find that\nthe assumption is warranted. The universe, so far as known to us, is so\nconstituted, that whatever is true in any one case, is true in all cases\nof a certain description; the only difficulty is, to find what\ndescription.\n\nThis universal fact, which is our warrant for all inferences from\nexperience, has been described by different philosophers in different\nforms of language: that the course of nature is uniform; that the universe\nis governed by general laws; and the like. One of the most usual of these\nmodes of expression, but also one of the most inadequate, is that which\nhas been brought into familiar use by the metaphysicians of the school of\nReid and Stewart. The disposition of the human mind to generalize from\nexperience\u2014a propensity considered by these philosophers as an instinct of\nour nature\u2014they usually describe under some such name as \u201cour intuitive\nconviction that the future will resemble the past.\u201d Now it has been well\npointed out by Mr. Bailey,(107) that (whether the tendency be or not an\noriginal and ultimate element of our nature), Time, in its modifications\nof past, present, and future, has no concern either with the belief\nitself, or with the grounds of it. We believe that fire will burn\nto-morrow, because it burned to-day and yesterday; but we believe, on\nprecisely the same grounds, that it burned before we were born, and that\nit burns this very day in Cochin-China. It is not from the past to the\nfuture, as past and future, that we infer, but from the known to the\nunknown; from facts observed to facts unobserved; from what we have\nperceived, or been directly conscious of, to what has not come within our\nexperience. In this last predicament is the whole region of the future;\nbut also the vastly greater portion of the present and of the past.\n\nWhatever be the most proper mode of expressing it, the proposition that\nthe course of nature is uniform, is the fundamental principle, or general\naxiom of Induction. It would yet be a great error to offer this large\ngeneralization as any explanation of the inductive process. On the\ncontrary, I hold it to be itself an instance of induction, and induction\nby no means of the most obvious kind. Far from being the first induction\nwe make, it is one of the last, or at all events one of those which are\nlatest in attaining strict philosophical accuracy. As a general maxim,\nindeed, it has scarcely entered into the minds of any but philosophers;\nnor even by them, as we shall have many opportunities of remarking, have\nits extent and limits been always very justly conceived. The truth is,\nthat this great generalization is itself founded on prior generalizations.\nThe obscurer laws of nature were discovered by means of it, but the more\nobvious ones must have been understood and assented to as general truths\nbefore it was ever heard of. We should never have thought of affirming\nthat all phenomena take place according to general laws, if we had not\nfirst arrived, in the case of a great multitude of phenomena, at some\nknowledge of the laws themselves; which could be done no otherwise than by\ninduction. In what sense, then, can a principle, which is so far from\nbeing our earliest induction, be regarded as our warrant for all the\nothers? In the only sense, in which (as we have already seen) the general\npropositions which we place at the head of our reasonings when we throw\nthem into syllogisms, ever really contribute to their validity. As\nArchbishop Whately remarks, every induction is a syllogism with the major\npremise suppressed; or (as I prefer expressing it) every induction may be\nthrown into the form of a syllogism, by supplying a major premise. If this\nbe actually done, the principle which we are now considering, that of the\nuniformity of the course of nature, will appear as the ultimate major\npremise of all inductions, and will, therefore, stand to all inductions in\nthe relation in which, as has been shown at so much length, the major\nproposition of a syllogism always stands to the conclusion; not\ncontributing at all to prove it, but being a necessary condition of its\nbeing proved; since no conclusion is proved, for which there can not be\nfound a true major premise.(108)\n\nThe statement, that the uniformity of the course of nature is the ultimate\nmajor premise in all cases of induction, may be thought to require some\nexplanation. The immediate major premise in every inductive argument, it\ncertainly is not. Of that, Archbishop Whately\u2019s must be held to be the\ncorrect account. The induction, \u201cJohn, Peter, etc., are mortal, therefore\nall mankind are mortal,\u201d may, as he justly says, be thrown into a\nsyllogism by prefixing as a major premise (what is at any rate a necessary\ncondition of the validity of the argument), namely, that what is true of\nJohn, Peter, etc., is true of all mankind. But how came we by this major\npremise? It is not self-evident; nay, in all cases of unwarranted\ngeneralization, it is not true. How, then, is it arrived at? Necessarily\neither by induction or ratiocination; and if by induction, the process,\nlike all other inductive arguments, may be thrown into the form of a\nsyllogism. This previous syllogism it is, therefore, necessary to\nconstruct. There is, in the long run, only one possible construction. The\nreal proof that what is true of John, Peter, etc., is true of all mankind,\ncan only be, that a different supposition would be inconsistent with the\nuniformity which we know to exist in the course of nature. Whether there\nwould be this inconsistency or not, may be a matter of long and delicate\ninquiry; but unless there would, we have no sufficient ground for the\nmajor of the inductive syllogism. It hence appears, that if we throw the\nwhole course of any inductive argument into a series of syllogisms, we\nshall arrive by more or fewer steps at an ultimate syllogism, which will\nhave for its major premise the principle, or axiom, of the uniformity of\nthe course of nature.(109)\n\nIt was not to be expected that in the case of this axiom, any more than of\nother axioms, there should be unanimity among thinkers with respect to the\ngrounds on which it is to be received as true. I have already stated that\nI regard it as itself a generalization from experience. Others hold it to\nbe a principle which, antecedently to any verification by experience, we\nare compelled by the constitution of our thinking faculty to assume as\ntrue. Having so recently, and at so much length, combated a similar\ndoctrine as applied to the axioms of mathematics, by arguments which are\nin a great measure applicable to the present case, I shall defer the more\nparticular discussion of this controverted point in regard to the\nfundamental axiom of induction, until a more advanced period of our\ninquiry.(110) At present it is of more importance to understand thoroughly\nthe import of the axiom itself. For the proposition, that the course of\nnature is uniform, possesses rather the brevity suitable to popular, than\nthe precision requisite in philosophical language: its terms require to be\nexplained, and a stricter than their ordinary signification given to them,\nbefore the truth of the assertion can be admitted.\n\n\u00a7 2. Every person\u2019s consciousness assures him that he does not always\nexpect uniformity in the course of events; he does not always believe that\nthe unknown will be similar to the known, that the future will resemble\nthe past. Nobody believes that the succession of rain and fine weather\nwill be the same in every future year as in the present. Nobody expects to\nhave the same dreams repeated every night. On the contrary, every body\nmentions it as something extraordinary, if the course of nature is\nconstant, and resembles itself, in these particulars. To look for\nconstancy where constancy is not to be expected, as for instance that a\nday which has once brought good fortune will always be a fortunate day, is\njustly accounted superstition.\n\nThe course of nature, in truth, is not only uniform, it is also infinitely\nvarious. Some phenomena are always seen to recur in the very same\ncombinations in which we met with them at first; others seem altogether\ncapricious; while some, which we had been accustomed to regard as bound\ndown exclusively to a particular set of combinations, we unexpectedly find\ndetached from some of the elements with which we had hitherto found them\nconjoined, and united to others of quite a contrary description. To an\ninhabitant of Central Africa, fifty years ago, no fact probably appeared\nto rest on more uniform experience than this, that all human beings are\nblack. To Europeans, not many years ago, the proposition, All swans are\nwhite, appeared an equally unequivocal instance of uniformity in the\ncourse of nature. Further experience has proved to both that they were\nmistaken; but they had to wait fifty centuries for this experience. During\nthat long time, mankind believed in a uniformity of the course of nature\nwhere no such uniformity really existed.\n\nAccording to the notion which the ancients entertained of induction, the\nforegoing were cases of as legitimate inference as any inductions\nwhatever. In these two instances, in which, the conclusion being false,\nthe ground of inference must have been insufficient, there was,\nnevertheless, as much ground for it as this conception of induction\nadmitted of. The induction of the ancients has been well described by\nBacon, under the name of \u201cInductio per enumerationem simplicem, ubi non\nreperitur instantia contradictoria.\u201d It consists in ascribing the\ncharacter of general truths to all propositions which are true in every\ninstance that we happen to know of. This is the kind of induction which is\nnatural to the mind when unaccustomed to scientific methods. The tendency,\nwhich some call an instinct, and which others account for by association,\nto infer the future from the past, the known from the unknown, is simply a\nhabit of expecting that what has been found true once or several times,\nand never yet found false, will be found true again. Whether the instances\nare few or many, conclusive or inconclusive, does not much affect the\nmatter: these are considerations which occur only on reflection; the\nunprompted tendency of the mind is to generalize its experience, provided\nthis points all in one direction; provided no other experience of a\nconflicting character comes unsought. The notion of seeking it, of\nexperimenting for it, of _interrogating_ nature (to use Bacon\u2019s\nexpression) is of much later growth. The observation of nature, by\nuncultivated intellects, is purely passive: they accept the facts which\npresent themselves, without taking the trouble of searching for more: it\nis a superior mind only which asks itself what facts are needed to enable\nit to come to a safe conclusion, and then looks out for these.\n\nBut though we have always a propensity to generalize from unvarying\nexperience, we are not always warranted in doing so. Before we can be at\nliberty to conclude that something is universally true because we have\nnever known an instance to the contrary, we must have reason to believe\nthat if there were in nature any instances to the contrary, we should have\nknown of them. This assurance, in the great majority of cases, we can not\nhave, or can have only in a very moderate degree. The possibility of\nhaving it, is the foundation on which we shall see hereafter that\ninduction by simple enumeration may in some remarkable cases amount\npractically to proof.(111) No such assurance, however, can be had, on any\nof the ordinary subjects of scientific inquiry. Popular notions are\nusually founded on induction by simple enumeration; in science it carries\nus but a little way. We are forced to begin with it; we must often rely on\nit provisionally, in the absence of means of more searching investigation.\nBut, for the accurate study of nature, we require a surer and a more\npotent instrument.\n\nIt was, above all, by pointing out the insufficiency of this rude and\nloose conception of Induction, that Bacon merited the title so generally\nawarded to him, of Founder of the Inductive Philosophy. The value of his\nown contributions to a more philosophical theory of the subject has\ncertainly been exaggerated. Although (along with some fundamental errors)\nhis writings contain, more or less fully developed, several of the most\nimportant principles of the Inductive Method, physical investigation has\nnow far outgrown the Baconian conception of Induction. Moral and political\ninquiry, indeed, are as yet far behind that conception. The current and\napproved modes of reasoning on these subjects are still of the same\nvicious description against which Bacon protested; the method almost\nexclusively employed by those professing to treat such matters\ninductively, is the very _inductio per enumerationem simplicem_ which he\ncondemns; and the experience which we hear so confidently appealed to by\nall sects, parties, and interests, is still, in his own emphatic words,\n_mera palpatio_.\n\n\u00a7 3. In order to a better understanding of the problem which the logician\nmust solve if he would establish a scientific theory of Induction, let us\ncompare a few cases of incorrect inductions with others which are\nacknowledged to be legitimate. Some, we know, which were believed for\ncenturies to be correct, were nevertheless incorrect. That all swans are\nwhite, can not have been a good induction, since the conclusion has turned\nout erroneous. The experience, however, on which the conclusion rested,\nwas genuine. From the earliest records, the testimony of the inhabitants\nof the known world was unanimous on the point. The uniform experience,\ntherefore, of the inhabitants of the known world, agreeing in a common\nresult, without one known instance of deviation from that result, is not\nalways sufficient to establish a general conclusion.\n\nBut let us now turn to an instance apparently not very dissimilar to this.\nMankind were wrong, it seems, in concluding that all swans were white: are\nwe also wrong, when we conclude that all men\u2019s heads grow above their\nshoulders, and never below, in spite of the conflicting testimony of the\nnaturalist Pliny? As there were black swans, though civilized people had\nexisted for three thousand years on the earth without meeting with them,\nmay there not also be \u201cmen whose heads do grow beneath their shoulders,\u201d\nnotwithstanding a rather less perfect unanimity of negative testimony from\nobservers? Most persons would answer No; it was more credible that a bird\nshould vary in its color, than that men should vary in the relative\nposition of their principal organs. And there is no doubt that in so\nsaying they would be right: but to say why they are right, would be\nimpossible, without entering more deeply than is usually done, into the\ntrue theory of Induction.\n\nAgain, there are cases in which we reckon with the most unfailing\nconfidence upon uniformity, and other cases in which we do not count upon\nit at all. In some we feel complete assurance that the future will\nresemble the past, the unknown be precisely similar to the known. In\nothers, however invariable may be the result obtained from the instances\nwhich have been observed, we draw from them no more than a very feeble\npresumption that the like result will hold in all other cases. That a\nstraight line is the shortest distance between two points, we do not doubt\nto be true even in the region of the fixed stars.(112) When a chemist\nannounces the existence and properties of a newly-discovered substance, if\nwe confide in his accuracy, we feel assured that the conclusions he has\narrived at will hold universally, though the induction be founded but on a\nsingle instance. We do not withhold our assent, waiting for a repetition\nof the experiment; or if we do, it is from a doubt whether the one\nexperiment was properly made, not whether if properly made it would be\nconclusive. Here, then, is a general law of nature, inferred without\nhesitation from a single instance; a universal proposition from a singular\none. Now mark another case, and contrast it with this. Not all the\ninstances which have been observed since the beginning of the world, in\nsupport of the general proposition that all crows are black, would be\ndeemed a sufficient presumption of the truth of the proposition, to\noutweigh the testimony of one unexceptionable witness who should affirm\nthat in some region of the earth not fully explored, he had caught and\nexamined a crow, and had found it to be gray.\n\nWhy is a single instance, in some cases, sufficient for a complete\ninduction, while in others, myriads of concurring instances, without a\nsingle exception known or presumed, go such a very little way toward\nestablishing a universal proposition? Whoever can answer this question\nknows more of the philosophy of logic than the wisest of the ancients, and\nhas solved the problem of induction.\n\n\n\n\n                               Chapter IV.\n\n\nOf Laws Of Nature.\n\n\n\u00a7 1. In the contemplation of that uniformity in the course of nature,\nwhich is assumed in every inference from experience, one of the first\nobservations that present themselves is, that the uniformity in question\nis not properly uniformity, but uniformities. The general regularity\nresults from the co-existence of partial regularities. The course of\nnature in general is constant, because the course of each of the various\nphenomena that compose it is so. A certain fact invariably occurs whenever\ncertain circumstances are present, and does not occur when they are\nabsent; the like is true of another fact; and so on. From these separate\nthreads of connection between parts of the great whole which we term\nnature, a general tissue of connection unavoidably weaves itself, by which\nthe whole is held together. If A is always accompanied by D, B by E, and C\nby F, it follows that A B is accompanied by D E, A C by D F, B C by E F,\nand finally A B C by D E F; and thus the general character of regularity\nis produced, which, along with and in the midst of infinite diversity,\npervades all nature.\n\nThe first point, therefore, to be noted in regard to what is called the\nuniformity of the course of nature, is, that it is itself a complex fact,\ncompounded of all the separate uniformities which exist in respect to\nsingle phenomena. These various uniformities, when ascertained by what is\nregarded as a sufficient induction, we call, in common parlance, Laws of\nNature. Scientifically speaking, that title is employed in a more\nrestricted sense, to designate the uniformities when reduced to their most\nsimple expression. Thus in the illustration already employed, there were\nseven uniformities; all of which, if considered sufficiently certain,\nwould, in the more lax application of the term, be called laws of nature.\nBut of the seven, three alone are properly distinct and independent: these\nbeing presupposed, the others follow of course. The first three,\ntherefore, according to the stricter acceptation, are called laws of\nnature; the remainder not; because they are in truth mere _cases_ of the\nfirst three; virtually included in them; said, therefore, to _result_ from\nthem: whoever affirms those three has already affirmed all the rest.\n\nTo substitute real examples for symbolical ones, the following are three\nuniformities, or call them laws of nature: the law that air has weight,\nthe law that pressure on a fluid is propagated equally in all directions,\nand the law that pressure in one direction, not opposed by equal pressure\nin the contrary direction, produces motion, which does not cease until\nequilibrium is restored. From these three uniformities we should be able\nto predict another uniformity, namely, the rise of the mercury in the\nTorricellian tube. This, in the stricter use of the phrase, is not a law\nof nature. It is the result of laws of nature. It is a _case_ of each and\nevery one of the three laws: and is the only occurrence by which they\ncould all be fulfilled. If the mercury were not sustained in the\nbarometer, and sustained at such a height that the column of mercury were\nequal in weight to a column of the atmosphere of the same diameter; here\nwould be a case, either of the air not pressing upon the surface of the\nmercury with the force which is called its weight, or of the downward\npressure on the mercury not being propagated equally in an upward\ndirection, or of a body pressed in one direction and not in the direction\nopposite, either not moving in the direction in which it is pressed, or\nstopping before it had attained equilibrium. If we knew, therefore, the\nthree simple laws, but had never tried the Torricellian experiment, we\nmight _deduce_ its result from those laws. The known weight of the air,\ncombined with the position of the apparatus, would bring the mercury\nwithin the first of the three inductions; the first induction would bring\nit within the second, and the second within the third, in the manner which\nwe characterized in treating of Ratiocination. We should thus come to know\nthe more complex uniformity, independently of specific experience, through\nour knowledge of the simpler ones from which it results; though, for\nreasons which will appear hereafter, _verification_ by specific experience\nwould still be desirable, and might possibly be indispensable.\n\nComplex uniformities which, like this, are mere cases of simpler ones, and\nhave, therefore, been virtually affirmed in affirming those, may with\npropriety be called _laws_, but can scarcely, in the strictness of\nscientific speech, be termed Laws of Nature. It is the custom in science,\nwherever regularity of any kind can be traced, to call the general\nproposition which expresses the nature of that regularity, a law; as when,\nin mathematics, we speak of the law of decrease of the successive terms of\na converging series. But the expression _law of nature_ has generally been\nemployed with a sort of tacit reference to the original sense of the word\nlaw, namely, the expression of the will of a superior. When, therefore, it\nappeared that any of the uniformities which were observed in nature, would\nresult spontaneously from certain other uniformities, no separate act of\ncreative will being supposed necessary for the production of the\nderivative uniformities, these have not usually been spoken of as laws of\nnature. According to one mode of expression, the question, What are the\nlaws of nature? may be stated thus: What are the fewest and simplest\nassumptions, which being granted, the whole existing order of nature would\nresult? Another mode of stating it would be thus: What are the fewest\ngeneral propositions from which all the uniformities which exist in the\nuniverse might be deductively inferred?\n\nEvery great advance which marks an epoch in the progress of science, has\nconsisted in a step made toward the solution of this problem. Even a\nsimple colligation of inductions already made, without any fresh extension\nof the inductive inference, is already an advance in that direction. When\nKepler expressed the regularity which exists in the observed motions of\nthe heavenly bodies, by the three general propositions called his laws,\nhe, in so doing, pointed out three simple suppositions which, instead of a\nmuch greater number, would suffice to construct the whole scheme of the\nheavenly motions, so far as it was known up to that time. A similar and\nstill greater step was made when these laws, which at first did not seem\nto be included in any more general truths, were discovered to be cases of\nthe three laws of motion, as obtaining among bodies which mutually tend\ntoward one another with a certain force, and have had a certain\ninstantaneous impulse originally impressed upon them. After this great\ndiscovery, Kepler\u2019s three propositions, though still called laws, would\nhardly, by any person accustomed to use language with precision, be termed\nlaws of nature: that phrase would be reserved for the simpler and more\ngeneral laws into which Newton is said to have resolved them.\n\nAccording to this language, every well-grounded inductive generalization\nis either a law of nature, or a result of laws of nature, capable, if\nthose laws are known, of being predicted from them. And the problem of\nInductive Logic may be summed up in two questions: how to ascertain the\nlaws of nature; and how, after having ascertained them, to follow them\ninto their results. On the other hand, we must not suffer ourselves to\nimagine that this mode of statement amounts to a real analysis, or to any\nthing but a mere verbal transformation of the problem; for the expression,\nLaws of Nature, _means_ nothing but the uniformities which exist among\nnatural phenomena (or, in other words, the results of induction), when\nreduced to their simplest expression. It is, however, something to have\nadvanced so far, as to see that the study of nature is the study of laws,\nnot _a_ law; of uniformities, in the plural number: that the different\nnatural phenomena have their separate rules or modes of taking place,\nwhich, though much intermixed and entangled with one another, may, to a\ncertain extent, be studied apart: that (to resume our former metaphor) the\nregularity which exists in nature is a web composed of distinct threads,\nand only to be understood by tracing each of the threads separately; for\nwhich purpose it is often necessary to unravel some portion of the web,\nand exhibit the fibres apart. The rules of experimental inquiry are the\ncontrivances for unraveling the web.\n\n\u00a7 2. In thus attempting to ascertain the general order of nature by\nascertaining the particular order of the occurrence of each one of the\nphenomena of nature, the most scientific proceeding can be no more than an\nimproved form of that which was primitively pursued by the human\nunderstanding, while undirected by science. When mankind first formed the\nidea of studying phenomena according to a stricter and surer method than\nthat which they had in the first instance spontaneously adopted, they did\nnot, conformably to the well-meant but impracticable precept of Descartes,\nset out from the supposition that nothing had been already ascertained.\nMany of the uniformities existing among phenomena are so constant, and so\nopen to observation, as to force themselves upon involuntary recognition.\nSome facts are so perpetually and familiarly accompanied by certain\nothers, that mankind learned, as children learn, to expect the one where\nthey found the other, long before they knew how to put their expectation\ninto words by asserting, in a proposition, the existence of a connection\nbetween those phenomena. No science was needed to teach that food\nnourishes, that water drowns, or quenches thirst, that the sun gives light\nand heat, that bodies fall to the ground. The first scientific inquirers\nassumed these and the like as known truths, and set out from them to\ndiscover others which were unknown: nor were they wrong in so doing,\nsubject, however, as they afterward began to see, to an ulterior revision\nof these spontaneous generalizations themselves, when the progress of\nknowledge pointed out limits to them, or showed their truth to be\ncontingent on some circumstance not originally attended to. It will\nappear, I think, from the subsequent part of our inquiry, that there is no\nlogical fallacy in this mode of proceeding; but we may see already that\nany other mode is rigorously impracticable: since it is impossible to\nframe any scientific method of induction, or test of the correctness of\ninductions, unless on the hypothesis that some inductions deserving of\nreliance have been already made.\n\nLet us revert, for instance, to one of our former illustrations, and\nconsider why it is that, with exactly the same amount of evidence, both\nnegative and positive, we did not reject the assertion that there are\nblack swans, while we should refuse credence to any testimony which\nasserted that there were men wearing their heads underneath their\nshoulders. The first assertion was more credible than the latter. But why\nmore credible? So long as neither phenomenon had been actually witnessed,\nwhat reason was there for finding the one harder to be believed than the\nother? Apparently because there is less constancy in the colors of\nanimals, than in the general structure of their anatomy. But how do we\nknow this? Doubtless, from experience. It appears, then, that we need\nexperience to inform us, in what degree, and in what cases, or sorts of\ncases, experience is to be relied on. Experience must be consulted in\norder to learn from it under what circumstances arguments from it will be\nvalid. We have no ulterior test to which we subject experience in general;\nbut we make experience its own test. Experience testifies, that among the\nuniformities which it exhibits or seems to exhibit, some are more to be\nrelied on than others; and uniformity, therefore, may be presumed, from\nany given number of instances, with a greater degree of assurance, in\nproportion as the case belongs to a class in which the uniformities have\nhitherto been found more uniform.\n\nThis mode of correcting one generalization by means of another, a narrower\ngeneralization by a wider, which common sense suggests and adopts in\npractice, is the real type of scientific Induction. All that art can do is\nbut to give accuracy and precision to this process, and adapt it to all\nvarieties of cases, without any essential alteration in its principle.\n\nThere are of course no means of applying such a test as that above\ndescribed, unless we already possess a general knowledge of the prevalent\ncharacter of the uniformities existing throughout nature. The\nindispensable foundation, therefore, of a scientific formula of induction,\nmust be a survey of the inductions to which mankind have been conducted in\nunscientific practice; with the special purpose of ascertaining what kinds\nof uniformities have been found perfectly invariable, pervading all\nnature, and what are those which have been found to vary with difference\nof time, place, or other changeable circumstances.\n\n\u00a7 3. The necessity of such a survey is confirmed by the consideration,\nthat the stronger inductions are the touch-stone to which we always\nendeavor to bring the weaker. If we find any means of deducing one of the\nless strong inductions from stronger ones, it acquires, at once, all the\nstrength of those from which it is deduced; and even adds to that\nstrength; since the independent experience on which the weaker induction\npreviously rested, becomes additional evidence of the truth of the better\nestablished law in which it is now found to be included. We may have\ninferred, from historical evidence, that the uncontrolled power of a\nmonarch, of an aristocracy, or of the majority, will often be abused: but\nwe are entitled to rely on this generalization with much greater assurance\nwhen it is shown to be a corollary from still better established facts;\nthe very low degree of elevation of character ever yet attained by the\naverage of mankind, and the little efficacy, for the most part, of the\nmodes of education hitherto practiced, in maintaining the predominance of\nreason and conscience over the selfish propensities. It is at the same\ntime obvious that even these more general facts derive an accession of\nevidence from the testimony which history bears to the effects of\ndespotism. The strong induction becomes still stronger when a weaker one\nhas been bound up with it.\n\nOn the other hand, if an induction conflicts with stronger inductions, or\nwith conclusions capable of being correctly deduced from them, then,\nunless on reconsideration it should appear that some of the stronger\ninductions have been expressed with greater universality than their\nevidence warrants, the weaker one must give way. The opinion so long\nprevalent that a comet, or any other unusual appearance in the heavenly\nregions, was the precursor of calamities to mankind, or to those at least\nwho witnessed it; the belief in the veracity of the oracles of Delphi or\nDodona; the reliance on astrology, or on the weather-prophecies in\nalmanacs, were doubtless inductions supposed to be grounded on\nexperience:(113) and faith in such delusions seems quite capable of\nholding out against a great multitude of failures, provided it be\nnourished by a reasonable number of casual coincidences between the\nprediction and the event. What has really put an end to these insufficient\ninductions, is their inconsistency with the stronger inductions\nsubsequently obtained by scientific inquiry, respecting the causes on\nwhich terrestrial events really depend; and where those scientific truths\nhave not yet penetrated, the same or similar delusions still prevail.\n\nIt may be affirmed as a general principle, that all inductions, whether\nstrong or weak, which can be connected by ratiocination, are confirmatory\nof one another; while any which lead deductively to consequences that are\nincompatible, become mutually each other\u2019s test, showing that one or other\nmust be given up, or at least more guardedly expressed. In the case of\ninductions which confirm each other, the one which becomes a conclusion\nfrom ratiocination rises to at least the level of certainty of the weakest\nof those from which it is deduced; while in general all are more or less\nincreased in certainty. Thus the Torricellian experiment, though a mere\ncase of three more general laws, not only strengthened greatly the\nevidence on which those laws rested, but converted one of them (the weight\nof the atmosphere) from a still doubtful generalization into a completely\nestablished doctrine.\n\nIf, then, a survey of the uniformities which have been ascertained to\nexist in nature, should point out some which, as far as any human purpose\nrequires certainty, may be considered quite certain and quite universal;\nthen by means of these uniformities we may be able to raise multitudes of\nother inductions to the same point in the scale. For if we can show, with\nrespect to any inductive inference, that either it must be true, or one of\nthese certain and universal inductions must admit of an exception; the\nformer generalization will attain the same certainty, and indefeasibleness\nwithin the bounds assigned to it, which are the attributes of the latter.\nIt will be proved to be a law; and if not a result of other and simpler\nlaws, it will be a law of nature.\n\nThere are such certain and universal inductions; and it is because there\nare such, that a Logic of Induction is possible.\n\n\n\n\n                                Chapter V.\n\n\nOf The Law Of Universal Causation.\n\n\n\u00a7 1. The phenomena of nature exist in two distinct relations to one\nanother; that of simultaneity, and that of succession. Every phenomenon is\nrelated, in a uniform manner, to some phenomena that co-exist with it, and\nto some that have preceded and will follow it.\n\nOf the uniformities which exist among synchronous phenomena, the most\nimportant, on every account, are the laws of number; and next to them\nthose of space, or, in other words, of extension and figure. The laws of\nnumber are common to synchronous and successive phenomena. That two and\ntwo make four, is equally true whether the second two follow the first two\nor accompany them. It is as true of days and years as of feet and inches.\nThe laws of extension and figure (in other words, the theorems of\ngeometry, from its lowest to its highest branches) are, on the contrary,\nlaws of simultaneous phenomena only. The various parts of space, and of\nthe objects which are said to fill space, co-exist; and the unvarying laws\nwhich are the subject of the science of geometry, are an expression of the\nmode of their co-existence.\n\nThis is a class of laws, or in other words, of uniformities, for the\ncomprehension and proof of which it is not necessary to suppose any lapse\nof time, any variety of facts or events succeeding one another. The\npropositions of geometry are independent of the succession of events. All\nthings which possess extension, or, in other words, which fill space, are\nsubject to geometrical laws. Possessing extension, they possess figure;\npossessing figure, they must possess some figure in particular, and have\nall the properties which geometry assigns to that figure. If one body be a\nsphere and another a cylinder, of equal height and diameter, the one will\nbe exactly two-thirds of the other, let the nature and quality of the\nmaterial be what it will. Again, each body, and each point of a body, must\noccupy some place or position among other bodies; and the position of two\nbodies relatively to each other, of whatever nature the bodies be, may be\nunerringly inferred from the position of each of them relatively to any\nthird body.\n\nIn the laws of number, then, and in those of space, we recognize in the\nmost unqualified manner, the rigorous universality of which we are in\nquest. Those laws have been in all ages the type of certainty, the\nstandard of comparison for all inferior degrees of evidence. Their\ninvariability is so perfect, that it renders us unable even to conceive\nany exception to them; and philosophers have been led, though (as I have\nendeavored to show) erroneously, to consider their evidence as lying not\nin experience, but in the original constitution of the intellect. If,\ntherefore, from the laws of space and number, we were able to deduce\nuniformities of any other description, this would be conclusive evidence\nto us that those other uniformities possessed the same rigorous certainty.\nBut this we can not do. From laws of space and number alone, nothing can\nbe deduced but laws of space and number.\n\nOf all truths relating to phenomena, the most valuable to us are those\nwhich relate to the order of their succession. On a knowledge of these is\nfounded every reasonable anticipation of future facts, and whatever power\nwe possess of influencing those facts to our advantage. Even the laws of\ngeometry are chiefly of practical importance to us as being a portion of\nthe premises from which the order of the succession of phenomena may be\ninferred. Inasmuch as the motion of bodies, the action of forces, and the\npropagation of influences of all sorts, take place in certain lines and\nover definite spaces, the properties of those lines and spaces are an\nimportant part of the laws to which those phenomena are themselves\nsubject. Again, motions, forces, or other influences, and times, are\nnumerable quantities; and the properties of number are applicable to them\nas to all other things. But though the laws of number and space are\nimportant elements in the ascertainment of uniformities of succession,\nthey can do nothing toward it when taken by themselves. They can only be\nmade instrumental to that purpose when we combine with them additional\npremises, expressive of uniformities of succession already known. By\ntaking, for instance, as premises these propositions, that bodies acted\nupon by an instantaneous force move with uniform velocity in straight\nlines; that bodies acted upon by a continuous force move with accelerated\nvelocity in straight lines; and that bodies acted upon by two forces in\ndifferent directions move in the diagonal of a parallelogram, whose sides\nrepresent the direction and quantity of those forces; we may by combining\nthese truths with propositions relating to the properties of straight\nlines and of parallelograms (as that a triangle is half a parallelogram of\nthe same base and altitude), deduce another important uniformity of\nsuccession, viz., that a body moving round a centre of force describes\nareas proportional to the times. But unless there had been laws of\nsuccession in our premises, there could have been no truths of succession\nin our conclusions. A similar remark might be extended to every other\nclass of phenomena really peculiar; and, had it been attended to, would\nhave prevented many chimerical attempts at demonstrations of the\nindemonstrable, and explanations which do not explain.\n\nIt is not, therefore, enough for us that the laws of space, which are only\nlaws of simultaneous phenomenon, and the laws of number, which though true\nof successive phenomena do not relate to their succession, possess the\nrigorous certainty and universality of which we are in search. We must\nendeavor to find some law of succession which has those same attributes,\nand is therefore fit to be made the foundation of processes for\ndiscovering, and of a test for verifying, all other uniformities of\nsuccession. This fundamental law must resemble the truths of geometry in\ntheir most remarkable peculiarity, that of never being, in any instance\nwhatever, defeated or suspended by any change of circumstances.\n\nNow among all those uniformities in the succession of phenomena, which\ncommon observation is sufficient to bring to light, there are very few\nwhich have any, even apparent, pretension to this rigorous\nindefeasibility: and of those few, one only has been found capable of\ncompletely sustaining it. In that one, however, we recognize a law which\nis universal also in another sense; it is co-extensive with the entire\nfield of successive phenomena, all instances whatever of succession being\nexamples of it. This law is the Law of Causation. The truth that every\nfact which has a beginning has a cause, is co-extensive with human\nexperience.\n\nThis generalization may appear to some minds not to amount to much, since\nafter all it asserts only this: \u201cit is a law, that every event depends on\nsome law:\u201d \u201cit is a law, that there is a law for every thing.\u201d We must\nnot, however, conclude that the generality of the principle is merely\nverbal; it will be found on inspection to be no vague or unmeaning\nassertion, but a most important and really fundamental truth.\n\n\u00a7 2. The notion of Cause being the root of the whole theory of Induction,\nit is indispensable that this idea should, at the very outset of our\ninquiry, be, with the utmost practicable degree of precision, fixed and\ndetermined. If, indeed, it were necessary for the purpose of inductive\nlogic that the strife should be quelled, which has so long raged among the\ndifferent schools of metaphysicians, respecting the origin and analysis of\nour idea of causation; the promulgation, or at least the general\nreception, of a true theory of induction, might be considered desperate\nfor a long time to come. But the science of the Investigation of Truth by\nmeans of Evidence, is happily independent of many of the controversies\nwhich perplex the science of the ultimate constitution of the human mind,\nand is under no necessity of pushing the analysis of mental phenomenon to\nthat extreme limit which alone ought to satisfy a metaphysician.\n\nI premise, then, that when in the course of this inquiry I speak of the\ncause of any phenomenon, I do not mean a cause which is not itself a\nphenomenon; I make no research into the ultimate or ontological cause of\nany thing. To adopt a distinction familiar in the writings of the Scotch\nmetaphysicians, and especially of Reid, the causes with which I concern\nmyself are not _efficient_, but _physical_ causes. They are causes in that\nsense alone, in which one physical fact is said to be the cause of\nanother. Of the efficient causes of phenomena, or whether any such causes\nexist at all, I am not called upon to give an opinion. The notion of\ncausation is deemed, by the schools of metaphysics most in vogue at the\npresent moment, to imply a mysterious and most powerful tie, such as can\nnot, or at least does not, exist between any physical fact and that other\nphysical fact on which it is invariably consequent, and which is popularly\ntermed its cause: and thence is deduced the supposed necessity of\nascending higher, into the essences and inherent constitution of things,\nto find the true cause, the cause which is not only followed by, but\nactually produces, the effect. No such necessity exists for the purposes\nof the present inquiry, nor will any such doctrine be found in the\nfollowing pages. The only notion of a cause, which the theory of induction\nrequires, is such a notion as can be gained from experience. The Law of\nCausation, the recognition of which is the main pillar of inductive\nscience, is but the familiar truth, that invariability of succession is\nfound by observation to obtain between every fact in nature and some other\nfact which has preceded it; independently of all considerations respecting\nthe ultimate mode of production of phenomena, and of every other question\nregarding the nature of \u201cThings in themselves.\u201d\n\nBetween the phenomena, then, which exist at any instant, and the phenomena\nwhich exist at the succeeding instant, there is an invariable order of\nsuccession; and, as we said in speaking of the general uniformity of the\ncourse of nature, this web is composed of separate fibres; this collective\norder is made up of particular sequences, obtaining invariably among the\nseparate parts. To certain facts, certain facts always do, and, as we\nbelieve, will continue to, succeed. The invariable antecedent is termed\nthe cause; the invariable consequent, the effect. And the universality of\nthe law of causation consists in this, that every consequent is connected\nin this manner with some particular antecedent, or set of antecedents. Let\nthe fact be what it may, if it has begun to exist, it was preceded by some\nfact or facts, with which it is invariably connected. For every event\nthere exists some combination of objects or events, some given concurrence\nof circumstances, positive and negative, the occurrence of which is always\nfollowed by that phenomenon. We may not have found out what this\nconcurrence of circumstances may be; but we never doubt that there is such\na one, and that it never occurs without having the phenomenon in question\nas its effect or consequence. On the universality of this truth depends\nthe possibility of reducing the inductive process to rules. The undoubted\nassurance we have that there is a law to be found if we only knew how to\nfind it, will be seen presently to be the source from which the canons of\nthe Inductive Logic derive their validity.\n\n\u00a7 3. It is seldom, if ever, between a consequent and a single antecedent,\nthat this invariable sequence subsists. It is usually between a consequent\nand the sum of several antecedents; the concurrence of all of them being\nrequisite to produce, that is, to be certain of being followed by, the\nconsequent. In such cases it is very common to single out one only of the\nantecedents under the denomination of Cause, calling the others merely\nConditions. Thus, if a person eats of a particular dish, and dies in\nconsequence, that is, would not have died if he had not eaten of it,\npeople would be apt to say that eating of that dish was the cause of his\ndeath. There needs not, however, be any invariable connection between\neating of the dish and death; but there certainly is, among the\ncircumstances which took place, some combination or other on which death\nis invariably consequent: as, for instance, the act of eating of the dish,\ncombined with a particular bodily constitution, a particular state of\npresent health, and perhaps even a certain state of the atmosphere; the\nwhole of which circumstances perhaps constituted in this particular case\nthe _conditions_ of the phenomenon, or, in other words, the set of\nantecedents which determined it, and but for which it would not have\nhappened. The real Cause, is the whole of these antecedents; and we have,\nphilosophically speaking, no right to give the name of cause to one of\nthem, exclusively of the others. What, in the case we have supposed,\ndisguises the incorrectness of the expression, is this: that the various\nconditions, except the single one of eating the food, were not _events_\n(that is, instantaneous changes, or successions of instantaneous changes)\nbut _states_, possessing more or less of permanency; and might therefore\nhave preceded the effect by an indefinite length of duration, for want of\nthe event which was requisite to complete the required concurrence of\nconditions: while as soon as that event, eating the food, occurs, no other\ncause is waited for, but the effect begins immediately to take place: and\nhence the appearance is presented of a more immediate and close connection\nbetween the effect and that one antecedent, than between the effect and\nthe remaining conditions. But though we may think proper to give the name\nof cause to that one condition, the fulfillment of which completes the\ntale, and brings about the effect without further delay; this condition\nhas really no closer relation to the effect than any of the other\nconditions has. All the conditions were equally indispensable to the\nproduction of the consequent; and the statement of the cause is\nincomplete, unless in some shape or other we introduce them all. A man\ntakes mercury, goes out-of-doors, and catches cold. We say, perhaps, that\nthe cause of his taking cold was exposure to the air. It is clear,\nhowever, that his having taken mercury may have been a necessary condition\nof his catching cold; and though it might consist with usage to say that\nthe cause of his attack was exposure to the air, to be accurate we ought\nto say that the cause was exposure to the air while under the effect of\nmercury.\n\nIf we do not, when aiming at accuracy, enumerate all the conditions, it is\nonly because some of them will in most cases be understood without being\nexpressed, or because for the purpose in view they may without detriment\nbe overlooked. For example, when we say, the cause of a man\u2019s death was\nthat his foot slipped in climbing a ladder, we omit as a thing unnecessary\nto be stated the circumstance of his weight, though quite as indispensable\na condition of the effect which took place. When we say that the assent of\nthe crown to a bill makes it law, we mean that the assent, being never\ngiven until all the other conditions are fulfilled, makes up the sum of\nthe conditions, though no one now regards it as the principal one. When\nthe decision of a legislative assembly has been determined by the casting\nvote of the chairman, we sometimes say that this one person was the cause\nof all the effects which resulted from the enactment. Yet we do not really\nsuppose that his single vote contributed more to the result than that of\nany other person who voted in the affirmative; but, for the purpose we\nhave in view, which is to insist on his individual responsibility, the\npart which any other person had in the transaction is not material.\n\nIn all these instances the fact which was dignified with the name of\ncause, was the one condition which came last into existence. But it must\nnot be supposed that in the employment of the term this or any other rule\nis always adhered to. Nothing can better show the absence of any\nscientific ground for the distinction between the cause of a phenomenon\nand its conditions, than the capricious manner in which we select from\namong the conditions that which we choose to denominate the cause. However\nnumerous the conditions may be, there is hardly any of them which may not,\naccording to the purpose of our immediate discourse, obtain that nominal\npre-eminence. This will be seen by analyzing the conditions of some one\nfamiliar phenomenon. For example, a stone thrown into water falls to the\nbottom. What are the conditions of this event? In the first place there\nmust be a stone, and water, and the stone must be thrown into the water;\nbut these suppositions forming part of the enunciation of the phenomenon\nitself, to include them also among the conditions would be a vicious\ntautology; and this class of conditions, therefore, have never received\nthe name of cause from any but the Aristotelians, by whom they were called\nthe _material_ cause, _causa materialis_. The next condition is, there\nmust be an earth: and accordingly it is often said, that the fall of a\nstone is caused by the earth; or by a power or property of the earth, or a\nforce exerted by the earth, all of which are merely roundabout ways of\nsaying that it is caused by the earth; or, lastly, the earth\u2019s attraction;\nwhich also is only a technical mode of saying that the earth causes the\nmotion, with the additional particularity that the motion is toward the\nearth, which is not a character of the cause, but of the effect. Let us\nnow pass to another condition. It is not enough that the earth should\nexist; the body must be within that distance from it, in which the earth\u2019s\nattraction preponderates over that of any other body. Accordingly we may\nsay, and the expression would be confessedly correct, that the cause of\nthe stone\u2019s falling is its being _within the sphere_ of the earth\u2019s\nattraction. We proceed to a further condition. The stone is immersed in\nwater: it is therefore a condition of its reaching the ground, that its\nspecific gravity exceed that of the surrounding fluid, or in other words\nthat it surpass in weight an equal volume of water. Accordingly any one\nwould be acknowledged to speak correctly who said, that the cause of the\nstone\u2019s going to the bottom is its exceeding in specific gravity the fluid\nin which it is immersed.\n\nThus we see that each and every condition of the phenomenon may be taken\nin its turn, and, with equal propriety in common parlance, but with equal\nimpropriety in scientific discourse, may be spoken of as if it were the\nentire cause. And in practice, that particular condition is usually styled\nthe cause, whose share in the matter is superficially the most\nconspicuous, or whose requisiteness to the production of the effect we\nhappen to be insisting on at the moment. So great is the force of this\nlast consideration, that it sometimes induces us to give the name of cause\neven to one of the negative conditions. We say, for example, The army was\nsurprised because the sentinel was off his post. But since the sentinel\u2019s\nabsence was not what created the enemy, or put the soldiers asleep, how\ndid it cause them to be surprised? All that is really meant is, that the\nevent would not have happened if he had been at his duty. His being off\nhis post was no producing cause, but the mere absence of a preventing\ncause: it was simply equivalent to his non-existence. From nothing, from a\nmere negation, no consequences can proceed. All effects are connected, by\nthe law of causation, with some set of _positive_ conditions; negative\nones, it is true, being almost always required in addition. In other\nwords, every fact or phenomenon which has a beginning, invariably arises\nwhen some certain combination of positive facts exists, provided certain\nother positive facts do not exist.\n\nThere is, no doubt, a tendency (which our first example, that of death\nfrom taking a particular food, sufficiently illustrates) to associate the\nidea of causation with the proximate antecedent _event_, rather than with\nany of the antecedent _states_, or permanent facts, which may happen also\nto be conditions of the phenomenon; the reason being that the event not\nonly exists, but begins to exist immediately previous; while the other\nconditions may have pre-existed for an indefinite time. And this tendency\nshows itself very visibly in the different logical fictions which are\nresorted to, even by men of science, to avoid the necessity of giving the\nname of cause to any thing which had existed for an indeterminate length\nof time before the effect. Thus, rather than say that the earth causes the\nfall of bodies, they ascribe it to a _force_ exerted by the earth, or an\n_attraction_ by the earth, abstractions which they can represent to\nthemselves as exhausted by each effort, and therefore constituting at each\nsuccessive instant a fresh fact, simultaneous with, or only immediately\npreceding, the effect. Inasmuch as the coming of the circumstance which\ncompletes the assemblage of conditions, is a change or event, it thence\nhappens that an event is always the antecedent in closest apparent\nproximity to the consequent: and this may account for the illusion which\ndisposes us to look upon the proximate event as standing more peculiarly\nin the position of a cause than any of the antecedent states. But even\nthis peculiarity, of being in closer proximity to the effect than any\nother of its conditions, is, as we have already seen, far from being\nnecessary to the common notion of a cause; with which notion, on the\ncontrary, any one of the conditions, either positive or negative, is\nfound, on occasion, completely to accord.(114)\n\nThe cause, then, philosophically speaking, is the sum total of the\nconditions, positive and negative taken together; the whole of the\ncontingencies of every description, which being realized, the consequent\ninvariably follows. The negative conditions, however, of any phenomenon, a\nspecial enumeration of which would generally be very prolix, may be all\nsummed up under one head, namely, the absence of preventing or\ncounteracting causes. The convenience of this mode of expression is mainly\ngrounded on the fact, that the effects of any cause in counteracting\nanother cause may in most cases be, with strict scientific exactness,\nregarded as a mere extension of its own proper and separate effects. If\ngravity retards the upward motion of a projectile, and deflects it into a\nparabolic trajectory, it produces, in so doing, the very same kind of\neffect, and even (as mathematicians know) the same quantity of effect, as\nit does in its ordinary operation of causing the fall of bodies when\nsimply deprived of their support. If an alkaline solution mixed with an\nacid destroys its sourness, and prevents it from reddening vegetable\nblues, it is because the specific effect of the alkali is to combine with\nthe acid, and form a compound with totally different qualities. This\nproperty, which causes of all descriptions possess, of preventing the\neffects of other causes by virtue (for the most part) of the same laws\naccording to which they produce their own,(115) enables us, by\nestablishing the general axiom that all causes are liable to be\ncounteracted in their effects by one another, to dispense with the\nconsideration of negative conditions entirely, and limit the notion of\ncause to the assemblage of the positive conditions of the phenomenon: one\nnegative condition invariably understood, and the same in all instances\n(namely, the absence of counteracting causes) being sufficient, along with\nthe sum of the positive conditions, to make up the whole set of\ncircumstances on which the phenomenon is dependent.\n\n\u00a7 4. Among the positive conditions, as we have seen that there are some to\nwhich, in common parlance, the term cause is more readily and frequently\nawarded, so there are others to which it is, in ordinary circumstances,\nrefused. In most cases of causation a distinction is commonly drawn\nbetween something which acts, and some other thing which is acted upon;\nbetween an _agent_ and a _patient_. Both of these, it would be universally\nallowed, are conditions of the phenomenon; but it would be thought absurd\nto call the latter the cause, that title being reserved for the former.\nThe distinction, however, vanishes on examination, or rather is found to\nbe only verbal; arising from an incident of mere expression, namely, that\nthe object said to be acted upon, and which is considered as the scene in\nwhich the effect takes place, is commonly included in the phrase by which\nthe effect is spoken of, so that if it were also reckoned as part of the\ncause, the seeming incongruity would arise of its being supposed to cause\nitself. In the instance which we have already had, of falling bodies, the\nquestion was thus put: What is the cause which makes a stone fall? and if\nthe answer had been \u201cthe stone itself,\u201d the expression would have been in\napparent contradiction to the meaning of the word cause. The stone,\ntherefore, is conceived as the patient, and the earth (or, according to\nthe common and most unphilosophical practice, an occult quality of the\nearth) is represented as the agent or cause. But that there is nothing\nfundamental in the distinction may be seen from this, that it is quite\npossible to conceive the stone as causing its own fall, provided the\nlanguage employed be such as to save the mere verbal incongruity. We might\nsay that the stone moves toward the earth by the properties of the matter\ncomposing it; and according to this mode of presenting the phenomenon, the\nstone itself might without impropriety be called the agent; though, to\nsave the established doctrine of the inactivity of matter, men usually\nprefer here also to ascribe the effect to an occult quality, and say that\nthe cause is not the stone itself, but the _weight_ or _gravitation_ of\nthe stone.\n\nThose who have contended for a radical distinction between agent and\npatient, have generally conceived the agent as that which causes some\nstate of, or some change in the state of, another object which is called\nthe patient. But a little reflection will show that the license we assume\nof speaking of phenomena as _states_ of the various objects which take\npart in them (an artifice of which so much use has been made by some\nphilosophers, Brown in particular, for the apparent explanation of\nphenomena), is simply a sort of logical fiction, useful sometimes as one\namong several modes of expression, but which should never be supposed to\nbe the enunciation of a scientific truth. Even those attributes of an\nobject which might seem with greatest propriety to be called states of the\nobject itself, its sensible qualities, its color, hardness, shape, and the\nlike, are in reality (as no one has pointed out more clearly than Brown\nhimself) phenomena of causation, in which the substance is distinctly the\nagent, or producing cause, the patient being our own organs, and those of\nother sentient beings. What we call states of objects, are always\nsequences into which the objects enter, generally as antecedents or\ncauses; and things are never more active than in the production of those\nphenomena in which they are said to be acted upon. Thus, in the example of\na stone falling to the earth, according to the theory of gravitation the\nstone is as much an agent as the earth, which not only attracts, but is\nitself attracted by, the stone. In the case of a sensation produced in our\norgans, the laws of our organization, and even those of our minds, are as\ndirectly operative in determining the effect produced, as the laws of the\noutward object. Though we call prussic acid the agent of a person\u2019s death,\nthe whole of the vital and organic properties of the patient are as\nactively instrumental as the poison, in the chain of effects which so\nrapidly terminates his sentient existence. In the process of education, we\nmay call the teacher the agent, and the scholar only the material acted\nupon; yet in truth all the facts which pre-existed in the scholar\u2019s mind\nexert either co-operating or counteracting agencies in relation to the\nteacher\u2019s efforts. It is not light alone which is the agent in vision, but\nlight coupled with the active properties of the eye and brain, and with\nthose of the visible object. The distinction between agent and patient is\nmerely verbal: patients are always agents; in a great proportion, indeed,\nof all natural phenomena, they are so to such a degree as to react\nforcibly on the causes which acted upon them: and even when this is not\nthe case, they contribute, in the same manner as any of the other\nconditions, to the production of the effect of which they are vulgarly\ntreated as the mere theatre. All the positive conditions of a phenomenon\nare alike agents, alike active; and in any expression of the cause which\nprofesses to be complete, none of them can with reason be excluded, except\nsuch as have already been implied in the words used for describing the\neffect; nor by including even these would there be incurred any but a\nmerely verbal impropriety.\n\n\u00a7 5. There is a case of causation which calls for separate notice, as it\npossesses a peculiar feature, and presents a greater degree of complexity\nthan the common case. It often happens that the effect, or one of the\neffects, of a cause, is, not to produce of itself a certain phenomenon,\nbut to fit something else for producing it. In other words, there is a\ncase of causation in which the effect is to invest an object with a\ncertain property. When sulphur, charcoal, and nitre are put together in\ncertain proportions and in a certain manner, the effect is, not an\nexplosion, but that the mixture acquires a property by which, in given\ncircumstances, it will explode. The various causes, natural and\nartificial, which educate the human body or the human mind, have for their\nprincipal effect, not to make the body or mind immediately do any thing,\nbut to endow it with certain properties\u2014in other words, to give assurance\nthat in given circumstances certain results will take place in it, or as\nconsequences of it. Physiological agencies often have for the chief part\nof their operation to _predispose_ the constitution to some mode of\naction. To take a simpler instance than all these: putting a coat of white\npaint upon a wall does not merely produce in those who see it done, the\nsensation of white; it confers on the wall the permanent property of\ngiving that kind of sensation. Regarded in reference to the sensation, the\nputting on of the paint is a condition of a condition; it is a condition\nof the wall\u2019s causing that particular fact. The wall may have been painted\nyears ago, but it has acquired a property which has lasted till now, and\nwill last longer; the antecedent condition necessary to enable the wall to\nbecome in its turn a condition, has been fulfilled once for all. In a case\nlike this, where the immediate consequent in the sequence is a property\nproduced in an object, no one now supposes the property to be a\nsubstantive entity \u201cinherent\u201d in the object. What has been produced is\nwhat, in other language, may be called a state of preparation in an object\nfor producing an effect. The ingredients of the gunpowder have been\nbrought into a state of preparation for exploding as soon as the other\nconditions of an explosion shall have occurred. In the case of the\ngunpowder, this state of preparation consists in a certain collocation of\nits particles relatively to one another. In the example of the wall, it\nconsists in a new collocation of two things relatively to each other\u2014the\nwall and the paint. In the example of the molding influences on the human\nmind, its being a collocation at all is only conjectural; for, even on the\nmaterialistic hypothesis, it would remain to be proved that the increased\nfacility with which the brain sums up a column of figures when it has been\nlong trained to calculation, is the result of a permanent new arrangement\nof some of its material particles. We must, therefore, content ourselves\nwith what we know, and must include among the effects of causes, the\ncapacities given to objects of being causes of other effects. This\ncapacity is not a real thing existing in the objects; it is but a name for\nour conviction that they will act in a particular manner when certain new\ncircumstances arise. We may invest this assurance of future events with a\nfictitious objective existence, by calling it a state of the object. But\nunless the state consists, as in the case of the gunpowder it does, in a\ncollocation of particles, it expresses no present fact; it is but the\ncontingent future fact brought back under another name.\n\nIt may be thought that this form of causation requires us to admit an\nexception to the doctrine that the conditions of a phenomenon\u2014the\nantecedents required for calling it into existence\u2014must all be found among\nthe facts immediately, not remotely, preceding its commencement. But what\nwe have arrived at is not a correction, it is only an explanation, of that\ndoctrine. In the enumeration of the conditions required for the occurrence\nof any phenomenon, it always has to be included that objects must be\npresent, possessed of given properties. It is a condition of the\nphenomenon explosion that an object should be present, of one or other of\ncertain kinds, which for that reason are called explosive. The presence of\none of these objects is a condition immediately precedent to the\nexplosion. The condition which is not immediately precedent is the cause\nwhich produced, not the explosion, but the explosive property. The\nconditions of the explosion itself were all present immediately before it\ntook place, and the general law, therefore, remains intact.\n\n\u00a7 6. It now remains to advert to a distinction which is of first-rate\nimportance both for clearing up the notion of cause, and for obviating a\nvery specious objection often made against the view which we have taken of\nthe subject.\n\nWhen we define the cause of any thing (in the only sense in which the\npresent inquiry has any concern with causes) to be \u201cthe antecedent which\nit invariably follows,\u201d we do not use this phrase as exactly synonymous\nwith \u201cthe antecedent which it invariably _has_ followed in our past\nexperience.\u201d Such a mode of conceiving causation would be liable to the\nobjection very plausibly urged by Dr. Reid, namely, that according to this\ndoctrine night must be the cause of day, and day the cause of night; since\nthese phenomena have invariably succeeded one another from the beginning\nof the world. But it is necessary to our using the word cause, that we\nshould believe not only that the antecedent always _has_ been followed by\nthe consequent, but that, as long as the present constitution of\nthings(116) endures, it always _will_ be so. And this would not be true of\nday and night. We do not believe that night will be followed by day under\nall imaginable circumstances, but only that it will be so _provided_ the\nsun rises above the horizon. If the sun ceased to rise, which, for aught\nwe know, may be perfectly compatible with the general laws of matter,\nnight would be, or might be, eternal. On the other hand, if the sun is\nabove the horizon, his light not extinct, and no opaque body between us\nand him, we believe firmly that unless a change takes place in the\nproperties of matter, this combination of antecedents will be followed by\nthe consequent, day; that if the combination of antecedents could be\nindefinitely prolonged, it would be always day; and that if the same\ncombination had always existed, it would always have been day, quite\nindependently of night as a previous condition. Therefore is it that we do\nnot call night the cause, nor even a condition, of day. The existence of\nthe sun (or some such luminous body), and there being no opaque medium in\na straight line(117) between that body and the part of the earth where we\nare situated, are the sole conditions; and the union of these, without the\naddition of any superfluous circumstance, constitutes the cause. This is\nwhat writers mean when they say that the notion of cause involves the idea\nof necessity. If there be any meaning which confessedly belongs to the\nterm necessity, it is _unconditionalness_. That which is necessary, that\nwhich _must_ be, means that which will be, whatever supposition we may\nmake in regard to all other things. The succession of day and night\nevidently is not necessary in this sense. It is conditional on the\noccurrence of other antecedents. That which will be followed by a given\nconsequent when, and only when, some third circumstance also exists, is\nnot the cause, even though no case should ever have occurred in which the\nphenomenon took place without it.\n\nInvariable sequence, therefore, is not synonymous with causation, unless\nthe sequence, besides being invariable, is unconditional. There are\nsequences, as uniform in past experience as any others whatever, which yet\nwe do not regard as cases of causation, but as conjunctions in some sort\naccidental. Such, to an accurate thinker, is that of day and night. The\none might have existed for any length of time, and the other not have\nfollowed the sooner for its existence; it follows only if certain other\nantecedents exist; and where those antecedents existed, it would follow in\nany case. No one, probably, ever called night the cause of day; mankind\nmust so soon have arrived at the very obvious generalization, that the\nstate of general illumination which we call day would follow from the\npresence of a sufficiently luminous body, whether darkness had preceded or\nnot.\n\nWe may define, therefore, the cause of a phenomenon, to be the antecedent,\nor the concurrence of antecedents, on which it is invariably and\n_unconditionally_ consequent. Or if we adopt the convenient modification\nof the meaning of the word cause, which confines it to the assemblage of\npositive conditions without the negative, then instead of\n\u201cunconditionally,\u201d we must say, \u201csubject to no other than negative\nconditions.\u201d\n\nTo some it may appear, that the sequence between night and day being\ninvariable in our experience, we have as much ground in this case as\nexperience can give in any case, for recognizing the two phenomena as\ncause and effect; and that to say that more is necessary\u2014to require a\nbelief that the succession is unconditional, or, in other words, that it\nwould be invariable under all changes of circumstances, is to acknowledge\nin causation an element of belief not derived from experience. The answer\nto this is, that it is experience itself which teaches us that one\nuniformity of sequence is conditional and another unconditional. When we\njudge that the succession of night and day is a derivative sequence,\ndepending on something else, we proceed on grounds of experience. It is\nthe evidence of experience which convinces us that day could equally exist\nwithout being followed by night, and that night could equally exist\nwithout being followed by day. To say that these beliefs are \u201cnot\ngenerated by our mere observation of sequence,\u201d(118) is to forget that\ntwice in every twenty-four hours, when the sky is clear, we have an\n_experimentum crucis_ that the cause of day is the sun. We have an\nexperimental knowledge of the sun which justifies us on experimental\ngrounds in concluding, that if the sun were always above the horizon there\nwould be day, though there had been no night, and that if the sun were\nalways below the horizon there would be night, though there had been no\nday. We thus know from experience that the succession of night and day is\nnot unconditional. Let me add, that the antecedent which is only\nconditionally invariable, is not the invariable antecedent. Though a fact\nmay, in experience, have always been followed by another fact, yet if the\nremainder of our experience teaches us that it might not always be so\nfollowed, or if the experience itself is such as leaves room for a\npossibility that the known cases may not correctly represent all possible\ncases, the hitherto invariable antecedent is not accounted the cause; but\nwhy? Because we are not sure that it _is_ the invariable antecedent.\n\nSuch cases of sequence as that of day and night not only do not contradict\nthe doctrine which resolves causation into invariable sequence, but are\nnecessarily implied in that doctrine. It is evident, that from a limited\nnumber of unconditional sequences, there will result a much greater number\nof conditional ones. Certain causes being given, that is, certain\nantecedents which are unconditionally followed by certain consequents; the\nmere co-existence of these causes will give rise to an unlimited number of\nadditional uniformities. If two causes exist together, the effects of both\nwill exist together; and if many causes co-exist, these causes (by what we\nshall term hereafter the intermixture of their laws) will give rise to new\neffects, accompanying or succeeding one another in some particular order,\nwhich order will be invariable while the causes continue to co-exist, but\nno longer. The motion of the earth in a given orbit round the sun, is a\nseries of changes which follow one another as antecedents and consequents,\nand will continue to do so while the sun\u2019s attraction, and the force with\nwhich the earth tends to advance in a direct line through space, continue\nto co-exist in the same quantities as at present. But vary either of these\ncauses, and this particular succession of motions would cease to take\nplace. The series of the earth\u2019s motions, therefore, though a case of\nsequence invariable within the limits of human experience, is not a case\nof causation. It is not unconditional.\n\nThis distinction between the relations of succession which, so far as we\nknow, are unconditional, and those relations, whether of succession or of\nco-existence, which, like the earth\u2019s motions, or the succession of day\nand night, depend on the existence or on the co-existence of other\nantecedent facts\u2014corresponds to the great division which Dr. Whewell and\nother writers have made of the field of science, into the investigation of\nwhat they term the Laws of Phenomena, and the investigation of causes; a\nphraseology, as I conceive, not philosophically sustainable, inasmuch as\nthe ascertainment of causes, such causes as the human faculties can\nascertain, namely, causes which are themselves phenomena, is, therefore,\nmerely the ascertainment of other and more universal Laws of Phenomena.\nAnd let me here observe, that Dr. Whewell, and in some degree even Sir\nJohn Herschel, seem to have misunderstood the meaning of those writers\nwho, like M. Comt\u00e9, limit the sphere of scientific investigation to Laws\nof Phenomena, and speak of the inquiry into causes as vain and futile. The\ncauses which M. Comt\u00e9 designates as inaccessible, are efficient causes.\nThe investigation of physical, as opposed to efficient, causes (including\nthe study of all the active forces in Nature, considered as facts of\nobservation) is as important a part of M. Comt\u00e9\u2019s conception of science as\nof Dr. Whewell\u2019s. His objection to the _word_ cause is a mere matter of\nnomenclature, in which, as a matter of nomenclature, I consider him to be\nentirely wrong. \u201cThose,\u201d it is justly remarked by Mr. Bailey,(119) \u201cwho,\nlike M. Comt\u00e9, object to designate _events_ as causes, are objecting\nwithout any real ground to a mere but extremely convenient generalization,\nto a very useful common name, the employment of which involves, or needs\ninvolve, no particular theory.\u201d To which it may be added, that by\nrejecting this form of expression, M. Comt\u00e9 leaves himself without any\nterm for marking a distinction which, however incorrectly expressed, is\nnot only real, but is one of the fundamental distinctions in science;\nindeed it is on this alone, as we shall hereafter find, that the\npossibility rests of framing a rigorous Canon of Induction. And as things\nleft without a name are apt to be forgotten, a Canon of that description\nis not one of the many benefits which the philosophy of Induction has\nreceived from M. Comt\u00e9\u2019s great powers.\n\n\u00a7 7. Does a cause always stand with its effect in the relation of\nantecedent and consequent? Do we not often say of two simultaneous facts\nthat they are cause and effect\u2014as when we say that fire is the cause of\nwarmth, the sun and moisture the cause of vegetation, and the like? Since\na cause does not necessarily perish because its effect has been produced,\nthe two things do very generally co-exist; and there are some appearances,\nand some common expressions, seeming to imply not only that causes may,\nbut that they must, be contemporaneous with their effects. _Cessante caus\u00e2\ncessat et effectus_, has been a dogma of the schools: the necessity for\nthe continued existence of the cause in order to the continuance of the\neffect, seems to have been once a generally received doctrine. Kepler\u2019s\nnumerous attempts to account for the motions of the heavenly bodies on\nmechanical principles, were rendered abortive by his always supposing that\nthe agency which set those bodies in motion must continue to operate in\norder to keep up the motion which it at first produced. Yet there were at\nall times many familiar instances of the continuance of effects, long\nafter their causes had ceased. A _coup de soleil_ gives a person\nbrain-fever: will the fever go off as soon as he is moved out of the\nsunshine? A sword is run through his body: must the sword remain in his\nbody in order that he may continue dead? A plowshare once made, remains a\nplowshare, without any continuance of heating and hammering, and even\nafter the man who heated and hammered it has been gathered to his fathers.\nOn the other hand, the pressure which forces up the mercury in an\nexhausted tube must be continued in order to sustain it in the tube. This\n(it may be replied) is because another force is acting without\nintermission, the force of gravity, which would restore it to its level,\nunless counterpoised by a force equally constant. But again: a tight\nbandage causes pain, which pain will sometimes go off as soon as the\nbandage is removed. The illumination which the sun diffuses over the earth\nceases when the sun goes down.\n\nThere is, therefore, a distinction to be drawn. The conditions which are\nnecessary for the first production of a phenomenon, are occasionally also\nnecessary for its continuance; though more commonly its continuance\nrequires no condition except negative ones. Most things, once produced,\ncontinue as they are, until something changes or destroys them; but some\nrequire the permanent presence of the agencies which produced them at\nfirst. These may, if we please, be considered as instantaneous phenomena,\nrequiring to be renewed at each instant by the cause by which they were at\nfirst generated. Accordingly, the illumination of any given point of space\nhas always been looked upon as an instantaneous fact, which perishes and\nis perpetually renewed as long as the necessary conditions subsist. If we\nadopt this language we avoid the necessity of admitting that the\ncontinuance of the cause is ever required to maintain the effect. We may\nsay, it is not required to maintain, but to reproduce, the effect, or else\nto counteract some force tending to destroy it. And this may be a\nconvenient phraseology. But it is only a phraseology. The fact remains,\nthat in some cases (though those are a minority) the continuance of the\nconditions which produced an effect is necessary to the continuance of the\neffect.\n\nAs to the ulterior question, whether it is strictly necessary that the\ncause, or assemblage of conditions, should precede, by ever so short an\ninstant, the production of the effect (a question raised and argued with\nmuch ingenuity by Sir John Herschel in an Essay already quoted),(120) the\ninquiry is of no consequence for our present purpose. There certainly are\ncases in which the effect follows without any interval perceptible by our\nfaculties; and when there is an interval, we can not tell by how many\nintermediate links imperceptible to us that interval may really be filled\nup. But even granting that an effect may commence simultaneously with its\ncause, the view I have taken of causation is in no way practically\naffected. Whether the cause and its effect be necessarily successive or\nnot, the beginning of a phenomenon is what implies a cause, and causation\nis the law of the succession of phenomena. If these axioms be granted, we\ncan afford, though I see no necessity for doing so, to drop the words\nantecedent and consequent as applied to cause and effect. I have no\nobjection to define a cause, the assemblage of phenomena, which occurring,\nsome other phenomenon invariably commences, or has its origin. Whether the\neffect coincides in point of time with, or immediately follows, the\nhindmost of its conditions, is immaterial. At all events, it does not\nprecede it; and when we are in doubt, between two co-existent phenomena,\nwhich is cause and which effect, we rightly deem the question solved if we\ncan ascertain which of them preceded the other.\n\n\u00a7 8. It continually happens that several different phenomena, which are\nnot in the slightest degree dependent or conditional on one another, are\nfound all to depend, as the phrase is, on one and the same agent; in other\nwords, one and the same phenomenon is seen to be followed by several sorts\nof effects quite heterogeneous, but which go on simultaneously one with\nanother; provided, of course, that all other conditions requisite for each\nof them also exist. Thus, the sun produces the celestial motions; it\nproduces daylight, and it produces heat. The earth causes the fall of\nheavy bodies, and it also, in its capacity of a great magnet, causes the\nphenomena of the magnetic needle. A crystal of galena causes the\nsensations of hardness, of weight, of cubical form, of gray color, and\nmany others between which we can trace no interdependence. The purpose to\nwhich the phraseology of Properties and Powers is specially adapted, is\nthe expression of this sort of cases. When the same phenomenon is followed\n(either subject or not to the presence of other conditions) by effects of\ndifferent and dissimilar orders, it is usual to say that each different\nsort of effect is produced by a different property of the cause. Thus we\ndistinguish the attractive or gravitative property of the earth, and its\nmagnetic property: the gravitative, luminiferous, and calorific properties\nof the sun: the color, shape, weight, and hardness of a crystal. These are\nmere phrases, which explain nothing, and add nothing to our knowledge of\nthe subject; but, considered as abstract names denoting the connection\nbetween the different effects produced and the object which produces them,\nthey are a very powerful instrument of abridgment, and of that\nacceleration of the process of thought which abridgment accomplishes.\n\nThis class of considerations leads to a conception which we shall find to\nbe of great importance, that of a Permanent Cause, or original natural\nagent. There exist in nature a number of permanent causes, which have\nsubsisted ever since the human race has been in existence, and for an\nindefinite and probably an enormous length of time previous. The sun, the\nearth, and planets, with their various constituents, air, water, and other\ndistinguishable substances, whether simple or compound, of which nature is\nmade up, are such Permanent Causes. These have existed, and the effects or\nconsequences which they were fitted to produce have taken place (as often\nas the other conditions of the production met), from the very beginning of\nour experience. But we can give no account of the origin of the Permanent\nCauses themselves. Why these particular natural agents existed originally\nand no others, or why they are commingled in such and such proportions,\nand distributed in such and such a manner throughout space, is a question\nwe can not answer. More than this: we can discover nothing regular in the\ndistribution itself; we can reduce it to no uniformity, to no law. There\nare no means by which, from the distribution of these causes or agents in\none part of space, we could conjecture whether a similar distribution\nprevails in another. The co-existence, therefore, of Primeval Causes\nranks, to us, among merely casual concurrences: and all those sequences or\nco-existences among the effects of several such causes, which, though\ninvariable while those causes co-exist, would, if the co-existence\nterminated, terminate along with it, we do not class as cases of\ncausation, or laws of nature: we can only calculate on finding these\nsequences or co-existences where we know by direct evidence, that the\nnatural agents on the properties of which they ultimately depend, are\ndistributed in the requisite manner. These Permanent Causes are not always\nobjects; they are sometimes events, that is to say, periodical cycles of\nevents, that being the only mode in which events can possess the property\nof permanence. Not only, for instance, is the earth itself a permanent\ncause, or primitive natural agent, but the earth\u2019s rotation is so too: it\nis a cause which has produced, from the earliest period (by the aid of\nother necessary conditions), the succession of day and night, the ebb and\nflow of the sea, and many other effects, while, as we can assign no cause\n(except conjecturally) for the rotation itself, it is entitled to be\nranked as a primeval cause. It is, however, only the _origin_ of the\nrotation which is mysterious to us: once begun, its continuance is\naccounted for by the first law of motion (that of the permanence of\nrectilinear motion once impressed) combined with the gravitation of the\nparts of the earth toward one another.\n\nAll phenomena without exception which begin to exist, that is, all except\nthe primeval causes, are effects either immediate or remote of those\nprimitive facts, or of some combination of them. There is no Thing\nproduced, no event happening, in the known universe, which is not\nconnected by a uniformity, or invariable sequence, with some one or more\nof the phenomena which preceded it; insomuch that it will happen again as\noften as those phenomena occur again, and as no other phenomenon having\nthe character of a counteracting cause shall co-exist. These antecedent\nphenomena, again, were connected in a similar manner with some that\npreceded them; and so on, until we reach, as the ultimate step attainable\nby us, either the properties of some one primeval cause, or the\nconjunction of several. The whole of the phenomena of nature were\ntherefore the necessary, or, in other words, the unconditional,\nconsequences of some former collocation of the Permanent Causes.\n\nThe state of the whole universe at any instant, we believe to be the\nconsequence of its state at the previous instant; insomuch that one who\nknew all the agents which exist at the present moment, their collocation\nin space, and all their properties, in other words, the laws of their\nagency, could predict the whole subsequent history of the universe, at\nleast unless some new volition of a power capable of controlling the\nuniverse should supervene.(121) And if any particular state of the entire\nuniverse could ever recur a second time, all subsequent states would\nreturn too, and history would, like a circulating decimal of many figures,\nperiodically repeat itself:\n\n\n    Jam redit et virgo, redeunt Saturnia regna....\n    Alter erit tum Tiphys, et altera qu\u00e6 vehat Argo\n    Delectos heroas; erunt quoque altera bella,\n    Atque iterum ad Trojam magnus mittetur Achilles.\n\n\nAnd though things do not really revolve in this eternal round, the whole\nseries of events in the history of the universe, past and future, is not\nthe less capable, in its own nature, of being constructed _a priori_ by\nany one whom we can suppose acquainted with the original distribution of\nall natural agents, and with the whole of their properties, that is, the\nlaws of succession existing between them and their effects: saving the far\nmore than human powers of combination and calculation which would be\nrequired, even in one possessing the data, for the actual performance of\nthe task.\n\n\u00a7 9. Since every thing which occurs is determined by laws of causation and\ncollocations of the original causes, it follows that the co-existences\nwhich are observable among effects can not be themselves the subject of\nany similar set of laws, distinct from laws of causation. Uniformities\nthere are, as well of co-existence as of succession, among effects; but\nthese must in all cases be a mere result either of the identity or of the\nco-existence of their causes: if the causes did not co-exist, neither\ncould the effects. And these causes being also effects of prior causes,\nand these of others, until we reach the primeval causes, it follows that\n(except in the case of effects which can be traced immediately or remotely\nto one and the same cause) the co-existences of phenomena can in no case\nbe universal, unless the co-existences of the primeval causes to which the\neffects are ultimately traceable can be reduced to a universal law: but we\nhave seen that they can not. There are, accordingly, no original and\nindependent, in other words no unconditional, uniformities of\nco-existence, between effects of different causes; if they co-exist, it is\nonly because the causes have casually co-existed. The only independent and\nunconditional co-existences which are sufficiently invariable to have any\nclaim to the character of laws, are between different and mutually\nindependent effects of the same cause; in other words, between different\nproperties of the same natural agent. This portion of the Laws of Nature\nwill be treated of in the latter part of the present Book, under the name\nof the Specific Properties of Kinds.\n\n\u00a7 10. Since the first publication of the present treatise, the sciences of\nphysical nature have made a great advance in generalization, through the\ndoctrine known as the Conservation or Persistence of Force. This imposing\nedifice of theory, the building and laying out of which has for some time\nbeen the principal occupation of the most systematic minds among physical\ninquirers, consists of two stages: one, of ascertained fact, the other\ncontaining a large element of hypothesis.\n\nTo begin with the first. It is proved by numerous facts, both natural and\nof artificial production, that agencies which had been regarded as\ndistinct and independent sources of force\u2014heat, electricity, chemical\naction, nervous and muscular action, momentum of moving bodies\u2014are\ninterchangeable, in definite and fixed quantities, with one another. It\nhad long been known that these dissimilar phenomena had the power, under\ncertain conditions, of producing one another: what is new in the theory is\na more accurate estimation of what this production consists in. What\nhappens is, that the whole or part of the one kind of phenomena\ndisappears, and is replaced by phenomena of one of the other descriptions,\nand that there is an equivalence in quantity between the phenomena that\nhave disappeared and those which have been produced, insomuch that if the\nprocess be reversed, the very same quantity which had disappeared will\nre-appear, without increase or diminution. Thus the amount of heat which\nwill raise the temperature of a pound of water one degree of the\nthermometer, will, if expended, say in the expansion of steam, lift a\nweight of 772 pounds one foot, or a weight of one pound 772 feet: and the\nsame exact quantity of heat can, by certain means, be recovered, through\nthe expenditure of exactly that amount of mechanical motion.\n\nThe establishment of this comprehensive law has led to a change in the\nlanguage in which the scientific world had been accustomed to speak of\nwhat are called the Forces of nature. Before this correlation between\nphenomena most unlike one another had been ascertained, their unlikeness\nhad caused them to be referred to so many distinct forces. Now that they\nare known to be convertible into one another without loss, they are spoken\nof as all of them results of one and the same force, manifesting itself in\ndifferent modes. This force (it is said) can only produce a limited and\ndefinite quantity of effect, but always does produce that definite\nquantity; and produces it, according to circumstances, in one or another\nof the forms, or divides it among several, but so as (according to a scale\nof numerical equivalents established by experiment) always to make up the\nsame sum; and no one of the manifestations can be produced, save by the\ndisappearance of the equivalent quantity of another, which in its turn, in\nappropriate circumstances, will re-appear undiminished. This mutual\ninterchangeability of the forces of nature, according to fixed numerical\nequivalents, is the part of the new doctrine which rests on irrefragable\nfact.\n\nTo make the statement true, however, it is necessary to add, that an\nindefinite and perhaps immense interval of time may elapse between the\ndisappearance of the force in one form and its re-appearance in another. A\nstone thrown up into the air with a given force, and falling back\nimmediately, will, by the time it reaches the earth, recover the exact\namount of mechanical momentum which was expended in throwing it up,\ndeduction being made of a small portion of motion which has been\ncommunicated to the air. But if the stone has lodged on a height, it may\nnot fall back for years, or perhaps ages, and until it does, the force\nexpended in raising it is temporarily lost, being represented only by\nwhat, in the language of the new theory, is called potential energy. The\ncoal imbedded in the earth is considered by the theory as a vast reservoir\nof force, which has remained dormant for many geological periods, and will\nso remain until, by being burned, it gives out the stored-up force in the\nform of heat. Yet it is not supposed that this force is a material thing\nwhich can be confined by bounds, as used to be thought of latent heat when\nthat important phenomenon was first discovered. What is meant is that when\nthe coal does at last, by combustion, generate a quantity of heat\n(transformable like all other heat into mechanical momentum, and the other\nforms of force), this extrication of heat is the re-appearance of a force\nderived from the sun\u2019s rays, expended myriads of ages ago in the\nvegetation of the organic substances which were the material of the coal.\n\nLet us now pass to the higher stage of the theory of Conservation of\nForce; the part which is no longer a generalization of proved fact, but a\ncombination of fact and hypothesis. Stated in few words, it is as follows:\nThat the Conservation of Force is really the Conservation of Motion; that\nin the various interchanges between the forms of force, it is always\nmotion that is transformed into motion. To establish this, it is necessary\nto assume motions which are hypothetical. The supposition is, that there\nare motions which manifest themselves to our senses only as heat,\nelectricity, etc., being molecular motions; oscillations, invisible to us,\namong the minute particles of bodies; and that these molecular motions are\ntransmutable into molar motions (motions of masses), and molar motions\ninto molecular. Now there is a real basis of fact for this supposition: we\nhave positive evidence of the existence of molecular motion in these\nmanifestations of force. In the case of chemical action, for instance, the\nparticles separate and form new combinations, often with a great visible\ndisturbance of the mass. In the case of heat, the evidence is equally\nconclusive, since heat expands bodies (that is, causes their particles to\nmove _from_ one another); and if of sufficient amount, changes their mode\nof aggregation from solid to liquid, or from liquid to gaseous. Again, the\nmechanical actions which produce heat\u2014friction, and the collision of\nbodies\u2014must from the nature of the case produce a shock, that is, an\ninternal motion of particles, which indeed, we find, is often so violent\nas to break them permanently asunder. Such facts are thought to warrant\nthe inference, that it is not, as was supposed, heat that causes the\nmotion of particles, but the motion of particles that causes heat; the\noriginal cause of both being the previous motion (whether molar or\nmolecular\u2014collision of bodies or combustion of fuel) which formed the\nheating agency. This inference already contains hypothesis; but at least\nthe supposed cause, the intestine motion of molecules, is a _vera causa_.\nBut in order to reduce the Conservation of Force to Conservation of\nMotion, it was necessary to attribute to motion the heat propagated,\nthrough apparently empty space, from the sun. This required the\nsupposition (already made for the explanation of the laws of light) of a\nsubtle ether pervading space, which, though impalpable to us, must have\nthe property which constitutes matter, that of resistance, since waves are\npropagated through it by an impulse from a given point. The ether must be\nsupposed (a supposition not required by the theory of light) to penetrate\ninto the minute interstices of all bodies. The vibratory motion supposed\nto be taking place in the heated mass of the sun, is considered as\nimparted from that mass to the particles of the surrounding ether, and\nthrough them to the particles of the same ether in the interstices of\nterrestrial bodies; and this, too, with a sufficient mechanical force to\nthrow the particles of those bodies into a state of similar vibration,\nproducing the expansion of their mass, and the sensation of heat in\nsentient creatures. All this is hypothesis, though, of its legitimacy as\nhypothesis, I do not mean to express any doubt. It would seem to follow as\na consequence from this theory, that Force may and should be defined,\nmatter in motion. This definition, however, will not stand, for, as has\nalready been seen, the matter needs not be in _actual_ motion. It is not\nnecessary to suppose that the motion afterward manifested, is actually\ntaking place among the molecules of the coal during its sojourn in the\nearth;(122) certainly not in the stone which is at rest on the eminence to\nwhich it has been raised. The true definition of Force must be, not\nmotion, but Potentiality of Motion; and what the doctrine, if established,\namounts to, is, not that there is at all times the same quantity of actual\nmotion in the universe; but that the possibilities of motion are limited\nto a definite quantity, which can not be added to, but which can not be\nexhausted; and that all actual motion which takes place in Nature is a\ndraft upon this limited stock. It needs not all of it have ever existed as\nactual motion. There is a vast amount of potential motion in the universe\nin the form of gravitation, which it would be a great abuse of hypothesis\nto suppose to have been stored up by the expenditure of an equal amount of\nactual motion in some former state of the universe. Nor does the motion\nproduced by gravity take place, so far as we know, at the expense of any\nother motion, either molar or molecular.\n\nIt is proper to consider whether the adoption of this theory as a\nscientific truth, involving as it does a change in the conception hitherto\nentertained of the most general physical agencies, requires any\nmodification in the view I have taken of Causation as a law of nature. As\nit appears to me, none whatever. The manifestations which the theory\nregards as modes of motion, are as much distinct and separate phenomena\nwhen referred to a single force, as when attributed to several. Whether\nthe phenomenon is called a transformation of force or the generation of\none, it has its own set or sets of antecedents, with which it is connected\nby invariable and unconditional sequence; and that set, or those sets, of\nantecedents are its cause. The relation of the Conservation theory to the\nprinciple of Causation is discussed in much detail, and very\ninstructively, by Professor Bain, in the second volume of his Logic. The\nchief practical conclusion drawn by him, bearing on Causation, is, that we\nmust distinguish in the assemblage of conditions which constitutes the\nCause of a phenomenon, two elements: one, the presence of a force; the\nother, the collocation or position of objects which is required in order\nthat the force may undergo the particular transmutation which constitutes\nthe phenomenon. Now, it might always have been said with acknowledged\ncorrectness, that a force and a collocation were both of them necessary to\nproduce any phenomenon. The law of causation is, that change can only be\nproduced by change. Along with any number of stationary antecedents, which\nare collocations, there must be at least one changing antecedent, which is\na force. To produce a bonfire, there must not only be fuel, and air, and a\nspark, which are collocations, but chemical action between the air and the\nmaterials, which is a force. To grind corn, there must be a certain\ncollocation of the parts composing a mill, relatively to one another and\nto the corn; but there must also be the gravitation of water, or the\nmotion of wind, to supply a force. But as the force in these cases was\nregarded as a property of the objects in which it is embodied, it seemed\ntautology to say that there must be the collocation _and_ the force. As\nthe collocation must be a collocation of objects possessing the\nforce-giving property, the collocation, so understood, included the force.\n\nHow, then, shall we have to express these facts, if the theory be finally\nsubstantiated that all Force is reducible to a previous Motion? We shall\nhave to say, that one of the conditions of every phenomenon is an\nantecedent Motion. But it will have to be explained that this needs not be\n_actual_ motion. The coal which supplies the force exerted in combustion\nis not shown to have been exerting that force in the form of molecular\nmotion in the pit; it was not even exerting pressure. The stone on the\neminence _is_ exerting a pressure, but only equivalent to its weight, not\nto the additional momentum it would acquire by falling. The antecedent,\ntherefore, is not a force in action; and we can still only call it a\nproperty of the objects, by which they would exert a force on the\noccurrence of a fresh collocation. The collocation, therefore, still\nincludes the force. The force said to be stored up, is simply a particular\nproperty which the object has acquired. The cause we are in search of, is\na collocation of objects possessing that particular property. When,\nindeed, we inquire further into the cause from which they derive that\nproperty, the new conception introduced by the Conservation theory comes\nin: the property is itself an effect, and its cause, according to the\ntheory, is a former motion of exactly equivalent amount, which has been\nimpressed on the particles of the body, perhaps at some very distant\nperiod. But the case is simply one of those we have already considered, in\nwhich the efficacy of a cause consists in its investing an object with a\nproperty. The force said to be laid up, and merely potential, is no more a\nreally existing thing than any other properties of objects are really\nexisting things. The expression is a mere artifice of language, convenient\nfor describing the phenomena: it is unnecessary to suppose that any thing\nhas been in continuous existence except an abstract potentiality. A force\nsuspended in its operation, neither manifesting itself by motion nor by\npressure, is not an existing fact, but a name for our conviction that in\nappropriate circumstances a fact would take place. We know that a pound\nweight, were it to fall from the earth into the sun, would acquire in\nfalling a momentum equal to millions of pounds; but we do not credit the\npound weight with more of actually existing force than is equal to the\npressure it is now exerting on the earth, and that is exactly a pound. We\nmight as well say that a force of millions of pounds exists in a pound, as\nthat the force which will manifest itself when the coal is burned is a\nreal thing existing in the coal. What is fixed in the coal is only a\ncertain property: it has become fit to be the antecedent of an effect\ncalled combustion, which partly consists in giving out, under certain\nconditions, a given definite quantity of heat.\n\nWe thus see that no new general conception of Causation is introduced by\nthe Conservation theory. The indestructibility of Force no more interferes\nwith the theory of Causation than the indestructibility of Matter, meaning\nby matter the element of resistance in the sensible world. It only enables\nus to understand better than before the nature and laws of some of the\nsequences.\n\nThis better understanding, however, enables us, with Mr. Bain, to admit,\nas one of the tests for distinguishing causation from mere concomitance,\nthe expenditure or transfer of energy. If the effect, or any part of the\neffect, to be accounted for, consists in putting matter in motion, then\nany of the objects present which has lost motion has contributed to the\neffect; and this is the true meaning of the proposition that the cause is\nthat one of the antecedents which exerts active force.\n\n\u00a7 11. It is proper in this place to advert to a rather ancient doctrine\nrespecting causation, which has been revived during the last few years in\nmany quarters, and at present gives more signs of life than any other\ntheory of causation at variance with that set forth in the preceding\npages.\n\nAccording to the theory in question, Mind, or to speak move precisely,\nWill, is the only cause of phenomena. The type of Causation, as well as\nthe exclusive source from which we derive the idea, is our own voluntary\nagency. Here, and here only (it is said), we have direct evidence of\ncausation. We know that we can move our bodies. Respecting the phenomena\nof inanimate nature, we have no other direct knowledge than that of\nantecedence and sequence. But in the case of our voluntary actions, it is\naffirmed that we are conscious of power before we have experience of\nresults. An act of volition, whether followed by an effect or not, is\naccompanied by a consciousness of effort, \u201cof force exerted, of power in\naction, which is necessarily causal, or causative.\u201d This feeling of energy\nor force, inherent in an act of will, is knowledge _a priori_; assurance,\nprior to experience, that we have the power of causing effects. Volition,\ntherefore, it is asserted, is something more than an unconditional\nantecedent; it is a cause, in a different sense from that in which\nphysical phenomena are said to cause one another: it is an Efficient\nCause. From this the transition is easy to the further doctrine, that\nVolition is the _sole_ Efficient Cause of all phenomena. \u201cIt is\ninconceivable that dead force could continue unsupported for a moment\nbeyond its creation. We can not even conceive of change or phenomena\nwithout the energy of a mind.\u201d \u201cThe word _action_\u201d itself, says another\nwriter of the same school, \u201chas no real significance except when applied\nto the doings of an intelligent agent. Let any one conceive, if he can, of\nany power, energy, or force inherent in a lump of matter.\u201d Phenomena may\nhave the semblance of being produced by physical causes, but they are in\nreality produced, say these writers, by the immediate agency of mind. All\nthings which do not proceed from a human (or, I suppose, an animal) will\nproceed, they say, directly from divine will. The earth is not moved by\nthe combination of a centripetal and a projectile force; this is but a\nmode of speaking, which serves to facilitate our conceptions. It is moved\nby the direct volition of an omnipotent Being, in a path coinciding with\nthat which we deduce from the hypothesis of these two forces.\n\nAs I have so often observed, the general question of the existence of\nEfficient Causes does not fall within the limits of our subject; but a\ntheory which represents them as capable of being subjects of human\nknowledge, and which passes off as efficient causes what are only physical\nor phenomenal causes, belongs as much to Logic as to metaphysics, and is a\nfit subject for discussion here.\n\nTo my apprehension, a volition is not an efficient, but simply a physical\ncause. Our will causes our bodily actions in the same sense, and in no\nother, in which cold causes ice, or a spark causes an explosion of\ngunpowder. The volition, a state of our mind, is the antecedent; the\nmotion of our limbs in conformity to the volition, is the consequent. This\nsequence I conceive to be not a subject of direct consciousness, in the\nsense intended by the theory. The antecedent, indeed, and the consequent,\nare subjects of consciousness. But the connection between them is a\nsubject of experience. I can not admit that our consciousness of the\nvolition contains in itself any _a priori_ knowledge that the muscular\nmotion will follow. If our nerves of motion were paralyzed, or our muscles\nstiff and inflexible, and had been so all our lives, I do not see the\nslightest ground for supposing that we should ever (unless by information\nfrom other people) have known any thing of volition as a physical power,\nor been conscious of any tendency in feelings of our mind to produce\nmotions of our body, or of other bodies. I will not undertake to say\nwhether we should in that case have had the physical feeling which I\nsuppose is meant when these writers speak of \u201cconsciousness of effort:\u201d I\nsee no reason why we should not; since that physical feeling is probably a\nstate of nervous sensation beginning and ending in the brain, without\ninvolving the motory apparatus: but we certainly should not have\ndesignated it by any term equivalent to effort, since effort implies\nconsciously aiming at an end, which we should not only in that case have\nhad no reason to do, but could not even have had the idea of doing. If\nconscious at all of this peculiar sensation, we should have been conscious\nof it, I conceive, only as a kind of uneasiness, accompanying our feelings\nof desire.\n\nIt is well argued by Sir William Hamilton against the theory in question,\nthat it \u201cis refuted by the consideration that between the overt fact of\ncorporeal movement of which we are cognizant, and the internal act of\nmental determination of which we are also cognizant, there intervenes a\nnumerous series of intermediate agencies of which we have no knowledge;\nand, consequently, that we can have no consciousness of any causal\nconnection between the extreme links of this chain, the volition to move\nand the limb moving, as this hypothesis asserts. No one is immediately\nconscious, for example, of moving his arm through his volition. Previously\nto this ultimate movement, muscles, nerves, a multitude of solid and fluid\nparts, must be set in motion by the will, but of this motion we know, from\nconsciousness, absolutely nothing. A person struck with paralysis is\nconscious of no inability in his limb to fulfill the determinations of his\nwill; and it is only after having willed, and finding that his limbs do\nnot obey his volition, that he learns by this experience, that the\nexternal movement does not follow the internal act. But as the paralytic\nlearns after the volition that his limbs do not obey his mind; so it is\nonly after volition that the man in health learns, that his limbs do obey\nthe mandates of his will.\u201d(123)\n\nThose against whom I am contending have never produced, and do not pretend\nto produce, any positive evidence(124) that the power of our will to move\nour bodies would be known to us independently of experience. What they\nhave to say on the subject is, that the production of physical events by a\nwill seems to carry its own explanation with it, while the action of\nmatter upon matter seems to require something else to explain it; and is\neven, according to them, \u201cinconceivable\u201d on any other supposition than\nthat some will intervenes between the apparent cause and its apparent\neffect. They thus rest their case on an appeal to the inherent laws of our\nconceptive faculty; mistaking, as I apprehend, for the laws of that\nfaculty its acquired habits, grounded on the spontaneous tendencies of its\nuncultured state. The succession between the will to move a limb and the\nactual motion is one of the most direct and instantaneous of all sequences\nwhich come under our observation, and is familiar to every moment\u2019s\nexperience from our earliest infancy; more familiar than any succession of\nevents exterior to our bodies, and especially more so than any other case\nof the apparent origination (as distinguished from the mere communication)\nof motion. Now, it is the natural tendency of the mind to be always\nattempting to facilitate its conception of unfamiliar facts by\nassimilating them to others which are familiar. Accordingly, our voluntary\nacts, being the most familiar to us of all cases of causation, are, in the\ninfancy and early youth of the human race, spontaneously taken as the type\nof causation in general, and all phenomena are supposed to be directly\nproduced by the will of some sentient being. This original Fetichism I\nshall not characterize in the words of Hume, or of any follower of Hume,\nbut in those of a religious metaphysician, Dr. Reid, in order more\neffectually to show the unanimity which exists on the subject among all\ncompetent thinkers.\n\n\u201cWhen we turn our attention to external objects, and begin to exercise our\nrational faculties about them, we find that there are some motions and\nchanges in them which we have power to produce, and that there are many\nwhich must have some other cause. Either the objects must have life and\nactive power, as we have, or they must be moved or changed by something\nthat has life and active power, as external objects are moved by us.\n\n\u201cOur first thoughts seem to be, that the objects in which we perceive such\nmotion have understanding and active power as we have. \u2018Savages,\u2019 says the\nAbb\u00e9 Raynal, \u2018wherever they see motion which they can not account for,\nthere they suppose a soul.\u2019 All men may be considered as savages in this\nrespect, until they are capable of instruction, and of using their\nfaculties in a more perfect manner than savages do.\n\n\u201cThe Abb\u00e9 Raynal\u2019s observation is sufficiently confirmed, both from fact,\nand from the structure of all languages.\n\n\u201cRude nations do really believe sun, moon, and stars, earth, sea, and air,\nfountains, and lakes, to have understanding and active power. To pay\nhomage to them, and implore their favor, is a kind of idolatry natural to\nsavages.\n\n\u201cAll languages carry in their structure the marks of their being formed\nwhen this belief prevailed. The distinction of verbs and participles into\nactive and passive, which is found in all languages, must have been\noriginally intended to distinguish what is really active from what is\nmerely passive; and in all languages, we find active verbs applied to\nthose objects, in which, according to the Abb\u00e9 Raynal\u2019s observation,\nsavages suppose a soul.\n\n\u201cThus we say the sun rises and sets, and comes to the meridian, the moon\nchanges, the sea ebbs and flows, the winds blow. Languages were formed by\nmen who believed these objects to have life and active power in\nthemselves. It was therefore proper and natural to express their motions\nand changes by active verbs.\n\n\u201cThere is no surer way of tracing the sentiments of nations before they\nhave records, than by the structure of their language, which,\nnotwithstanding the changes produced in it by time, will always retain\nsome signatures of the thoughts of those by whom it was invented. When we\nfind the same sentiments indicated in the structure of all languages,\nthose sentiments must have been common to the human species when languages\nwere invented.\n\n\u201cWhen a few, of superior intellectual abilities, find leisure for\nspeculation, they begin to philosophize, and soon discover, that many of\nthose objects which at first they believed to be intelligent and active\nare really lifeless and passive. This is a very important discovery. It\nelevates the mind, emancipates from many vulgar superstitions, and invites\nto further discoveries of the same kind.\n\n\u201cAs philosophy advances, life and activity in natural objects retires, and\nleaves them dead and inactive. Instead of moving voluntarily, we find them\nto be moved necessarily; instead of acting, we find them to be acted upon;\nand Nature appears as one great machine, where one wheel is turned by\nanother, that by a third; and how far this necessary succession may reach,\nthe philosopher does not know.\u201d(125)\n\nThere is, then, a spontaneous tendency of the intellect to account to\nitself for all cases of causation by assimilating them to the intentional\nacts of voluntary agents like itself. This is the instinctive philosophy\nof the human mind in its earliest stage, before it has become familiar\nwith any other invariable sequences than those between its own volitions\nor those of other human beings and their voluntary acts. As the notion of\nfixed laws of succession among external phenomena gradually establishes\nitself, the propensity to refer all phenomena to voluntary agency slowly\ngives way before it. The suggestions, however, of daily life continuing to\nbe more powerful than those of scientific thought, the original\ninstinctive philosophy maintains its ground in the mind, underneath the\ngrowths obtained by cultivation, and keeps up a constant resistance to\ntheir throwing their roots deep into the soil. The theory against which I\nam contending derives its nourishment from that substratum. Its strength\ndoes not lie in argument, but in its affinity to an obstinate tendency of\nthe infancy of the human mind.\n\nThat this tendency, however, is not the result of an inherent mental law,\nis proved by superabundant evidence. The history of science, from its\nearliest dawn, shows that mankind have not been unanimous in thinking\neither that the action of matter upon matter was not conceivable, or that\nthe action of mind upon matter was. To some thinkers, and some schools of\nthinkers, both in ancient and in modern times, this last has appeared much\nmore inconceivable than the former. Sequences entirely physical and\nmaterial, as soon as they had become sufficiently familiar to the human\nmind, came to be thought perfectly natural, and were regarded not only as\nneeding no explanation themselves, but as being capable of affording it to\nothers, and even of serving as the ultimate explanation of things in\ngeneral.\n\nOne of the ablest recent supporters of the Volitional theory has furnished\nan explanation, at once historically true and philosophically acute, of\nthe failure of the Greek philosophers in physical inquiry, in which, as I\nconceive, he unconsciously depicts his own state of mind. \u201cTheir\nstumbling-block was one as to the nature of the evidence they had to\nexpect for their conviction.... They had not seized the idea that they\nmust not expect to understand the processes of outward causes, but only\ntheir results; and consequently, the whole physical philosophy of the\nGreeks was an attempt to identify mentally the effect with its cause, to\nfeel after some not only necessary but natural connection, where they\nmeant by natural that which would _per se_ carry some presumption to their\nown mind.... They wanted to see some _reason_ why the physical antecedent\nshould produce this particular consequent, and their only attempts were in\ndirections where they could find such reasons.\u201d(126) In other words, they\nwere not content merely to know that one phenomenon was always followed by\nanother; they thought that they had not attained the true aim of science,\nunless they could perceive something in the nature of the one phenomenon\nfrom which it might have been known or presumed _previous to trial_ that\nit would be followed by the other: just what the writer, who has so\nclearly pointed out their error, thinks that he perceives in the nature of\nthe phenomenon Volition. And to complete the statement of the case, he\nshould have added that these early speculators not only made this their\naim, but were quite satisfied with their success in it; not only sought\nfor causes which should carry in their mere statement evidence of their\nefficiency, but fully believed that they had found such causes. The\nreviewer can see plainly that this was an error, because _he_ does not\nbelieve that there exist any relations between material phenomena which\ncan account for their producing one another; but the very fact of the\npersistency of the Greeks in this error, shows that their minds were in a\nvery different state: they were able to derive from the assimilation of\nphysical facts to other physical facts, the kind of mental satisfaction\nwhich we connect with the word explanation, and which the reviewer would\nhave us think can only be found in referring phenomena to a will. When\nThales and Hippo held that moisture was the universal cause, and external\nelement, of which all other things were but the infinitely various\nsensible manifestations; when Anaximenes predicated the same thing of air,\nPythagoras of numbers, and the like, they all thought that they had found\na real explanation; and were content to rest in this explanation as\nultimate. The ordinary sequences of the external universe appeared to\nthem, no less than to their critic, to be inconceivable without the\nsupposition of some universal agency to connect the antecedents with the\nconsequents; but they did not think that Volition, exerted by minds, was\nthe only agency which fulfilled this requirement. Moisture, or air, or\nnumbers, carried to their minds a precisely similar impression of making\nintelligible what was otherwise inconceivable, and gave the same full\nsatisfaction to the demands of their conceptive faculty.\n\nIt was not the Greeks alone, who \u201cwanted to see some reason why the\nphysical antecedent should produce this particular consequent,\u201d some\nconnection \u201cwhich would _per se_ carry some presumption to their own\nmind.\u201d Among modern philosophers, Leibnitz laid it down as a self-evident\nprinciple that all physical causes without exception must contain in their\nown nature something which makes it intelligible that they should be able\nto produce the effects which they do produce. Far from admitting Volition\nas the only kind of cause which carried internal evidence of its own\npower, and as the real bond of connection between physical antecedents and\ntheir consequents, he demanded some naturally and _per se_ efficient\nphysical antecedent as the bond of connection between Volition itself and\nits effects. He distinctly refused to admit the will of God as a\nsufficient explanation of any thing except miracles; and insisted upon\nfinding something that would account _better_ for the phenomena of nature\nthan a mere reference to divine volition.(127)\n\nAgain, and conversely, the action of mind upon matter (which, we are now\ntold, not only needs no explanation itself, but is the explanation of all\nother effects), has appeared to some thinkers to be itself the grand\ninconceivability. It was to get over this very difficulty that the\nCartesians invented the system of Occasional Causes. They could not\nconceive that thoughts in a mind could produce movements in a body, or\nthat bodily movements could produce thoughts. They could see no necessary\nconnection, no relation _a priori_, between a motion and a thought. And as\nthe Cartesians, more than any other school of philosophical speculation\nbefore or since, made their own minds the measure of all things, and\nrefused, on principle, to believe that Nature had done what they were\nunable to see any reason why she must do, they affirmed it to be\nimpossible that a material and a mental fact could be causes one of\nanother. They regarded them as mere Occasions on which the real agent,\nGod, thought fit to exert his power as a Cause. When a man wills to move\nhis foot, it is not his will that moves it, but God (they said) moves it\non the occasion of his will. God, according to this system, is the only\nefficient cause, not _qu\u00e2_ mind, or _qu\u00e2_ endowed with volition, but _qu\u00e2_\nomnipotent. This hypothesis was, as I said, originally suggested by the\nsupposed inconceivability of any real mutual action between Mind and\nMatter; but it was afterward extended to the action of Matter upon Matter,\nfor on a nicer examination they found this inconceivable too, and\ntherefore, according to their logic, impossible. The _deus ex machin\u00e2_ was\nultimately called in to produce a spark on the occasion of a flint and\nsteel coming together, or to break an egg on the occasion of its falling\non the ground.\n\nAll this, undoubtedly, shows that it is the disposition of mankind in\ngeneral, not to be satisfied with knowing that one fact is invariably\nantecedent and another consequent, but to look out for something which may\nseem to explain their being so. But we also see that this demand may be\ncompletely satisfied by an agency purely physical, provided it be much\nmore familiar than that which it is invoked to explain. To Thales and\nAnaximenes, it appeared inconceivable that the antecedents which we see in\nnature should produce the consequents; but perfectly natural that water,\nor air, should produce them. The writers whom I oppose declare this\ninconceivable, but can conceive that mind, or volition, is _per se_ an\nefficient cause: while the Cartesians could not conceive even that, but\nperemptorily declared that no mode of production of any fact whatever was\nconceivable, except the direct agency of an omnipotent being; thus giving\nadditional proof of what finds new confirmation in every stage of the\nhistory of science: that both what persons can, and what they can not,\nconceive, is very much an affair of accident, and depends altogether on\ntheir experience, and their habits of thought; that by cultivating the\nrequisite associations of ideas, people may make themselves unable to\nconceive any given thing; and may make themselves able to conceive most\nthings, however inconceivable these may at first appear; and the same\nfacts in each person\u2019s mental history which determine what is or is not\nconceivable to him, determine also which among the various sequences in\nnature will appear to him so natural and plausible, as to need no other\nproof of their existence; to be evident by their own light, independent\nequally of experience and of explanation.\n\nBy what rule is any one to decide between one theory of this description\nand another? The theorists do not direct us to any external evidence; they\nappeal each to his own subjective feelings. One says, the succession C B\nappears to me more natural, conceivable, and credible _per se_, than the\nsuccession A B; you are therefore mistaken in thinking that B depends upon\nA; I am certain, though I can give no other evidence of it, that C comes\nin between A and B, and is the real and only cause of B. The other\nanswers, the successions C B and A B appear to me equally natural and\nconceivable, or the latter more so than the former: A is quite capable of\nproducing B without any other intervention. A third agrees with the first\nin being unable to conceive that A can produce B, but finds the sequence D\nB still more natural than C B, or of nearer kin to the subject-matter, and\nprefers his D theory to the C theory. It is plain that there is no\nuniversal law operating here, except the law that each person\u2019s\nconceptions are governed and limited by his individual experiences and\nhabits of thought. We are warranted in saying of all three, what each of\nthem already believes of the other two, namely, that they exalt into an\noriginal law of the human intellect and of outward nature one particular\nsequence of phenomena, which appears to them more natural and more\nconceivable than other sequences, only because it is more familiar. And\nfrom this judgment I am unable to except the theory, that Volition is an\nEfficient Cause.\n\nI am unwilling to leave the subject without adverting to the additional\nfallacy contained in the corollary from this theory; in the inference that\nbecause Volition is an efficient cause, therefore it is the only cause,\nand the direct agent in producing even what is apparently produced by\nsomething else. Volitions are not known to produce any thing directly\nexcept nervous action, for the will influences even the muscles only\nthrough the nerves. Though it were granted, then, that every phenomenon\nhas an efficient, and not merely a phenomenal cause, and that volition, in\nthe case of the peculiar phenomena which are known to be produced by it,\nis that efficient cause; are we therefore to say, with these writers, that\nsince we know of no other efficient cause, and ought not to assume one\nwithout evidence, there _is_ no other, and volition is the direct cause of\nall phenomena? A more outrageous stretch of inference could hardly be\nmade. Because among the infinite variety of the phenomena of nature there\nis one, namely, a particular mode of action of certain nerves, which has\nfor its cause, and as we are now supposing for its efficient cause, a\nstate of our mind; and because this is the only efficient cause of which\nwe are conscious, being the only one of which in the nature of the case we\n_can_ be conscious, since it is the only one which exists within\nourselves; does this justify us in concluding that all other phenomena\nmust have the same kind of efficient cause with that one eminently\nspecial, narrow, and peculiarly human or animal, phenomenon? The nearest\nparallel to this specimen of generalization is suggested by the recently\nrevived controversy on the old subject of Plurality of Worlds, in which\nthe contending parties have been so conspicuously successful in\noverthrowing one another. Here also we have experience only of a single\ncase, that of the world in which we live, but that this is inhabited we\nknow absolutely, and without possibility of doubt. Now if on this evidence\nany one were to infer that every heavenly body without exception, sun,\nplanet, satellite, comet, fixed star or nebula, is inhabited, and must be\nso from the inherent constitution of things, his inference would exactly\nresemble that of the writers who conclude that because volition is the\nefficient cause of our own bodily motions, it must be the efficient cause\nof every thing else in the universe. It is true there are cases in which,\nwith acknowledged propriety, we generalize from a single instance to a\nmultitude of instances. But they must be instances which resemble the one\nknown instance, and not such as have no circumstance in common with it\nexcept that of being instances. I have, for example, no direct evidence\nthat any creature is alive except myself, yet I attribute, with full\nassurance, life and sensation to other human beings and animals. But I do\nnot conclude that all other things are alive merely because I am. I\nascribe to certain other creatures a life like my own, because they\nmanifest it by the same sort of indications by which mine is manifested. I\nfind that their phenomena and mine conform to the same laws, and it is for\nthis reason that I believe both to arise from a similar cause. Accordingly\nI do not extend the conclusion beyond the grounds for it. Earth, fire,\nmountains, trees, are remarkable agencies, but their phenomena do not\nconform to the same laws as my actions do, and I therefore do not believe\nearth or fire, mountains or trees, to possess animal life. But the\nsupporters of the Volition Theory ask us to infer that volition causes\nevery thing, for no reason except that it causes one particular thing;\nalthough that one phenomenon, far from being a type of all natural\nphenomena, is eminently peculiar; its laws bearing scarcely any\nresemblance to those of any other phenomenon, whether of inorganic or of\norganic nature.\n\nNOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.\n\n\n    The author of the Second Burnett Prize Essay (Dr. Tulloch), who\n    has employed a considerable number of pages in controverting the\n    doctrines of the preceding chapter, has somewhat surprised me by\n    denying a fact, which I imagined too well known to require\n    proof\u2014that there have been philosophers who found in physical\n    explanations of phenomena the same complete mental satisfaction\n    which we are told is only given by volitional explanation, and\n    others who denied the Volitional Theory on the same ground of\n    inconceivability on which it is defended. The assertion of the\n    Essayist is countersigned still more positively by an able\n    reviewer of the Essay:(128) \u201cTwo illustrations,\u201d says the\n    reviewer, \u201care advanced by Mr. Mill: the case of Thales and\n    Anaximenes, stated by him to have maintained, the one Moisture and\n    the other Air to be the origin of all things; and that of\n    Descartes and Leibnitz, whom he asserts to have found the action\n    of Mind upon Matter the grand inconceivability. In\n    counter-statement as to the first of these cases the author\n    shows\u2014what we believe now hardly admits of doubt\u2014that the Greek\n    philosophers distinctly recognized as beyond and above their\n    primal material source, the \u03bd\u03bf\u1fe6\u03c2, or Divine Intelligence, as the\n    efficient and originating Source of all; and as to the second, by\n    proof that it was the _mode_, not the _fact_, of that action on\n    matter, which was represented as inconceivable.\u201d\n\n    A greater quantity of historical error has seldom been comprised\n    in a single sentence. With regard to Thales, the assertion that he\n    considered water as a mere material in the hands of \u03bd\u03bf\u1fe6\u03c2 rests on\n    a passage of Cicero _de Natur\u00e2 Deorum_; and whoever will refer to\n    any of the accurate historians of philosophy, will find that they\n    treat this as a mere fancy of Cicero, resting on no authority,\n    opposed to all the evidence; and make surmises as to the manner in\n    which Cicero may have been led into the error. (See Rutter, vol.\n    i., p. 211, 2d ed.; Brandis, vol. i., pp. 118\u20139, 1st ed.; Preller,\n    _Historia Philosophi\u00e6 Gr\u00e6co-Roman\u00e6_, p. 10. \u201cSchiefe Ansicht,\n    durchaus zu verwerfen;\u201d \u201caugenscheinlich folgernd statt zu\n    berichten;\u201d \u201cquibus vera sententia Thaletis plane detorquetur,\u201d\n    are the expressions of these writers.) As for Anaximenes, he even\n    according to Cicero, maintained, not that air was the material out\n    of which God made the world, but that the air was a god:\n    \u201cAnaximenes a\u00ebra deum statuit;\u201d or, according to St. Augustine,\n    that it was the material out of which the gods were made; \u201cnon\n    tamen ab ipsis [Diis] a\u00ebrem factum, sed ipsos ex a\u00ebre ortos\n    credidit.\u201d Those who are not familiar with the metaphysical\n    terminology of antiquity, must not be misled by finding it stated\n    that Anaximenes attributed \u03c8\u03c5\u03c7\u1f74 (translated _soul_, or _life_) to\n    his universal element, the air. The Greek philosophers\n    acknowledged several kinds of \u03c8\u03c5\u03c7\u1f74, the nutritive, the sensitive,\n    and the intellective.(129) Even the moderns, with admitted\n    correctness, attribute life to plants. As far as we can make out\n    the meaning of Anaximenes, he made choice of Air as the universal\n    agent, on the ground that it is perpetually in motion, without any\n    apparent cause external to itself: so that he conceived it as\n    exercising spontaneous force, and as the principle of life and\n    activity in all things, men and gods inclusive. If this be not\n    representing it as the Efficient Cause the dispute altogether has\n    no meaning.\n\n    If either Anaximenes, or Thales, or any of their contemporaries,\n    had held the doctrine that \u03bd\u03bf\u1fe6\u03c2 was the Efficient Cause, that\n    doctrine could not have been reputed, as it was throughout\n    antiquity, to have originated with Anaxagoras. The testimony of\n    Aristotle, in the first book of his Metaphysics, is perfectly\n    decisive with respect to these early speculations. After\n    enumerating four kinds of causes, or rather four different\n    meanings of the word Cause, viz., the Essence of a thing, the\n    Matter of it, the Origin of Motion (Efficient Cause), and the End\n    or Final Cause, he proceeds to say, that most of the early\n    philosophers recognized only the second kind of Cause, the Matter\n    of a thing, \u03c4\u1f70\u03c2 \u1f10\u03bd \u1f55\u03bb\u03b7\u03c2 \u03b5\u1f36\u03b4\u03b5\u03b9 \u03bc\u03cc\u03bd\u03b1\u03c2 \u1fa0\u03ae\u03b8\u03b7\u03c3\u03b1\u03bd \u1f00\u03c1\u03c7\u1f70\u03c2 \u03b5\u1f37\u03bd\u03b1\u03b9 \u03c0\u03ac\u03bd\u03c4\u03c9\u03bd. As\n    his first example he specifies Thales, whom he describes as taking\n    the lead in this view of the subject, \u1f41 \u03c4\u1fc6\u03c2 \u03c4\u03bf\u03b9\u03b1\u03cd\u03c4\u03b7\u03c2 \u1f00\u03c1\u03c7\u03b7\u03b3\u1f78\u03c2\n    \u03c6\u03b9\u03bb\u03bf\u03c3\u03bf\u03c6\u03af\u03b1\u03c2, and goes on to Hippon, Anaximenes, Diogenes (of\n    Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.\n    Anaxagoras, however (he proceeds to say), taught a different\n    doctrine, as we _know_, and it is _alleged_ that Hermotimus of\n    Clazomen\u00e6 taught it before him. Anaxagoras represented, that even\n    if these various theories of the universal material were true,\n    there would be need of some other cause to account for the\n    transformations of the materials, since the material can not\n    originate its own changes: \u03bf\u1f50 \u03b3\u1f70\u03c1 \u03b4\u1f74 \u03c4\u03cc \u03b3\u03b5 \u1f51\u03c0\u03bf\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf\u03bd \u03b1\u1f50\u03c4\u1f78 \u03c0\u03bf\u03b9\u03b5\u1f76\n    \u03bc\u03b5\u03c4\u03b1\u03b2\u03ac\u03bb\u03bb\u03b5\u03b9\u03bd \u1f11\u03b1\u1fe6\u03c4\u03bf; \u03bb\u03ad\u03b3\u03c9 \u03b4\u1fbd \u03bf\u1f30\u03bf\u03bd \u03bf\u1f50\u03c4\u03b5 \u03c4\u1f78 \u03be\u03cd\u03bb\u03bf\u03bd \u03bf\u1f54\u03c4\u03b5 \u1f41 \u03c7\u03b1\u03bb\u03ba\u1f78\u03c2 \u03b1\u1f34\u03c4\u03b9\u03bf\u03c2\n    \u03c4\u03bf\u1fe6 \u03bc\u03b5\u03c4\u03b1\u03b2\u03ac\u03bb\u03bb\u03b5\u03b9\u03bd \u1f11\u03ba\u03ac\u03c4\u03b5\u03c1\u03bf\u03bd \u03b1\u1f50\u03c4\u1ff6\u03bd, \u03bf\u1f50\u03b4\u1f72 \u03c0\u03bf\u03b9\u03b5\u1fd6 \u03c4\u1f78 \u03bc\u1f72\u03bd \u03be\u03cd\u03bb\u03bf\u03bd \u03ba\u03bb\u03af\u03bd\u03b7\u03bd \u1f41\n    \u03b4\u03ad \u03c7\u03b1\u03bb\u03ba\u1f78\u03c2 \u1f00\u03bd\u03b4\u03c1\u03b9\u03ac\u03bd\u03c4\u03b1, \u1f00\u03bb\u03bb\u1fbd \u1f11\u03c4\u03b5\u03c1\u03cc\u03bd \u03c4\u03b9 \u03c4\u1fc6\u03c2 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u1fc6\u03c2 \u03b1\u1f34\u03c4\u03b9\u03bf\u03bd, viz.,\n    the other kind of cause, \u1f44\u03b8\u03b5\u03bd \u1f21 \u1f00\u03c1\u03c7\u1f74 \u03c4\u1fc6\u03c2 \u03ba\u03b9\u03bd\u03ae\u03c3\u03b5\u03c9\u03c2\u2014an Efficient\n    Cause. Aristotle expresses great approbation of this doctrine\n    (which he says made its author appear the only sober man among\n    persons raving, \u03bf\u1f30\u03bf\u03bd \u03bd\u03ae\u03c6\u03c9\u03bd \u1f10\u03c6\u03ac\u03bd\u03b7 \u03c0\u03b1\u03c1\u1fbd \u03b5\u1f30\u03ba\u1fc6 \u03bb\u03ad\u03b3\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf\u1fe6\u03c2\n    \u03c0\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03bd); but while describing the influence which it exercised\n    over subsequent speculation, he remarks that the philosophers\n    against whom this, as he thinks, insuperable difficulty was urged,\n    had not felt it to be any difficulty: \u03bf\u1f50\u03b4\u03ad\u03bd \u1f10\u03b4\u03c5\u03c3\u03c7\u03b5\u03c1\u03ac\u03bd\u03b1\u03bd \u1f10\u03bd\n    \u1f11\u03b1\u03c5\u03c4\u03bf\u1fd6\u03c2. It is surely unnecessary to say more in proof of the\n    matter of fact which Dr. Tulloch and his reviewer disbelieve.\n\n    Having pointed out what he thinks the error of these early\n    speculators in not recognizing the need of an efficient cause,\n    Aristotle goes on to mention two other efficient causes to which\n    they might have had recourse, instead of intelligence: \u03c4\u03cd\u03c7\u03b7,\n    chance, and \u03c4\u1f78 \u03b1\u1f50\u03c4\u03bf\u03bc\u03ac\u03c4\u03bf\u03bd, spontaneity. He indeed puts these aside\n    as not sufficiently worthy causes for the order in the universe,\n    \u03bf\u1f50\u03b4\u1fbd \u03b1\u1f51 \u03c4\u03c9\u1ff7 \u03b1\u1f50\u03c4\u03bf\u03bc\u03ac\u03c4\u1ff3 \u03ba\u03b1\u1f76 \u03c4\u1fc7 \u03c4\u03cd\u03c7\u1fc3 \u03c4\u03bf\u03c3\u03bf\u1fe6\u03c4\u03bf\u03bd \u1f10\u03c0\u03b9\u03c4\u03c1\u03ad\u03c8\u03b1\u03b9 \u03c0\u03c1\u1fb6\u03b3\u03bc\u03b1 \u03ba\u03b1\u03bb\u1ff6\u03c2\n    \u03b5\u1f30\u03c7\u03b5\u03bd; but he does not reject them as incapable of producing _any_\n    effect, but only as incapable of producing _that_ effect. He\n    himself recognizes \u03c4\u03cd\u03c7\u03b7 and \u03c4\u1f78 \u03b1\u1f50\u03c4\u03bf\u03bc\u03ac\u03c4\u03bf\u03bd as co-ordinate agents\n    with Mind in producing the phenomena of the universe; the\n    department allotted to them being composed of all the classes of\n    phenomena which are not supposed to follow any uniform law. By\n    thus including Chance among efficient causes, Aristotle fell into\n    an error which philosophy has now outgrown, but which is by no\n    means so alien to the spirit even of modern speculation as it may\n    at first sight appear. Up to quite a recent period philosophers\n    went on ascribing, and many of them have not yet ceased to\n    ascribe, a real existence to the results of abstraction. Chance\n    could make out as good a title to that dignity as many other of\n    the mind\u2019s abstract creations: it had had a name given to it, and\n    why should it not be a reality? As for \u03c4\u1f78 \u03b1\u1f50\u03c4\u03bf\u03bc\u03ac\u03c4\u03bf\u03bd, it is\n    recognized even yet as one of the modes of origination of\n    phenomena by all those thinkers who maintain what is called the\n    Freedom of the Will. The same self-determining power which that\n    doctrine attributes to volitions, was supposed by the ancients to\n    be possessed also by some other natural phenomena: a circumstance\n    which throws considerable light on more than one of the supposed\n    invincible necessities of belief. I have introduced it here,\n    because this belief of Aristotle, or rather of the Greek\n    philosophers generally, is as fatal as the doctrines of Thales and\n    the Ionic school to the theory that the human mind is compelled by\n    its constitution to conceive volition as the origin of all force,\n    and the efficient cause of all phenomena.(130)\n\n    With regard to the modern philosophers (Leibnitz and the\n    Cartesians) whom I had cited as having maintained that the action\n    of mind upon matter, so far from being the only conceivable origin\n    of material phenomena, is itself inconceivable; the attempt to\n    rebut this argument by asserting that the mode, not the fact, of\n    the action of mind on matter was represented as inconceivable, is\n    an abuse of the privilege of writing confidently about authors\n    without reading them; for any knowledge whatever of Leibnitz would\n    have taught those who thus speak of him, that the inconceivability\n    of the mode, and the impossibility of the thing, were in his mind\n    convertible expressions. What was his famous Principle of the\n    Sufficient Reason, the very corner-stone of his Philosophy, from\n    which the Pre-established Harmony, the doctrine of Monads, and all\n    the opinions most characteristic of Leibnitz, were corollaries? It\n    was, that nothing exists, the existence of which is not capable of\n    being proved and explained _a priori_; the proof and explanation\n    in the case of contingent facts being derived from the nature of\n    their causes; which could not be the causes unless there was\n    something in their nature showing them to be capable of producing\n    those particular effects. And this \u201csomething\u201d which accounts for\n    the production of physical effects, he was able to find in many\n    physical causes, but could not find it in any finite minds, which\n    therefore he unhesitatingly asserted to be incapable of producing\n    any physical effects whatever. \u201cOn ne saurait concevoir,\u201d he says,\n    \u201cune action r\u00e9ciproque de la mati\u00e8re et de l\u2019intelligence l\u2019une\n    sur l\u2019autre,\u201d and there is therefore (he contends) no choice but\n    between the Occasional Causes of the Cartesians and his own\n    Pre-established Harmony, according to which there is no more\n    connection between our volitions and our muscular actions than\n    there is between two clocks which are wound up to strike at the\n    same instant. But he felt no similar difficulty as to physical\n    causes; and throughout his speculations, as in the passage I have\n    already cited respecting gravitation, he distinctly refuses to\n    consider as part of the order of nature any fact which is not\n    explicable from the nature of its physical cause.\n\n    With regard to the Cartesians (not Descartes; I did not make that\n    mistake, though the reviewer of Dr. Tulloch\u2019s Essay attributes it\n    to me) I take a passage almost at random from Malebranche, who is\n    the best known of the Cartesians, and, though not the inventor of\n    the system of Occasional Causes, is its principal expositor. In\n    Part II., chap. iii., of his Sixth Book, having first said that\n    matter can not have the power of moving itself, he proceeds to\n    argue that neither can mind have the power of moving it. \u201cQuand on\n    examine l\u2019id\u00e9e que l\u2019on a de tous les esprits finis, on ne voit\n    point de liaison n\u00e9cessaire entre leur volont\u00e9 et le mouvement de\n    quelque corps que ce soit, on voit au contraire qu\u2019il n\u2019y en a\n    point, et qu\u2019il n\u2019y en peut avoir\u201d (there is nothing in the idea\n    of finite mind which can account for its causing the motion of a\n    body); \u201con doit aussi conclure, si on vent raisonner selon ses\n    lumi\u00e8res, qu\u2019il n\u2019y a aucun esprit cr\u00e9\u00e9 qui puisse remuer quelque\n    corps que ce soit comme cause v\u00e9ritable on principale, de m\u00eame que\n    l\u2019on a dit qu\u2019aucun corps ne se pouvait remuer soi-m\u00eame:\u201d thus the\n    idea of Mind is according to him as incompatible as the idea of\n    Matter with the exercise of active force. But when, he continues,\n    we consider not a created but a Divine Mind, the case is altered;\n    for the idea of a Divine Mind includes omnipotence; and the idea\n    of omnipotence does contain the idea of being able to move bodies.\n    Thus it is the nature of omnipotence which renders the motion of\n    bodies even by the Divine Mind credible or conceivable, while, so\n    far as depended on the mere nature of mind, it would have been\n    inconceivable and incredible. If Malebranche had not believed in\n    an omnipotent Being, he would have held all action of mind on body\n    to be a demonstrated impossibility.(131)\n\n    A doctrine more precisely the reverse of the Volitional theory of\n    causation can not well be imagined. The Volitional theory is, that\n    we know by intuition or by direct experience the action of our own\n    mental volitions on matter; that we may hence infer all other\n    action upon matter to be that of volition, and might thus know,\n    without any other evidence, that matter is under the government of\n    a Divine Mind. Leibnitz and the Cartesians, on the contrary,\n    maintain that our volitions do not and can not act upon matter,\n    and that it is only the existence of an all-governing Being, and\n    that Being omnipotent, which can account for the sequence between\n    our volitions and our bodily actions. When we consider that each\n    of these two theories, which, as theories of causation, stand at\n    the opposite extremes of possible divergence from one another,\n    invokes not only as its evidence, but as its sole evidence, the\n    absolute inconceivability of any theory but itself, we are enabled\n    to measure the worth of this kind of evidence: and when we find\n    the Volitional theory entirely built upon the assertion that by\n    our mental constitution we are compelled to recognize our\n    volitions as efficient causes, and then find other thinkers\n    maintaining that we know that they are not and can not be such\n    causes, and can not conceive them to be so, I think we have a\n    right to say that this supposed law of our mental constitution\n    does not exist.\n\n    Dr. Tulloch (pp. 45\u201347) thinks it a sufficient answer to this,\n    that Leibnitz and the Cartesians were Theists, and believed the\n    will of God to be an efficient cause. Doubtless they did, and the\n    Cartesians even believed (though Leibnitz did not) that it is the\n    only such cause. Dr. Tulloch mistakes the nature of the question.\n    I was not writing on Theism, as Dr. Tulloch is, but against a\n    particular theory of causation, which, if it be unfounded, can\n    give no effective support to Theism or to any thing else. I found\n    it asserted that volition is the only efficient cause, on the\n    ground that no other efficient cause is conceivable. To this\n    assertion I oppose the instances of Leibnitz and of the\n    Cartesians, who affirmed with equal positiveness that volition as\n    an efficient cause is itself not conceivable, and that\n    omnipotence, which renders all things conceivable, can alone take\n    away the impossibility. This I thought, and think, a conclusive\n    answer to the argument on which this theory of causation avowedly\n    depends. But I certainly did not imagine that Theism was bound up\n    with that theory; nor expected to be charged with denying Leibnitz\n    and the Cartesians to be Theists because I denied that they held\n    the theory.\n\n\n\n\n                               Chapter VI.\n\n\nOn The Composition Of Causes.\n\n\n\u00a7 1. To complete the general notion of causation on which the rules of\nexperimental inquiry into the laws of nature must be founded, one\ndistinction still remains to be pointed out: a distinction so radical, and\nof so much importance, as to require a chapter to itself.\n\nThe preceding discussions have rendered us familiar with the case in which\nseveral agents, or causes, concur as conditions to the production of an\neffect; a case, in truth, almost universal, there being very few effects\nto the production of which no more than one agent contributes. Suppose,\nthen, that two different agents, operating jointly, are followed, under a\ncertain set of collateral conditions, by a given effect. If either of\nthese agents, instead of being joined with the other, had operated alone,\nunder the same set of conditions in all other respects, some effect would\nprobably have followed, which would have been different from the joint\neffect of the two, and more or less dissimilar to it. Now, if we happen to\nknow what would be the effect of each cause when acting separately from\nthe other, we are often able to arrive deductively, or _a priori_, at a\ncorrect prediction of what will arise from their conjunct agency. To\nrender this possible, it is only necessary that the same law which\nexpresses the effect of each cause acting by itself, shall also correctly\nexpress the part due to that cause of the effect which follows from the\ntwo together. This condition is realized in the extensive and important\nclass of phenomena commonly called mechanical, namely the phenomena of the\ncommunication of motion (or of pressure, which is tendency to motion) from\none body to another. In this important class of cases of causation, one\ncause never, properly speaking, defeats or frustrates another; both have\ntheir full effect. If a body is propelled in two directions by two forces,\none tending to drive it to the north and the other to the east, it is\ncaused to move in a given time exactly as far in both directions as the\ntwo forces would separately have carried it; and is left precisely where\nit would have arrived if it had been acted upon first by one of the two\nforces, and afterward by the other. This law of nature is called, in\ndynamics, the principle of the Composition of Forces; and in imitation of\nthat well-chosen expression, I shall give the name of the Composition of\nCauses to the principle which is exemplified in all cases in which the\njoint effect of several causes is identical with the sum of their separate\neffects.\n\nThis principle, however, by no means prevails in all departments of the\nfield of nature. The chemical combination of two substances produces, as\nis well known, a third substance, with properties different from those of\neither of the two substances separately, or of both of them taken\ntogether. Not a trace of the properties of hydrogen or of oxygen is\nobservable in those of their compound, water. The taste of sugar of lead\nis not the sum of the tastes of its component elements, acetic acid and\nlead or its oxide; nor is the color of blue vitriol a mixture of the\ncolors of sulphuric acid and copper. This explains why mechanics is a\ndeductive or demonstrative science, and chemistry not. In the one, we can\ncompute the effects of combinations of causes, whether real or\nhypothetical, from the laws which we know to govern those causes when\nacting separately, because they continue to observe the same laws when in\ncombination which they observe when separate: whatever would have happened\nin consequence of each cause taken by itself, happens when they are\ntogether, and we have only to cast up the results. Not so in the phenomena\nwhich are the peculiar subject of the science of chemistry. There most of\nthe uniformities to which the causes conform when separate, cease\naltogether when they are conjoined; and we are not, at least in the\npresent state of our knowledge, able to foresee what result will follow\nfrom any new combination until we have tried the specific experiment.\n\nIf this be true of chemical combinations, it is still more true of those\nfar more complex combinations of elements which constitute organized\nbodies; and in which those extraordinary new uniformities arise which are\ncalled the laws of life. All organized bodies are composed of parts\nsimilar to those composing inorganic nature, and which have even\nthemselves existed in an inorganic state; but the phenomena of life, which\nresult from the juxtaposition of those parts in a certain manner, bear no\nanalogy to any of the effects which would be produced by the action of the\ncomponent substances considered as mere physical agents. To whatever\ndegree we might imagine our knowledge of the properties of the several\ningredients of a living body to be extended and perfected, it is certain\nthat no mere summing up of the separate actions of those elements will\never amount to the action of the living body itself. The tongue, for\ninstance, is, like all other parts of the animal frame, composed of\ngelatine, fibrine, and other products of the chemistry of digestion; but\nfrom no knowledge of the properties of those substances could we ever\npredict that it could taste, unless gelatine or fibrine could themselves\ntaste; for no elementary fact can be in the conclusion which was not in\nthe premises.\n\nThere are thus two different modes of the conjunct action of causes; from\nwhich arise two modes of conflict, or mutual interference, between laws of\nnature. Suppose, at a given point of time and space, two or more causes,\nwhich, if they acted separately, would produce effects contrary, or at\nleast conflicting with each other; one of them tending to undo, wholly or\npartially, what the other tends to do. Thus the expansive force of the\ngases generated by the ignition of gunpowder tends to project a bullet\ntoward the sky, while its gravity tends to make it fall to the ground. A\nstream running into a reservoir at one end tends to fill it higher and\nhigher, while a drain at the other extremity tends to empty it. Now, in\nsuch cases as these, even if the two causes which are in joint action\nexactly annul one another, still the laws of both are fulfilled; the\neffect is the same as if the drain had been open for half an hour\nfirst,(132) and the stream had flowed in for as long afterward. Each agent\nproduces the same amount of effect as if it had acted separately, though\nthe contrary effect which was taking place during the same time\nobliterated it as fast as it was produced. Here, then, are two causes,\nproducing by their joint operations an effect which at first seems quite\ndissimilar to those which they produce separately, but which on\nexamination proves to be really the sum of those separate effects. It will\nbe noticed that we here enlarge the idea of the sum of two effects, so as\nto include what is commonly called their difference, but which is in\nreality the result of the addition of opposites; a conception to which\nmankind are indebted for that admirable extension of the algebraical\ncalculus, which has so vastly increased its powers as an instrument of\ndiscovery, by introducing into its reasonings (with the sign of\nsubtraction prefixed, and under the name of Negative Quantities) every\ndescription whatever of positive phenomena, provided they are of such a\nquality in reference to those previously introduced, that to add the one\nis equivalent to subtracting an equal quantity of the other.\n\nThere is, then, one mode of the mutual interference of laws of nature, in\nwhich, even when the concurrent causes annihilate each other\u2019s effects,\neach exerts its full efficacy according to its own law\u2014its law as a\nseparate agent. But in the other description of cases, the agencies which\nare brought together cease entirely, and a totally different set of\nphenomena arise: as in the experiment of two liquids which, when mixed in\ncertain proportions, instantly become, not a larger amount of liquid, but\na solid mass.\n\n\u00a7 2. This difference between the case in which the joint effect of causes\nis the sum of their separate effects, and the case in which it is\nheterogeneous to them\u2014between laws which work together without alteration,\nand laws which, when called upon to work together, cease and give place to\nothers\u2014is one of the fundamental distinctions in nature. The former case,\nthat of the Composition of Causes, is the general one; the other is always\nspecial and exceptional. There are no objects which do not, as to some of\ntheir phenomena, obey the principle of the Composition of Causes; none\nthat have not some laws which are rigidly fulfilled in every combination\ninto which the objects enter. The weight of a body, for instance, is a\nproperty which it retains in all the combinations in which it is placed.\nThe weight of a chemical compound, or of an organized body, is equal to\nthe sum of the weights of the elements which compose it. The weight either\nof the elements or of the compound will vary, if they be carried farther\nfrom their centre of attraction, or brought nearer to it; but whatever\neffects the one effects the other. They always remain precisely equal. So,\nagain, the component parts of a vegetable or animal substance do not lose\ntheir mechanical and chemical properties as separate agents, when, by a\npeculiar mode of juxtaposition, they, as an aggregate whole, acquire\nphysiological or vital properties in addition. Those bodies continue, as\nbefore, to obey mechanical and chemical laws, in so far as the operation\nof those laws is not counteracted by the new laws which govern them as\norganized beings; when, in short, a concurrence of causes takes place\nwhich calls into action new laws bearing no analogy to any that we can\ntrace in the separate operation of the causes, the new laws, while they\nsupersede one portion of the previous laws, may co-exist with another\nportion, and may even compound the effect of those previous laws with\ntheir own.\n\nAgain, laws which were themselves generated in the second mode, may\ngenerate others in the first. Though there are laws which, like those of\nchemistry and physiology, owe their existence to a breach of the principle\nof Composition of Causes, it does not follow that these peculiar, or, as\nthey might be termed, _heteropathic_ laws, are not capable of composition\nwith one another. The causes which by one combination have had their laws\naltered, may carry their new laws with them unaltered into their ulterior\ncombinations. And hence there is no reason to despair of ultimately\nraising chemistry and physiology to the condition of deductive sciences;\nfor though it is impossible to deduce all chemical and physiological\ntruths from the laws or properties of simple substances or elementary\nagents, they may possibly be deducible from laws which commence when these\nelementary agents are brought together into some moderate number of not\nvery complex combinations. The Laws of Life will never be deducible from\nthe mere laws of the ingredients, but the prodigiously complex Facts of\nLife may all be deducible from comparatively simple laws of life; which\nlaws (depending indeed on combinations, but on comparatively simple\ncombinations, of antecedents) may, in more complex circumstances, be\nstrictly compounded with one another, and with the physical and chemical\nlaws of the ingredients. The details of the vital phenomena, even now,\nafford innumerable exemplifications of the Composition of Causes; and in\nproportion as these phenomena are more accurately studied, there appears\nmore reason to believe that the same laws which operate in the simpler\ncombinations of circumstances do, in fact, continue to be observed in the\nmore complex. This will be found equally true in the phenomena of mind;\nand even in social and political phenomena, the results of the laws of\nmind. It is in the case of chemical phenomena that the least progress has\nyet been made in bringing the special laws under general ones from which\nthey may be deduced; but there are even in chemistry many circumstances to\nencourage the hope that such general laws will hereafter be discovered.\nThe different actions of a chemical compound will never, undoubtedly, be\nfound to be the sums of the actions of its separate elements; but there\nmay exist, between the properties of the compound and those of its\nelements, some constant relation, which, if discoverable by a sufficient\ninduction, would enable us to foresee the sort of compound which will\nresult from a new combination before we have actually tried it, and to\njudge of what sort of elements some new substance is compounded before we\nhave analyzed it. The law of definite proportions, first discovered in its\nfull generality by Dalton, is a complete solution of this problem in one,\nthough but a secondary aspect, that of quantity; and in respect to\nquality, we have already some partial generalizations, sufficient to\nindicate the possibility of ultimately proceeding farther. We can\npredicate some common properties of the kind of compounds which result\nfrom the combination, in each of the small number of possible proportions,\nof any acid whatever with any base. We have also the curious law,\ndiscovered by Berthollet, that two soluble salts mutually decompose one\nanother whenever the new combinations which result produce an insoluble\ncompound, or one less soluble than the two former. Another uniformity is\nthat called the law of isomorphism; the identity of the crystalline forms\nof substances which possess in common certain peculiarities of chemical\ncomposition.(133) Thus it appears that even heteropathic laws, such laws\nof combined agency as are not compounded of the laws of the separate\nagencies, are yet, at least in some cases, derived from them according to\na fixed principle. There may, therefore, be laws of the generation of laws\nfrom others dissimilar to them; and in chemistry, these undiscovered laws\nof the dependence of the properties of the compound on the properties of\nits elements, may, together with the laws of the elements themselves,\nfurnish the premises by which the science is perhaps destined one day to\nbe rendered deductive.\n\nIt would seem, therefore, that there is no class of phenomena in which the\nComposition of Causes does not obtain: that as a general rule, causes in\ncombination produce exactly the same effects as when acting singly: but\nthat this rule, though general, is not universal: that in some instances,\nat some particular points in the transition from separate to united\naction, the laws change, and an entirely new set of effects are either\nadded to, or take the place of, those which arise from the separate agency\nof the same causes: the laws of these new effects being again susceptible\nof composition, to an indefinite extent, like the laws which they\nsuperseded.\n\n\u00a7 3. That effects are proportional to their causes is laid down by some\nwriters as an axiom in the theory of causation; and great use is sometimes\nmade of this principle in reasonings respecting the laws of nature, though\nit is encumbered with many difficulties and apparent exceptions, which\nmuch ingenuity has been expended in showing not to be real ones. This\nproposition, in so far as it is true, enters as a particular case into the\ngeneral principle of the Composition of Causes; the causes compounded\nbeing, in this instance, homogeneous; in which case, if in any, their\njoint effect might be expected to be identical with the sum of their\nseparate effects. If a force equal to one hundred weight will raise a\ncertain body along an inclined plane, a force equal to two hundred weight\nwill raise two bodies exactly similar, and thus the effect is proportional\nto the cause. But does not a force equal to two hundred weight actually\ncontain in itself two forces each equal to one hundred weight, which, if\nemployed apart, would separately raise the two bodies in question? The\nfact, therefore, that when exerted jointly they raise both bodies at once,\nresults from the Composition of Causes, and is a mere instance of the\ngeneral fact that mechanical forces are subject to the law of Composition.\nAnd so in every other case which can be supposed. For the doctrine of the\nproportionality of effects to their causes can not of course be applicable\nto cases in which the augmentation of the cause alters the kind of effect;\nthat is, in which the surplus quantity superadded to the cause does not\nbecome compounded with it, but the two together generate an altogether new\nphenomenon. Suppose that the application of a certain quantity of heat to\na body merely increases its bulk, that a double quantity melts it, and a\ntriple quantity decomposes it: these three effects being heterogeneous, no\nratio, whether corresponding or not to that of the quantities of heat\napplied, can be established between them. Thus the supposed axiom of the\nproportionality of effects to their causes fails at the precise point\nwhere the principle of the Composition of Causes also fails; viz., where\nthe concurrence of causes is such as to determine a change in the\nproperties of the body generally, and render it subject to new laws, more\nor less dissimilar to those to which it conformed in its previous state.\nThe recognition, therefore, of any such law of proportionality is\nsuperseded by the more comprehensive principle, in which as much of it as\nis true is implicitly asserted.(134)\n\nThe general remarks on causation, which seemed necessary as an\nintroduction to the theory of the inductive process, may here terminate.\nThat process is essentially an inquiry into cases of causation. All the\nuniformities which exist in the succession of phenomena, and most of the\nuniformities in their co-existence, are either, as we have seen,\nthemselves laws of causation, or consequences resulting from, and\ncorollaries capable of being deduced from, such laws. If we could\ndetermine what causes are correctly assigned to what effects, and what\neffects to what causes, we should be virtually acquainted with the whole\ncourse of nature. All those uniformities which are mere results of\ncausation might then be explained and accounted for; and every individual\nfact or event might be predicted, provided we had the requisite data, that\nis, the requisite knowledge of the circumstances which, in the particular\ninstance, preceded it.\n\nTo ascertain, therefore, what are the laws of causation which exist in\nnature; to determine the effect of every cause, and the causes of all\neffects, is the main business of Induction; and to point out how this is\ndone is the chief object of Inductive Logic.\n\n\n\n\n                               Chapter VII.\n\n\nOn Observation And Experiment.\n\n\n\u00a7 1. It results from the preceding exposition, that the process of\nascertaining what consequents, in nature, are invariably connected with\nwhat antecedents, or in other words what phenomena are related to each\nother as causes and effects, is in some sort a process of analysis. That\nevery fact which begins to exist has a cause, and that this cause must be\nfound in some fact or concourse of facts which immediately preceded the\noccurrence, may be taken for certain. The whole of the present facts are\nthe infallible result of all past facts, and more immediately of all the\nfacts which existed at the moment previous. Here, then, is a great\nsequence, which we know to be uniform. If the whole prior state of the\nentire universe could again recur, it would again be followed by the\npresent state. The question is, how to resolve this complex uniformity\ninto the simpler uniformities which compose it, and assign to each portion\nof the vast antecedent the portion of the consequent which is attendant on\nit.\n\nThis operation, which we have called analytical, inasmuch as it is the\nresolution of a complex whole into the component elements, is more than a\nmerely mental analysis. No mere contemplation of the phenomena, and\npartition of them by the intellect alone, will of itself accomplish the\nend we have now in view. Nevertheless, such a mental partition is an\nindispensable first step. The order of nature, as perceived at a first\nglance, presents at every instant a chaos followed by another chaos. We\nmust decompose each chaos into single facts. We must learn to see in the\nchaotic antecedent a multitude of distinct antecedents, in the chaotic\nconsequent a multitude of distinct consequents. This, supposing it done,\nwill not of itself tell us on which of the antecedents each consequent is\ninvariably attendant. To determine that point, we must endeavor to effect\na separation of the facts from one another, not in our minds only, but in\nnature. The mental analysis, however, must take place first. And every one\nknows that in the mode of performing it, one intellect differs immensely\nfrom another. It is the essence of the act of observing; for the observer\nis not he who merely sees the thing which is before his eyes, but he who\nsees what parts that thing is composed of. To do this well is a rare\ntalent. One person, from inattention, or attending only in the wrong\nplace, overlooks half of what he sees; another sets down much more than he\nsees, confounding it with what he imagines, or with what he infers;\nanother takes note of the _kind_ of all the circumstances, but being\ninexpert in estimating their degree, leaves the quantity of each vague and\nuncertain; another sees indeed the whole, but makes such an awkward\ndivision of it into parts, throwing things into one mass which require to\nbe separated, and separating others which might more conveniently be\nconsidered as one, that the result is much the same, sometimes even worse,\nthan if no analysis had been attempted at all. It would be possible to\npoint out what qualities of mind, and modes of mental culture, fit a\nperson for being a good observer: that, however, is a question not of\nLogic, but of the Theory of Education, in the most enlarged sense of the\nterm. There is not properly an Art of Observing. There may be rules for\nobserving. But these, like rules for inventing, are properly instructions\nfor the preparation of one\u2019s own mind; for putting it into the state in\nwhich it will be most fitted to observe, or most likely to invent. They\nare, therefore, essentially rules of self-education, which is a different\nthing from Logic. They do not teach how to do the thing, but how to make\nourselves capable of doing it. They are an art of strengthening the limbs,\nnot an art of using them.\n\nThe extent and minuteness of observation which may be requisite, and the\ndegree of decomposition to which it may be necessary to carry the mental\nanalysis, depend on the particular purpose in view. To ascertain the state\nof the whole universe at any particular moment is impossible, but would\nalso be useless. In making chemical experiments, we do not think it\nnecessary to note the position of the planets; because experience has\nshown, as a very superficial experience is sufficient to show, that in\nsuch cases that circumstance is not material to the result: and\naccordingly, in the ages when men believed in the occult influences of the\nheavenly bodies, it might have been unphilosophical to omit ascertaining\nthe precise condition of those bodies at the moment of the experiment. As\nto the degree of minuteness of the mental subdivision, if we were obliged\nto break down what we observe into its very simplest elements, that is,\nliterally into single facts, it would be difficult to say where we should\nfind them; we can hardly ever affirm that our divisions of any kind have\nreached the ultimate unit. But this, too, is fortunately unnecessary. The\nonly object of the mental separation is to suggest the requisite physical\nseparation, so that we may either accomplish it ourselves, or seek for it\nin nature; and we have done enough when we have carried the subdivision as\nfar as the point at which we are able to see what observations or\nexperiments we require. It is only essential, at whatever point our mental\ndecomposition of facts may for the present have stopped, that we should\nhold ourselves ready and able to carry it further as occasion requires,\nand should not allow the freedom of our discriminating faculty to be\nimprisoned by the swathes and bands of ordinary classification; as was the\ncase with all early speculative inquirers, not excepting the Greeks, to\nwhom it seldom occurred that what was called by one abstract name might,\nin reality, be several phenomena, or that there was a possibility of\ndecomposing the facts of the universe into any elements but those which\nordinary language already recognized.\n\n\u00a7 2. The different antecedents and consequents being, then, supposed to\nbe, so far as the case requires, ascertained and discriminated from one\nanother, we are to inquire which is connected with which. In every\ninstance which comes under our observation, there are many antecedents and\nmany consequents. If those antecedents could not be severed from one\nanother except in thought, or if those consequents never were found apart,\nit would be impossible for us to distinguish (_a posteriori_ at least) the\nreal laws, or to assign to any cause its effect, or to any effect its\ncause. To do so, we must be able to meet with some of the antecedents\napart from the rest, and observe what follows from them; or some of the\nconsequents, and observe by what they are preceded. We must, in short,\nfollow the Baconian rule of _varying the circumstances_. This is, indeed,\nonly the first rule of physical inquiry, and not, as some have thought,\nthe sole rule; but it is the foundation of all the rest.\n\nFor the purpose of varying the circumstances, we may have recourse\n(according to a distinction commonly made) either to observation or to\nexperiment; we may either _find_ an instance in nature suited to our\npurposes, or, by an artificial arrangement of circumstances, _make_ one.\nThe value of the instance depends on what it is in itself, not on the mode\nin which it is obtained: its employment for the purposes of induction\ndepends on the same principles in the one case and in the other; as the\nuses of money are the same whether it is inherited or acquired. There is,\nin short, no difference in kind, no real logical distinction, between the\ntwo processes of investigation. There are, however, practical distinctions\nto which it is of considerable importance to advert.\n\n\u00a7 3. The first and most obvious distinction between Observation and\nExperiment is, that the latter is an immense extension of the former. It\nnot only enables us to produce a much greater number of variations in the\ncircumstances than nature spontaneously offers, but also, in thousands of\ncases, to produce the precise _sort_ of variation which we are in want of\nfor discovering the law of the phenomenon; a service which nature, being\nconstructed on a quite different scheme from that of facilitating our\nstudies, is seldom so friendly as to bestow upon us. For example, in order\nto ascertain what principle in the atmosphere enables it to sustain life,\nthe variation we require is that a living animal should be immersed in\neach component element of the atmosphere separately. But nature does not\nsupply either oxygen or azote in a separate state. We are indebted to\nartificial experiment for our knowledge that it is the former, and not the\nlatter, which supports respiration; and for our knowledge of the very\nexistence of the two ingredients.\n\nThus far the advantage of experimentation over simple observation is\nuniversally recognized: all are aware that it enables us to obtain\ninnumerable combinations of circumstances which are not to be found in\nnature, and so add to nature\u2019s experiments a multitude of experiments of\nour own. But there is another superiority (or, as Bacon would have\nexpressed it, another prerogative) of instances artificially obtained over\nspontaneous instances\u2014of our own experiments over even the same\nexperiments when made by nature\u2014which is not of less importance, and which\nis far from being felt and acknowledged in the same degree.\n\nWhen we can produce a phenomenon artificially, we can take it, as it were,\nhome with us, and observe it in the midst of circumstances with which in\nall other respects we are accurately acquainted. If we desire to know what\nare the effects of the cause A, and are able to produce A by means at our\ndisposal, we can generally determine at our own discretion, so far as is\ncompatible with the nature of the phenomenon A, the whole of the\ncircumstances which shall be present along with it: and thus, knowing\nexactly the simultaneous state of every thing else which is within the\nreach of A\u2019s influence, we have only to observe what alteration is made in\nthat state by the presence of A.\n\nFor example, by the electric machine we can produce, in the midst of known\ncircumstances, the phenomena which nature exhibits on a grander scale in\nthe form of lightning and thunder. Now let any one consider what amount of\nknowledge of the effects and laws of electric agency mankind could have\nobtained from the mere observation of thunder-storms, and compare it with\nthat which they have gained, and may expect to gain, from electrical and\ngalvanic experiments. This example is the more striking, now that we have\nreason to believe that electric action is of all natural phenomena (except\nheat) the most pervading and universal, which, therefore, it might\nantecedently have been supposed could stand least in need of artificial\nmeans of production to enable it to be studied; while the fact is so much\nthe contrary, that without the electric machine, the Leyden jar, and the\nvoltaic battery, we probably should never have suspected the existence of\nelectricity as one of the great agents in nature; the few electric\nphenomena we should have known of would have continued to be regarded\neither as supernatural, or as a sort of anomalies and eccentricities in\nthe order of the universe.\n\nWhen we have succeeded in insulating the phenomenon which is the subject\nof inquiry, by placing it among known circumstances, we may produce\nfurther variations of circumstances to any extent, and of such kinds as we\nthink best calculated to bring the laws of the phenomenon into a clear\nlight. By introducing one well-defined circumstance after another into the\nexperiment, we obtain assurance of the manner in which the phenomenon\nbehaves under an indefinite variety of possible circumstances. Thus,\nchemists, after having obtained some newly-discovered substance in a pure\nstate (that is, having made sure that there is nothing present which can\ninterfere with and modify its agency), introduce various other substances,\none by one, to ascertain whether it will combine with them, or decompose\nthem, and with what result; and also apply heat, or electricity, or\npressure, to discover what will happen to the substance under each of\nthese circumstances.\n\nBut if, on the other hand, it is out of our power to produce the\nphenomenon, and we have to seek for instances in which nature produces it,\nthe task before us is very different.\n\nInstead of being able to choose what the concomitant circumstances shall\nbe, we now have to discover what they are; which, when we go beyond the\nsimplest and most accessible cases, it is next to impossible to do with\nany precision and completeness. Let us take, as an exemplification of a\nphenomenon which we have no means of fabricating artificially, a human\nmind. Nature produces many; but the consequence of our not being able to\nproduce them by art is, that in every instance in which we see a human\nmind developing itself, or acting upon other things, we see it surrounded\nand obscured by an indefinite multitude of unascertainable circumstances,\nrendering the use of the common experimental methods almost delusive. We\nmay conceive to what extent this is true, if we consider, among other\nthings, that whenever Nature produces a human mind, she produces, in close\nconnection with it, a body; that is, a vast complication of physical\nfacts, in no two cases perhaps exactly similar, and most of which (except\nthe mere structure, which we can examine in a sort of coarse way after it\nhas ceased to act), are radically out of the reach of our means of\nexploration. If, instead of a human mind, we suppose the subject of\ninvestigation to be a human society or State, all the same difficulties\nrecur in a greatly augmented degree.\n\nWe have thus already come within sight of a conclusion, which the progress\nof the inquiry will, I think, bring before us with the clearest evidence:\nnamely, that in the sciences which deal with phenomena in which artificial\nexperiments are impossible (as in the case of astronomy), or in which they\nhave a very limited range (as in mental philosophy, social science, and\neven physiology), induction from direct experience is practiced at a\ndisadvantage in most cases equivalent to impracticability; from which it\nfollows that the methods of those sciences, in order to accomplish any\nthing worthy of attainment, must be to a great extent, if not principally,\ndeductive. This is already known to be the case with the first of the\nsciences we have mentioned, astronomy; that it is not generally recognized\nas true of the others, is probably one of the reasons why they are not in\na more advanced state.\n\n\u00a7 4. If what is called pure observation is at so great a disadvantage,\ncompared with artificial experimentation, in one department of the direct\nexploration of phenomena, there is another branch in which the advantage\nis all on the side of the former.\n\nInductive inquiry having for its object to ascertain what causes are\nconnected with what effects, we may begin this search at either end of the\nroad which leads from the one point to the other: we may either inquire\ninto the effects of a given cause or into the causes of a given effect.\nThe fact that light blackens chloride of silver might have been discovered\neither by experiments on light, trying what effect it would produce on\nvarious substances, or by observing that portions of the chloride had\nrepeatedly become black, and inquiring into the circumstances. The effect\nof the urali poison might have become known either by administering it to\nanimals, or by examining how it happened that the wounds which the Indians\nof Guiana inflict with their arrows prove so uniformly mortal. Now it is\nmanifest from the mere statement of the examples, without any theoretical\ndiscussion, that artificial experimentation is applicable only to the\nformer of these modes of investigation. We can take a cause, and try what\nit will produce; but we can not take an effect, and try what it will be\nproduced by. We can only watch till we see it produced, or are enabled to\nproduce it by accident.\n\nThis would be of little importance, if it always depended on our choice\nfrom which of the two ends of the sequence we would undertake our\ninquiries. But we have seldom any option. As we can only travel from the\nknown to the unknown, we are obliged to commence at whichever end we are\nbest acquainted with. If the agent is more familiar to us than its\neffects, we watch for, or contrive, instances of the agent, under such\nvarieties of circumstances as are open to us, and observe the result. If,\non the contrary, the conditions on which a phenomenon depends are obscure,\nbut the phenomenon itself familiar, we must commence our inquiry from the\neffect. If we are struck with the fact that chloride of silver has been\nblackened, and have no suspicion of the cause, we have no resource but to\ncompare instances in which the fact has chanced to occur, until by that\ncomparison we discover that in all those instances the substances had been\nexposed to light. If we knew nothing of the Indian arrows but their fatal\neffect, accident alone could turn our attention to experiments on the\nurali; in the regular course of investigation, we could only inquire, or\ntry to observe, what had been done to the arrows in particular instances.\n\nWherever, having nothing to guide us to the cause, we are obliged to set\nout from the effect, and to apply the rule of varying the circumstances to\nthe consequents, not the antecedents, we are necessarily destitute of the\nresource of artificial experimentation. We can not, at our choice, obtain\nconsequents, as we can antecedents, under any set of circumstances\ncompatible with their nature. There are no means of producing effects but\nthrough their causes, and by the supposition the causes of the effect in\nquestion are not known to us. We have, therefore, no expedient but to\nstudy it where it offers itself spontaneously. If nature happens to\npresent us with instances sufficiently varied in their circumstances, and\nif we are able to discover, either among the proximate antecedents or\namong some other order of antecedents, something which is always found\nwhen the effect is found, however various the circumstances, and never\nfound when it is not, we may discover, by mere observation without\nexperiment, a real uniformity in nature.\n\nBut though this is certainly the most favorable case for sciences of pure\nobservation, as contrasted with those in which artificial experiments are\npossible, there is in reality no case which more strikingly illustrates\nthe inherent imperfection of direct induction when not founded on\nexperimentation. Suppose that, by a comparison of cases of the effect, we\nhave found an antecedent which appears to be, and perhaps is, invariably\nconnected with it: we have not yet proved that antecedent to be the cause\nuntil we have reversed the process, and produced the effect by means of\nthat antecedent. If we can produce the antecedent artificially, and if,\nwhen we do so, the effect follows, the induction is complete; that\nantecedent is the cause of that consequent.(135) But we have then added\nthe evidence of experiment to that of simple observation. Until we had\ndone so, we had only proved _invariable_ antecedence within the limits of\nexperience, but not _unconditional_ antecedence, or causation. Until it\nhad been shown by the actual production of the antecedent under known\ncircumstances, and the occurrence thereupon of the consequent, that the\nantecedent was really the condition on which it depended; the uniformity\nof succession which was proved to exist between them might, for aught we\nknew, be (like the succession of day and night) not a case of causation at\nall; both antecedent and consequent might be successive stages of the\neffect of an ulterior cause. Observation, in short, without experiment\n(supposing no aid from deduction) can ascertain sequences and\nco-existences, but can not prove causation.\n\nIn order to see these remarks verified by the actual state of the\nsciences, we have only to think of the condition of natural history. In\nzoology, for example, there is an immense number of uniformities\nascertained, some of co-existence, others of succession, to many of which,\nnotwithstanding considerable variations of the attendant circumstances, we\nknow not any exception: but the antecedents, for the most part, are such\nas we can not artificially produce; or if we can, it is only by setting in\nmotion the exact process by which nature produces them; and this being to\nus a mysterious process, of which the main circumstances are not only\nunknown but unobservable, we do not succeed in obtaining the antecedents\nunder known circumstances. What is the result? That on this vast subject,\nwhich affords so much and such varied scope for observation, we have made\nmost scanty progress in ascertaining any laws of causation. We know not\nwith certainty, in the case of most of the phenomena that we find\nconjoined, which is the condition of the other; which is cause, and which\neffect, or whether either of them is so, or they are not rather conjunct\neffects of causes yet to be discovered, complex results of laws hitherto\nunknown.\n\nAlthough some of the foregoing observations may be, in technical\nstrictness of arrangement, premature in this place, it seemed that a few\ngeneral remarks on the difference between sciences of mere observation and\nsciences of experimentation, and the extreme disadvantage under which\ndirectly inductive inquiry is necessarily carried on in the former, were\nthe best preparation for discussing the methods of direct induction; a\npreparation rendering superfluous much that must otherwise have been\nintroduced, with some inconvenience, into the heart of that discussion. To\nthe consideration of these methods we now proceed.\n\n\n\n\n                              Chapter VIII.\n\n\nOf The Four Methods Of Experimental Inquiry.\n\n\n\u00a7 1. The simplest and most obvious modes of singling out from among the\ncircumstances which precede or follow a phenomenon, those with which it is\nreally connected by an invariable law, are two in number. One is, by\ncomparing together different instances in which the phenomenon occurs. The\nother is, by comparing instances in which the phenomenon does occur, with\ninstances in other respects similar in which it does not. These two\nmethods may be respectively denominated, the Method of Agreement, and the\nMethod of Difference.\n\nIn illustrating these methods, it will be necessary to bear in mind the\ntwofold character of inquiries into the laws of phenomena; which may be\neither inquiries into the cause of a given effect, or into the effects or\nproperties of a given cause. We shall consider the methods in their\napplication to either order of investigation, and shall draw our examples\nequally from both.\n\nWe shall denote antecedents by the large letters of the alphabet, and the\nconsequents corresponding to them by the small. Let A, then, be an agent\nor cause, and let the object of our inquiry be to ascertain what are the\neffects of this cause. If we can either find, or produce, the agent A in\nsuch varieties of circumstances that the different cases have no\ncircumstance in common except A; then whatever effect we find to be\nproduced in all our trials, is indicated as the effect of A. Suppose, for\nexample, that A is tried along with B and C, and that the effect is _a b\nc_; and suppose that A is next tried with D and E, but without B and C,\nand that the effect is _a d e_. Then we may reason thus: _b_ and _c_ are\nnot effects of A, for they were not produced by it in the second\nexperiment; nor are _d_ and _e_, for they were not produced in the first.\nWhatever is really the effect of A must have been produced in both\ninstances; now this condition is fulfilled by no circumstance except _a_.\nThe phenomenon _a_ can not have been the effect of B or C, since it was\nproduced where they were not; nor of D or E, since it was produced where\nthey were not. Therefore it is the effect of A.\n\nFor example, let the antecedent A be the contact of an alkaline substance\nand an oil. This combination being tried under several varieties of\ncircumstances, resembling each other in nothing else, the results agree in\nthe production of a greasy and detersive or saponaceous substance: it is\ntherefore concluded that the combination of an oil and an alkali causes\nthe production of a soap. It is thus we inquire, by the Method of\nAgreement, into the effect of a given cause.\n\nIn a similar manner we may inquire into the cause of a given effect. Let\n_a_ be the effect. Here, as shown in the last chapter, we have only the\nresource of observation without experiment: we can not take a phenomenon\nof which we know not the origin, and try to find its mode of production by\nproducing it: if we succeeded in such a random trial it could only be by\naccident. But if we can observe a in two different combinations, _a b c_\nand _a d e_; and if we know, or can discover, that the antecedent\ncircumstances in these cases respectively were A B C and A D E, we may\nconclude by a reasoning similar to that in the preceding example, that A\nis the antecedent connected with the consequent _a_ by a law of causation.\nB and C, we may say, can not be causes of _a_, since on its second\noccurrence they were not present; nor are D and E, for they were not\npresent on its first occurrence. A, alone of the five circumstances, was\nfound among the antecedents of _a_ in both instances.\n\nFor example, let the effect _a_ be crystallization. We compare instances\nin which bodies are known to assume crystalline structure, but which have\nno other point of agreement; and we find them to have one, and as far as\nwe can observe, only one, antecedent in common: the deposition of a solid\nmatter from a liquid state, either a state of fusion or of solution. We\nconclude, therefore, that the solidification of a substance from a liquid\nstate is an invariable antecedent of its crystallization.\n\nIn this example we may go further, and say, it is not only the invariable\nantecedent but the cause; or at least the proximate event which completes\nthe cause. For in this case we are able, after detecting the antecedent A,\nto produce it artificially, and by finding that _a_ follows it, verify the\nresult of our induction. The importance of thus reversing the proof was\nstrikingly manifested when, by keeping a phial of water charged with\nsiliceous particles undisturbed for years, a chemist (I believe Dr.\nWollaston) succeeded in obtaining crystals of quartz; and in the equally\ninteresting experiment in which Sir James Hall produced artificial marble\nby the cooling of its materials from fusion under immense pressure: two\nadmirable examples of the light which may be thrown upon the most secret\nprocesses of Nature by well-contrived interrogation of her.\n\nBut if we can not artificially produce the phenomenon A, the conclusion\nthat it is the cause of _a_ remains subject to very considerable doubt.\nThough an invariable, it may not be the unconditional antecedent of _a_,\nbut may precede it as day precedes night or night day. This uncertainty\narises from the impossibility of assuring ourselves that A is the _only_\nimmediate antecedent common to both the instances. If we could be certain\nof having ascertained all the invariable antecedents, we might be sure\nthat the unconditional invariable antecedent, or cause, must be found\nsomewhere among them. Unfortunately it is hardly ever possible to\nascertain all the antecedents, unless the phenomenon is one which we can\nproduce artificially. Even then, the difficulty is merely lightened, not\nremoved: men knew how to raise water in pumps long before they adverted to\nwhat was really the operating circumstance in the means they employed,\nnamely, the pressure of the atmosphere on the open surface of the water.\nIt is, however, much easier to analyze completely a set of arrangements\nmade by ourselves, than the whole complex mass of the agencies which\nnature happens to be exerting at the moment of the production of a given\nphenomenon. We may overlook some of the material circumstances in an\nexperiment with an electrical machine; but we shall, at the worst, be\nbetter acquainted with them than with those of a thunder-storm.\n\nThe mode of discovering and proving laws of nature, which we have now\nexamined, proceeds on the following axiom: Whatever circumstances can be\nexcluded, without prejudice to the phenomenon, or can be absent\nnotwithstanding its presence, is not connected with it in the way of\ncausation. The casual circumstances being thus eliminated, if only one\nremains, that one is the cause which we are in search of: if more than\none, they either are, or contain among them, the cause; and so, _mutatis\nmutandis_, of the effect. As this method proceeds by comparing different\ninstances to ascertain in what they agree, I have termed it the Method of\nAgreement; and we may adopt as its regulating principal the following\ncanon:\n\nFIRST CANON.\n\n_If two or more instances of the phenomenon under investigation have only\none circumstance in common, the circumstance in which alone all the\ninstances agree, is the cause (or effect) of the given phenomenon._\n\nQuitting for the present the Method of Agreement, to which we shall almost\nimmediately return, we proceed to a still more potent instrument of the\ninvestigation of nature, the Method of Difference.\n\n\u00a7 2. In the Method of Agreement, we endeavored to obtain instances which\nagreed in the given circumstance but differed in every other: in the\npresent method we require, on the contrary, two instances resembling one\nanother in every other respect, but differing in the presence or absence\nof the phenomenon we wish to study. If our object be to discover the\neffects of an agent A, we must procure A in some set of ascertained\ncircumstances, as A B C, and having noted the effects produced, compare\nthem with the effect of the remaining circumstances B C, when A is absent.\nIf the effect of A B C is _a b c_, and the effect of B C _b c_, it is\nevident that the effect of A is _a_. So again, if we begin at the other\nend, and desire to investigate the cause of an effect _a_, we must select\nan instance, as _a b c_, in which the effect occurs, and in which the\nantecedents were A B C, and we must look out for another instance in which\nthe remaining circumstances, _b c_, occur without _a_. If the antecedents,\nin that instance, are B C, we know that the cause of _a_ must be A: either\nA alone, or A in conjunction with some of the other circumstances present.\n\nIt is scarcely necessary to give examples of a logical process to which we\nowe almost all the inductive conclusions we draw in daily life. When a man\nis shot through the heart, it is by this method we know that it was the\ngunshot which killed him: for he was in the fullness of life immediately\nbefore, all circumstances being the same, except the wound.\n\nThe axioms implied in this method are evidently the following. Whatever\nantecedent can not be excluded without preventing the phenomenon, is the\ncause, or a condition, of that phenomenon: whatever consequent can be\nexcluded, with no other difference in the antecedents than the absence of\na particular one, is the effect of that one. Instead of comparing\ndifferent instances of a phenomenon, to discover in what they agree, this\nmethod compares an instance of its occurrence with an instance of its\nnon-occurrence, to discover in what they differ. The canon which is the\nregulating principle of the Method of Difference may be expressed as\nfollows:\n\nSECOND CANON.\n\n_If an instance in which the phenomenon under investigation occurs, and an\ninstance in which it does not occur, have every circumstance in common\nsave one, that one occurring only in the former; the circumstance in which\nalone the two instances differ, is the effect, or the cause, or an\nindispensable part of the cause, of the phenomenon._\n\n\u00a7 3. The two methods which we have now stated have many features of\nresemblance, but there are also many distinctions between them. Both are\nmethods of _elimination_. This term (employed in the theory of equations\nto denote the process by which one after another of the elements of a\nquestion is excluded, and the solution made to depend on the relation\nbetween the remaining elements only) is well suited to express the\noperation, analogous to this, which has been understood since the time of\nBacon to be the foundation of experimental inquiry: namely, the successive\nexclusion of the various circumstances which are found to accompany a\nphenomenon in a given instance, in order to ascertain what are those among\nthem which can be absent consistently with the existence of the\nphenomenon. The Method of Agreement stands on the ground that whatever can\nbe eliminated, is not connected with the phenomenon by any law. The Method\nof Difference has for its foundation, that whatever can not be eliminated,\nis connected with the phenomenon by a law.\n\nOf these methods, that of Difference is more particularly a method of\nartificial experiment; while that of Agreement is more especially the\nresource employed where experimentation is impossible. A few reflections\nwill prove the fact, and point out the reason of it.\n\nIt is inherent in the peculiar character of the Method of Difference, that\nthe nature of the combinations which it requires is much more strictly\ndefined than in the Method of Agreement. The two instances which are to be\ncompared with one another must be exactly similar, in all circumstances\nexcept the one which we are attempting to investigate: they must be in the\nrelation of A B C and B C, or of _a b c_ and _b c_. It is true that this\nsimilarity of circumstances needs not extend to such as are already known\nto be immaterial to the result. And in the case of most phenomena we learn\nat once, from the commonest experience, that most of the co-existent\nphenomena of the universe may be either present or absent without\naffecting the given phenomenon; or, if present, are present indifferently\nwhen the phenomenon does not happen and when it does. Still, even limiting\nthe identity which is required between the two instances, A B C and B C,\nto such circumstances as are not already known to be indifferent, it is\nvery seldom that nature affords two instances, of which we can be assured\nthat they stand in this precise relation to one another. In the\nspontaneous operations of nature there is generally such complication and\nsuch obscurity, they are mostly either on so overwhelmingly large or on so\ninaccessibly minute a scale, we are so ignorant of a great part of the\nfacts which really take place, and even those of which we are not ignorant\nare so multitudinous, and therefore so seldom exactly alike in any two\ncases, that a spontaneous experiment, of the kind required by the Method\nof Difference, is commonly not to be found. When, on the contrary, we\nobtain a phenomenon by an artificial experiment, a pair of instances such\nas the method requires is obtained almost as a matter of course, provided\nthe process does not last a long time. A certain state of surrounding\ncircumstances existed before we commenced the experiment; this is B C. We\nthen introduce A; say, for instance, by merely bringing an object from\nanother part of the room, before there has been time for any change in the\nother elements. It is, in short (as M. Comt\u00e9 observes), the very nature of\nan experiment, to introduce into the pre-existing state of circumstances a\nchange perfectly definite. We choose a previous state of things with which\nwe are well acquainted, so that no unforeseen alteration in that state is\nlikely to pass unobserved; and into this we introduce, as rapidly as\npossible, the phenomenon which we wish to study; so that in general we are\nentitled to feel complete assurance that the pre-existing state, and the\nstate which we have produced, differ in nothing except the presence or\nabsence of that phenomenon. If a bird is taken from a cage, and instantly\nplunged into carbonic acid gas, the experimentalist may be fully assured\n(at all events after one or two repetitions) that no circumstance capable\nof causing suffocation had supervened in the interim, except the change\nfrom immersion in the atmosphere to immersion in carbonic acid gas. There\nis one doubt, indeed, which may remain in some cases of this description;\nthe effect may have been produced not by the change, but by the means\nemployed to produce the change. The possibility, however, of this last\nsupposition generally admits of being conclusively tested by other\nexperiments. It thus appears that in the study of the various kinds of\nphenomena which we can, by our voluntary agency, modify or control, we can\nin general satisfy the requisitions of the Method of Difference; but that\nby the spontaneous operations of nature those requisitions are seldom\nfulfilled.\n\nThe reverse of this is the case with the Method of Agreement. We do not\nhere require instances of so special and determinate a kind. Any instances\nwhatever, in which nature presents us with a phenomenon, may be examined\nfor the purposes of this method; and if all such instances agree in any\nthing, a conclusion of considerable value is already attained. We can\nseldom, indeed, be sure that the one point of agreement is the only one;\nbut this ignorance does not, as in the Method of Difference, vitiate the\nconclusion; the certainty of the result, as far as it goes, is not\naffected. We have ascertained one invariable antecedent or consequent,\nhowever many other invariable antecedents or consequents may still remain\nunascertained. If A B C, A D E, A F G, are all equally followed by a, then\na is an invariable consequent of A. If _a b c_, _a d e_, _a f g_, all\nnumber A among their antecedents, then A is connected as an antecedent, by\nsome invariable law, with _a_. But to determine whether this invariable\nantecedent is a cause, or this invariable consequent an effect, we must be\nable, in addition, to produce the one by means of the other; or, at least,\nto obtain that which alone constitutes our assurance of having produced\nany thing, namely, an instance in which the effect, _a_, has come into\nexistence, with no other change in the pre-existing circumstances than the\naddition of A. And this, if we can do it, is an application of the Method\nof Difference, not of the Method of Agreement.\n\nIt thus appears to be by the Method of Difference alone that we can ever,\nin the way of direct experience, arrive with certainty at causes. The\nMethod of Agreement leads only to laws of phenomena (as some writers call\nthem, but improperly, since laws of causation are also laws of phenomena):\nthat is, to uniformities, which either are not laws of causation, or in\nwhich the question of causation must for the present remain undecided. The\nMethod of Agreement is chiefly to be resorted to, as a means of suggesting\napplications of the Method of Difference (as in the last example the\ncomparison of A B C, A D E, A F G, suggested that A was the antecedent on\nwhich to try the experiment whether it could produce _a_); or as an\ninferior resource, in case the Method of Difference is impracticable;\nwhich, as we before showed, generally arises from the impossibility of\nartificially producing the phenomena. And hence it is that the Method of\nAgreement, though applicable in principle to either case, is more\nemphatically the method of investigation on those subjects where\nartificial experimentation is impossible; because on those it is,\ngenerally, our only resource of a directly inductive nature; while, in the\nphenomena which we can produce at pleasure, the Method of Difference\ngenerally affords a more efficacious process, which will ascertain causes\nas well as mere laws.\n\n\u00a7 4. There are, however, many cases in which, though our power of\nproducing the phenomenon is complete, the Method of Difference either can\nnot be made available at all, or not without a previous employment of the\nMethod of Agreement. This occurs when the agency by which we can produce\nthe phenomenon is not that of one single antecedent, but a combination of\nantecedents, which we have no power of separating from each other, and\nexhibiting apart. For instance, suppose the subject of inquiry to be the\ncause of the double refraction of light. We can produce this phenomenon at\npleasure, by employing any one of the many substances which are known to\nrefract light in that peculiar manner. But if, taking one of those\nsubstances, as Iceland spar, for example, we wish to determine on which of\nthe properties of Iceland spar this remarkable phenomenon depends, we can\nmake no use, for that purpose, of the Method of Difference; for we can not\nfind another substance precisely resembling Iceland spar except in some\none property. The only mode, therefore, of prosecuting this inquiry is\nthat afforded by the Method of Agreement; by which, in fact, through a\ncomparison of all the known substances which have the property of doubly\nrefracting light, it was ascertained that they agree in the circumstance\nof being crystalline substances; and though the converse does not hold,\nthough all crystalline substances have not the property of double\nrefraction, it was concluded, with reason, that there is a real connection\nbetween these two properties; that either crystalline structure, or the\ncause which gives rise to that structure, is one of the conditions of\ndouble refraction.\n\nOut of this employment of the Method of Agreement arises a peculiar\nmodification of that method, which is sometimes of great avail in the\ninvestigation of nature. In cases similar to the above, in which it is not\npossible to obtain the precise pair of instances which our second canon\nrequires\u2014instances agreeing in every antecedent except A, or in every\nconsequent except _a_, we may yet be able, by a double employment of the\nMethod of Agreement, to discover in what the instances which contain A or\n_a_ differ from those which do not.\n\nIf we compare various instances in which _a_ occurs, and find that they\nall have in common the circumstance A, and (as far as can be observed) no\nother circumstance, the Method of Agreement, so far, bears testimony to a\nconnection between A and _a_. In order to convert this evidence of\nconnection into proof of causation by the direct Method of Difference, we\nought to be able, in some one of these instances, as for example, A B C,\nto leave out A, and observe whether by doing so, _a_ is prevented. Now\nsupposing (what is often the case) that we are not able to try this\ndecisive experiment; yet, provided we can by any means discover what would\nbe its result if we could try it, the advantage will be the same. Suppose,\nthen, that as we previously examined a variety of instances in which _a_\noccurred, and found them to agree in containing A, so we now observe a\nvariety of instances in which _a_ does not occur, and find them agree in\nnot containing A; which establishes, by the Method of Agreement, the same\nconnection between the absence of A and the absence of _a_, which was\nbefore established between their presence. As, then, it had been shown\nthat whenever A is present _a_ is present, so, it being now shown that\nwhen A is taken away a is removed along with it, we have by the one\nproposition A B C, _a b c_, by the other B C, _b c_, the positive and\nnegative instances which the Method of Difference requires.\n\nThis method may be called the Indirect Method of Difference, or the Joint\nMethod of Agreement and Difference; and consists in a double employment of\nthe Method of Agreement, each proof being independent of the other, and\ncorroborating it. But it is not equivalent to a proof by the direct Method\nof Difference. For the requisitions of the Method of Difference are not\nsatisfied, unless we can be quite sure either that the instances\naffirmative of _a_ agree in no antecedent whatever but A, or that the\ninstances negative of _a_ agree in nothing but the negation of A. Now, if\nit were possible, which it never is, to have this assurance, we should not\nneed the joint method; for either of the two sets of instances separately\nwould then be sufficient to prove causation. This indirect method,\ntherefore, can only be regarded as a great extension and improvement of\nthe Method of Agreement, but not as participating in the more cogent\nnature of the Method of Difference. The following may be stated as its\ncanon:\n\nTHIRD CANON.\n\n_If two or more instances in which the phenomenon occurs have only one\ncircumstance in common, while two or more instances in which it does not\noccur have nothing in common save the absence of that circumstance, the\ncircumstance in which alone the two sets of instances differ, is the\neffect, or the cause, or an indispensable part of the cause, of the\nphenomenon._\n\nWe shall presently see that the Joint Method of Agreement and Difference\nconstitutes, in another respect not yet adverted to, an improvement upon\nthe common Method of Agreement, namely, in being unaffected by a\ncharacteristic imperfection of that method, the nature of which still\nremains to be pointed out. But as we can not enter into this exposition\nwithout introducing a new element of complexity into this long and\nintricate discussion, I shall postpone it to a subsequent chapter, and\nshall at once proceed to a statement of two other methods, which will\ncomplete the enumeration of the means which mankind possess for exploring\nthe laws of nature by specific observation and experience.\n\n\u00a7 5. The first of these has been aptly denominated the Method of Residues.\nIts principle is very simple. Subducting from any given phenomenon all the\nportions which, by virtue of preceding inductions, can be assigned to\nknown causes, the remainder will be the effect of the antecedents which\nhad been overlooked, or of which the effect was as yet an unknown\nquantity.\n\nSuppose, as before, that we have the antecedents A B C, followed by the\nconsequents _a b c_, and that by previous inductions (founded, we will\nsuppose, on the Method of Difference) we have ascertained the causes of\nsome of these effects, or the effects of some of these causes; and are\nthence apprised that the effect of A is _a_, and that the effect of B is\n_b_. Subtracting the sum of these effects from the total phenomenon, there\nremains _c_, which now, without any fresh experiments, we may know to be\nthe effect of C. This Method of Residues is in truth a peculiar\nmodification of the Method of Difference. If the instance A B C, _a b c_,\ncould have been compared with a single instance A B, _a b_, we should have\nproved C to be the cause of _c_, by the common process of the Method of\nDifference. In the present case, however, instead of a single instance A\nB, we have had to study separately the causes A and B, and to infer from\nthe effects which they produce separately what effect they must produce in\nthe case A B C, where they act together. Of the two instances, therefore,\nwhich the Method of Difference requires\u2014the one positive, the other\nnegative\u2014the negative one, or that in which the given phenomenon is\nabsent, is not the direct result of observation and experiment, but has\nbeen arrived at by deduction. As one of the forms of the Method of\nDifference, the Method of Residues partakes of its rigorous certainty,\nprovided the previous inductions, those which gave the effects of A and B,\nwere obtained by the same infallible method, and provided we are certain\nthat C is the _only_ antecedent to which the residual phenomenon _c_ can\nbe referred; the only agent of which we had not already calculated and\nsubducted the effect. But as we can never be quite certain of this, the\nevidence derived from the Method of Residues is not complete unless we can\nobtain C artificially, and try it separately, or unless its agency, when\nonce suggested, can be accounted for, and proved deductively from known\nlaws.\n\nEven with these reservations, the Method of Residues is one of the most\nimportant among our instruments of discovery. Of all the methods of\ninvestigating laws of nature, this is the most fertile in unexpected\nresults: often informing us of sequences in which neither the cause nor\nthe effect were sufficiently conspicuous to attract of themselves the\nattention of observers. The agent C may be an obscure circumstance, not\nlikely to have been perceived unless sought for, nor likely to have been\nsought for until attention had been awakened by the insufficiency of the\nobvious causes to account for the whole of the effect. And _c_ may be so\ndisguised by its intermixture with _a_ and _b_, that it would scarcely\nhave presented itself spontaneously as a subject of separate study. Of\nthese uses of the method, we shall presently cite some remarkable\nexamples. The canon of the Method of Residues is as follows:\n\nFOURTH CANON.\n\n_Subduct from any phenomenon such part as is known by previous inductions\nto be the effect of certain antecedents, and the residue of the phenomenon\nis the effect of the remaining antecedents._\n\n\u00a7 6. There remains a class of laws which it is impracticable to ascertain\nby any of the three methods which I have attempted to characterize:\nnamely, the laws of those Permanent Causes, or indestructible natural\nagents, which it is impossible either to exclude or to isolate; which we\ncan neither hinder from being present, nor contrive that they shall be\npresent alone. It would appear at first sight that we could by no means\nseparate the effects of these agents from the effects of those other\nphenomena with which they can not be prevented from co-existing. In\nrespect, indeed, to most of the permanent causes, no such difficulty\nexists; since, though we can not eliminate them as co-existing facts, we\ncan eliminate them as influencing agents, by simply trying our experiment\nin a local situation beyond the limits of their influence. The pendulum,\nfor example, has its oscillations disturbed by the vicinity of a mountain:\nwe remove the pendulum to a sufficient distance from the mountain, and the\ndisturbance ceases: from these data we can determine by the Method of\nDifference, the amount of effect due to the mountain; and beyond a certain\ndistance every thing goes on precisely as it would do if the mountain\nexercised no influence whatever, which, accordingly, we, with sufficient\nreason, conclude to be the fact.\n\nThe difficulty, therefore, in applying the methods already treated of to\ndetermine the effects of Permanent Causes, is confined to the cases in\nwhich it is impossible for us to get out of the local limits of their\ninfluence. The pendulum can be removed from the influence of the mountain,\nbut it can not be removed from the influence of the earth: we can not take\naway the earth from the pendulum, nor the pendulum from the earth, to\nascertain whether it would continue to vibrate if the action which the\nearth exerts upon it were withdrawn. On what evidence, then, do we ascribe\nits vibrations to the earth\u2019s influence? Not on any sanctioned by the\nMethod of Difference; for one of the two instances, the negative instance,\nis wanting. Nor by the Method of Agreement; for though all pendulums agree\nin this, that during their oscillations the earth is always present, why\nmay we not as well ascribe the phenomenon to the sun, which is equally a\nco-existent fact in all the experiments? It is evident that to establish\neven so simple a fact of causation as this, there was required some method\nover and above those which we have yet examined.\n\nAs another example, let us take the phenomenon Heat. Independently of all\nhypothesis as to the real nature of the agency so called, this fact is\ncertain, that we are unable to exhaust any body of the whole of its heat.\nIt is equally certain that no one ever perceived heat not emanating from a\nbody. Being unable, then, to separate Body and Heat, we can not effect\nsuch a variation of circumstances as the foregoing three methods require;\nwe can not ascertain, by those methods, what portion of the phenomena\nexhibited by any body is due to the heat contained in it. If we could\nobserve a body with its heat, and the same body entirely divested of heat,\nthe Method of Difference would show the effect due to the heat, apart from\nthat due to the body. If we could observe heat under circumstances\nagreeing in nothing but heat, and therefore not characterized also by the\npresence of a body, we could ascertain the effects of heat, from an\ninstance of heat with a body and an instance of heat without a body, by\nthe Method of Agreement; or we could determine by the Method of Difference\nwhat effect was due to the body, when the remainder which was due to the\nheat would be given by the Method of Residues. But we can do none of these\nthings; and without them the application of any of the three methods to\nthe solution of this problem would be illusory. It would be idle, for\ninstance, to attempt to ascertain the effect of heat by subtracting from\nthe phenomena exhibited by a body all that is due to its other properties;\nfor as we have never been able to observe any bodies without a portion of\nheat in them, effects due to that heat might form a part of the very\nresults which we were affecting to subtract, in order that the effect of\nheat might be shown by the residue.\n\nIf, therefore, there were no other methods of experimental investigation\nthan these three, we should be unable to determine the effects due to heat\nas a cause. But we have still a resource. Though we can not exclude an\nantecedent altogether, we may be able to produce, or nature may produce\nfor us some modification in it. By a modification is here meant, a change\nin it not amounting to its total removal. If some modification in the\nantecedent A is always followed by a change in the consequent _a_, the\nother consequents _b_ and _c_ remaining the same; or _vic\u00e8 versa_, if\nevery change in _a_ is found to have been preceded by some modification in\nA, none being observable in any of the other antecedents, we may safely\nconclude that _a_ is, wholly or in part, an effect traceable to A, or at\nleast in some way connected with it through causation. For example, in the\ncase of heat, though we can not expel it altogether from any body, we can\nmodify it in quantity, we can increase or diminish it; and doing so, we\nfind by the various methods of experimentation or observation already\ntreated of, that such increase or diminution of heat is followed by\nexpansion or contraction of the body. In this manner we arrive at the\nconclusion, otherwise unattainable by us, that one of the effects of heat\nis to enlarge the dimensions of bodies; or, what is the same thing in\nother words, to widen the distances between their particles.\n\nA change in a thing, not amounting to its total removal, that is, a change\nwhich leaves it still the same thing it was, must be a change either in\nits quantity, or in some of its variable relations to other things, of\nwhich variable relations the principal is its position in space. In the\nprevious example, the modification which was produced in the antecedent\nwas an alteration in its quantity. Let us now suppose the question to be,\nwhat influence the moon exerts on the surface of the earth. We can not try\nan experiment in the absence of the moon, so as to observe what\nterrestrial phenomena her annihilation would put an end to; but when we\nfind that all the variations in the _position_ of the moon are followed by\ncorresponding variations in the time and place of high water, the place\nbeing always either the part of the earth which is nearest to, or that\nwhich is most remote from, the moon, we have ample evidence that the moon\nis, wholly or partially, the cause which determines the tides. It very\ncommonly happens, as it does in this instance, that the variations of an\neffect are correspondent, or analogous, to those of its cause; as the moon\nmoves farther toward the east, the high-water point does the same: but\nthis is not an indispensable condition, as may be seen in the same\nexample, for along with that high-water point there is at the same instant\nanother high-water point diametrically opposite to it, and which,\ntherefore, of necessity, moves toward the west, as the moon, followed by\nthe nearer of the tide waves, advances toward the east: and yet both these\nmotions are equally effects of the moon\u2019s motion.\n\nThat the oscillations of the pendulum are caused by the earth, is proved\nby similar evidence. Those oscillations take place between equidistant\npoints on the two sides of a line, which, being perpendicular to the\nearth, varies with every variation in the earth\u2019s position, either in\nspace or relatively to the object. Speaking accurately, we only know by\nthe method now characterized, that all terrestrial bodies tend to the\nearth, and not to some unknown fixed point lying in the same direction. In\nevery twenty-four hours, by the earth\u2019s rotation, the line drawn from the\nbody at right angles to the earth coincides successively with all the\nradii of a circle, and in the course of six months the place of that\ncircle varies by nearly two hundred millions of miles; yet in all these\nchanges of the earth\u2019s position, the line in which bodies tend to fall\ncontinues to be directed toward it: which proves that terrestrial gravity\nis directed to the earth, and not, as was once fancied by some, to a fixed\npoint of space.\n\nThe method by which these results were obtained may be termed the Method\nof Concomitant Variations; it is regulated by the following canon:\n\nFIFTH CANON.\n\n_Whatever phenomenon varies in any manner whenever another phenomenon\nvaries in some particular manner, is either a cause or an effect of that\nphenomenon, or is connected with it through some fact of causation._\n\nThe last clause is subjoined, because it by no means follows when two\nphenomena accompany each other in their variations, that the one is cause\nand the other effect. The same thing may, and indeed must happen,\nsupposing them to be two different effects of a common cause: and by this\nmethod alone it would never be possible to ascertain which of the\nsuppositions is the true one. The only way to solve the doubt would be\nthat which we have so often adverted to, viz., by endeavoring to ascertain\nwhether we can produce the one set of variations by means of the other. In\nthe case of heat, for example, by increasing the temperature of a body we\nincrease its bulk, but by increasing its bulk we do not increase its\ntemperature; on the contrary (as in the rarefaction of air under the\nreceiver of an air-pump), we generally diminish it: therefore heat is not\nan effect, but a cause, of increase of bulk. If we can not ourselves\nproduce the variations, we must endeavor, though it is an attempt which is\nseldom successful, to find them produced by nature in some case in which\nthe preexisting circumstances are perfectly known to us.\n\nIt is scarcely necessary to say, that in order to ascertain the uniform\nconcomitance of variations in the effect with variations in the cause, the\nsame precautions must be used as in any other case of the determination of\nan invariable sequence. We must endeavor to retain all the other\nantecedents unchanged, while that particular one is subjected to the\nrequisite series of variations; or, in other words, that we may be\nwarranted in inferring causation from concomitance of variations, the\nconcomitance itself must be proved by the Method of Difference.\n\nIt might at first appear that the Method of Concomitant Variations assumes\na new axiom, or law of causation in general, namely, that every\nmodification of the cause is followed by a change in the effect. And it\ndoes usually happen that when a phenomenon A causes a phenomenon _a_, any\nvariation in the quantity or in the various relations of A, is uniformly\nfollowed by a variation in the quantity or relations of _a_. To take a\nfamiliar instance, that of gravitation. The sun causes a certain tendency\nto motion in the earth; here we have cause and effect; but that tendency\nis _toward_ the sun, and therefore varies in direction as the sun varies\nin the relation of position; and, moreover, the tendency varies in\nintensity, in a certain numerical correspondence to the sun\u2019s distance\nfrom the earth, that is, according to another relation of the sun. Thus we\nsee that there is not only an invariable connection between the sun and\nthe earth\u2019s gravitation, but that two of the relations of the sun, its\nposition with respect to the earth and its distance from the earth, are\ninvariably connected as antecedents with the quantity and direction of the\nearth\u2019s gravitation. The cause of the earth\u2019s gravitating at all, is\nsimply the sun; but the cause of its gravitating with a given intensity\nand in a given direction, is the existence of the sun in a given direction\nand at a given distance. It is not strange that a modified cause, which is\nin truth a different cause, should produce a different effect.\n\nAlthough it is for the most part true that a modification of the cause is\nfollowed by a modification of the effect, the Method of Concomitant\nVariations does not, however, presuppose this as an axiom. It only\nrequires the converse proposition: that any thing on whose modifications,\nmodifications of an effect are invariably consequent, must be the cause\n(or connected with the cause) of that effect; a proposition, the truth of\nwhich is evident; for if the thing itself had no influence on the effect,\nneither could the modifications of the thing have any influence. If the\nstars have no power over the fortunes of mankind, it is implied in the\nvery terms that the conjunctions or oppositions of different stars can\nhave no such power.\n\nAlthough the most striking applications of the Method of Concomitant\nVariations take place in the cases in which the Method of Difference,\nstrictly so called, is impossible, its use is not confined to those cases;\nit may often usefully follow after the Method of Difference, to give\nadditional precision to a solution which that has found. When by the\nMethod of Difference it has first been ascertained that a certain object\nproduces a certain effect, the Method of Concomitant Variations may be\nusefully called in, to determine according to what law the quantity or the\ndifferent relations of the effect follow those of the cause.\n\n\u00a7 7. The case in which this method admits of the most extensive\nemployment, is that in which the variations of the cause are variations of\nquantity. Of such variations we may in general affirm with safety, that\nthey will be attended not only with variations, but with similar\nvariations, of the effect: the proposition that more of the cause is\nfollowed by more of the effect, being a corollary from the principle of\nthe Composition of Causes, which, as we have seen, is the general rule of\ncausation; cases of the opposite description, in which causes change their\nproperties on being conjoined with one another, being, on the contrary,\nspecial and exceptional. Suppose, then, that when A changes in quantity,\n_a_ also changes in quantity, and in such a manner that we can trace the\nnumerical relation which the changes of the one bear to such changes of\nthe other as take place within our limits of observation. We may then,\nwith certain precautions, safely conclude that the same numerical relation\nwill hold beyond those limits. If, for instance, we find that when A is\ndouble, _a_ is double; that when A is treble or quadruple, _a_ is treble\nor quadruple; we may conclude that if A were a half or a third, _a_ would\nbe a half or a third, and finally, that if A were annihilated, _a_ would\nbe annihilated; and that _a_ is wholly the effect of A, or wholly the\neffect of the same cause with A. And so with any other numerical relation\naccording to which A and _a_ would vanish simultaneously; as, for\ninstance, if _a_ were proportional to the square of A. If, on the other\nhand, _a_ is not wholly the effect of A, but yet varies when A varies, it\nis probably a mathematical function not of A alone, but of A and something\nelse: its changes, for example, may be such as would occur if part of it\nremained constant, or varied on some other principle, and the remainder\nvaried in some numerical relations to the variations of A. In that case,\nwhen A diminishes, _a_ will be seen to approach not toward zero, but\ntoward some other limit; and when the series of variations is such as to\nindicate what that limit is, if constant, or the law of its variation, if\nvariable, the limit will exactly measure how much of _a_ is the effect of\nsome other and independent cause, and the remainder will be the effect of\nA (or of the cause of A).\n\nThese conclusions, however, must not be drawn without certain precautions.\nIn the first place, the possibility of drawing them at all, manifestly\nsupposes that we are acquainted not only with the variations, but with the\nabsolute quantities both of A and _a_. If we do not know the total\nquantities, we can not, of course, determine the real numerical relation\naccording to which those quantities vary. It is, therefore, an error to\nconclude, as some have concluded, that because increase of heat expands\nbodies, that is, increases the distance between their particles, therefore\nthe distance is wholly the effect of heat, and that if we could entirely\nexhaust the body of its heat, the particles would be in complete contact.\nThis is no more than a guess, and of the most hazardous sort, not a\nlegitimate induction: for since we neither know how much heat there is in\nany body, nor what is the real distance between any two of its particles,\nwe can not judge whether the contraction of the distance does or does not\nfollow the diminution of the quantity of heat according to such a\nnumerical relation that the two quantities would vanish simultaneously.\n\nIn contrast with this, let us consider a case in which the absolute\nquantities are known; the case contemplated in the first law of motion:\nviz., that all bodies in motion continue to move in a straight line with\nuniform velocity until acted upon by some new force. This assertion is in\nopen opposition to first appearances; all terrestrial objects, when in\nmotion, gradually abate their velocity, and at last stop; which\naccordingly the ancients, with their _inductio per enumerationem\nsimplicem_, imagined to be the law. Every moving body, however, encounters\nvarious obstacles, as friction, the resistance of the atmosphere, etc.,\nwhich we know by daily experience to be causes capable of destroying\nmotion. It was suggested that the whole of the retardation might be owing\nto these causes. How was this inquired into? If the obstacles could have\nbeen entirely removed, the case would have been amenable to the Method of\nDifference. They could not be removed, they could only be diminished, and\nthe case, therefore, admitted only of the Method of Concomitant\nVariations. This accordingly being employed, it was found that every\ndiminution of the obstacles diminished the retardation of the motion: and\ninasmuch as in this case (unlike the case of heat) the total quantities\nboth of the antecedent and of the consequent were known, it was\npracticable to estimate, with an approach to accuracy, both the amount of\nthe retardation and the amount of the retarding causes, or resistances,\nand to judge how near they both were to being exhausted; and it appeared\nthat the effect dwindled as rapidly, and at each step was as far on the\nroad toward annihilation, as the cause was. The simple oscillation of a\nweight suspended from a fixed point, and moved a little out of the\nperpendicular, which in ordinary circumstances lasts but a few minutes,\nwas prolonged in Borda\u2019s experiments to more than thirty hours, by\ndiminishing as much as possible the friction at the point of suspension,\nand by making the body oscillate in a space exhausted as nearly as\npossible of its air. There could therefore be no hesitation in assigning\nthe whole of the retardation of motion to the influence of the obstacles;\nand since, after subducting this retardation from the total phenomenon,\nthe remainder was a uniform velocity, the result was the proposition known\nas the first law of motion.\n\nThere is also another characteristic uncertainty affecting the inference\nthat the law of variation which the quantities observe within our limits\nof observation, will hold beyond those limits. There is, of course, in the\nfirst instance, the possibility that beyond the limits, and in\ncircumstances therefore of which we have no direct experience, some\ncounteracting cause might develop itself; either a new agent or a new\nproperty of the agents concerned, which lies dormant in the circumstances\nwe are able to observe. This is an element of uncertainty which enters\nlargely into all our predictions of effects; but it is not peculiarly\napplicable to the Method of Concomitant Variations. The uncertainty,\nhowever, of which I am about to speak, is characteristic of that method;\nespecially in the cases in which the extreme limits of our observation are\nvery narrow, in comparison with the possible variations in the quantities\nof the phenomena. Any one who has the slightest acquaintance with\nmathematics, is aware that very different laws of variation may produce\nnumerical results which differ but slightly from one another within narrow\nlimits; and it is often only when the absolute amounts of variation are\nconsiderable, that the difference between the results given by one law and\nby another becomes appreciable. When, therefore, such variations in the\nquantity of the antecedents as we have the means of observing are small in\ncomparison with the total quantities, there is much danger lest we should\nmistake the numerical law, and be led to miscalculate the variations which\nwould take place beyond the limits; a miscalculation which would vitiate\nany conclusion respecting the dependence of the effect upon the cause,\nthat could be founded on those variations. Examples are not wanting of\nsuch mistakes. \u201cThe formul\u00e6,\u201d says Sir John Herschel,(136) \u201cwhich have\nbeen empirically deduced for the elasticity of steam (till very recently),\nand those for the resistance of fluids, and other similar subjects,\u201d when\nrelied on beyond the limits of the observations from which they were\ndeduced, \u201chave almost invariably failed to support the theoretical\nstructures which have been erected on them.\u201d\n\nIn this uncertainty, the conclusion we may draw from the concomitant\nvariations of _a_ and A, to the existence of an invariable and exclusive\nconnection between them, or to the permanency of the same numerical\nrelation between their variations when the quantities are much greater or\nsmaller than those which we have had the means of observing, can not be\nconsidered to rest on a complete induction. All that in such a case can be\nregarded as proved on the subject of causation is, that there is some\nconnection between the two phenomena; that A, or something which can\ninfluence A, must be _one_ of the causes which collectively determine _a_.\nWe may, however, feel assured that the relation which we have observed to\nexist between the variations of A and _a_, will hold true in all cases\nwhich fall between the same extreme limits; that is, wherever the utmost\nincrease or diminution in which the result has been found by observation\nto coincide with the law, is not exceeded.\n\nThe four methods which it has now been attempted to describe, are the only\npossible modes of experimental inquiry\u2014of direct induction _a posteriori_,\nas distinguished from deduction: at least, I know not, nor am able to\nimagine any others. And even of these, the Method of Residues, as we have\nseen, is not independent of deduction; though, as it also requires\nspecific experience, it may, without impropriety, be included among\nmethods of direct observation and experiment.\n\nThese, then, with such assistance as can be obtained from Deduction,\ncompose the available resources of the human mind for ascertaining the\nlaws of the succession of phenomena. Before proceeding to point out\ncertain circumstances by which the employment of these methods is\nsubjected to an immense increase of complication and of difficulty, it is\nexpedient to illustrate the use of the methods, by suitable examples drawn\nfrom actual physical investigations. These, accordingly, will form the\nsubject of the succeeding chapter.\n\n\n\n\n                               Chapter IX.\n\n\nMiscellaneous Examples Of The Four Methods.\n\n\n\u00a7 1. I shall select, as a first example, an interesting speculation of one\nof the most eminent of theoretical chemists, Baron Liebig. The object in\nview is to ascertain the immediate cause of the death produced by metallic\npoisons.\n\nArsenious acid, and the salts of lead, bismuth, copper, and mercury, if\nintroduced into the animal organism, except in the smallest doses, destroy\nlife. These facts have long been known, as insulated truths of the lowest\norder of generalization; but it was reserved for Liebig, by an apt\nemployment of the first two of our methods of experimental inquiry, to\nconnect these truths together by a higher induction, pointing out what\nproperty, common to all these deleterious substances, is the really\noperating cause of their fatal effect.\n\nWhen solutions of these substances are placed in sufficiently close\ncontact with many animal products, albumen, milk, muscular fibre, and\nanimal membranes, the acid or salt leaves the water in which it was\ndissolved, and enters into combination with the animal substance, which\nsubstance, after being thus acted upon, is found to have lost its tendency\nto spontaneous decomposition, or putrefaction.\n\nObservation also shows, in cases where death has been produced by these\npoisons, that the parts of the body with which the poisonous substances\nhave been brought into contact, do not afterward putrefy.\n\nAnd, finally, when the poison has been supplied in too small a quantity to\ndestroy life, eschars are produced, that is, certain superficial portions\nof the tissues are destroyed, which are afterward thrown off by the\nreparative process taking place in the healthy parts.\n\nThese three sets of instances admit of being treated according to the\nMethod of Agreement. In all of them the metallic compounds are brought\ninto contact with the substances which compose the human or animal body;\nand the instances do not seem to agree in any other circumstance. The\nremaining antecedents are as different, and even opposite, as they could\npossibly be made; for in some the animal substances exposed to the action\nof the poisons are in a state of life, in others only in a state of\norganization, in others not even in that. And what is the result which\nfollows in all the cases? The conversion of the animal substance (by\ncombination with the poison) into a chemical compound, held together by so\npowerful a force as to resist the subsequent action of the ordinary causes\nof decomposition. Now, organic life (the necessary condition of sensitive\nlife) consisting in a continual state of decomposition and recomposition\nof the different organs and tissues, whatever incapacitates them for this\ndecomposition destroys life. And thus the proximate cause of the death\nproduced by this description of poisons is ascertained, as far as the\nMethod of Agreement can ascertain it.\n\nLet us now bring our conclusion to the test of the Method of Difference.\nSetting out from the cases already mentioned, in which the antecedent is\nthe presence of substances forming with the tissues a compound incapable\nof putrefaction, (and _a fortiori_ incapable of the chemical actions which\nconstitute life), and the consequent is death, either of the whole\norganism, or of some portion of it; let us compare with these cases other\ncases, as much resembling them as possible, but in which that effect is\nnot produced. And, first, \u201cmany insoluble basic salts of arsenious acid\nare known not to be poisonous. The substance called alkargen, discovered\nby Bunsen, which contains a very large quantity of arsenic, and approaches\nvery closely in composition to the organic arsenious compounds found in\nthe body, has not the slightest injurious action upon the organism.\u201d Now\nwhen these substances are brought into contact with the tissues in any\nway, they do not combine with them; they do not arrest their progress to\ndecomposition. As far, therefore, as these instances go, it appears that\nwhen the effect is absent, it is by reason of the absence of that\nantecedent which we had already good ground for considering as the\nproximate cause.\n\nBut the rigorous conditions of the Method of Difference are not yet\nsatisfied; for we can not be sure that these unpoisonous bodies agree with\nthe poisonous substances in every property, except the particular one of\nentering into a difficultly decomposable compound with the animal tissues.\nTo render the method strictly applicable, we need an instance, not of a\ndifferent substance, but of one of the very same substances, in\ncircumstances which would prevent it from forming, with the tissues, the\nsort of compound in question; and then, if death does not follow, our case\nis made out. Now such instances are afforded by the antidotes to these\npoisons. For example, in case of poisoning by arsenious acid, if hydrated\nperoxide of iron is administered, the destructive agency is instantly\nchecked. Now this peroxide is known to combine with the acid, and form a\ncompound, which, being insoluble, can not act at all on animal tissues.\nSo, again, sugar is a well-known antidote to poisoning by salts of copper;\nand sugar reduces those salts either into metallic copper, or into the red\nsub-oxide, neither of which enters into combination with animal matter.\nThe disease called painter\u2019s colic, so common in manufactories of\nwhite-lead, is unknown where the workmen are accustomed to take, as a\npreservative, sulphuric acid lemonade (a solution of sugar rendered acid\nby sulphuric acid). Now diluted sulphuric acid has the property of\ndecomposing all compounds of lead with organic matter, or of preventing\nthem from being formed.\n\nThere is another class of instances, of the nature required by the Method\nof Difference, which seem at first sight to conflict with the theory.\nSoluble salts of silver, such for instance as the nitrate, have the same\nstiffening antiseptic effect on decomposing animal substances as corrosive\nsublimate and the most deadly metallic poisons; and when applied to the\nexternal parts of the body, the nitrate is a powerful caustic, depriving\nthose parts of all active vitality, and causing them to be thrown off by\nthe neighboring living structures, in the form of an eschar. The nitrate\nand the other salts of silver ought, then, it would seem, if the theory be\ncorrect, to be poisonous; yet they may be administered internally with\nperfect impunity. From this apparent exception arises the strongest\nconfirmation which the theory has yet received. Nitrate of silver, in\nspite of its chemical properties, does not poison when introduced into the\nstomach; but in the stomach, as in all animal liquids, there is common\nsalt; and in the stomach there is also free muriatic acid. These\nsubstances operate as natural antidotes, combining with the nitrate, and\nif its quantity is not too great, immediately converting it into chloride\nof silver, a substance very slightly soluble, and therefore incapable of\ncombining with the tissues, although to the extent of its solubility it\nhas a medicinal influence, though an entirely different class of organic\nactions.\n\nThe preceding instances have afforded an induction of a high order of\nconclusiveness, illustrative of the two simplest of our four methods;\nthough not rising to the maximum of certainty which the Method of\nDifference, in its most perfect exemplification, is capable of affording.\nFor (let us not forget) the positive instance and the negative one which\nthe rigor of that method requires, ought to differ only in the presence or\nabsence of one single circumstance. Now, in the preceding argument, they\ndiffer in the presence or absence not of a single _circumstance_, but of a\nsingle _substance_: and as every substance has innumerable properties,\nthere is no knowing what number of real differences are involved in what\nis nominally and apparently only one difference. It is conceivable that\nthe antidote, the peroxide of iron for example, may counteract the poison\nthrough some other of its properties than that of forming an insoluble\ncompound with it; and if so, the theory would fall to the ground, so far\nas it is supported by that instance. This source of uncertainty, which is\na serious hinderance to all extensive generalizations in chemistry, is,\nhowever, reduced in the present case to almost the lowest degree possible,\nwhen we find that not only one substance, but many substances, possess the\ncapacity of acting as antidotes to metallic poisons, and that all these\nagree in the property of forming insoluble compounds with the poisons,\nwhile they can not be ascertained to agree in any other property\nwhatsoever. We have thus, in favor of the theory, all the evidence which\ncan be obtained by what we termed the Indirect Method of Difference, or\nthe Joint Method of Agreement and Difference; the evidence of which,\nthough it never can amount to that of the Method of Difference properly so\ncalled, may approach indefinitely near to it.\n\n\u00a7 2. Let the object be(137) to ascertain the law of what is termed\n_induced_ electricity; to find under what conditions any electrified body,\nwhether positively or negatively electrified, gives rise to a contrary\nelectric state in some other body adjacent to it.\n\nThe most familiar exemplification of the phenomenon to be investigated is\nthe following. Around the prime conductors of an electrical machine the\natmosphere to some distance, or any conducting surface suspended in that\natmosphere, is found to be in an electric condition opposite to that of\nthe prime conductor itself. Near and around the positive prime conductor\nthere is negative electricity, and near and around the negative prime\nconductor there is positive electricity. When pith balls are brought near\nto either of the conductors, they become electrified with the opposite\nelectricity to it; either receiving a share from the already electrified\natmosphere by conduction, or acted upon by the direct inductive influence\nof the conductor itself: they are then attracted by the conductor to which\nthey are in opposition; or, if withdrawn in their electrified state, they\nwill be attracted by any other oppositely charged body. In like manner the\nhand, if brought near enough to the conductor, receives or gives an\nelectric discharge; now we have no evidence that a charged conductor can\nbe suddenly discharged unless by the approach of a body oppositely\nelectrified. In the case, therefore, of the electric machine, it appears\nthat the accumulation of electricity in an insulated conductor is always\naccompanied by the excitement of the contrary electricity in the\nsurrounding atmosphere, and in every conductor placed near the former\nconductor. It does not seem possible, in this case, to produce one\nelectricity by itself.\n\nLet us now examine all the other instances which we can obtain, resembling\nthis instance in the given consequent, namely, the evolution of an\nopposite electricity in the neighborhood of an electrified body. As one\nremarkable instance we have the Leyden jar; and after the splendid\nexperiments of Faraday in complete and final establishment of the\nsubstantial identity of magnetism and electricity, we may cite the magnet,\nboth the natural and the electro-magnet, in neither of which it is\npossible to produce one kind of electricity by itself, or to charge one\npole without charging an opposite pole with the contrary electricity at\nthe same time. We can not have a magnet with one pole: if we break a\nnatural loadstone into a thousand pieces, each piece will have its two\noppositely electrified poles complete within itself. In the voltaic\ncircuit, again, we can not have one current without its opposite. In the\nordinary electric machine, the glass cylinder or plate, and the rubber,\nacquire opposite electricities.\n\nFrom all these instances, treated by the Method of Agreement, a general\nlaw appears to result. The instances embrace all the known modes in which\na body can become charged with electricity; and in all of them there is\nfound, as a concomitant or consequent, the excitement of the opposite\nelectric state in some other body or bodies. It seems to follow that the\ntwo facts are invariably connected, and that the excitement of electricity\nin any body has for one of its necessary conditions the possibility of a\nsimultaneous excitement of the opposite electricity in some neighboring\nbody.\n\nAs the two contrary electricities can only be produced together, so they\ncan only cease together. This may be shown by an application of the Method\nof Difference to the example of the Leyden jar. It needs scarcely be here\nremarked that in the Leyden jar, electricity can be accumulated and\nretained in considerable quantity, by the contrivance of having two\nconducting surfaces of equal extent, and parallel to each other through\nthe whole of that extent, with a non-conducting substance such as glass\nbetween them. When one side of the jar is charged positively, the other is\ncharged negatively, and it was by virtue of this fact that the Leyden jar\nserved just now as an instance in our employment of the Method of\nAgreement. Now it is impossible to discharge one of the coatings unless\nthe other can be discharged at the same time. A conductor held to the\npositive side can not convey away any electricity unless an equal quantity\nbe allowed to pass from the negative side: if one coating be perfectly\ninsulated, the charge is safe. The dissipation of one must proceed _pari\npassu_ with that of the other.\n\nThe law thus strongly indicated admits of corroboration by the Method of\nConcomitant Variations. The Leyden jar is capable of receiving a much\nhigher charge than can ordinarily be given to the conductor of an\nelectrical machine. Now in the case of the Leyden jar, the metallic\nsurface which receives the induced electricity is a conductor exactly\nsimilar to that which receives the primary charge, and is therefore as\nsusceptible of receiving and retaining the one electricity, as the\nopposite surface of receiving and retaining the other; but in the machine,\nthe neighboring body which is to be oppositely electrified is the\nsurrounding atmosphere, or any body casually brought near to the\nconductor; and as these are generally much inferior in their capacity of\nbecoming electrified, to the conductor itself, their limited power imposes\na corresponding limit to the capacity of the conductor for being charged.\nAs the capacity of the neighboring body for supporting the opposition\nincreases, a higher charge becomes possible: and to this appears to be\nowing the great superiority of the Leyden jar.\n\nA further and most decisive confirmation by the Method of Difference, is\nto be found in one of Faraday\u2019s experiments in the course of his\nresearches on the subject of Induced Electricity.\n\nSince common or machine electricity, and voltaic electricity, may be\nconsidered for the present purpose to be identical, Faraday wished to know\nwhether, as the prime conductor develops opposite electricity upon a\nconductor in its vicinity, so a voltaic current running along a wire would\ninduce an opposite current upon another wire laid parallel to it at a\nshort distance. Now this case is similar to the cases previously examined,\nin every circumstance except the one to which we have ascribed the effect.\nWe found in the former instances that whenever electricity of one kind was\nexcited in one body, electricity of the opposite kind must be excited in a\nneighboring body. But in Faraday\u2019s experiment this indispensable\nopposition exists within the wire itself. From the nature of a voltaic\ncharge, the two opposite currents necessary to the existence of each other\nare both accommodated in one wire; and there is no need of another wire\nplaced beside it to contain one of them, in the same way as the Leyden jar\nmust have a positive and a negative surface. The exciting cause can and\ndoes produce all the effect which its laws require, independently of any\nelectric excitement of a neighboring body. Now the result of the\nexperiment with the second wire was, that no opposite current was\nproduced. There was an instantaneous effect at the closing and breaking of\nthe voltaic circuit; electric inductions appeared when the two wires were\nmoved to and from one another; but these are phenomena of a different\nclass. There was no induced electricity in the sense in which this is\npredicated of the Leyden jar; there was no sustained current running up\nthe one wire while an opposite current ran down the neighboring wire; and\nthis alone would have been a true parallel case to the other.\n\nIt thus appears by the combined evidence of the Method of Agreement, the\nMethod of Concomitant Variations, and the most rigorous form of the Method\nof Difference, that neither of the two kinds of electricity can be excited\nwithout an equal excitement of the other and opposite kind: that both are\neffects of the same cause; that the possibility of the one is a condition\nof the possibility of the other, and the quantity of the one an impassable\nlimit to the quantity of the other. A scientific result of considerable\ninterest in itself, and illustrating those three methods in a manner both\ncharacteristic and easily intelligible.(138)\n\n\u00a7 3. Our third example shall be extracted from Sir John Herschel\u2019s\n_Discourse __ course on the Study of Natural Philosophy_, a work replete\nwith happily-selected exemplifications of inductive processes from almost\nevery department of physical science, and in which alone, of all books\nwhich I have met with, the four methods of induction are distinctly\nrecognized, though not so clearly characterized and defined, nor their\ncorrelation so fully shown, as has appeared to me desirable. The present\nexample is described by Sir John Herschel as \u201cone of the most beautiful\nspecimens\u201d which can be cited \u201cof inductive experimental inquiry lying\nwithin a moderate compass;\u201d the theory of dew, first promulgated by the\nlate Dr. Wells, and now universally adopted by scientific authorities. The\npassages in inverted commas are extracted verbatim from the\nDiscourse.(139)\n\n\u201cSuppose _dew_ were the phenomenon proposed, whose cause we would know. In\nthe first place\u201d we must determine precisely what we mean by dew: what the\nfact really is whose cause we desire to investigate. \u201cWe must separate dew\nfrom rain, and the moisture of fogs, and limit the application of the term\nto what is really meant, which is the spontaneous appearance of moisture\non substances exposed in the open air when no rain or _visible_ wet is\nfalling.\u201d This answers to a preliminary operation which will be\ncharacterized in the ensuing book, treating of operations subsidiary to\ninduction.(140)\n\n\u201cNow, here we have analogous phenomena in the moisture which bedews a cold\nmetal or stone when we breathe upon it; that which appears on a glass of\nwater fresh from the well in hot weather; that which appears on the inside\nof windows when sudden rain or hail chills the external air; that which\nruns down our walls when, after a long frost, a warm, moist thaw comes\non.\u201d Comparing these cases, we find that they all contain the phenomenon\nwhich was proposed as the subject of investigation. Now \u201call these\ninstances agree in one point, the coldness of the object dewed, in\ncomparison with the air in contact with it.\u201d But there still remains the\nmost important case of all, that of nocturnal dew: does the same\ncircumstance exist in this case? \u201cIs it a fact that the object dewed _is_\ncolder than the air? Certainly not, one would at first be inclined to say;\nfor what is to _make_ it so? But ... the experiment is easy: we have only\nto lay a thermometer in contact with the dewed substance, and hang one at\na little distance above it, out of reach of its influence. The experiment\nhas been therefore made, the question has been asked, and the answer has\nbeen invariably in the affirmative. Whenever an object contracts dew, it\n_is_ colder than the air.\u201d\n\nHere, then, is a complete application of the Method of Agreement,\nestablishing the fact of an invariable connection between the deposition\nof dew on a surface, and the coldness of that surface compared with the\nexternal air. But which of these is cause, and which effect? or are they\nboth effects of something else? On this subject the Method of Agreement\ncan afford us no light: we must call in a more potent method. \u201cWe must\ncollect more facts, or, which comes to the same thing, vary the\ncircumstances; since every instance in which the circumstances differ is a\nfresh fact: and especially, we must note the contrary or negative cases,\n_i.e._, where no dew is produced:\u201d a comparison between instances of dew\nand instances of no dew, being the condition necessary to bring the Method\nof Difference into play.\n\n\u201cNow, first, no dew is produced on the surface of polished metals, but it\n_is_ very copiously on glass, both exposed with their faces upward, and in\nsome cases the under side of a horizontal plate of glass is also dewed.\u201d\nHere is an instance in which the effect is produced, and another instance\nin which it is not produced; but we can not yet pronounce, as the canon of\nthe Method of Difference requires, that the latter instance agrees with\nthe former in all its circumstances except one; for the differences\nbetween glass and polished metals are manifold, and the only thing we can\nas yet be sure of is, that the cause of dew will be found among the\ncircumstances by which the former substance is distinguished from the\nlatter. But if we could be sure that glass, and the various other\nsubstances on which dew is deposited, have only one quality in common, and\nthat polished metals and the other substances on which dew is not\ndeposited, have also nothing in common but the one circumstance of not\nhaving the one quality which the others have; the requisitions of the\nMethod of Difference would be completely satisfied, and we should\nrecognize, in that quality of the substances, the cause of dew. This,\naccordingly, is the path of inquiry which is next to be pursued.\n\n\u201cIn the cases of polished metal and polished glass, the contrast shows\nevidently that the _substance_ has much to do with the phenomenon;\ntherefore let the substance _alone_ be diversified as much as possible, by\nexposing polished surfaces of various kinds. This done, a _scale of\nintensity_ becomes obvious. Those polished substances are found to be most\nstrongly dewed which conduct heat worst; while those which conduct heat\nwell, resist dew most effectually.\u201d The complication increases; here is\nthe Method of Concomitant Variations called to our assistance; and no\nother method was practicable on this occasion; for the quality of\nconducting heat could not be excluded, since all substances conduct heat\nin some degree. The conclusion obtained is, that _c\u00e6teris paribus_ the\ndeposition of dew is in some proportion to the power which the body\npossesses of resisting the passage of heat; and that this, therefore (or\nsomething connected with this), must be at least one of the causes which\nassist in producing the deposition of dew on the surface.\n\n\u201cBut if we expose rough surfaces instead of polished, we sometimes find\nthis law interfered with. Thus, roughened iron, especially if painted over\nor blackened, becomes dewed sooner than varnished paper; the kind of\n_surface_, therefore, has a great influence. Expose, then, the _same_\nmaterial in very diversified states, as to surface\u201d (that is, employ the\nMethod of Difference to ascertain concomitance of variations), \u201cand\nanother scale of intensity becomes at once apparent; those _surfaces_\nwhich _part with their heat_ most readily by radiation are found to\ncontract dew most copiously.\u201d Here, therefore, are the requisites for a\nsecond employment of the Method of Concomitant Variations; which in this\ncase also is the only method available, since all substances radiate heat\nin some degree or other. The conclusion obtained by this new application\nof the method is, that _c\u00e6teris paribus_ the deposition of dew is also in\nsome proportion to the power of radiating heat; and that the quality of\ndoing this abundantly (or some cause on which that quality depends) is\nanother of the causes which promote the deposition of dew on the\nsubstance.\n\n\u201cAgain, the influence ascertained to exist of _substance_ and _surface_\nleads us to consider that of _texture_: and here, again, we are presented\non trial with remarkable differences, and with a third scale of intensity,\npointing out substances of a close, firm texture, such as stones, metals,\netc., as unfavorable, but those of a loose one, as cloth, velvet, wool,\neider-down, cotton, etc., as eminently favorable to the contraction of\ndew.\u201d The Method of Concomitant Variations is here, for the third time,\nhad recourse to; and, as before, from necessity, since the texture of no\nsubstance is absolutely firm or absolutely loose. Looseness of texture,\ntherefore, or something which is the cause of that quality, is another\ncircumstance which promotes the deposition of dew; but this third course\nresolves itself into the first, viz., the quality of resisting the passage\nof heat: for substances of loose texture \u201care precisely those which are\nbest adapted for clothing, or for impeding the free passage of heat from\nthe skin into the air, so as to allow their outer surfaces to be very\ncold, while they remain warm within;\u201d and this last is, therefore, an\ninduction (from fresh instances) simply _corroborative_ of a former\ninduction.\n\nIt thus appears that the instances in which much dew is deposited, which\nare very various, agree in this, and, so far as we are able to observe, in\nthis only, that they either radiate heat rapidly or conduct it slowly:\nqualities between which there is no other circumstance of agreement than\nthat by virtue of either, the body tends to lose heat from the surface\nmore rapidly than it can be restored from within. The instances, on the\ncontrary, in which no dew, or but a small quantity of it, is formed, and\nwhich are also extremely various, agree (as far as we can observe) in\nnothing except in _not_ having this same property. We seem, therefore, to\nhave detected the characteristic difference between the substances on\nwhich dew is produced and those on which it is not produced. And thus have\nbeen realized the requisitions of what we have termed the Indirect Method\nof Difference, or the Joint Method of Agreement and Difference. The\nexample afforded of this indirect method, and of the manner in which the\ndata are prepared for it by the Methods of Agreement and of Concomitant\nVariations, is the most important of all the illustrations of induction\nafforded by this interesting speculation.\n\nWe might now consider the question, on what the deposition of dew depends,\nto be completely solved, if we could be quite sure that the substances on\nwhich dew is produced differ from those on which it is not, in _nothing_\nbut in the property of losing heat from the surface faster than the loss\ncan be repaired from within. And though we never can have that complete\ncertainty, this is not of so much importance as might at first be\nsupposed; for we have, at all events, ascertained that even if there be\nany other quality hitherto unobserved which is present in all the\nsubstances which contract dew, and absent in those which do not, this\nother property must be one which, in all that great number of substances,\nis present or absent exactly where the property of being a better radiator\nthan conductor is present or absent; an extent of coincidence which\naffords a strong presumption of a community of cause, and a consequent\ninvariable co-existence between the two properties; so that the property\nof being a better radiator than conductor, if not itself the cause, almost\ncertainly always accompanies the cause, and for purposes of prediction, no\nerror is likely to be committed by treating it as if it were really such.\n\nReverting now to an earlier stage of the inquiry, let us remember that we\nhad ascertained that, in every instance where dew is formed, there is\nactual coldness of the surface below the temperature of the surrounding\nair; but we were not sure whether this coldness was the cause of dew, or\nits effect. This doubt we are now able to resolve. We have found that, in\nevery such instance, the substance is one which, by its own properties or\nlaws, would, if exposed in the night, become colder than the surrounding\nair. The coldness, therefore, being accounted for independently of the\ndew, while it is proved that there is a connection between the two, it\nmust be the dew which depends on the coldness; or, in other words, the\ncoldness is the cause of the dew.\n\nThis law of causation, already so amply established, admits, however, of\nefficient additional corroboration in no less than three ways. First, by\ndeduction from the known laws of aqueous vapor when diffused through air\nor any other gas; and though we have not yet come to the Deductive Method,\nwe will not omit what is necessary to render this speculation complete. It\nis known by direct experiment that only a limited quantity of water can\nremain suspended in the state of vapor at each degree of temperature, and\nthat this maximum grows less and less as the temperature diminishes. From\nthis it follows, deductively, that if there is already as much vapor\nsuspended as the air will contain at its existing temperature, any\nlowering of that temperature will cause a portion of the vapor to be\ncondensed, and become water. But again, we know deductively, from the laws\nof heat, that the contact of the air with a body colder than itself will\nnecessarily lower the temperature of the stratum of air immediately\napplied to its surface; and will, therefore, cause it to part with a\nportion of its water, which accordingly will, by the ordinary laws of\ngravitation or cohesion, attach itself to the surface of the body, thereby\nconstituting dew. This deductive proof, it will have been seen, has the\nadvantage of at once proving causation as well as co-existence; and it has\nthe additional advantage that it also accounts for the exceptions to the\noccurrence of the phenomenon, the cases in which, although the body is\ncolder than the air, yet no dew is deposited; by showing that this will\nnecessarily be the case when the air is so under-supplied with aqueous\nvapor, comparatively to its temperature, that even when somewhat cooled by\nthe contact of the colder body it can still continue to hold in suspension\nall the vapor which was previously suspended in it: thus in a very dry\nsummer there are no dews, in a very dry winter no hoar-frost. Here,\ntherefore, is an additional condition of the production of dew, which the\nmethods we previously made use of failed to detect, and which might have\nremained still undetected, if recourse had not been had to the plan of\ndeducing the effect from the ascertained properties of the agents known to\nbe present.\n\nThe second corroboration of the theory is by direct experiment, according\nto the canon of the Method of Difference. We can, by cooling the surface\nof any body, find in all cases some temperature (more or less inferior to\nthat of the surrounding air, according to its hygrometric condition) at\nwhich dew will begin to be deposited. Here, too, therefore, the causation\nis directly proved. We can, it is true, accomplish this only on a small\nscale, but we have ample reason to conclude that the same operation, if\nconducted in nature\u2019s great laboratory, would equally produce the effect.\n\nAnd, finally, even on that great scale we are able to verify the result.\nThe case is one of those rare cases, as we have shown them to be, in which\nnature works the experiment for us in the same manner in which we\nourselves perform it; introducing into the previous state of things a\nsingle and perfectly definite new circumstance, and manifesting the effect\nso rapidly that there is not time for any other material change in the\npre-existing circumstances. \u201cIt is observed that dew is never copiously\ndeposited in situations much screened from the open sky, and not at all in\na cloudy night; but _if the clouds withdraw even for a few minutes, and\nleave a clear opening, a deposition of dew presently begins_, and goes on\nincreasing... Dew formed in clear intervals will often even evaporate\nagain when the sky becomes thickly overcast.\u201d The proof, therefore, is\ncomplete, that the presence or absence of an uninterrupted communication\nwith the sky causes the deposition or non-deposition of dew. Now, since a\nclear sky is nothing but the absence of clouds, and it is a known property\nof clouds, as of all other bodies between which and any given object\nnothing intervenes but an elastic fluid, that they tend to raise or keep\nup the superficial temperature of the object by radiating heat to it, we\nsee at once that the disappearance of clouds will cause the surface to\ncool; so that nature, in this case, produces a change in the antecedent by\ndefinite and known means, and the consequent follows accordingly: a\nnatural experiment which satisfies the requisitions of the Method of\nDifference.(141)\n\nThe accumulated proof of which the Theory of Dew has been found\nsusceptible, is a striking instance of the fullness of assurance which the\ninductive evidence of laws of causation may attain, in cases in which the\ninvariable sequence is by no means obvious to a superficial view.\n\n\u00a7 4. The admirable physiological investigations of Dr. Brown-S\u00e9quard\nafford brilliant examples of the application of the Inductive Methods to a\nclass of inquiries in which, for reasons which will presently be given,\ndirect induction takes place under peculiar difficulties and\ndisadvantages. As one of the most apt instances, I select his speculation\n(in the proceedings of the Royal Society for May 16, 1861) on the\nrelations between muscular irritability, cadaveric rigidity, and\nputrefaction.\n\nThe law which Dr. Brown-S\u00e9quard\u2019s investigation tends to establish, is the\nfollowing: \u201cThe greater the degree of muscular irritability at the time of\ndeath, the later the cadaveric rigidity sets in, and the longer it lasts,\nand the later also putrefaction appears, and the slower it progresses.\u201d\nOne would say at first sight that the method here required must be that of\nConcomitant Variations. But this is a delusive appearance, arising from\nthe circumstance that the conclusion to be tested is itself a fact of\nconcomitant variations. For the establishment of that fact any of the\nMethods may be put in requisition, and it will be found that the fourth\nMethod, though really employed, has only a subordinate place in this\nparticular investigation.\n\nThe evidences by which Dr. Brown-S\u00e9quard establishes the law may be\nenumerated as follows:\n\n1st. Paralyzed muscles have greater irritability than healthy muscles.\nNow, paralyzed muscles are later in assuming the cadaveric rigidity than\nhealthy muscles, the rigidity lasts longer, and putrefaction sets in\nlater, and proceeds more slowly.\n\nBoth these propositions had to be proved by experiment; and for the\nexperiments which prove them, science is also indebted to Dr.\nBrown-S\u00e9quard. The former of the two\u2014that paralyzed muscles have greater\nirritability than healthy muscles\u2014he ascertained in various ways, but most\ndecisively by \u201ccomparing the duration of irritability in a paralyzed\nmuscle and in the corresponding healthy one of the opposite side, while\nthey are both submitted to the same excitation.\u201d He \u201coften found, in\nexperimenting in that way, that the paralyzed muscle remained irritable\ntwice, three times, or even four times as long as the healthy one.\u201d This\nis a case of induction by the Method of Difference. The two limbs, being\nthose of the same animal, were presumed to differ in no circumstance\nmaterial to the case except the paralysis, to the presence and absence of\nwhich, therefore, the difference in the muscular irritability was to be\nattributed. This assumption of complete resemblance in all material\ncircumstances save one, evidently could not be safely made in any one pair\nof experiments, because the two legs of any given animal might be\naccidentally in very different pathological conditions; but if, besides\ntaking pains to avoid any such difference, the experiment was repeated\nsufficiently often in different animals to exclude the supposition that\nany abnormal circumstance could be present in them all, the conditions of\nthe Method of Difference were adequately secured.\n\nIn the same manner in which Dr. Brown-S\u00e9quard proved that paralyzed\nmuscles have greater irritability, he also proved the correlative\nproposition respecting cadaveric rigidity and putrefaction. Having, by\nsection of the roots of the sciatic nerve, and again of a lateral half of\nthe spinal cord, produced paralysis in one hind leg of an animal while the\nother remained healthy, he found that not only did muscular irritability\nlast much longer in the paralyzed limb, but rigidity set in later and\nended later, and putrefaction began later and was less rapid than on the\nhealthy side. This is a common case of the Method of Difference, requiring\nno comment. A further and very important corroboration was obtained by the\nsame method. When the animal was killed, not shortly after the section of\nthe nerve, but a month later, the effect was reversed; rigidity set in\nsooner, and lasted a shorter time, than in the healthy muscles. But after\nthis lapse of time, the paralyzed muscles, having been kept by the\nparalysis in a state of rest, had lost a great part of their irritability,\nand instead of more, had become less irritable than those on the healthy\nside. This gives the A B C, _a b c_, and B C, b c, of the Method of\nDifference. One antecedent, increased irritability, being changed, and the\nother circumstances being the same, the consequence did not follow; and,\nmoreover, when a new antecedent, contrary to the first, was supplied, it\nwas followed by a contrary consequent. This instance is attended with the\nspecial advantage of proving that the retardation and prolongation of the\nrigidity do not depend directly on the paralysis, since that was the same\nin both the instances; but specifically on one effect of the paralysis,\nnamely, the increased irritability; since they ceased when it ceased, and\nwere reversed when it was reversed.\n\n2d. Diminution of the temperature of muscles before death increases their\nirritability. But diminution of their temperature also retards cadaveric\nrigidity and putrefaction.\n\nBoth these truths were first made known by Dr. Brown-S\u00e9quard himself,\nthrough experiments which conclude according to the Method of Difference.\nThere is nothing in the nature of the process requiring specific analysis.\n\n3d. Muscular exercise, prolonged to exhaustion, diminishes the muscular\nirritability. This is a well-known truth, dependent on the most general\nlaws of muscular action, and proved by experiments under the Method of\nDifference, constantly repeated. Now, it has been shown by observation\nthat overdriven cattle, if killed before recovery from their fatigue,\nbecome rigid and putrefy in a surprisingly short time. A similar fact has\nbeen observed in the case of animals hunted to death; cocks killed during\nor shortly after a fight; and soldiers slain in the field of battle. These\nvarious cases agree in no circumstance, directly connected with the\nmuscles, except that these have just been subjected to exhausting\nexercise. Under the canon, therefore, of the Method of Agreement, it may\nbe inferred that there is a connection between the two facts. The Method\nof Agreement, indeed, as has been shown, is not competent to prove\ncausation. The present case, however, is already known to be a case of\ncausation, it being certain that the state of the body after death must\nsomehow depend upon its state at the time of death. We are, therefore,\nwarranted in concluding that the single circumstance in which all the\ninstances agree, is the part of the antecedent which is the cause of that\nparticular consequent.\n\n4th. In proportion as the nutrition of muscles is in a good state, their\nirritability is high. This fact also rests on the general evidence of the\nlaws of physiology, grounded on many familiar applications of the Method\nof Difference. Now, in the case of those who die from accident or\nviolence, with their muscles in a good state of nutrition, the muscular\nirritability continues long after death, rigidity sets in late, and\npersists long without the putrefactive change. On the contrary, in cases\nof disease in which nutrition has been diminished for a long time before\ndeath, all these effects are reversed. These are the conditions of the\nJoint Method of Agreement and Difference. The cases of retarded and long\ncontinued rigidity here in question agree only in being preceded by a high\nstate of nutrition of the muscles; the cases of rapid and brief rigidity\nagree only in being preceded by a low state of muscular nutrition; a\nconnection is, therefore, inductively proved between the degree of the\nnutrition, and the slowness and prolongation of the rigidity.\n\n5th. Convulsions, like exhausting exercise, but in a still greater degree,\ndiminish the muscular irritability. Now, when death follows violent and\nprolonged convulsions, as in tetanus, hydrophobia, some cases of cholera,\nand certain poisons, rigidity sets in very rapidly, and after a very brief\nduration, gives place to putrefaction. This is another example of the\nMethod of Agreement, of the same character with No. 3.\n\n6th. The series of instances which we shall take last, is of a more\ncomplex character, and requires a more minute analysis.\n\nIt has long been observed that in some cases of death by lightning,\ncadaveric rigidity either does not take place at all, or is of such\nextremely brief duration as to escape notice, and that in these cases\nputrefaction is very rapid. In other cases, however, the usual cadaveric\nrigidity appears. There must be some difference in the cause, to account\nfor this difference in the effect. Now, \u201cdeath by lightning may be the\nresult of, 1st, a syncope by fright, or in consequence of a direct or\nreflex influence of lightning on the par vagum; 2d, hemorrhage in or\naround the brain, or in the lungs, the pericardium, etc.; 3d, concussion,\nor some other alteration in the brain;\u201d none of which phenomena have any\nknown property capable of accounting for the suppression, or almost\nsuppression, of the cadaveric rigidity. But the cause of death may also be\nthat the lightning produces \u201ca violent convulsion of every muscle in the\nbody,\u201d of which, if of sufficient intensity, the known effect would be\nthat \u201cmuscular irritability ceases almost at once.\u201d If Dr. Brown-S\u00e9quard\u2019s\ngeneralization is a true law, these will be the very cases in which\nrigidity is so much abridged as to escape notice; and the cases in which,\non the contrary, rigidity takes place as usual, will be those in which the\nstroke of lightning operates in some of the other modes which have been\nenumerated. How, then, is this brought to the test? By experiments, not on\nlightning, which can not be commanded at pleasure, but on the same natural\nagency in a manageable form, that of artificial galvanism. Dr.\nBrown-S\u00e9quard galvanized the entire bodies of animals immediately after\ndeath. Galvanism can not operate in any of the modes in which the stroke\nof lightning may have operated, except the single one of producing\nmuscular convulsions. If, therefore, after the bodies have been\ngalvanized, the duration of rigidity is much shortened and putrefaction\nmuch accelerated, it is reasonable to ascribe the same effects when\nproduced by lightning to the property which galvanism shares with\nlightning, and not to those which it does not. Now this Dr. Brown-S\u00e9quard\nfound to be the fact. The galvanic experiment was tried with charges of\nvery various degrees of strength; and the more powerful the charge, the\nshorter was found to be the duration of rigidity, and the more speedy and\nrapid the putrefaction. In the experiment in which the charge was\nstrongest, and the muscular irritability most promptly destroyed, the\nrigidity only lasted fifteen minutes. On the principle, therefore, of the\nMethod of Concomitant Variations, it may be inferred that the duration of\nthe rigidity depends on the degree of the irritability; and that if the\ncharge had been as much stronger than Dr. Brown-S\u00e9quard\u2019s strongest, as a\nstroke of lightning must be stronger than any electric shock which we can\nproduce artificially, the rigidity would have been shortened in a\ncorresponding ratio, and might have disappeared altogether. This\nconclusion having been arrived at, the case of an electric shock, whether\nnatural or artificial, becomes an instance, in addition to all those\nalready ascertained, of correspondence between the irritability of the\nmuscle and the duration of rigidity.\n\nAll these instances are summed up in the following statement: \u201cThat when\nthe degree of muscular irritability at the time of death is considerable,\neither in consequence of a good state of nutrition, as in persons who die\nin full health from an accidental cause, or in consequence of rest, as in\ncases of paralysis, or on account of the influence of cold, cadaveric\nrigidity in all these cases sets in late and lasts long, and putrefaction\nappears late, and progresses slowly;\u201d but \u201cthat when the degree of\nmuscular irritability at the time of death is slight, either in\nconsequence of a bad state of nutrition, or of exhaustion from\noverexertion, or from convulsions caused by disease or poison, cadaveric\nrigidity sets in and ceases soon, and putrefaction appears and progresses\nquickly.\u201d These facts present, in all their completeness, the conditions\nof the Joint Method of Agreement and Difference. Early and brief rigidity\ntakes place in cases which agree only in the circumstance of a low state\nof muscular irritability. Rigidity begins late and lasts long in cases\nwhich agree only in the contrary circumstance, of a muscular irritability\nhigh and unusually prolonged. It follows that there is a connection\nthrough causation between the degree of muscular irritability after death,\nand the tardiness and prolongation of the cadaveric rigidity.\n\nThis investigation places in a strong light the value and efficacy of the\nJoint Method. For, as we have already seen, the defect of that Method is,\nthat like the Method of Agreement, of which it is only an improved form,\nit can not prove causation. But in the present case (as in one of the\nsteps in the argument which led up to it) causation is already proved;\nsince there could never be any doubt that the rigidity altogether, and the\nputrefaction which follows it, are caused by the fact of death: the\nobservations and experiments on which this rests are too familiar to need\nanalysis, and fall under the Method of Difference. It being, therefore,\nbeyond doubt that the aggregate antecedent, the death, is the actual cause\nof the whole train of consequents, whatever of the circumstances attending\nthe death can be shown to be followed in all its variations by variations\nin the effect under investigation, must be the particular feature of the\nfact of death on which that effect depends. The degree of muscular\nirritability at the time of death fulfills this condition. The only point\nthat could be brought into question, would be whether the effect depended\non the irritability itself, or on something which always accompanied the\nirritability: and this doubt is set at rest by establishing, as the\ninstances do, that by whatever cause the high or low irritability is\nproduced, the effect equally follows; and can not, therefore, depend upon\nthe causes of irritability, nor upon the other effects of those causes,\nwhich are as various as the causes themselves, but upon the irritability,\nsolely.\n\n\u00a7 5. The last two examples will have conveyed to any one by whom they have\nbeen duly followed, so clear a conception of the use and practical\nmanagement of three of the four methods of experimental inquiry, as to\nsupersede the necessity of any further exemplification of them. The\nremaining method, that of Residues, not having found a place in any of the\npreceding investigations, I shall quote from Sir John Herschel some\nexamples of that method, with the remarks by which they are introduced.\n\n\u201cIt is by this process, in fact, that science, in its present advanced\nstate, is chiefly promoted. Most of the phenomena which Nature presents\nare very complicated; and when the effects of all known causes are\nestimated with exactness, and subducted, the residual facts are constantly\nappearing in the form of phenomena altogether new, and leading to the most\nimportant conclusions.\n\n\u201cFor example: the return of the comet predicted by Professor Eucke a great\nmany times in succession, and the general good agreement of its calculated\nwith its observed place during any one of its periods of visibility, would\nlead us to say that its gravitation toward the sun and planets is the sole\nand sufficient cause of all the phenomena of its orbitual motion; but when\nthe effect of this cause is strictly calculated and subducted from the\nobserved motion, there is found to remain behind a _residual phenomenon_,\nwhich would never have been otherwise ascertained to exist, which is a\nsmall anticipation of the time of its re-appearance, or a diminution of\nits periodic time, which can not be accounted for by gravity, and whose\ncause is therefore to be inquired into. Such an anticipation would be\ncaused by the resistance of a medium disseminated through the celestial\nregions; and as there are other good reasons for believing this to be a\n_vera causa_\u201d (an actually existing antecedent), \u201cit has therefore been\nascribed to such a resistance.(142)\n\n\u201cM. Arago, having suspended a magnetic needle by a silk thread, and set it\nin vibration, observed, that it came much sooner to a state of rest when\nsuspended over a plate of copper, than when no such plate was beneath it.\nNow, in both cases there were two _ver\u00e6 caus\u00e6_\u201d (antecedents known to\nexist) \u201cwhy it _should_ come at length to rest, viz., the resistance of\nthe air, which opposes, and at length destroys, all motions performed in\nit; and the want of perfect mobility in the silk thread. But the effect of\nthese causes being exactly known by the observation made in the absence of\nthe copper, and being thus allowed for and subducted, a residual\nphenomenon appeared, in the fact that a retarding influence was exerted by\nthe copper itself; and this fact, once ascertained, speedily led to the\nknowledge of an entirely new and unexpected class of relations.\u201d This\nexample belongs, however, not to the Method of Residues but to the Method\nof Difference, the law being ascertained by a direct comparison of the\nresults of two experiments, which differed in nothing but the presence or\nabsence of the plate of copper. To have made it exemplify the Method of\nResidues, the effect of the resistance of the air and that of the rigidity\nof the silk should have been calculated _a priori_, from the laws obtained\nby separate and foregone experiments.\n\n\u201cUnexpected and peculiarly striking confirmations of inductive laws\nfrequently occur in the form of residual phenomena, in the course of\ninvestigations of a widely different nature from those which gave rise to\nthe inductions themselves. A very elegant example may be cited in the\nunexpected confirmation of the law of the development of heat in elastic\nfluids by compression, which is afforded by the phenomena of sound. The\ninquiry into the cause of sound had led to conclusions respecting its mode\nof propagation, from which its velocity in the air could be precisely\ncalculated. The calculations were performed; but, when compared with fact,\nthough the agreement was quite sufficient to show the general correctness\nof the cause and mode of propagation assigned, yet the _whole_ velocity\ncould not be shown to arise from this theory. There was still a residual\nvelocity to be accounted for, which placed dynamical philosophers for a\nlong time in great dilemma. At length Laplace struck on the happy idea,\nthat this might arise from the _heat_ developed in the act of that\ncondensation which necessarily takes place at every vibration by which\nsound is conveyed. The matter was subjected to exact calculation, and the\nresult was at once the complete explanation of the residual phenomenon,\nand a striking confirmation of the general law of the development of heat\nby compression, under circumstances beyond artificial imitation.\u201d\n\n\u201cMany of the new elements of chemistry have been detected in the\ninvestigation of residual phenomena. Thus Arfwedson discovered lithia by\nperceiving an excess of weight in the sulphate produced from a small\nportion of what he considered as magnesia present in a mineral he had\nanalyzed. It is on this principle, too, that the small concentrated\nresidues of great operations in the arts are almost sure to be the\nlurking-places of new chemical ingredients: witness iodine, brome,\nselenium, and the new metals accompanying platina in the experiments of\nWollaston and Tennant. It was a happy thought of Glauber to examine what\nevery body else threw away.\u201d(143)\n\n\u201cAlmost all the greatest discoveries in Astronomy,\u201d says the same\nauthor,(144) \u201chave resulted from the consideration of residual phenomena\nof a quantitative or numerical kind.... It was thus that the grand\ndiscovery of the precession of the equinoxes resulted as a residual\nphenomenon, from the imperfect explanation of the return of the seasons by\nthe return of the sun to the same apparent place among the fixed stars.\nThus, also, aberration and nutation resulted as residual phenomena from\nthat portion of the changes of the apparent places of the fixed stars\nwhich was left unaccounted for by precession. And thus again the apparent\nproper motions of the stars are the observed residues of their apparent\nmovements outstanding and unaccounted for by strict calculation of the\neffects of precession, nutation, and aberration. The nearest approach\nwhich human theories can make to perfection is to diminish this residue,\nthis _caput mortuum_ of observation, as it may be considered, as much as\npracticable, and, if possible, to reduce it to nothing, either by showing\nthat something has been neglected in our estimation of known causes, or by\nreasoning upon it as a new fact, and on the principle of the inductive\nphilosophy ascending from the effect to its cause or causes.\u201d\n\nThe disturbing effects mutually produced by the earth and planets upon\neach other\u2019s motions were first brought to light as residual phenomena, by\nthe difference which appeared between the observed places of those bodies,\nand the places calculated on a consideration solely of their gravitation\ntoward the sun. It was this which determined astronomers to consider the\nlaw of gravitation as obtaining between all bodies whatever, and therefore\nbetween all particles of matter; their first tendency having been to\nregard it as a force acting only between each planet or satellite and the\ncentral body to whose system it belonged. Again, the catastrophists, in\ngeology, be their opinion right or wrong, support it on the plea, that\nafter the effect of all causes now in operation has been allowed for,\nthere remains in the existing constitution of the earth a large residue of\nfacts, proving the existence at former periods either of other forces, or\nof the same forces in a much greater degree of intensity. To add one more\nexample: those who assert, what no one has shown any real ground for\nbelieving, that there is in one human individual, one sex, or one race of\nmankind over another, an inherent and inexplicable superiority in mental\nfaculties, could only substantiate their proposition by subtracting from\nthe differences of intellect which we in fact see, all that can be traced\nby known laws either to the ascertained differences of physical\norganization, or to the differences which have existed in the outward\ncircumstances in which the subjects of the comparison have hitherto been\nplaced. What these causes might fail to account for would constitute a\nresidual phenomenon, which and which alone would be evidence of an\nulterior original distinction, and the measure of its amount. But the\nasserters of such supposed differences have not provided themselves with\nthese necessary logical conditions of the establishment of their doctrine.\n\nThe spirit of the Method of Residues being, it is hoped, sufficiently\nintelligible from these examples, and the other three methods having\nalready been so fully exemplified, we may here close our exposition of the\nfour methods, considered as employed in the investigation of the simpler\nand more elementary order of the combinations of phenomena.\n\n\u00a7 6. Dr. Whewell has expressed a very unfavorable opinion of the utility\nof the Four Methods, as well as of the aptness of the examples by which I\nhave attempted to illustrate them. His words are these:(145)\n\n\u201cUpon these methods, the obvious thing to remark is, that they take for\ngranted the very thing which is most difficult to discover, the reduction\nof the phenomena to formul\u00e6 such as are here presented to us. When we have\nany set of complex facts offered to us; for instance, those which were\noffered in the cases of discovery which I have mentioned\u2014the facts of the\nplanetary paths, of falling bodies, of refracted rays, of cosmical\nmotions, of chemical analysis; and when, in any of these cases, we would\ndiscover the law of nature which governs them, or, if any one chooses so\nto term it, the feature in which all the cases agree, where are we to look\nfor our A, B, C, and _a_, _b_, _c_? Nature does not present to us the\ncases in this form; and how are we to reduce them to this form? You say\n_when_ we find the combination of A B C with _a b c_ and A B D with _a b\nd_, then we may draw our inference. Granted; but when and where are we to\nfind such combinations? Even now that the discoveries are made, who will\npoint out to us what are the A, B, C, and _a_, _b_, _c_, elements of the\ncases which have just been enumerated? Who will tell us which of the\nmethods of inquiry those historically real and successful inquiries\nexemplify? Who will carry these formul\u00e6 through the history of the\nsciences, as they have really grown up, and show us that these four\nmethods have been operative in their formation; or that any light is\nthrown upon the steps of their progress by reference to these formul\u00e6?\u201d\n\nHe adds that, in this work, the methods have not been applied \u201cto a large\nbody of conspicuous and undoubted examples of discovery, extending along\nthe whole history of science;\u201d which ought to have been done in order that\nthe methods might be shown to possess the \u201cadvantage\u201d (which he claims as\nbelonging to his own) of being those \u201cby which all great discoveries in\nscience have really been made.\u201d\u2014(P. 277.)\n\nThere is a striking similarity between the objections here made against\nCanons of Induction, and what was alleged, in the last century, by as able\nmen as Dr. Whewell, against the acknowledged Canon of Ratiocination. Those\nwho protested against the Aristotelian Logic said of the Syllogism, what\nDr. Whewell says of the Inductive Methods, that it \u201ctakes for granted the\nvery thing which is most difficult to discover, the reduction of the\nargument to formul\u00e6 such as are here presented to us.\u201d The grand\ndifficulty, they said, is to obtain your syllogism, not to judge of its\ncorrectness when obtained. On the matter of fact, both they and Dr.\nWhewell are right. The greatest difficulty in both cases is, first, that\nof obtaining the evidence, and next, of reducing it to the form which\ntests its conclusiveness. But if we try to reduce it without knowing what\nit is to be reduced to, we are not likely to make much progress. It is a\nmore difficult thing to solve a geometrical problem, than to judge whether\na proposed solution is correct: but if people were not able to judge of\nthe solution when found, they would have little chance of finding it. And\nit can not be pretended that to judge of an induction when found is\nperfectly easy, is a thing for which aids and instruments are superfluous;\nfor erroneous inductions, false inferences from experience, are quite as\ncommon, on some subjects much commoner than true ones. The business of\nInductive Logic is to provide rules and models (such as the Syllogism and\nits rules are for ratiocination) to which if inductive arguments conform,\nthose arguments are conclusive, and not otherwise. This is what the Four\nMethods profess to be, and what I believe they are universally considered\nto be by experimental philosophers, who had practiced all of them long\nbefore any one sought to reduce the practice to theory.\n\nThe assailants of the Syllogism had also anticipated Dr. Whewell in the\nother branch of his argument. They said that no discoveries were ever made\nby syllogism; and Dr. Whewell says, or seems to say, that none were ever\nmade by the Four Methods of Induction. To the former objectors, Archbishop\nWhately very pertinently answered, that their argument, if good at all,\nwas good against the reasoning process altogether; for whatever can not be\nreduced to syllogism, is not reasoning. And Dr. Whewell\u2019s argument, if\ngood at all, is good against all inferences from experience. In saying\nthat no discoveries were ever made by the Four Methods, he affirms that\nnone were ever made by observation and experiment; for assuredly if any\nwere, it was by processes reducible to one or other of those methods.\n\nThis difference between us accounts for the dissatisfaction which my\nexamples give him; for I did not select them with a view to satisfy any\none who required to be convinced that observation and experiment are modes\nof acquiring knowledge: I confess that in the choice of them I thought\nonly of illustration, and of facilitating the _conception_ of the Methods\nby concrete instances. If it had been my object to justify the processes\nthemselves as means of investigation, there would have been no need to\nlook far off, or make use of recondite or complicated instances. As a\nspecimen of a truth ascertained by the Method of Agreement, I might have\nchosen the proposition, \u201cDogs bark.\u201d This dog, and that dog, and the other\ndog, answer to A B C, A D E, A F G. The circumstance of being a dog\nanswers to A. Barking answers to _a_. As a truth made known by the Method\nof Difference, \u201cFire burns\u201d might have sufficed. Before I touch the fire I\nam not burned; this is B C: I touch it, and am burned; this is A B C, _a_\nB C.\n\nSuch familiar experimental processes are not regarded as inductions by Dr.\nWhewell; but they are perfectly homogeneous with those by which, even on\nhis own showing, the pyramid of science is supplied with its base. In vain\nhe attempts to escape from this conclusion by laying the most arbitrary\nrestrictions on the choice of examples admissible as instances of\nInduction: they must neither be such as are still matter of discussion (p.\n265), nor must any of them be drawn from mental and social subjects (p.\n269), nor from ordinary observation and practical life (pp. 241\u2013247). They\nmust be taken exclusively from the generalizations by which scientific\nthinkers have ascended to great and comprehensive laws of natural\nphenomena. Now it is seldom possible, in these complicated inquiries, to\ngo much beyond the initial steps, without calling in the instrument of\nDeduction, and the temporary aid of hypothesis; as I myself, in common\nwith Dr. Whewell, have maintained against the purely empirical school.\nSince, therefore, such cases could not conveniently be selected to\nillustrate the principles of mere observation and experiment, Dr. Whewell\nis misled by their absence into representing the Experimental Methods as\nserving no purpose in scientific investigation; forgetting that if those\nmethods had not supplied the first generalizations, there would have been\nno materials for his own conception of Induction to work upon.\n\nHis challenge, however, to point out which of the four methods are\nexemplified in certain important cases of scientific inquiry, is easily\nanswered. \u201cThe planetary paths,\u201d as far as they are a case of induction at\nall,(146) fall under the Method of Agreement. The law of \u201cfalling bodies,\u201d\nnamely, that they describe spaces proportional to the squares of the\ntimes, was historically a deduction from the first law of motion; but the\nexperiments by which it was verified, and by which it might have been\ndiscovered, were examples of the Method of Agreement; and the apparent\nvariation from the true law, caused by the resistance of the air, was\ncleared up by experiments _in vacuo_, constituting an application of the\nMethod of Difference. The law of \u201crefracted rays\u201d (the constancy of the\nratio between the sines of incidence and of refraction for each refracting\nsubstance) was ascertained by direct measurement, and therefore by the\nMethod of Agreement. The \u201ccosmical motions\u201d were determined by highly\ncomplex processes of thought, in which Deduction was predominant, but the\nMethods of Agreement and of Concomitant Variations had a large part in\nestablishing the empirical laws. Every case without exception of \u201cchemical\nanalysis\u201d constitutes a well-marked example of the Method of Difference.\nTo any one acquainted with the subjects\u2014to Dr. Whewell himself, there\nwould not be the smallest difficulty in setting out \u201cthe A B C and _a b c_\nelements\u201d of these cases.\n\nIf discoveries are ever made by observation and experiment without\nDeduction, the four methods are methods of discovery: but even if they\nwere not methods of discovery, it would not be the less true that they are\nthe sole methods of Proof; and in that character, even the results of\ndeduction are amenable to them. The great generalizations which begin as\nHypotheses, must end by being proved, and are in reality (as will be shown\nhereafter) proved, by the Four Methods. Now it is with Proof, as such,\nthat Logic is principally concerned. This distinction has indeed no chance\nof finding favor with Dr. Whewell; for it is the peculiarity of his\nsystem, not to recognize, in cases of Induction, any necessity for proof.\nIf, after assuming an hypothesis and carefully collating it with facts,\nnothing is brought to light inconsistent with it, that is, if experience\ndoes not _dis_prove it, he is content: at least until a simpler\nhypothesis, equally consistent with experience, presents itself. If this\nbe Induction, doubtless there is no necessity for the four methods. But to\nsuppose that it is so, appears to me a radical misconception of the nature\nof the evidence of physical truths.\n\nSo real and practical is the need of a test for induction, similar to the\nsyllogistic test of ratiocination, that inferences which bid defiance to\nthe most elementary notions of inductive logic are put forth without\nmisgiving by persons eminent in physical science, as soon as they are off\nthe ground on which they are conversant with the facts, and not reduced to\njudge only by the arguments; and as for educated persons in general, it\nmay be doubted if they are better judges of a good or a bad induction than\nthey were before Bacon wrote. The improvement in the results of thinking\nhas seldom extended to the processes; or has reached, if any process, that\nof investigation only, not that of proof. A knowledge of many laws of\nnature has doubtless been arrived at, by framing hypotheses and finding\nthat the facts corresponded to them; and many errors have been got rid of\nby coming to a knowledge of facts which were inconsistent with them, but\nnot by discovering that the mode of thought which led to the errors was\nitself faulty, and might have been known to be such independently of the\nfacts which disproved the specific conclusion. Hence it is, that while the\nthoughts of mankind have on many subjects worked themselves practically\nright, the thinking power remains as weak as ever: and on all subjects on\nwhich the facts which would check the result are not accessible, as in\nwhat relates to the invisible world, and even, as has been seen lately, to\nthe visible world of the planetary regions, men of the greatest scientific\nacquirements argue as pitiably as the merest ignoramus. For though they\nhave made many sound inductions, they have not learned from them (and Dr.\nWhewell thinks there is no necessity that they should learn) the\nprinciples of inductive _evidence_.\n\n\n\n\n                                Chapter X.\n\n\nOf Plurality Of Causes, And Of The Intermixture Of Effects.\n\n\n\u00a7 1. In the preceding exposition of the four methods of observation and\nexperiment, by which we contrive to distinguish among a mass of\nco-existent phenomena the particular effect due to a given cause, or the\nparticular cause which gave birth to a given effect, it has been necessary\nto suppose, in the first instance, for the sake of simplification, that\nthis analytical operation is encumbered by no other difficulties than what\nare essentially inherent in its nature; and to represent to ourselves,\ntherefore, every effect, on the one hand as connected exclusively with a\nsingle cause, and on the other hand as incapable of being mixed and\nconfounded with any other co-existent effect. We have regarded _a b c d\ne_, the aggregate of the phenomena existing at any moment, as consisting\nof dissimilar facts, _a_, _b_, _c_, _d_, and _e_, for each of which one,\nand only one, cause needs be sought; the difficulty being only that of\nsingling out this one cause from the multitude of antecedent\ncircumstances, A, B, C, D, and E. The cause indeed may not be simple; it\nmay consist of an assemblage of conditions; but we have supposed that\nthere was only one possible assemblage of conditions from which the given\neffect could result.\n\nIf such were the fact, it would be comparatively an easy task to\ninvestigate the laws of nature. But the supposition does not hold in\neither of its parts. In the first place, it is not true that the same\nphenomenon is always produced by the same cause: the effect _a_ may\nsometimes arise from A, sometimes from B. And, secondly, the effects of\ndifferent causes are often not dissimilar, but homogeneous, and marked out\nby no assignable boundaries from one another: A and B may produce not _a_\nand _b_, but different portions of an effect _a_. The obscurity and\ndifficulty of the investigation of the laws of phenomena is singularly\nincreased by the necessity of adverting to these two circumstances:\nIntermixture of Effects, and Plurality of Causes. To the latter, being the\nsimpler of the two considerations, we shall first direct our attention.\n\nIt is not true, then, that one effect must be connected with only one\ncause, or assemblage of conditions; that each phenomenon can be produced\nonly in one way. There are often several independent modes in which the\nsame phenomenon could have originated. One fact may be the consequent in\nseveral invariable sequences; it may follow, with equal uniformity, any\none of several antecedents, or collections of antecedents. Many causes may\nproduce mechanical motion; many causes may produce some kinds of\nsensation; many causes may produce death. A given effect may really be\nproduced by a certain cause, and yet be perfectly capable of being\nproduced without it.\n\n\u00a7 2. One of the principal consequences of this fact of Plurality of Causes\nis, to render the first of the inductive methods, that of Agreement,\nuncertain. To illustrate that method, we supposed two instances, A B C\nfollowed by _a b c_, and A D E followed by _a d e_. From these instances\nit might apparently be concluded that A is an invariable antecedent of\n_a_, and even that it is the unconditional invariable antecedent, or\ncause, if we could be sure that there is no other antecedent common to the\ntwo cases. That this difficulty may not stand in the way, let us suppose\nthe two cases positively ascertained to have no antecedent in common\nexcept A. The moment, however, that we let in the possibility of a\nplurality of causes, the conclusion fails. For it involves a tacit\nsupposition, that _a_ must have been produced in both instances by the\nsame cause. If there can possibly have been two causes, those two may, for\nexample, be C and E: the one may have been the cause of _a_ in the former\nof the instances, the other in the latter, A having no influence in either\ncase.\n\nSuppose, for example, that two great artists or great philosophers, that\ntwo extremely selfish or extremely generous characters, were compared\ntogether as to the circumstances of their education and history, and the\ntwo cases were found to agree only in one circumstance: would it follow\nthat this one circumstance was the cause of the quality which\ncharacterized both those individuals? Not at all; for the causes which may\nproduce any type of character are very numerous; and the two persons might\nequally have agreed in their character, though there had been no manner of\nresemblance in their previous history.\n\nThis, therefore, is a characteristic imperfection of the Method of\nAgreement, from which imperfection the Method of Difference is free. For\nif we have two instances, A B C and B C, of which B C gives _b c_, and A\nbeing added converts it into _a b c_, it is certain that in this instance\nat least, A was either the cause of _a_, or an indispensable portion of\nits cause, even though the cause which produces it in other instances may\nbe altogether different. Plurality of Causes, therefore, not only does not\ndiminish the reliance due to the Method of Difference, but does not even\nrender a greater number of observations or experiments necessary: two\ninstances, the one positive and the other negative, are still sufficient\nfor the most complete and rigorous induction. Not so, however, with the\nMethod of Agreement. The conclusions which that yields, when the number of\ninstances compared is small, are of no real value, except as, in the\ncharacter of suggestions, they may lead either to experiments bringing\nthem to the test of the Method of Difference, or to reasonings which may\nexplain and verify them deductively.\n\nIt is only when the instances, being indefinitely multiplied and varied,\ncontinue to suggest the same result, that this result acquires any high\ndegree of independent value. If there are but two instances, A B C and A D\nE, though these instances have no antecedent in common except A, yet as\nthe effect may possibly have been produced in the two cases by different\ncauses, the result is at most only a slight probability in favor of A;\nthere may be causation, but it is almost equally probable that there was\nonly a coincidence. But the oftener we repeat the observation, varying the\ncircumstances, the more we advance toward a solution of this doubt. For if\nwe try A F G, A H K, etc., all unlike one another except in containing the\ncircumstance A, and if we find the effect _a_ entering into the result in\nall these cases, we must suppose one of two things, either that it is\ncaused by A, or that it has as many different causes as there are\ninstances. With each addition, therefore, to the number of instances, the\npresumption is strengthened in favor of A. The inquirer, of course, will\nnot neglect, if an opportunity present itself, to exclude A from some one\nof these combinations, from A H K for instance, and by trying H K\nseparately, appeal to the Method of Difference in aid of the Method of\nAgreement. By the Method of Difference alone can it be ascertained that A\nis the cause of _a_; but that it is either the cause, or another effect of\nthe same cause, may be placed beyond any reasonable doubt by the Method of\nAgreement, provided the instances are very numerous as well as\nsufficiently various.\n\nAfter how great a multiplication, then, of varied instances, all agreeing\nin no other antecedent except A, is the supposition of a plurality of\ncauses sufficiently rebutted, and the conclusion that _a_ is connected\nwith A divested of the characteristic imperfection, and reduced to a\nvirtual certainty? This is a question which we can not be exempted from\nanswering: but the consideration of it belongs to what is called the\nTheory of Probability, which will form the subject of a chapter hereafter.\nIt is seen, however, at once, that the conclusion does amount to a\npractical certainty after a sufficient number of instances, and that the\nmethod, therefore, is not radically vitiated by the characteristic\nimperfection. The result of these considerations is only, in the first\nplace, to point out a new source of inferiority in the Method of Agreement\nas compared with other modes of investigation, and new reasons for never\nresting contented with the results obtained by it, without attempting to\nconfirm them either by the Method of Difference, or by connecting them\ndeductively with some law or laws already ascertained by that superior\nmethod. And, in the second place, we learn from this the true theory of\nthe value of mere _number_ of instances in inductive inquiry. The\nPlurality of Causes is the only reason why mere number is of any\nimportance. The tendency of unscientific inquirers is to rely too much on\nnumber, without analyzing the instances; without looking closely enough\ninto their nature to ascertain what circumstances are or are not\neliminated by means of them. Most people hold their conclusions with a\ndegree of assurance proportioned to the mere _mass_ of the experience on\nwhich they appear to rest; not considering that by the addition of\ninstances to instances, all of the same kind, that is, differing from one\nanother only in points already recognized as immaterial, nothing whatever\nis added to the evidence of the conclusion. A single instance eliminating\nsome antecedent which existed in all the other cases, is of more value\nthan the greatest multitude of instances which are reckoned by their\nnumber alone. It is necessary, no doubt, to assure ourselves, by\nrepetition of the observation or experiment, that no error has been\ncommitted concerning the individual facts observed; and until we have\nassured ourselves of this, instead of varying the circumstances, we can\nnot too scrupulously repeat the same experiment or observation without any\nchange. But when once this assurance has been obtained, the multiplication\nof instances which do not exclude any more circumstances is entirely\nuseless, provided there have been already enough to exclude the\nsupposition of Plurality of Causes.\n\nIt is of importance to remark, that the peculiar modification of the\nMethod of Agreement, which, as partaking in some degree of the nature of\nthe Method of Difference, I have called the Joint Method of Agreement and\nDifference, is not affected by the characteristic imperfection now pointed\nout. For, in the joint method, it is supposed not only that the instances\nin which _a_ is, agree only in containing A, but also that the instances\nin which _a_ is not, agree only in not containing A. Now, if this be so, A\nmust be not only the cause of _a_, but the only possible cause: for if\nthere were another, as for example B, then in the instances in which _a_\nis not, B must have been absent as well as A, and it would not be true\nthat these instances agree _only_ in not containing A. This, therefore,\nconstitutes an immense advantage of the joint method over the simple\nMethod of Agreement. It may seem, indeed, that the advantage does not\nbelong so much to the joint method, as to one of its two premises (if they\nmay be so called), the negative premise. The Method of Agreement, when\napplied to negative instances, or those in which a phenomenon does _not_\ntake place, is certainly free from the characteristic imperfection which\naffects it in the affirmative case. The negative premise, it might\ntherefore be supposed, could be worked as a simple case of the Method of\nAgreement, without requiring an affirmative premise to be joined with it.\nBut though this is true in principle, it is generally altogether\nimpossible to work the Method of Agreement by negative instances without\npositive ones; it is so much more difficult to exhaust the field of\nnegation than that of affirmation. For instance, let the question be what\nis the cause of the transparency of bodies; with what prospect of success\ncould we set ourselves to inquire directly in what the multifarious\nsubstances which are _not_ transparent agree? But we might hope much\nsooner to seize some point of resemblance among the comparatively few and\ndefinite species of objects which _are_ transparent; and this being\nattained, we should quite naturally be put upon examining whether the\n_absence_ of this one circumstance be not precisely the point in which all\nopaque substances will be found to resemble.\n\nThe Joint Method of Agreement and Difference, therefore, or as I have\notherwise called it, the Indirect Method of Difference (because, like the\nMethod of Difference properly so-called, it proceeds by ascertaining how\nand in what the cases where the phenomenon is present differ from those in\nwhich it is absent) is, after the Direct Method of Difference, the most\npowerful of the remaining instruments of inductive investigation; and in\nthe sciences which depend on pure observation, with little or no aid from\nexperiment, this method, so well exemplified in the speculation on the\ncause of dew, is the primary resource, so far as direct appeals to\nexperience are concerned.\n\n\u00a7 3. We have thus far treated Plurality of Causes only as a possible\nsupposition, which, until removed, renders our inductions uncertain; and\nhave only considered by what means, where the plurality does not really\nexist, we may be enabled to disprove it. But we must also consider it as a\ncase actually occurring in nature, and which, as often as it does occur,\nour methods of induction ought to be capable of ascertaining and\nestablishing. For this, however, there is required no peculiar method.\nWhen an effect is really producible by two or more causes, the process for\ndetecting them is in no way different from that by which we discover\nsingle causes. They may (first) be discovered as separate sequences, by\nseparate sets of instances. One set of observations or experiments shows\nthat the sun is a cause of heat, another that friction is a source of it,\nanother that percussion, another that electricity, another that chemical\naction is such a source. Or (secondly) the plurality may come to light in\nthe course of collating a number of instances, when we attempt to find\nsome circumstance in which they all agree, and fail in doing so. We find\nit impossible to trace, in all the cases in which the effect is met with,\nany common circumstance. We find that we can eliminate _all_ the\nantecedents; that no one of them is present in all the instances, no one\nof them indispensable to the effect. On closer scrutiny, however, it\nappears that though no one is always present, one or other of several\nalways is. If, on further analysis, we can detect in these any common\nelement, we may be able to ascend from them to some one cause which is the\nreally operative circumstance in them all. Thus it is now thought that in\nthe production of heat by friction, percussion, chemical action, etc., the\nultimate source is one and the same. But if (as continually happens) we\ncan not take this ulterior step, the different antecedents must be set\ndown provisionally as distinct causes, each sufficient of itself to\nproduce the effect.\n\nWe here close our remarks on the Plurality of Causes, and proceed to the\nstill more peculiar and more complex case of the Intermixture of Effects,\nand the interference of causes with one another: a case constituting the\nprincipal part of the complication and difficulty of the study of nature;\nand with which the four only possible methods of directly inductive\ninvestigation by observation and experiment, are, for the most part, as\nwill appear presently, quite unequal to cope. The instrument of Deduction\nalone is adequate to unravel the complexities proceeding from this source;\nand the four methods have little more in their power than to supply\npremises for, and a verification of, our deductions.\n\n\u00a7 4. A concurrence of two or more causes, not separately producing each\nits own effect, but interfering with or modifying the effects of one\nanother, takes place, as has already been explained in two different ways.\nIn the one, which is exemplified by the joint operation of different\nforces in mechanics, the separate effects of all the causes continue to be\nproduced, but are compounded with one another, and disappear in one total.\nIn the other, illustrated by the case of chemical action, the separate\neffects cease entirely, and are succeeded by phenomena altogether\ndifferent, and governed by different laws.\n\nOf these cases the former is by far the more frequent, and this case it is\nwhich, for the most part, eludes the grasp of our experimental methods.\nThe other and exceptional case is essentially amenable to them. When the\nlaws of the original agents cease entirely, and a phenomenon makes its\nappearance, which, with reference to those laws, is quite heterogeneous;\nwhen, for example, two gaseous substances, hydrogen and oxygen, on being\nbrought together, throw off their peculiar properties, and produce the\nsubstance called water; in such cases the new fact may be subjected to\nexperimental inquiry, like any other phenomenon; and the elements which\nare said to compose it may be considered as the mere agents of its\nproduction\u2014the conditions on which it depends, the facts which make up its\ncause.\n\nThe _effects_ of the new phenomenon, the _properties_ of water, for\ninstance, are as easily found by experiment as the effects of any other\ncause. But to discover the _cause_ of it, that is, the particular\nconjunction of agents from which it results, is often difficult enough. In\nthe first place, the origin and actual production of the phenomenon are\nmost frequently inaccessible to our observation. If we could not have\nlearned the composition of water until we found instances in which it was\nactually produced from oxygen and hydrogen, we should have been forced to\nwait until the casual thought struck some one of passing an electric spark\nthrough a mixture of the two gases, or inserting a lighted taper into it,\nmerely to try what would happen. Besides, many substances, though they can\nbe analyzed, can not by any known artificial means be recompounded.\nFurther, even if we could have ascertained, by the Method of Agreement,\nthat oxygen and hydrogen were both present when water is produced, no\nexperimentation on oxygen and hydrogen separately, no knowledge of their\nlaws, could have enabled us deductively to infer that they would produce\nwater. We require a specific experiment on the two combined.\n\nUnder these difficulties, we should generally have been indebted for our\nknowledge of the causes of this class of effects, not to any inquiry\ndirected specifically toward that end, but either to accident, or to the\ngradual progress of experimentation on the different combinations of which\nthe producing agents are susceptible; if it were not for a peculiarity\nbelonging to effects of this description, that they often, under some\nparticular combination of circumstances, reproduce their causes. If water\nresults from the juxtaposition of hydrogen and oxygen whenever this can be\nmade sufficiently close and intimate, so, on the other hand, if water\nitself be placed in certain situations, hydrogen and oxygen are reproduced\nfrom it: an abrupt termination is put to the new laws, and the agents\nre-appear separately with their own properties as at first. What is called\nchemical analysis is the process of searching for the causes of a\nphenomenon among its effects, or rather among the effects produced by the\naction of some other causes upon it.\n\nLavoisier, by heating mercury to a high temperature in a close vessel\ncontaining air, found that the mercury increased in weight, and became\nwhat was then called red precipitate, while the air, on being examined\nafter the experiment, proved to have lost weight, and to have become\nincapable of supporting life or combustion. When red precipitate was\nexposed to a still greater heat, it became mercury again, and gave off a\ngas which did support life and flame. Thus the agents which by their\ncombination produced red precipitate, namely, the mercury and the gas,\nreappear as effects resulting from that precipitate when acted upon by\nheat. So, if we decompose water by means of iron filings, we produce two\neffects, rust and hydrogen. Now rust is already known, by experiments upon\nthe component substances, to be an effect of the union of iron and oxygen:\nthe iron we ourselves supplied, but the oxygen must have been produced\nfrom the water. The result, therefore, is that water has disappeared, and\nhydrogen and oxygen have appeared in its stead; or, in other words, the\noriginal laws of these gaseous agents, which had been suspended by the\nsuperinduction of the new laws called the properties of water, have again\nstarted into existence, and the causes of water are found among its\neffects.\n\nWhere two phenomena, between the laws or properties of which, considered\nin themselves, no connection can be traced, are thus reciprocally cause\nand effect, each capable in its turn of being produced from the other, and\neach, when it produces the other, ceasing itself to exist (as water is\nproduced from oxygen and hydrogen, and oxygen and hydrogen are reproduced\nfrom water); this causation of the two phenomena by one another, each\nbeing generated by the other\u2019s destruction, is properly transformation.\nThe idea of chemical composition is an idea of transformation, but of a\ntransformation which is incomplete; since we consider the oxygen and\nhydrogen to be present in the water _as_ oxygen and hydrogen, and capable\nof being discovered in it if our senses were sufficiently keen: a\nsupposition (for it is no more) grounded solely on the fact that the\nweight of the water is the sum of the separate weights of the two\ningredients. If there had not been this exception to the entire\ndisappearance, in the compound, of the laws of the separate ingredients;\nif the combined agents had not, in this one particular of weight,\npreserved their own laws, and produced a joint result equal to the sum of\ntheir separate results; we should never, probably, have had the notion now\nimplied by the words chemical composition; and, in the facts of water\nproduced from hydrogen and oxygen, and hydrogen and oxygen produced from\nwater, as the transformation would have been complete, we should have seen\nonly a transformation.\n\nIn these cases, where the heteropathic effect (as we called it in a former\nchapter)(147) is but a transformation of its cause, or in other words,\nwhere the effect and its cause are reciprocally such, and mutually\nconvertible into each other; the problem of finding the cause resolves\nitself into the far easier one of finding an effect, which is the kind of\ninquiry that admits of being prosecuted by direct experiment. But there\nare other cases of heteropathic effects to which this mode of\ninvestigation is not applicable. Take, for instance, the heteropathic laws\nof mind; that portion of the phenomena of our mental nature which are\nanalogous to chemical rather than to dynamical phenomena; as when a\ncomplex passion is formed by the coalition of several elementary impulses,\nor a complex emotion by several simple pleasures or pains, of which it is\nthe result without being the aggregate, or in any respect homogeneous with\nthem. The product, in these cases, is generated by its various factors;\nbut the factors can not be reproduced from the product; just as a youth\ncan grow into an old man, but an old man can not grow into a youth. We can\nnot ascertain from what simple feelings any of our complex states of mind\nare generated, as we ascertain the ingredients of a chemical compound, by\nmaking it, in its turn, generate them. We can only, therefore, discover\nthese laws by the slow process of studying the simple feelings themselves,\nand ascertaining synthetically, by experimenting on the various\ncombinations of which they are susceptible, what they, by their mutual\naction upon one another, are capable of generating.\n\n\u00a7 5. It might have been supposed that the other, and apparently simpler\nvariety of the mutual interference of causes, where each cause continues\nto produce its own proper effect according to the same laws to which it\nconforms in its separate state, would have presented fewer difficulties to\nthe inductive inquirer than that of which we have just finished the\nconsideration. It presents, however, so far as direct induction apart from\ndeduction is concerned, infinitely greater difficulties. When a\nconcurrence of causes gives rise to a new effect, bearing no relation to\nthe separate effects of those causes, the resulting phenomenon stands\nforth undisguised, inviting attention to its peculiarity, and presenting\nno obstacle to our recognizing its presence or absence among any number of\nsurrounding phenomena. It admits, therefore, of being easily brought under\nthe canons of Induction, provided instances can be obtained such as those\ncanons require; and the non-occurrence of such instances, or the want of\nmeans to produce them artificially, is the real and only difficulty in\nsuch investigations; a difficulty not logical but in some sort physical.\nIt is otherwise with cases of what, in a preceding chapter, has been\ndenominated the Composition of Causes. There, the effects of the separate\ncauses do not terminate and give place to others, thereby ceasing to form\nany part of the phenomenon to be investigated; on the contrary, they still\ntake place, but are intermingled with, and disguised by, the homogeneous\nand closely allied effects of other causes. They are no longer _a_, _b_,\n_c_, _d_, _e_, existing side by side, and continuing to be separately\ndiscernible; they are +_a_, \u2013_a_, \u00bd_b_, _\u2013b_, 2_b_, etc.; some of which\ncancel one another, while many others do not appear distinguishably, but\nmerge in one sum; forming altogether a result, between which and the\ncauses whereby it was produced there is often an insurmountable difficulty\nin tracing by observation any fixed relation whatever.\n\nThe general idea of the Composition of Causes has been seen to be, that\nthough two or more laws interfere with one another, and apparently\nfrustrate or modify one another\u2019s operation, yet in reality all are\nfulfilled, the collective effect being the exact sum of the effects of the\ncauses taken separately. A familiar instance is that of a body kept in\nequilibrium by two equal and contrary forces. One of the forces if acting\nalone would carry the body in a given time a certain distance to the west,\nthe other if acting alone would carry it exactly as far toward the east;\nand the result is the same as if it had been first carried to the west as\nfar as the one force would carry it, and then back toward the east as far\nas the other would carry it\u2014that is, precisely the same distance; being\nultimately left where it was found at first.\n\nAll laws of causation are liable to be in this manner counteracted, and\nseemingly frustrated, by coming into conflict with other laws, the\nseparate result of which is opposite to theirs, or more or less\ninconsistent with it. And hence, with almost every law, many instances in\nwhich it really is entirely fulfilled, do not, at first sight, appear to\nbe cases of its operation at all. It is so in the example just adduced: a\nforce in mechanics means neither more nor less than a cause of motion, yet\nthe sum of the effects of two causes of motion may be rest. Again, a body\nsolicited by two forces in directions making an angle with one another,\nmoves in the diagonal; and it seems a paradox to say that motion in the\ndiagonal is the sum of two motions in two other lines. Motion, however, is\nbut change of place, and at every instant the body is in the exact place\nit would have been in if the forces had acted during alternate instants\ninstead of acting in the same instant (saving that if we suppose two\nforces to act successively which are in truth simultaneous we must of\ncourse allow them double the time). It is evident, therefore, that each\nforce has had, during each instant, all the effect which belonged to it;\nand that the modifying influence which one of two concurrent causes is\nsaid to exercise with respect to the other may be considered as exerted\nnot over the action of the cause itself, but over the effect after it is\ncompleted. For all purposes of predicting, calculating, or explaining\ntheir joint result, causes which compound their effects may be treated as\nif they produced simultaneously each of them its own effect, and all these\neffects co-existed visibly.\n\nSince the laws of causes are as really fulfilled when the causes are said\nto be counteracted by opposing causes, as when they are left to their own\nundisturbed action, we must be cautious not to express the laws in such\nterms as would render the assertion of their being fulfilled in those\ncases a contradiction. If, for instance, it were stated as a law of nature\nthat a body to which a force is applied moves in the direction of the\nforce, with a velocity proportioned to the force directly, and to its own\nmass inversely; when in point of fact some bodies to which a force is\napplied do not move at all, and those which do move (at least in the\nregion of our earth) are, from the very first, retarded by the action of\ngravity and other resisting forces, and at last stopped altogether; it is\nclear that the general proposition, though it would be true under a\ncertain hypothesis, would not express the facts as they actually occur. To\naccommodate the expression of the law to the real phenomena, we must say,\nnot that the object moves, but that it _tends_ to move, in the direction\nand with the velocity specified. We might, indeed, guard our expression in\na different mode, by saying that the body moves in that manner unless\nprevented, or except in so far as prevented, by some counteracting cause.\nBut the body does not only move in that manner unless counteracted; it\n_tends_ to move in that manner even when counteracted; it still exerts, in\nthe original direction, the same energy of movement as if its first\nimpulse had been undisturbed, and produces, by that energy, an exactly\nequivalent quantity of effect. This is true even when the force leaves the\nbody as it found it, in a state of absolute rest; as when we attempt to\nraise a body of three tons\u2019 weight with a force equal to one ton. For if,\nwhile we are applying this force, wind or water or any other agent\nsupplies an additional force just exceeding two tons, the body will be\nraised; thus proving that the force we applied exerted its full effect, by\nneutralizing an equivalent portion of the weight which it was insufficient\naltogether to overcome. And if, while we are exerting this force of one\nton upon the object in a direction contrary to that of gravity, it be put\ninto a scale and weighed, it will be found to have lost a ton of its\nweight, or, in other words, to press downward with a force only equal to\nthe difference of the two forces.\n\nThese facts are correctly indicated by the expression _tendency_. All laws\nof causation, in consequence of their liability to be counteracted,\nrequire to be stated in words affirmative of tendencies only, and not of\nactual results. In those sciences of causation which have an accurate\nnomenclature, there are special words which signify a tendency to the\nparticular effect with which the science is conversant; thus _pressure_,\nin mechanics, is synonymous with tendency to motion, and forces are not\nreasoned on as causing actual motion, but as exerting pressure. A similar\nimprovement in terminology would be very salutary in many other branches\nof science.\n\nThe habit of neglecting this necessary element in the precise expression\nof the laws of nature, has given birth to the popular prejudice that all\ngeneral truths have exceptions; and much unmerited distrust has thence\naccrued to the conclusions of science, when they have been submitted to\nthe judgment of minds insufficiently disciplined and cultivated. The rough\ngeneralizations suggested by common observation usually have exceptions;\nbut principles of science, or, in other words, laws of causation, have\nnot. \u201cWhat is thought to be an exception to a principle\u201d (to quote words\nused on a different occasion), \u201cis always some other and distinct\nprinciple cutting into the former; some other force which impinges(148)\nagainst the first force, and deflects it from its direction. There are not\na law and an exception to that law, the law acting in ninety-nine cases,\nand the exception in one. There are two laws, each possibly acting in the\nwhole hundred cases, and bringing about a common effect by their conjunct\noperation. If the force which, being the less conspicuous of the two, is\ncalled the _disturbing_ force, prevails sufficiently over the other force\nin some one case, to constitute that case what is commonly called an\nexception, the same disturbing force probably acts as a modifying cause in\nmany other cases which no one will call exceptions.\n\n\u201cThus if it were stated to be a law of nature that all heavy bodies fall\nto the ground, it would probably be said that the resistance of the\natmosphere, which prevents a balloon from falling, constitutes the balloon\nan exception to that pretended law of nature. But the real law is, that\nall heavy bodies _tend_ to fall; and to this there is no exception, not\neven the sun and moon; for even they, as every astronomer knows, tend\ntoward the earth, with a force exactly equal to that with which the earth\ntends toward them. The resistance of the atmosphere might, in the\nparticular case of the balloon, from a misapprehension of what the law of\ngravitation is, be said to _prevail over_ the law; but its disturbing\neffect is quite as real in every other case, since though it does not\nprevent, it retards the fall of all bodies whatever. The rule, and the\nso-called exception, do not divide the cases between them; each of them is\na comprehensive rule extending to all cases. To call one of these\nconcurrent principles an exception to the other, is superficial, and\ncontrary to the correct principles of nomenclature and arrangement. An\neffect of precisely the same kind, and arising from the same cause, ought\nnot to be placed in two different categories, merely as there does or does\nnot exist another cause preponderating over it.\u201d(149)\n\n\u00a7 6. We have now to consider according to what method these complex\neffects, compounded of the effects of many causes, are to be studied; how\nwe are enabled to trace each effect to the concurrence of causes in which\nit originated, and ascertain the conditions of its recurrence\u2014the\ncircumstances in which it may be expected again to occur. The conditions\nof a phenomenon which arises from a composition of causes, may be\ninvestigated either deductively or experimentally.\n\nThe case, it is evident, is naturally susceptible of the deductive mode of\ninvestigation. The law of an effect of this description is a result of the\nlaws of the separate causes on the combination of which it depends, and\nis, therefore, in itself capable of being deduced from these laws. This is\ncalled the method _a priori_. The other, or _a posteriori_ method,\nprofesses to proceed according to the canons of experimental inquiry.\nConsidering the whole assemblage of concurrent causes which produced the\nphenomenon, as one single cause, it attempts to ascertain the cause in the\nordinary manner, by a comparison of instances. This second method\nsubdivides itself into two different varieties. If it merely collates\ninstances of the effect, it is a method of pure observation. If it\noperates upon the causes, and tries different combinations of them, in\nhopes of ultimately hitting the precise combination which will produce the\ngiven total effect, it is a method of experiment.\n\nIn order more completely to clear up the nature of each of these three\nmethods, and determine which of them deserves the preference, it will be\nexpedient (conformably to a favorite maxim of Lord Chancellor Eldon, to\nwhich, though it has often incurred philosophical ridicule, a deeper\nphilosophy will not refuse its sanction) to \u201cclothe them in\ncircumstances.\u201d We shall select for this purpose a case which as yet\nfurnishes no very brilliant example of the success of any of the three\nmethods, but which is all the more suited to illustrate the difficulties\ninherent in them. Let the subject of inquiry be, the conditions of health\nand disease in the human body; or (for greater simplicity) the conditions\nof recovery from a given disease; and in order to narrow the question\nstill more, let it be limited, in the first instance, to this one inquiry:\nIs, or is not, some particular medicament (mercury, for instance) a remedy\nfor the given disease.\n\nNow, the deductive method would set out from known properties of mercury,\nand known laws of the human body, and by reasoning from these, would\nattempt to discover whether mercury will act upon the body when in the\nmorbid condition supposed, in such a manner as would tend to restore\nhealth. The experimental method would simply administer mercury in as many\ncases as possible, noting the age, sex, temperament, and other\npeculiarities of bodily constitution, the particular form or variety of\nthe disease, the particular stage of its progress, etc., remarking in\nwhich of these cases it was attended with a salutary effect, and with what\ncircumstances it was on those occasions combined. The method of simple\nobservation would compare instances of recovery, to find whether they\nagreed in having been preceded by the administration of mercury; or would\ncompare instances of recovery with instances of failure, to find cases\nwhich, agreeing in all other respects, differed only in the fact that\nmercury had been administered, or that it had not.\n\n\u00a7 7. That the last of these three modes of investigation is applicable to\nthe case, no one has ever seriously contended. No conclusions of value on\na subject of such intricacy ever were obtained in that way. The utmost\nthat could result would be a vague general impression for or against the\nefficacy of mercury, of no avail for guidance unless confirmed by one of\nthe other two methods. Not that the results, which this method strives to\nobtain, would not be of the utmost possible value if they could be\nobtained. If all the cases of recovery which presented themselves, in an\nexamination extending to a great number of instances, were cases in which\nmercury had been administered, we might generalize with confidence from\nthis experience, and should have obtained a conclusion of real value. But\nno such basis for generalization can we, in a case of this description,\nhope to obtain. The reason is that which we have spoken of as constituting\nthe characteristic imperfection of the Method of Agreement, Plurality of\nCauses. Supposing even that mercury does tend to cure the disease, so many\nother causes, both natural and artificial, also tend to cure it, that\nthere are sure to be abundant instances of recovery in which mercury has\nnot been administered, unless, indeed, the practice be to administer it in\nall cases; on which supposition it will equally be found in the cases of\nfailure.\n\nWhen an effect results from the union of many causes, the share which each\nhas in the determination of the effect can not in general be great, and\nthe effect is not likely, even in its presence or absence, still less in\nits variations, to follow, even approximately, any one of the causes.\nRecovery from a disease is an event to which, in every case, many\ninfluences must concur. Mercury may be one such influence; but from the\nvery fact that there are many other such, it will necessarily happen that\nalthough mercury is administered, the patient, for want of other\nconcurring influences, will often not recover, and that he often will\nrecover when it is not administered, the other favorable influences being\nsufficiently powerful without it. Neither, therefore, will the instances\nof recovery agree in the administration of mercury, nor will the instances\nof failure agree in its non-administration. It is much if, by multiplied\nand accurate returns from hospitals and the like, we can collect that\nthere are rather more recoveries and rather fewer failures when mercury is\nadministered than when it is not; a result of very secondary value even as\na guide to practice, and almost worthless as a contribution to the theory\nof the subject.(150)\n\n\u00a7 8. The inapplicability of the method of simple observation to ascertain\nthe conditions of effects dependent on many concurring causes, being thus\nrecognized, we shall next inquire whether any greater benefit can be\nexpected from the other branch of the _a posteriori_ method, that which\nproceeds by directly trying different combinations of causes, either\nartificially produced or found in nature, and taking notice what is their\neffect; as, for example, by actually trying the effect of mercury in as\nmany different circumstances as possible. This method differs from the one\nwhich we have just examined in turning our attention directly to the\ncauses or agents, instead of turning it to the effect, recovery from the\ndisease. And since, as a general rule, the effects of causes are far more\naccessible to our study than the causes of effects, it is natural to think\nthat this method has a much better chance of proving successful than the\nformer.\n\nThe method now under consideration is called the Empirical Method; and in\norder to estimate it fairly, we must suppose it to be completely, not\nincompletely, empirical. We must exclude from it every thing which\npartakes of the nature not of an experimental but of a deductive\noperation. If, for instance, we try experiments with mercury upon a person\nin health, in order to ascertain the general laws of its action upon the\nhuman body, and then reason from these laws to determine how it will act\nupon persons affected with a particular disease, this may be a really\neffectual method; but this is deduction. The experimental method does not\nderive the law of a complex case from the simpler laws which conspire to\nproduce it, but makes its experiments directly upon the complex case. We\nmust make entire abstraction of all knowledge of the simpler tendencies,\nthe _modi operandi_ of mercury in detail. Our experimentation must aim at\nobtaining a direct answer to the specific question, Does or does not\nmercury tend to cure the particular disease?\n\nLet us see, therefore, how far the case admits of the observance of those\nrules of experimentation which it is found necessary to observe in other\ncases. When we devise an experiment to ascertain the effect of a given\nagent, there are certain precautions which we never, if we can help it,\nomit. In the first place, we introduce the agent into the midst of a set\nof circumstances which we have exactly ascertained. It needs hardly be\nremarked how far this condition is from being realized in any case\nconnected with the phenomena of life; how far we are from knowing what are\nall the circumstances which pre-exist in any instance in which mercury is\nadministered to a living being. This difficulty, however, though\ninsuperable in most cases, may not be so in all; there are sometimes\nconcurrences of many causes, in which we yet know accurately what the\ncauses are. Moreover, the difficulty may be attenuated by sufficient\nmultiplication of experiments, in circumstances rendering it improbable\nthat any of the unknown causes should exist in them all. But when we have\ngot clear of this obstacle, we encounter another still more serious. In\nother cases, when we intend to try an experiment, we do not reckon it\nenough that there be no circumstance in the case the presence of which is\nunknown to us. We require, also, that none of the circumstances which we\ndo know shall have effects susceptible of being confounded with those of\nthe agents whose properties we wish to study. We take the utmost pains to\nexclude all causes capable of composition with the given cause; or, if\nforced to let in any such causes, we take care to make them such that we\ncan compute and allow for their influence, so that the effect of the given\ncause may, after the subduction of those other effects, be apparent as a\nresidual phenomenon.\n\nThese precautions are inapplicable to such cases as we are now\nconsidering. The mercury of our experiment being tried with an unknown\nmultitude (or even let it be a known multitude) of other influencing\ncircumstances, the mere fact of their being influencing circumstances\nimplies that they disguise the effect of the mercury, and preclude us from\nknowing whether it has any effect or not. Unless we already knew what and\nhow much is owing to every other circumstance (that is, unless we suppose\nthe very problem solved which we are considering the means of solving), we\ncan not tell that those other circumstances may not have produced the\nwhole of the effect, independently or even in spite of the mercury. The\nMethod of Difference, in the ordinary mode of its use, namely, by\ncomparing the state of things following the experiment with the state\nwhich preceded it, is thus, in the case of intermixture of effects,\nentirely unavailing; because other causes than that whose effect we are\nseeking to determine have been operating during the transition. As for the\nother mode of employing the Method of Difference, namely, by comparing,\nnot the same case at two different periods, but different cases, this in\nthe present instance is quite chimerical. In phenomena so complicated it\nis questionable if two cases, similar in all respects but one, ever\noccurred; and were they to occur, we could not possibly know that they\nwere so exactly similar.\n\nAny thing like a scientific use of the method of experiment, in these\ncomplicated cases, is therefore out of the question. We can generally,\neven in the most favorable cases, only discover by a succession of trials,\nthat a certain cause is _very often_ followed by a certain effect. For, in\none of these conjunct effects, the portion which is determined by any one\nof the influencing agents, is usually, as we before remarked, but small;\nand it must be a more potent cause than most, if even the tendency which\nit really exerts is not thwarted by other tendencies in nearly as many\ncases as it is fulfilled. Some causes indeed there are which are more\npotent than any counteracting causes to which they are commonly exposed;\nand accordingly there are some truths in medicine which are sufficiently\nproved by direct experiment. Of these the most familiar are those that\nrelate to the efficacy of the substances known as Specifics for particular\ndiseases, \u201cquinine, colchicum, lime-juice, cod-liver oil,\u201d(151) and a few\nothers. Even these are not invariably followed by success; but they\nsucceed in so large a proportion of cases, and against such powerful\nobstacles, that their _tendency_ to restore health in the disorders for\nwhich they are prescribed may be regarded as an experimental truth.(152)\n\nIf so little can be done by the experimental method to determine the\nconditions of an effect of many combined causes, in the case of medical\nscience; still less is this method applicable to a class of phenomena more\ncomplicated than even those of physiology, the phenomena of politics and\nhistory. There, Plurality of Causes exists in almost boundless excess, and\neffects are, for the most part, inextricably interwoven with one another.\nTo add to the embarrassment, most of the inquiries in political science\nrelate to the production of effects of a most comprehensive description,\nsuch as the public wealth, public security, public morality, and the like:\nresults liable to be affected directly or indirectly either in _plus_ or\nin _minus_ by nearly every fact which exists, or event which occurs, in\nhuman society. The vulgar notion, that the safe methods on political\nsubjects are those of Baconian induction\u2014that the true guide is not\ngeneral reasoning, but specific experience\u2014will one day be quoted as among\nthe most unequivocal marks of a low state of the speculative faculties in\nany age in which it is accredited. Nothing can be more ludicrous than the\nsort of parodies on experimental reasoning which one is accustomed to meet\nwith, not in popular discussion only, but in grave treatises, when the\naffairs of nations are the theme. \u201cHow,\u201d it is asked, \u201ccan an institution\nbe bad, when the country has prospered under it?\u201d \u201cHow can such or such\ncauses have contributed to the prosperity of one country, when another has\nprospered without them?\u201d Whoever makes use of an argument of this kind,\nnot intending to deceive, should be sent back to learn the elements of\nsome one of the more easy physical sciences. Such reasoners ignore the\nfact of Plurality of Causes in the very case which affords the most signal\nexample of it. So little could be concluded, in such a case, from any\npossible collation of individual instances, that even the impossibility,\nin social phenomena, of making artificial experiments, a circumstance\notherwise so prejudicial to directly inductive inquiry, hardly affords, in\nthis case, additional reason of regret. For even if we could try\nexperiments upon a nation or upon the human race, with as little scruple\nas M. Magendie tried them on dogs and rabbits, we should never succeed in\nmaking two instances identical in every respect except the presence or\nabsence of some one definite circumstance. The nearest approach to an\nexperiment in the philosophical sense, which takes place in politics, is\nthe introduction of a new operative element into national affairs by some\nspecial and assignable measure of government, such as the enactment or\nrepeal of a particular law. But where there are so many influences at\nwork, it requires some time for the influence of any new cause upon\nnational phenomena to become apparent; and as the causes operating in so\nextensive a sphere are not only infinitely numerous, but in a state of\nperpetual alteration, it is always certain that before the effect of the\nnew cause becomes conspicuous enough to be a subject of induction, so many\nof the other influencing circumstances will have changed as to vitiate the\nexperiment.(153)\n\nTwo, therefore, of the three possible methods for the study of phenomena\nresulting from the composition of many causes, being, from the very nature\nof the case, inefficient and illusory, there remains only the third\u2014that\nwhich considers the causes separately, and infers the effect from the\nbalance of the different tendencies which produce it: in short, the\ndeductive, or _a priori_ method. The more particular consideration of this\nintellectual process requires a chapter to itself.\n\n\n\n\n                               Chapter XI.\n\n\nOf The Deductive Method.\n\n\n\u00a7 1. The mode of investigation which, from the proved inapplicability of\ndirect methods of observation and experiment, remains to us as the main\nsource of the knowledge we possess or can acquire respecting the\nconditions and laws of recurrence, of the more complex phenomena, is\ncalled, in its most general expression, the Deductive Method; and consists\nof three operations: the first, one of direct induction; the second, of\nratiocination; the third, of verification.\n\nI call the first step in the process an inductive operation, because there\nmust be a direct induction as the basis of the whole; though in many\nparticular investigations the place of the induction may be supplied by a\nprior deduction; but the premises of this prior deduction must have been\nderived from induction.\n\nThe problem of the Deductive Method is, to find the law of an effect, from\nthe laws of the different tendencies of which it is the joint result. The\nfirst requisite, therefore, is to know the laws of those tendencies; the\nlaw of each of the concurrent causes: and this supposes a previous process\nof observation or experiment upon each cause separately; or else a\nprevious deduction, which also must depend for its ultimate premises on\nobservation or experiment. Thus, if the subject be social or historical\nphenomena, the premises of the Deductive Method must be the laws of the\ncauses which determine that class of phenomena; and those causes are human\nactions, together with the general outward circumstances under the\ninfluence of which mankind are placed, and which constitute man\u2019s position\non the earth. The Deductive Method, applied to social phenomena, must\nbegin, therefore, by investigating, or must suppose to have been already\ninvestigated, the laws of human action, and those properties of outward\nthings by which the actions of human beings in society are determined.\nSome of these general truths will naturally be obtained by observation and\nexperiment, others by deduction: the more complex laws of human action,\nfor example, may be deduced from the simpler ones; but the simple or\nelementary laws will always, and necessarily, have been obtained by a\ndirectly inductive process.\n\nTo ascertain, then, the laws of each separate cause which takes a share in\nproducing the effect, is the first desideratum of the Deductive Method. To\nknow what the causes are which must be subjected to this process of study,\nmay or may not be difficult. In the case last mentioned, this first\ncondition is of easy fulfillment. That social phenomena depend on the acts\nand mental impressions of human beings, never could have been a matter of\nany doubt, however imperfectly it may have been known either by what laws\nthose impressions and actions are governed, or to what social consequences\ntheir laws naturally lead. Neither, again, after physical science had\nattained a certain development, could there be any real doubt where to\nlook for the laws on which the phenomena of life depend, since they must\nbe the mechanical and chemical laws of the solid and fluid substances\ncomposing the organized body and the medium in which it subsists, together\nwith the peculiar vital laws of the different tissues constituting the\norganic structure. In other cases, really far more simple than these, it\nwas much less obvious in what quarter the causes were to be looked for: as\nin the case of the celestial phenomena. Until, by combining the laws of\ncertain causes, it was found that those laws explained all the facts which\nexperience had proved concerning the heavenly motions, and led to\npredictions which it always verified, mankind never knew that those _were_\nthe causes. But whether we are able to put the question before, or not\nuntil after, we have become capable of answering it, in either case it\nmust be answered; the laws of the different causes must be ascertained,\nbefore we can proceed to deduce from them the conditions of the effect.\n\nThe mode of ascertaining those laws neither is, nor can be any other than\nthe fourfold method of experimental inquiry, already discussed. A few\nremarks on the application of that method to cases of the Composition of\nCauses are all that is requisite.\n\nIt is obvious that we can not expect to find the law of a tendency by an\ninduction from cases in which the tendency is counteracted. The laws of\nmotion could never have been brought to light from the observation of\nbodies kept at rest by the equilibrium of opposing forces. Even where the\ntendency is not, in the ordinary sense of the word, counteracted, but only\nmodified, by having its effects compounded with the effects arising from\nsome other tendency or tendencies, we are still in an unfavorable position\nfor tracing, by means of such cases, the law of the tendency itself. It\nwould have been scarcely possible to discover the law that every body in\nmotion tends to continue moving in a straight line, by an induction from\ninstances in which the motion is deflected into a curve, by being\ncompounded with the effect of an accelerating force. Notwithstanding the\nresources afforded in this description of cases by the Method of\nConcomitant Variations, the principles of a judicious experimentation\nprescribe that the law of each of the tendencies should be studied, if\npossible, in cases in which that tendency operates alone, or in\ncombination with no agencies but those of which the effect can, from\nprevious knowledge, be calculated and allowed for.\n\nAccordingly, in the cases, unfortunately very numerous and important, in\nwhich the causes do not suffer themselves to be separated and observed\napart, there is much difficulty in laying down with due certainty the\ninductive foundation necessary to support the deductive method. This\ndifficulty is most of all conspicuous in the case of physiological\nphenomena; it being seldom possible to separate the different agencies\nwhich collectively compose an organized body, without destroying the very\nphenomena which it is our object to investigate:\n\n\n    \u2014\u2014following life, in creatures we dissect,\n    We lose it, in the moment we detect.\n\n\nAnd for this reason I am inclined to the opinion that physiology (greatly\nand rapidly progressive as it now is) is embarrassed by greater natural\ndifficulties, and is probably susceptible of a less degree of ultimate\nperfection, than even the social science; inasmuch as it is possible to\nstudy the laws and operations of one human mind apart from other minds,\nmuch less imperfectly than we can study the laws of one organ or tissue of\nthe human body apart from the other organs or tissues.\n\nIt has been judiciously remarked that pathological facts, or, to speak in\ncommon language, diseases in their different forms and degrees afford in\nthe case of physiological investigation the most valuable equivalent to\nexperimentation properly so called; inasmuch as they often exhibit to us a\ndefinite disturbance in some one organ or organic function, the remaining\norgans and functions being, in the first instance at least, unaffected. It\nis true that from the perpetual actions and reactions which are going on\namong all parts of the organic economy, there can be no prolonged\ndisturbance in any one function without ultimately involving many of the\nothers; and when once it has done so, the experiment for the most part\nloses its scientific value. All depends on observing the early stages of\nthe derangement; which, unfortunately, are of necessity the least marked.\nIf, however, the organs and functions not disturbed in the first instance\nbecome affected in a fixed order of succession, some light is thereby\nthrown upon the action which one organ exercises over another: and we\noccasionally obtain a series of effects which we can refer with some\nconfidence to the original local derangement; but for this it is necessary\nthat we should know that the original derangement _was_ local. If it was\nwhat is termed constitutional; that is, if we do not know in what part of\nthe animal economy it took its rise, or the precise nature of the\ndisturbance which took place in that part, we are unable to determine\nwhich of the various derangements was cause and which effect; which of\nthem were produced by one another, and which by the direct, though perhaps\ntardy, action of the original cause.\n\nBesides natural pathological facts, we can produce pathological facts\nartificially: we can try experiments, even in the popular sense of the\nterm, by subjecting the living being to some external agent, such as the\nmercury of our former example, or the section of a nerve to ascertain the\nfunctions of different parts of the nervous system. As this\nexperimentation is not intended to obtain a direct solution of any\npractical question, but to discover general laws, from which afterward the\nconditions of any particular effect may be obtained by deduction, the best\ncases to select are those of which the circumstances can be best\nascertained: and such are generally not those in which there is any\npractical object in view. The experiments are best tried, not in a state\nof disease, which is essentially a changeable state, but in the condition\nof health, comparatively a fixed state. In the one, unusual agencies are\nat work, the results of which we have no means of predicting: in the\nother, the course of the accustomed physiological phenomena would, it may\ngenerally be presumed, remain undisturbed, were it not for the disturbing\ncause which we introduce.\n\nSuch, with the occasional aid of the Method of Concomitant Variations (the\nlatter not less encumbered than the more elementary methods by the\npeculiar difficulties of the subject), are our inductive resources for\nascertaining the laws of the causes considered separately, when we have it\nnot in our power to make trial of them in a state of actual separation.\nThe insufficiency of these resources is so glaring, that no one can be\nsurprised at the backward state of the science of physiology; in which\nindeed our knowledge of causes is so imperfect, that we can neither\nexplain, nor could without specific experience have predicted, many of the\nfacts which are certified to us by the most ordinary observation.\nFortunately, we are much better informed as to the empirical laws of the\nphenomena, that is, the uniformities respecting which we can not yet\ndecide whether they are cases of causation, or mere results of it. Not\nonly has the order in which the facts of organization and life\nsuccessively manifest themselves, from the first germ of existence to\ndeath, been found to be uniform, and very accurately ascertainable; but,\nby a great application of the Method of Concomitant Variations to the\nentire facts of comparative anatomy and physiology, the characteristic\norganic structure corresponding to each class of functions has been\ndetermined with considerable precision. Whether these organic conditions\nare the whole of the conditions, and in many cases whether they are\nconditions at all, or mere collateral effects of some common cause, we are\nquite ignorant; nor are we ever likely to know, unless we could construct\nan organized body and try whether it would live.\n\nUnder such disadvantages do we, in cases of this description, attempt the\ninitial, or inductive step, in the application of the Deductive Method to\ncomplex phenomena. But such, fortunately, is not the common case. In\ngeneral, the laws of the causes on which the effect depends may be\nobtained by an induction from comparatively simple instances, or, at the\nworst, by deduction from the laws of simpler causes, so obtained. By\nsimple instances are meant, of course, those in which the action of each\ncause was not intermixed or interfered with, or not to any great extent,\nby other causes whose laws were unknown. And only when the induction which\nfurnished the premises to the Deductive method rested on such instances\nhas the application of such a method to the ascertainment of the laws of a\ncomplex effect, been attended with brilliant results.\n\n\u00a7 2. When the laws of the causes have been ascertained, and the first\nstage of the great logical operation now under discussion satisfactorily\naccomplished, the second part follows; that of determining from the laws\nof the causes what effect any given combination of those causes will\nproduce. This is a process of calculation, in the wider sense of the term;\nand very often involves processes of calculation in the narrowest sense.\nIt is a ratiocination; and when our knowledge of the causes is so perfect\nas to extend to the exact numerical laws which they observe in producing\ntheir effects, the ratiocination may reckon among its premises the\ntheorems of the science of number, in the whole immense extent of that\nscience. Not only are the most advanced truths of mathematics often\nrequired to enable us to compute an effect, the numerical law of which we\nalready know; but, even by the aid of those most advanced truths, we can\ngo but a little way. In so simple a case as the common problem of three\nbodies gravitating toward one another, with a force directly as their mass\nand inversely as the square of the distance, all the resources of the\ncalculus have not hitherto sufficed to obtain any general solution, but an\napproximate one. In a case a little more complex, but still one of the\nsimplest which arise in practice, that of the motion of a projectile, the\ncauses which affect the velocity and range (for example) of a cannon-ball\nmay be all known and estimated: the force of the gunpowder, the angle of\nelevation, the density of the air, the strength and direction of the wind;\nbut it is one of the most difficult of mathematical problems to combine\nall these, so as to determine the effect resulting from their collective\naction.\n\nBesides the theorems of number, those of geometry also come in as\npremises, where the effects take place in space, and involve motion and\nextension, as in mechanics, optics, acoustics, astronomy. But when the\ncomplication increases, and the effects are under the influence of so many\nand such shifting causes as to give no room either for fixed numbers, or\nfor straight lines and regular curves (as in the case of physiological, to\nsay nothing of mental and social phenomena), the laws of number and\nextension are applicable, if at all, only on that large scale on which\nprecision of details becomes unimportant. Although these laws play a\nconspicuous part in the most striking examples of the investigation of\nnature by the Deductive Method, as for example in the Newtonian theory of\nthe celestial motions, they are by no means an indispensable part of every\nsuch process. All that is essential in it is reasoning from a general law\nto a particular case, that is, determining by means of the particular\ncircumstances of that case, what result is required in that instance to\nfulfill the law. Thus in the Torricellian experiment, if the fact that air\nhas weight had been previously known, it would have been easy, without any\nnumerical data, to deduce from the general law of equilibrium, that the\nmercury would stand in the tube at such a height that the column of\nmercury would exactly balance a column of the atmosphere of equal\ndiameter; because, otherwise, equilibrium would not exist.\n\nBy such ratiocinations from the separate laws of the causes, we may, to a\ncertain extent, succeed in answering either of the following questions:\nGiven a certain combination of causes, what effect will follow? and, What\ncombination of causes, if it existed, would produce a given effect? In the\none case, we determine the effect to be expected in any complex\ncircumstances of which the different elements are known: in the other case\nwe learn, according to what law\u2014under what antecedent conditions\u2014a given\ncomplex effect will occur.\n\n\u00a7 3. But (it may here be asked) are not the same arguments by which the\nmethods of direct observation and experiment were set aside as illusory\nwhen applied to the laws of complex phenomena, applicable with equal force\nagainst the Method of Deduction? When in every single instance a\nmultitude, often an unknown multitude, of agencies, are clashing and\ncombining, what security have we that in our computation _a priori_ we\nhave taken all these into our reckoning? How many must we not generally be\nignorant of? Among those which we know, how probable that some have been\noverlooked; and, even were all included, how vain the pretense of summing\nup the effects of many causes, unless we know accurately the numerical law\nof each\u2014a condition in most cases not to be fulfilled; and even when it is\nfulfilled, to make the calculation transcends, in any but very simple\ncases, the utmost power of mathematical science with all its most modern\nimprovements.\n\nThese objections have real weight, and would be altogether unanswerable,\nif there were no test by which, when we employ the Deductive Method, we\nmight judge whether an error of any of the above descriptions had been\ncommitted or not. Such a test, however, there is: and its application\nforms, under the name of Verification, the third essential component part\nof the Deductive Method; without which all the results it can give have\nlittle other value than that of conjecture. To warrant reliance on the\ngeneral conclusions arrived at by deduction, these conclusions must be\nfound, on careful comparison, to accord with the results of direct\nobservation wherever it can be had. If, when we have experience to compare\nwith them, this experience confirms them, we may safely trust to them in\nother cases of which our specific experience is yet to come. But if our\ndeductions have led to the conclusion that from a particular combination\nof causes a given effect would result, then in all known cases where that\ncombination can be shown to have existed, and where the effect has not\nfollowed, we must be able to show (or at least to make a probable surmise)\nwhat frustrated it: if we can not, the theory is imperfect, and not yet to\nbe relied upon. Nor is the verification complete, unless some of the cases\nin which the theory is borne out by the observed result are of at least\nequal complexity with any other cases in which its application could be\ncalled for.\n\nIf direct observation and collation of instances have furnished us with\nany empirical laws of the effect (whether true in all observed cases, or\nonly true for the most part), the most effectual verification of which the\ntheory could be susceptible, would be, that it led deductively to those\nempirical laws; that the uniformities, whether complete or incomplete,\nwhich were observed to exist among the phenomena, were accounted for by\nthe laws of the causes\u2014were such as could not but exist if those be really\nthe causes by which the phenomena are produced. Thus it was very\nreasonably deemed an essential requisite of any true theory of the causes\nof the celestial motions, that it should lead by deduction to Kepler\u2019s\nlaws; which, accordingly, the Newtonian theory did.\n\nIn order, therefore, to facilitate the verification of theories obtained\nby deduction, it is important that as many as possible of the empirical\nlaws of the phenomena should be ascertained, by a comparison of instances,\nconformably to the Method of Agreement: as well as (it must be added) that\nthe phenomena themselves should be described, in the most comprehensive as\nwell as accurate manner possible; by collecting from the observation of\nparts, the simplest possible correct expressions for the corresponding\nwholes: as when the series of the observed places of a planet was first\nexpressed by a circle, then by a system of epicycles, and subsequently by\nan ellipse.\n\nIt is worth remarking, that complex instances which would have been of no\nuse for the discovery of the simple laws into which we ultimately analyze\ntheir phenomena, nevertheless, when they have served to verify the\nanalysis, become additional evidence of the laws themselves. Although we\ncould not have got at the law from complex cases, still when the law, got\nat otherwise, is found to be in accordance with the result of a complex\ncase, that case becomes a new experiment on the law, and helps to confirm\nwhat it did not assist to discover. It is a new trial of the principle in\na different set of circumstances; and occasionally serves to eliminate\nsome circumstance not previously excluded, and the exclusion of which\nmight require an experiment impossible to be executed. This was strikingly\nconspicuous in the example formerly quoted, in which the difference\nbetween the observed and the calculated velocity of sound was ascertained\nto result from the heat extricated by the condensation which takes place\nin each sonorous vibration. This was a trial, in new circumstances, of the\nlaw of the development of heat by compression; and it added materially to\nthe proof of the universality of that law. Accordingly, any law of nature\nis deemed to have gained in point of certainty, by being found to explain\nsome complex case which had not previously been thought of in connection\nwith it; and this indeed is a consideration to which it is the habit of\nscientific inquirers to attach rather too much value than too little.\n\nTo the Deductive Method, thus characterized in its three constituent\nparts, Induction, Ratiocination, and Verification, the human mind is\nindebted for its most conspicuous triumphs in the investigation of nature.\nTo it we owe all the theories by which vast and complicated phenomena are\nembraced under a few simple laws, which, considered as the laws of those\ngreat phenomena, could never have been detected by their direct study. We\nmay form some conception of what the method has done for us from the case\nof the celestial motions: one of the simplest among the greater instances\nof the Composition of Causes, since (except in a few cases not of primary\nimportance) each of the heavenly bodies may be considered, without\nmaterial inaccuracy, to be never at one time influenced by the attraction\nof more than two bodies, the sun and one other planet or satellite;\nmaking, with the reaction of the body itself, and the force generated by\nthe body\u2019s own motion and acting in the direction of the tangent, only\nfour different agents on the concurrence of which the motions of that body\ndepend; a much smaller number, no doubt, than that by which any other of\nthe great phenomena of nature is determined or modified. Yet how could we\never have ascertained the combination of forces on which the motions of\nthe earth and planets are dependent, by merely comparing the orbits or\nvelocities of different planets, or the different velocities or positions\nof the same planet? Notwithstanding the regularity which manifests itself\nin those motions, in a degree so rare among the effects of concurrence of\ncauses; and although the periodical recurrence of exactly the same effect,\naffords positive proof that all the combinations of causes which occur at\nall, recur periodically; we should not have known what the causes were, if\nthe existence of agencies precisely similar on our own earth had not,\nfortunately, brought the causes themselves within the reach of\nexperimentation under simple circumstances. As we shall have occasion to\nanalyze, further on, this great example of the Method of Deduction, we\nshall not occupy any time with it here, but shall proceed to that\nsecondary application of the Deductive Method, the result of which is not\nto prove laws of phenomena, but to explain them.\n\n\n\n\n                               Chapter XII.\n\n\nOf The Explanation Of Laws Of Nature.\n\n\n\u00a7 1. The deductive operation by which we derive the law of an effect from\nthe laws of the causes, the concurrence of which gives rise to it, may be\nundertaken either for the purpose of discovering the law, or of explaining\na law already discovered. The word _explanation_ occurs so continually,\nand holds so important a place in philosophy, that a little time spent in\nfixing the meaning of it will be profitably employed.\n\nAn individual fact is said to be explained, by pointing out its cause,\nthat is, by stating the law or laws of causation, of which its production\nis an instance. Thus, a conflagration is explained, when it is proved to\nhave arisen from a spark falling into the midst of a heap of combustibles.\nAnd in a similar manner, a law or uniformity in nature is said to be\nexplained, when another law or laws are pointed out, of which that law\nitself is but a case, and from which it could be deduced.\n\n\u00a7 2. There are three distinguishable sets of circumstances in which a law\nof causation may be explained from, or, as it also is often expressed,\nresolved into, other laws.\n\nThe first is the case already so fully considered; an intermixture of\nlaws, producing a joint effect equal to the sum of the effects of the\ncauses taken separately. The law of the complex effect is explained, by\nbeing resolved into the separate laws of the causes which contribute to\nit. Thus, the law of the motion of a planet is resolved into the law of\nthe acquired force, which tends to produce a uniform motion in the\ntangent, and the law of the centripetal force, which tends to produce an\naccelerating motion toward the sun; the real motion being a compound of\nthe two.\n\nIt is necessary here to remark, that in this resolution of the law of a\ncomplex effect, the laws of which it is compounded are not the only\nelements. It is resolved into the laws of the separate causes, together\nwith the fact of their co-existence. The one is as essential an ingredient\nas the other; whether the object be to discover the law of the effect, or\nonly to explain it. To deduce the laws of the heavenly motions, we require\nnot only to know the law of a rectilineal and that of a gravitative force,\nbut the existence of both these forces in the celestial regions, and even\ntheir relative amount. The complex laws of causation are thus resolved\ninto two distinct kinds of elements: the one, simpler laws of causation,\nthe other (in the aptly selected expression of Dr. Chalmers) collocations;\nthe collocations consisting in the existence of certain agents or powers,\nin certain circumstances of place and time. We shall hereafter have\noccasion to return to this distinction, and to dwell on it at such length\nas dispenses with the necessity of further insisting on it here. The first\nmode, then, of the explanation of Laws of Causation, is when the law of an\neffect is resolved into the various tendencies of which it is the result,\ntogether with the laws of those tendencies.\n\n\u00a7 3. A second case is when, between what seemed the cause and what was\nsupposed to be its effect, further observation detects an intermediate\nlink; a fact caused by the antecedent, and in its turn causing the\nconsequent; so that the cause at first assigned is but the remote cause,\noperating through the intermediate phenomenon. A seemed the cause of C,\nbut it subsequently appeared that A was only the cause of B, and that it\nis B which was the cause of C. For example: mankind were aware that the\nact of touching an outward object caused a sensation. It was subsequently\ndiscovered that after we have touched the object, and before we experience\nthe sensation, some change takes place in a kind of thread called a nerve,\nwhich extends from our outward organs to the brain. Touching the object,\ntherefore, is only the remote cause of our sensation; that is, not the\ncause, properly speaking, but the cause of the cause; the real cause of\nthe sensation is the change in the state of the nerve. Future experience\nmay not only give us more knowledge than we now have of the particular\nnature of this change, but may also interpolate another link: between the\ncontact (for example) of the object with our outward organs, and the\nproduction of the change of state in the nerve, there may take place some\nelectric phenomenon, or some phenomenon of a nature not resembling the\neffects of any known agency. Hitherto, however, no such intermediate link\nhas been discovered; and the touch of the object must be considered,\nprovisionally, as the proximate cause of the affection of the nerve. The\nsequence, therefore, of a sensation of touch on contact with an object is\nascertained not to be an ultimate law; it is resolved, as the phrase is,\ninto two other laws\u2014the law that contact with an object produces an\naffection of the nerve, and the law that an affection of the nerve\nproduces sensation.\n\nTo take another example: the more powerful acids corrode or blacken\norganic compounds. This is a case of causation, but of remote causation;\nand is said to be explained when it is shown that there is an intermediate\nlink, namely, the separation of some of the chemical elements of the\norganic structure from the rest, and their entering into combination with\nthe acid. The acid causes this separation of the elements, and the\nseparation of the elements causes the disorganization, and often the\ncharring of the structure. So, again, chlorine extracts coloring matters\n(whence its efficacy in bleaching) and purifies the air from infection.\nThis law is resolved into the two following laws: Chlorine has a powerful\naffinity for bases of all kinds, particularly metallic bases and hydrogen:\nsuch bases are essential elements of coloring matters and contagious\ncompounds, which substances, therefore, are decomposed and destroyed by\nchlorine.\n\n\u00a7 4. It is of importance to remark, that when a sequence of phenomena is\nthus resolved into other laws, they are always laws more general than\nitself. The law that A is followed by C, is less general than either of\nthe laws which connect B with C and A with B. This will appear from very\nsimple considerations.\n\nAll laws of causation are liable to be counteracted or frustrated, by the\nnon-fulfillment of some negative condition; the tendency, therefore, of B\nto produce C may be defeated. Now the law that A produces B, is equally\nfulfilled whether B is followed by C or not; but the law that A produces C\nby means of B, is of course only fulfilled when B is really followed by C,\nand is, therefore, less general than the law that A produces B. It is also\nless general than the law that B produces C. For B may have other causes\nbesides A; and as A produces C only by means of B, while B produces C,\nwhether it has itself been produced by A or by any thing else, the second\nlaw embraces a greater number of instances, covers as it were a greater\nspace of ground, than the first.\n\nThus, in our former example, the law that the contact of an object causes\na change in the state of the nerve, is more general than the law that\ncontact with an object causes sensation, since, for aught we know, the\nchange in the nerve may equally take place when, from a counteracting\ncause, as, for instance, strong mental excitement, the sensation does not\nfollow; as in a battle, where wounds are sometimes received without any\nconsciousness of receiving them. And again, the law that change in the\nstate of a nerve produces sensation, is more general than the law that\ncontact with an object produces sensation; since the sensation equally\nfollows the change in the nerve when not produced by contact with an\nobject, but by some other cause; as in the well-known case, when a person\nwho has lost a limb feels the same sensation which he has been accustomed\nto call a pain in the limb.\n\nNot only are the laws of more immediate sequence into which the law of a\nremote sequence is resolved, laws of greater generality than that law is,\nbut (as a consequence of, or rather as implied in, their greater\ngenerality) they are more to be relied on; there are fewer chances of\ntheir being ultimately found not to be universally true. From the moment\nwhen the sequence of A and C is shown not to be immediate, but to depend\non an intervening phenomenon, then, however constant and invariable the\nsequence of A and C has hitherto been found, possibilities arise of its\nfailure, exceeding those which can effect either of the more immediate\nsequences, A, B, and B, C. The tendency of A to produce C may be defeated\nby whatever is capable of defeating either the tendency of A to produce B,\nor the tendency of B to produce C; it is, therefore, twice as liable to\nfailure as either of those more elementary tendencies; and the\ngeneralization that A is always followed by C, is twice as likely to be\nfound erroneous. And so of the converse generalization, that C is always\npreceded and caused by A; which will be erroneous not only if there should\nhappen to be a second immediate mode of production of C itself, but\nmoreover if there be a second mode of production of B, the immediate\nantecedent of C in the sequence.\n\nThe resolution of the one generalization into the other two, not only\nshows that there are possible limitations of the former, from which its\ntwo elements are exempt, but shows also where these are to be looked for.\nAs soon as we know that B intervenes between A and C, we also know that if\nthere be cases in which the sequence of A and C does not hold, these are\nmost likely to be found by studying the effects or the conditions of the\nphenomenon B.\n\nIt appears, then, that in the second of the three modes in which a law may\nbe resolved into other laws, the latter are more general, that is, extend\nto more cases, and are also less likely to require limitation from\nsubsequent experience, than the law which they serve to explain. They are\nmore nearly unconditional; they are defeated by fewer contingencies; they\nare a nearer approach to the universal truth of nature. The same\nobservations are still more evidently true with regard to the first of the\nthree modes of resolution. When the law of an effect of combined forces is\nresolved into the separate laws of the causes, the nature of the case\nimplies that the law of the effect is less general than the law of any of\nthe causes, since it only holds when they are combined; while the law of\nany one of the causes holds good both then, and also when that cause acts\napart from the rest.\n\nIt is also manifest that the complex law is liable to be oftener\nunfulfilled than any one of the simpler laws of which it is the result,\nsince every contingency which defeats any of the laws prevents so much of\nthe effect as depends on it, and thereby defeats the complex law. The mere\nrusting, for example, of some small part of a great machine, often\nsuffices entirely to prevent the effect which ought to result from the\njoint action of all the parts. The law of the effect of a combination of\ncauses is always subject to the whole of the negative conditions which\nattach to the action of all the causes severally.\n\nThere is another and an equally strong reason why the law of a complex\neffect must be less general than the laws of the causes which conspire to\nproduce it. The same causes, acting according to the same laws, and\ndiffering only in the proportions in which they are combined, often\nproduce effects which differ not merely in quantity, but in kind. The\ncombination of a centripetal with a projectile force, in the proportions\nwhich obtain in all the planets and satellites of our solar system, gives\nrise to an elliptical motion; but if the ratio of the two forces to each\nother were slightly altered, it is demonstrated that the motion produced\nwould be in a circle, or a parabola, or an hyperbola; and it is thought\nthat in the case of some comets one of these is probably the fact. Yet the\nlaw of the parabolic motion would be resolvable into the very same simple\nlaws into which that of the elliptical motion is resolved, namely, the law\nof the permanence of rectilineal motion, and the law of gravitation. If,\ntherefore, in the course of ages, some circumstance were to manifest\nitself which, without defeating the law of either of those forces, should\nmerely alter their proportion to one another (such as the shock of some\nsolid body, or even the accumulating effect of the resistance of the\nmedium in which astronomers have been led to surmise that the motions of\nthe heavenly bodies take place), the elliptical motion might be changed\ninto a motion in some other conic section; and the complex law, that the\nplanetary motions take place in ellipses, would be deprived of its\nuniversality, though the discovery would not at all detract from the\nuniversality of the simpler laws into which that complex law is resolved.\nThe law, in short, of each of the concurrent causes remains the same,\nhowever their collocations may vary; but the law of their joint effect\nvaries with every difference in the collocations. There needs no more to\nshow how much more general the elementary laws must be than any of the\ncomplex laws which are derived from them.\n\n\u00a7 5. Besides the two modes which have been treated of, there is a third\nmode in which laws are resolved into one another; and in this it is\nself-evident that they are resolved into laws more general than\nthemselves. This third mode is the _subsumption_ (as it has been called)\nof one law under another; or (what comes to the same thing) the gathering\nup of several laws into one more general law which includes them all. The\nmost splendid example of this operation was when terrestrial gravity and\nthe central force of the solar system were brought together under the\ngeneral law of gravitation. It had been proved antecedently that the earth\nand the other planets tend to the sun; and it had been known from the\nearliest times that terrestrial bodies tend toward the earth. These were\nsimilar phenomena; and to enable them both to be subsumed under one law,\nit was only necessary to prove that, as the effects were similar in\nquality so also they, as to quantity, conform to the same rules. This was\nfirst shown to be true of the moon, which agreed with terrestrial objects\nnot only in tending to a centre, but in the fact that this centre was the\nearth. The tendency of the moon toward the earth being ascertained to vary\nas the inverse square of the distance, it was deduced from this, by direct\ncalculation, that if the moon were as near to the earth as terrestrial\nobjects are, and the acquired force in the direction of the tangent were\nsuspended, the moon would fall toward the earth through exactly as many\nfeet in a second as those objects do by virtue of their weight. Hence the\ninference was irresistible, that the moon also tends to the earth by\nvirtue of its weight: and that the two phenomena, the tendency of the moon\nto the earth and the tendency of terrestrial objects to the earth, being\nnot only similar in quality, but, when in the same circumstances,\nidentical in quantity, are cases of one and the same law of causation. But\nthe tendency of the moon to the earth, and the tendency of the earth and\nplanets to the sun, were already known to be cases of the same law of\ncausation; and thus the law of all these tendencies, and the law of\nterrestrial gravity, were recognized as identical, and were subsumed under\none general law, that of gravitation.\n\nIn a similar manner, the laws of magnetic phenomena have more recently\nbeen subsumed under known laws of electricity. It is thus that the most\ngeneral laws of nature are usually arrived at: we mount to them by\nsuccessive steps. For, to arrive by correct induction at laws which hold\nunder such an immense variety of circumstances, laws so general as to be\nindependent of any varieties of space or time which we are able to\nobserve, requires for the most part many distinct sets of experiments or\nobservations, conducted at different times and by different people. One\npart of the law is first ascertained, afterward another part: one set of\nobservations teaches us that the law holds good under some conditions,\nanother that it holds good under other conditions, by combining which\nobservations we find that it holds good under conditions much more\ngeneral, or even universally. The general law, in this case, is literally\nthe sum of all the partial ones; it is a recognition of the same sequence\nin different sets of instances; and may, in fact, be regarded as merely\none step in the process of elimination. The tendency of bodies toward one\nanother, which we now call gravity, had at first been observed only on the\nearth\u2019s surface, where it manifested itself only as a tendency of all\nbodies toward the earth, and might, therefore, be ascribed to a peculiar\nproperty of the earth itself: one of the circumstances, namely, the\nproximity of the earth, had not been eliminated. To eliminate this\ncircumstance required a fresh set of instances in other parts of the\nuniverse: these we could not ourselves create; and though nature had\ncreated them for us, we were placed in very unfavorable circumstances for\nobserving them. To make these observations, fell naturally to the lot of a\ndifferent set of persons from those who studied terrestrial phenomena; and\nhad, indeed, been a matter of great interest at a time when the idea of\nexplaining celestial facts by terrestrial laws was looked upon as the\nconfounding of an indefeasible distinction. When, however, the celestial\nmotions were accurately ascertained, and the deductive processes\nperformed, from which it appeared that their laws and those of terrestrial\ngravity corresponded, those celestial observations became a set of\ninstances which exactly eliminated the circumstance of proximity to the\nearth; and proved that in the original case, that of terrestrial objects,\nit was not the earth, as such, that caused the motion or the pressure, but\nthe circumstance common to that case with the celestial instances, namely,\nthe presence of some great body within certain limits of distance.\n\n\u00a7 6. There are, then, three modes of explaining laws of causation, or,\nwhich is the same thing, resolving them into other laws. First, when the\nlaw of an effect of combined causes is resolved into the separate laws of\nthe causes, together with the fact of their combination. Secondly, when\nthe law which connects any two links, not proximate, in a chain of\ncausation, is resolved into the laws which connect each with the\nintermediate links. Both of these are cases of resolving one law into two\nor more; in the third, two or more are resolved into one: when, after the\nlaw has been shown to hold good in several different classes of cases, we\ndecide that what is true in each of these classes of cases, is true under\nsome more general supposition, consisting of what all those classes of\ncases have in common. We may here remark that this last operation involves\nnone of the uncertainties attendant on induction by the Method of\nAgreement, since we need not suppose the result to be extended by way of\ninference to any new class of cases different from those by the comparison\nof which it was engendered.\n\nIn all these three processes, laws are, as we have seen, resolved into\nlaws more general than themselves; laws extending to all the cases which\nthe former extended to, and others besides. In the first two modes they\nare also resolved into laws more certain, in other words, more universally\ntrue than themselves; they are, in fact, proved not to be themselves laws\nof nature, the character of which is to be universally true, but _results_\nof laws of nature, which may be only true conditionally, and for the most\npart. No difference of this sort exists in the third case; since here the\npartial laws are, in fact, the very same law as the general one, and any\nexception to them would be an exception to it too.\n\nBy all the three processes, the range of deductive science is extended;\nsince the laws, thus resolved, may be thenceforth deduced demonstratively\nfrom the laws into which they are resolved. As already remarked, the same\ndeductive process which proves a law or fact of causation if unknown,\nserves to explain it when known.\n\nThe word explanation is here used in its philosophical sense. What is\ncalled explaining one law of nature by another, is but substituting one\nmystery for another; and does nothing to render the general course of\nnature other than mysterious: we can no more assign a _why_ for the more\nextensive laws than for the partial ones. The explanation may substitute a\nmystery which has become familiar, and has grown to _seem_ not mysterious,\nfor one which is still strange. And this is the meaning of explanation, in\ncommon parlance. But the process with which we are here concerned often\ndoes the very contrary: it resolves a phenomenon with which we are\nfamiliar into one of which we previously knew little or nothing; as when\nthe common fact of the fall of heavy bodies was resolved into the tendency\nof all particles of matter toward one another. It must be kept constantly\nin view, therefore, that in science, those who speak of explaining any\nphenomenon mean (or should mean) pointing out not some more familiar, but\nmerely some more general, phenomenon, of which it is a partial\nexemplification; or some laws of causation which produce it by their joint\nor successive action, and from which, therefore, its conditions may be\ndetermined deductively. Every such operation brings us a step nearer\ntoward answering the question which was stated in a previous chapter as\ncomprehending the whole problem of the investigation of nature, viz.: what\nare the fewest assumptions, which being granted, the order of nature as it\nexists would be the result? What are the fewest, general propositions from\nwhich all the uniformities existing in nature could be deduced?\n\nThe laws, thus explained or resolved, are sometimes said to be _accounted\nfor_; but the expression is incorrect, if taken to mean any thing more\nthan what has been already stated. In minds not habituated to accurate\nthinking, there is often a confused notion that the general laws are the\n_causes_ of the partial ones; that the law of general gravitation, for\nexample, causes the phenomenon of the fall of bodies to the earth. But to\nassert this would be a misuse of the word cause: terrestrial gravity is\nnot an effect of general gravitation, but a _case_ of it; that is, one\nkind of the particular instances in which that general law obtains. To\naccount for a law of nature means, and can mean, nothing more than to\nassign other laws more general, together with collocations, which laws and\ncollocations being supposed, the partial law follows without any\nadditional supposition.\n\n\n\n\n                              Chapter XIII.\n\n\nMiscellaneous Examples Of The Explanation Of Laws Of Nature.\n\n\n\u00a7 1. The most striking example which the history of science presents, of\nthe explanation of laws of causation and other uniformities of sequence\namong special phenomena, by resolving them into laws of greater simplicity\nand generality, is the great Newtonian generalization; respecting which\ntypical instance, so much having already been said, it is sufficient to\ncall attention to the great number and variety of the special observed\nuniformities, which are in this case accounted for, either as particular\ncases, or as consequences, of one very simple law of universal nature. The\nsimple fact of a tendency of every particle of matter toward every other\nparticle, varying inversely as the square of the distance, explains the\nfall of bodies to the earth, the revolutions of the planets and\nsatellites, the motions (so far as known) of comets, and all the various\nregularities which have been observed in these special phenomena; such as\nthe elliptical orbits, and the variations from exact ellipses; the\nrelation between the solar distances of the planets and the duration of\ntheir revolutions; the precession of the equinoxes; the tides, and a vast\nnumber of minor astronomical truths.\n\nMention has also been made in the preceding chapter of the explanation of\nthe phenomena of magnetism from laws of electricity; the special laws of\nmagnetic agency having been affiliated by deduction to observed laws of\nelectric action, in which they have ever since been considered to be\nincluded as special cases. An example not so complete in itself, but even\nmore fertile in consequences, having been the starting-point of the really\nscientific study of physiology, is the affiliation, commenced by Bichat,\nand carried on by subsequent biologists, of the properties of the bodily\norgans, to the elementary properties of the tissues into which they are\nanatomically decomposed.\n\nAnother striking instance is afforded by Dalton\u2019s generalization, commonly\nknown as the atomic theory. It had been known from the very commencement\nof accurate chemical observation, that any two bodies combine chemically\nwith one another in only a certain number of proportions; but those\nproportions were in each case expressed by a percentage\u2014so many parts (by\nweight) of each ingredient, in 100 of the compound (say 35 and a fraction\nof one element, 64 and a fraction of the other); in which mode of\nstatement no relation was perceived between the proportion in which a\ngiven element combines with one substance, and that in which it combines\nwith others. The great step made by Dalton consisted in perceiving that a\nunit of weight might be established for each substance, such that by\nsupposing the substance to enter into all its combinations in the ratio\neither of that unit, or of some low multiple of that unit, all the\ndifferent proportions, previously expressed by percentages, were found to\nresult. Thus 1 being assumed as the unit of hydrogen, if 8 were then taken\nas that of oxygen, the combination of one unit of hydrogen with one unit\nof oxygen would produce the exact proportion of weight between the two\nsubstances which is known to exist in water; the combination of one unit\nof hydrogen with two units of oxygen would produce the proportion which\nexists in the other compound of the same two elements, called peroxide of\nhydrogen; and the combinations of hydrogen and of oxygen with all other\nsubstances, would correspond with the supposition that those elements\nenter into combination by single units, or twos, or threes, of the numbers\nassigned to them, 1 and 8, and the other substances by ones or twos or\nthrees of other determinate numbers proper to each. The result is that a\ntable of the equivalent numbers, or, as they are called, atomic weights,\nof all the elementary substances, comprises in itself, and scientifically\nexplains, all the proportions in which any substance, elementary or\ncompound, is found capable of entering into chemical combination with any\nother substance whatever.\n\n\u00a7 2. Some interesting cases of the explanation of old uniformities by\nnewly ascertained laws are afforded by the researches of Professor Graham.\nThat eminent chemist was the first who drew attention to the distinction\nwhich may be made of all substances into two classes, termed by him\ncrystalloids and colloids; or rather, of all states of matter into the\ncrystalloid and the colloidal states, for many substances are capable of\nexisting in either. When in the colloidal state, their sensible properties\nare very different from those of the same substance when crystallized, or\nwhen in a state easily susceptible of crystallization. Colloid substances\npass with extreme difficulty and slowness into the crystalline state, and\nare extremely inert in all the ordinary chemical relations. Substances in\nthe colloid state are almost always, when combined with water, more or\nless viscous or gelatinous. The most prominent examples of the state are\ncertain animal and vegetable substances, particularly gelatine, albumen,\nstarch, the gums, caramel, tannin, and some others. Among substances not\nof organic origin, the most notable instances are hydrated silicic acid,\nand hydrated alumina, with other metallic peroxides of the aluminous\nclass.\n\nNow it is found, that while colloidal substances are easily penetrated by\nwater, and by the solutions of crystalloid substances, they are very\nlittle penetrable by one another: which enabled Professor Graham to\nintroduce a highly effective process (termed dialysis) for separating the\ncrystalloid substances contained in any liquid mixture, by passing them\nthrough a thin septum of colloidal matter, which does not suffer any thing\ncolloidal to pass, or suffers it only in very minute quantity. This\nproperty of colloids enabled Mr. Graham to account for a number of special\nresults of observation, not previously explained.\n\nFor instance, \u201cwhile soluble crystalloids are always highly sapid, soluble\ncolloids are singularly insipid,\u201d as might be expected; for, as the\nsentient extremities of the nerves of the palate \u201care probably protected\nby a colloidal membrane,\u201d impermeable to other colloids, a colloid, when\ntasted, probably never reaches those nerves. Again, \u201cit has been observed\nthat vegetable gum is not digested in the stomach; the coats of that organ\ndialyse the soluble food, absorbing crystalloids, and rejecting all\ncolloids.\u201d One of the mysterious processes accompanying digestion, the\nsecretion of free muriatic acid by the coats of the stomach, obtains a\nprobable hypothetical explanation through the same law. Finally, much\nlight is thrown upon the observed phenomena of osmose (the passage of\nfluids outward and inward through animal membranes) by the fact that the\nmembranes are colloidal. In consequence, the water and saline solutions\ncontained in the animal body pass easily and rapidly through the\nmembranes, while the substances directly applicable to nutrition, which\nare mostly colloidal, are detained by them.(154)\n\nThe property which salt possesses of preserving animal substances from\nputrefaction is resolved by Liebig into two more general laws, the strong\nattraction of salt for water, and the necessity of the presence of water\nas a condition of putrefaction. The intermediate phenomenon which is\ninterpolated between the remote cause and the effect, can here be not\nmerely inferred but seen; for it is a familiar fact, that flesh upon which\nsalt has been thrown is speedily found swimming in brine.\n\nThe second of the two factors (as they may be termed) into which the\npreceding law has been resolved, the necessity of water to putrefaction,\nitself affords an additional example of the Resolution of Laws. The law\nitself is proved by the Method of Difference, since flesh completely dried\nand kept in a dry atmosphere does not putrefy; as we see in the case of\ndried provisions and human bodies in very dry climates. A deductive\nexplanation of this same law results from Liebig\u2019s speculations. The\nputrefaction of animal and other azotized bodies is a chemical process, by\nwhich they are gradually dissipated in a gaseous form, chiefly in that of\ncarbonic acid and ammonia; now to convert the carbon of the animal\nsubstance into carbonic acid requires oxygen, and to convert the azote\ninto ammonia requires hydrogen, which are the elements of water. The\nextreme rapidity of the putrefaction of azotized substances, compared with\nthe gradual decay of non-azotized bodies (such as wood and the like) by\nthe action of oxygen alone, he explains from the general law that\nsubstances are much more easily decomposed by the action of two different\naffinities upon two of their elements than by the action of only one.\n\n\u00a7 3. Among the many important properties of the nervous system which have\neither been first discovered or strikingly illustrated by Dr.\nBrown-S\u00e9quard, I select the reflex influence of the nervous system on\nnutrition and secretion. By reflex nervous action is meant, action which\none part of the nervous system exerts over another part, without any\nintermediate action on the brain, and consequently without consciousness;\nor which, if it does pass through the brain, at least produces its effects\nindependently of the will. There are many experiments which prove that\nirritation of a nerve in one part of the body may in this manner excite\npowerful action in another part; for example, food injected into the\nstomach through a divided \u0153sophagus, nevertheless produces secretion of\nsaliva; warm water injected into the bowels, and various other irritations\nof the lower intestines, have been found to excite secretion of the\ngastric juice, and so forth. The reality of the power being thus proved,\nits agency explains a great variety of apparently anomalous phenomena; of\nwhich I select the following from Dr. Brown-S\u00e9quard\u2019s _Lectures on the\nNervous System_:\n\nThe production of tears by irritation of the eye, or of the mucous\nmembrane of the nose;\n\nThe secretions of the eye and nose increased by exposure of other parts of\nthe body to cold;\n\nInflammation of the eye, especially when of traumatic origin, very\nfrequently excites a similar affection in the other eye, which may be\ncured by section of the intervening nerve;\n\nLoss of sight sometimes produced by neuralgia, and has been known to be at\nonce cured by the extirpation (for instance) of a carious tooth;\n\nEven cataract has been produced in a healthy eye by cataract in the other\neye, or by neuralgia, or by a wound of the frontal nerve;\n\nThe well-known phenomenon of a sudden stoppage of the heart\u2019s action, and\nconsequent death, produced by irritation of some of the nervous\nextremities; _e.g._, by drinking very cold water, or by a blow on the\nabdomen, or other sudden excitation of the abdominal sympathetic nerve,\nthough this nerve may be irritated to any extent without stopping the\nheart\u2019s action, if a section be made of the communicating nerves;\n\nThe extraordinary effects produced on the internal organs by an extensive\nburn on the surface of the body, consisting in violent inflammation of the\ntissues of the abdomen, chest, or head, which, when death ensues from this\nkind of injury, is one of the most frequent causes of it;\n\nParalysis and an\u00e6sthesia of one part of the body from neuralgia in another\npart; and muscular atrophy from neuralgia, even when there is no\nparalysis;\n\nTetanus produced by the lesion of a nerve. Dr. Brown-S\u00e9quard thinks it\nhighly probable that hydrophobia is a phenomenon of a similar nature;\n\nMorbid changes in the nutrition of the brain and spinal cord, manifesting\nthemselves by epilepsy, chorea, hysteria, and other diseases, occasioned\nby lesion of some of the nervous extremities in remote places, as by\nworms, calculi, tumors, carious bones, and in some cases even by very\nslight irritations of the skin.\n\n\u00a7 4. From the foregoing and similar instances, we may see the importance,\nwhen a law of nature previously unknown has been brought to light, or when\nnew light has been thrown upon a known law by experiment, of examining all\ncases which present the conditions necessary for bringing that law into\naction; a process fertile in demonstrations of special laws previously\nunsuspected, and explanations of others already empirically known.\n\nFor instance, Faraday discovered by experiment, that voltaic electricity\ncould be evolved from a natural magnet, provided a conducting body were\nset in motion at right angles to the direction of the magnet; and this he\nfound to hold not only of small magnets, but of that great magnet, the\nearth. The law being thus established experimentally, that electricity is\nevolved, by a magnet, and a conductor moving at right angles to the\ndirection of its poles, we may now look out for fresh instances in which\nthese conditions meet. Wherever a conductor moves or revolves at right\nangles to the direction of the earth\u2019s magnetic poles, there we may expect\nan evolution of electricity. In the northern regions, where the polar\ndirection is nearly perpendicular to the horizon, all horizontal motions\nof conductors will produce electricity; horizontal wheels, for example,\nmade of metal; likewise all running streams will evolve a current of\nelectricity, which will circulate round them; and the air thus charged\nwith electricity may be one of the causes of the Aurora Borealis. In the\nequatorial regions, on the contrary, upright wheels placed parallel to the\nequator will originate a voltaic circuit, and water-falls will naturally\nbecome electric.\n\nFor a second example, it has been proved, chiefly by the researches of\nProfessor Graham, that gases have a strong tendency to permeate animal\nmembranes, and diffuse themselves through the spaces which such membranes\ninclose, notwithstanding the presence of other gases in those spaces.\nProceeding from this general law, and reviewing a variety of cases in\nwhich gases lie contiguous to membranes, we are enabled to demonstrate or\nto explain the following more special laws: 1st. The human or animal body,\nwhen surrounded with any gas not already contained within the body,\nabsorbs it rapidly; such, for instance, as the gases of putrefying\nmatters: which helps to explain malaria. 2d. The carbonic acid gas of\neffervescing drinks, evolved in the stomach, permeates its membranes, and\nrapidly spreads through the system. 3d. Alcohol taken into the stomach\npasses into vapor, and spreads through the system with great rapidity\n(which, combined with the high combustibility of alcohol, or in other\nwords its ready combination with oxygen, may perhaps help to explain the\nbodily warmth immediately consequent on drinking spirituous liquors). 4th.\nIn any state of the body in which peculiar gases are formed within it,\nthese will rapidly exhale through all parts of the body; and hence the\nrapidity with which, in certain states of disease, the surrounding\natmosphere becomes tainted. 5th. The putrefaction of the interior parts of\na carcass will proceed as rapidly as that of the exterior, from the ready\npassage outward of the gaseous products. 6th. The exchange of oxygen and\ncarbonic acid in the lungs is not prevented, but rather promoted, by the\nintervention of the membrane of the lungs and the coats of the\nblood-vessels between the blood and the air. It is necessary, however,\nthat there should be a substance in the blood with which the oxygen of the\nair may immediately combine; otherwise, instead of passing into the blood,\nit would permeate the whole organism: and it is necessary that the\ncarbonic acid, as it is formed in the capillaries, should also find a\nsubstance in the blood with which it can combine; otherwise it would leave\nthe body at all points, instead of being discharged through the lungs.\n\n\u00a7 5. The following is a deduction which confirms, by explaining, the\nempirical generalization, that soda powders weaken the human system. These\npowders, consisting of a mixture of tartaric acid with bicarbonate of\nsoda, from which the carbonic acid is set free, must pass into the stomach\nas tartrate of soda. Now, neutral tartrates, citrates, and acetates of the\nalkalis are found, in their passage through the system, to be changed into\ncarbonates; and to convert a tartrate into a carbonate requires an\nadditional quantity of oxygen, the abstraction of which must lessen the\noxygen destined for assimilation with the blood, on the quantity of which\nthe vigorous action of the human system partly depends.\n\nThe instances of new theories agreeing with and explaining old\nempiricisms, are innumerable. All the just remarks made by experienced\npersons on human character and conduct, are so many special laws, which\nthe general laws of the human mind explain and resolve. The empirical\ngeneralizations on which the operations of the arts have usually been\nfounded, are continually justified and confirmed on the one hand, or\ncorrected and improved on the other, by the discovery of the simpler\nscientific laws on which the efficacy of those operations depends. The\neffects of the rotation of crops, of the various manures, and other\nprocesses of improved agriculture, have been for the first time resolved\nin our own day into known laws of chemical and organic action, by Davy,\nLiebig, and others. The processes of the medical art are even now mostly\nempirical: their efficacy is concluded, in each instance, from a special\nand most precarious experimental generalization: but as science advances\nin discovering the simple laws of chemistry and physiology, progress is\nmade in ascertaining the intermediate links in the series of phenomena,\nand the more general laws on which they depend; and thus, while the old\nprocesses are either exploded, or their efficacy, in so far as real,\nexplained, better processes, founded on the knowledge of proximate causes,\nare continually suggested and brought into use.(155) Many even of the\ntruths of geometry were generalizations from experience before they were\ndeduced from first principles. The quadrature of the cycloid is said to\nhave been first effected by measurement, or rather by weighing a cycloidal\ncard, and comparing its weight with that of a piece of similar card of\nknown dimensions.\n\n\u00a7 6. To the foregoing examples from physical science, let us add another\nfrom mental. The following is one of the simple laws of mind: Ideas of a\npleasurable or painful character form associations more easily and\nstrongly than other ideas, that is, they become associated after fewer\nrepetitions, and the association is more durable. This is an experimental\nlaw, grounded on the Method of Difference. By deduction from this law,\nmany of the more special laws which experience shows to exist among\nparticular mental phenomena may be demonstrated and explained: the ease\nand rapidity, for instance, with which thoughts connected with our\npassions or our more cherished interests are excited, and the firm hold\nwhich the facts relating to them have on our memory; the vivid\nrecollection we retain of minute circumstances which accompanied any\nobject or event that deeply interested us, and of the times and places in\nwhich we have been very happy or very miserable; the horror with which we\nview the accidental instrument of any occurrence which shocked us, or the\nlocality where it took place and the pleasure we derive from any memorial\nof past enjoyment; all these effects being proportional to the sensibility\nof the individual mind, and to the consequent intensity of the pain or\npleasure from which the association originated. It has been suggested by\nthe able writer of a biographical sketch of Dr. Priestley in a monthly\nperiodical,(156) that the same elementary law of our mental constitution,\nsuitably followed out, would explain a variety of mental phenomena\npreviously inexplicable, and in particular some of the fundamental\ndiversities of human character and genius. Associations being of two\nsorts, either between synchronous, or between successive impressions; and\nthe influence of the law which renders associations stronger in proportion\nto the pleasurable or painful character of the impressions, being felt\nwith peculiar force in the synchronous class of associations; it is\nremarked by the writer referred to, that in minds of strong organic\nsensibility synchronous associations will be likely to predominate,\nproducing a tendency to conceive things in pictures and in the concrete,\nrichly clothed in attributes and circumstances, a mental habit which is\ncommonly called Imagination, and is one of the peculiarities of the\npainter and the poet; while persons of more moderate susceptibility to\npleasure and pain will have a tendency to associate facts chiefly in the\norder of their succession, and such persons, if they possess mental\nsuperiority, will addict themselves to history or science rather than to\ncreative art. This interesting speculation the author of the present work\nhas endeavored, on another occasion, to pursue further, and to examine how\nfar it will avail toward explaining the peculiarities of the poetical\ntemperament.(157) It is at least an example which may serve, instead of\nmany others, to show the extensive scope which exists for deductive\ninvestigation in the important and hitherto so imperfect Science of Mind.\n\n\u00a7 7. The copiousness with which the discovery and explanation of special\nlaws of phenomena by deduction from simpler and more general ones has here\nbeen exemplified, was prompted by a desire to characterize clearly, and\nplace in its due position of importance, the Deductive Method; which, in\nthe present state of knowledge, is destined henceforth irrevocably to\npredominate in the course of scientific investigation. A revolution is\npeaceably and progressively effecting itself in philosophy, the reverse of\nthat to which Bacon has attached his name. That great man changed the\nmethod of the sciences from deductive to experimental, and it is now\nrapidly reverting from experimental to deductive. But the deductions which\nBacon abolished were from premises hastily snatched up, or arbitrarily\nassumed. The principles were neither established by legitimate canons of\nexperimental inquiry, nor the results tested by that indispensable element\nof a rational Deductive Method, verification by specific experience.\nBetween the primitive method of Deduction and that which I have attempted\nto characterize, there is all the difference which exists between the\nAristotelian physics and the Newtonian theory of the heavens.\n\nIt would, however, be a mistake to expect that those great\ngeneralizations, from which the subordinate truths of the more backward\nsciences will probably at some future period be deduced by reasoning (as\nthe truths of astronomy are deduced from the generalities of the Newtonian\ntheory), will be found in all, or even in most cases, among truths now\nknown and admitted. We may rest assured, that many of the most general\nlaws of nature are as yet entirely unthought of; and that many others,\ndestined hereafter to assume the same character, are known, if at all,\nonly as laws or properties of some limited class of phenomena; just as\nelectricity, now recognized as one of the most universal of natural\nagencies, was once known only as a curious property which certain\nsubstances acquired by friction, of first attracting and then repelling\nlight bodies. If the theories of heat, cohesion, crystallization, and\nchemical action are destined, as there can be little doubt that they are,\nto become deductive, the truths which will then be regarded as the\n_principia_ of those sciences would probably, if now announced, appear\nquite as novel(158) as the law of gravitation appeared to the\ncontemporaries of Newton; possibly even more so, since Newton\u2019s law, after\nall, was but an extension of the law of weight\u2014that is, of a\ngeneralization familiar from of old, and which already comprehended a not\ninconsiderable body of natural phenomena. The general laws of a similarly\ncommanding character, which we still look forward to the discovery of, may\nnot always find so much of their foundations already laid.\n\nThese general truths will doubtless make their first appearance in the\ncharacter of hypotheses; not proved, nor even admitting of proof, in the\nfirst instance, but assumed as premises for the purpose of deducing from\nthem the known laws of concrete phenomena. But this, though their initial,\ncan not be their final state. To entitle an hypothesis to be received as\none of the truths of nature, and not as a mere technical help to the human\nfaculties, it must be capable of being tested by the canons of legitimate\ninduction, and must actually have been submitted to that test. When this\nshall have been done, and done successfully, premises will have been\nobtained from which all the other propositions of the science will\nthenceforth be presented as conclusions, and the science will, by means of\na new and unexpected Induction, be rendered Deductive.\n\n\n\n\n                               Chapter XIV.\n\n\nOf The Limits To The Explanation Of Laws Of Nature; And Of Hypotheses.\n\n\n\u00a7 1. The preceding considerations have led us to recognize a distinction\nbetween two kinds of laws, or observed uniformities in nature: ultimate\nlaws, and what may be termed derivative laws. Derivative laws are such as\nare deducible from, and may, in any of the modes which we have pointed\nout, be resolved into, other and more general ones. Ultimate laws are\nthose which can not. We are not sure that any of the uniformities with\nwhich we are yet acquainted are ultimate laws; but we know that there must\nbe ultimate laws; and that every resolution of a derivative law into more\ngeneral laws brings us nearer to them.\n\nSince we are continually discovering that uniformities, not previously\nknown to be other than ultimate, are derivative, and resolvable into more\ngeneral laws; since (in other words) we are continually discovering the\nexplanation of some sequence which was previously known only as a fact; it\nbecomes an interesting question whether there are any necessary limits to\nthis philosophical operation, or whether it may proceed until all the\nuniform sequences in nature are resolved into some one universal law. For\nthis seems, at first sight, to be the ultimatum toward which the progress\nof induction by the Deductive Method, resting on a basis of observation\nand experiment, is tending. Projects of this kind were universal in the\ninfancy of philosophy; any speculations which held out a less brilliant\nprospect being in these early times deemed not worth pursuing. And the\nidea receives so much apparent countenance from the nature of the most\nremarkable achievements of modern science, that speculators are even now\nfrequently appearing, who profess either to have solved the problem, or to\nsuggest modes in which it may one day be solved. Even where pretensions of\nthis magnitude are not made, the character of the solutions which are\ngiven or sought of particular classes of phenomena, often involves such\nconceptions of what constitutes explanation, as would render the notion of\nexplaining all phenomena whatever by means of some one cause or law,\nperfectly admissible.\n\n\u00a7 2. It is, therefore, useful to remark that the ultimate Laws of Nature\ncan not possibly be less numerous than the distinguishable sensations or\nother feelings of our nature; those, I mean, which are distinguishable\nfrom one another in quality, and not merely in quantity or degree. For\nexample: since there is a phenomenon _sui generis_, called color, which\nour consciousness testifies to be not a particular degree of some other\nphenomenon, as heat or odor or motion, but intrinsically unlike all\nothers, it follows that there are ultimate laws of color; that though the\nfacts of color may admit of explanation, they never can be explained from\nlaws of heat or odor alone, or of motion alone, but that, however far the\nexplanation may be carried, there will always remain in it a law of color.\nI do not mean that it might not possibly be shown that some other\nphenomenon, some chemical or mechanical action, for example, invariably\nprecedes, and is the cause of, every phenomenon of color. But though this,\nif proved, would be an important extension of our knowledge of nature, it\nwould not explain how or why a motion, or a chemical action, can produce a\nsensation of color; and, however diligent might be our scrutiny of the\nphenomena, whatever number of hidden links we might detect in the chain of\ncausation terminating in the color, the last link would still be a law of\ncolor, not a law of motion, nor of any other phenomenon whatever. Nor does\nthis observation apply only to color, as compared with any other of the\ngreat classes of sensations; it applies to every particular color, as\ncompared with others. White color can in no manner be explained\nexclusively by the laws of the production of red color. In any attempt to\nexplain it, we can not but introduce, as one element of the explanation,\nthe proposition that some antecedent or other produces the sensation of\nwhite.\n\nThe ideal limit, therefore, of the explanation of natural phenomena\n(toward which as toward other ideal limits we are constantly tending,\nwithout the prospect of ever completely attaining it) would be to show\nthat each distinguishable variety of our sensations, or other states of\nconsciousness, has only one sort of cause; that, for example, whenever we\nperceive a white color, there is some one condition or set of conditions\nwhich is always present, and the presence of which always produces in us\nthat sensation. As long as there are several known modes of production of\na phenomenon (several different substances, for instance, which have the\nproperty of whiteness, and between which we can not trace any other\nresemblance) so long it is not impossible that one of these modes of\nproduction may be resolved into another, or that all of them may be\nresolved into some more general mode of production not hitherto\nrecognized. But when the modes of production are reduced to one, we can\nnot, in point of simplification, go any further. This one may not, after\nall, be the ultimate mode; there may be other links to be discovered\nbetween the supposed cause and the effect; but we can only further resolve\nthe known law, by introducing some other law hitherto unknown, which will\nnot diminish the number of ultimate laws.\n\nIn what cases, accordingly, has science been most successful in explaining\nphenomena, by resolving their complex laws into laws of greater simplicity\nand generality? Hitherto chiefly in cases of the propagation of various\nphenomena through space; and, first and principally, the most extensive\nand important of all facts of that description, mechanical motion. Now\nthis is exactly what might be expected from the principles here laid down.\nNot only is motion one of the most universal of all phenomena, it is also\n(as might be expected from that circumstance) one of those which,\napparently at least, are produced in the greatest number of ways; but the\nphenomenon itself is always, to our sensations, the same in every respect\nbut degree. Differences of duration or of velocity, are evidently\ndifferences in degree only; and differences of direction in space, which\nalone has any semblance of being a distinction in kind, entirely disappear\n(so far as our sensations are concerned) by a change in our own position;\nindeed, the very same motion appears to us, according to our position, to\ntake place in every variety of direction, and motions in every different\ndirection to take place in the same. And again, motion in a straight line\nand in a curve are no otherwise distinct than that the one is motion\ncontinuing in the same direction, the other is motion which at each\ninstant changes its direction. There is, therefore, according to the\nprinciples I have stated, no absurdity in supposing that all motion may be\nproduced in one and the same way, by the same kind of cause. Accordingly,\nthe greatest achievements in physical science have consisted in resolving\none observed law of the production of motion into the laws of other known\nmodes of production, or the laws of several such modes into one more\ngeneral mode; as when the fall of bodies to the earth, and the motions of\nthe planets, were brought under the one law of the mutual attraction of\nall particles of matter; when the motions said to be produced by magnetism\nwere shown to be produced by electricity; when the motions of fluids in a\nlateral direction, or even contrary to the direction of gravity, were\nshown to be produced by gravity; and the like. There is an abundance of\ndistinct causes of motion still unresolved into one another: gravitation,\nheat, electricity, chemical action, nervous action, and so forth; but\nwhether the efforts of the present generation of savants to resolve all\nthese different modes of production into one are ultimately successful or\nnot, the attempt so to resolve them is perfectly legitimate. For, though\nthese various causes produce, in other respects, sensations intrinsically\ndifferent, and are not, therefore, capable of being resolved into one\nanother, yet, in so far as they all produce motion, it is quite possible\nthat the immediate antecedent of the motion may in all these different\ncases be the same; nor is it impossible that these various agencies\nthemselves may, as the new doctrines assert, all of them have for their\nown immediate antecedent modes of molecular motion.\n\nWe need not extend our illustration to other cases, as, for instance, to\nthe propagation of light, sound, heat, electricity, etc., through space,\nor any of the other phenomena which have been found susceptible of\nexplanation by the resolution of their observed laws into more general\nlaws. Enough has been said to display the difference between the kind of\nexplanation and resolution of laws which is chimerical, and that of which\nthe accomplishment is the great aim of science; and to show into what sort\nof elements the resolution must be effected, if at all.(159)\n\n\u00a7 3. As, however, there is scarcely any one of the principles of a true\nmethod of philosophizing which does not require to be guarded against\nerrors on both sides, I must enter a caveat against another\nmisapprehension, of a kind directly contrary to the preceding. M. Comte,\namong other occasions on which he has condemned, with some asperity, any\nattempt to explain phenomena which are \u201cevidently primordial\u201d (meaning,\napparently, no more than that every peculiar phenomenon must have at least\none peculiar and therefore inexplicable law), has spoken of the attempt to\nfurnish any explanation of the color belonging to each substance, \u201cla\ncouleur \u00e9l\u00e9mentaire propre \u00e0 chaque substance,\u201d as essentially illusory.\n\u201cNo one,\u201d says he, \u201cin our time attempts to explain the particular\nspecific gravity of each substance or of each structure. Why should it be\notherwise as to the specific color, the notion of which is undoubtedly no\nless primordial?\u201d(160)\n\nNow although, as he elsewhere observes, a color must always remain a\ndifferent thing from a weight or a sound, varieties of color might\nnevertheless follow, or correspond to, given varieties of weight, or\nsound, or some other phenomenon as different as these are from color\nitself. It is one question what a thing is, and another what it depends\non; and though to ascertain the conditions of an elementary phenomenon is\nnot to obtain any new insight into the nature of the phenomenon itself,\nthat is no reason against attempting to discover the conditions. The\ninterdict against endeavoring to reduce distinctions of color to any\ncommon principle, would have held equally good against a like attempt on\nthe subject of distinctions of sound; which nevertheless have been found\nto be immediately preceded and caused by distinguishable varieties in the\nvibrations of elastic bodies; though a sound, no doubt, is quite as\ndifferent as a color is from any motion of particles, vibratory or\notherwise. We might add, that, in the case of colors, there are strong\npositive indications that they are not ultimate properties of the\ndifferent kinds of substances, but depend on conditions capable of being\nsuperinduced upon all substances; since there is no substance which can\nnot, according to the kind of light thrown upon it, be made to assume\nalmost any color; and since almost every change in the mode of aggregation\nof the particles of the same substance is attended with alterations in its\ncolor, and in its optical properties generally.\n\nThe really weak point in the attempts which have been made to account for\ncolors by the vibrations of a fluid, is not that the attempt itself is\nunphilosophical, but that the existence of the fluid, and the fact of its\nvibratory motion, are not proved, but are assumed, on no other ground than\nthe facility they are supposed to afford of explaining the phenomena. And\nthis consideration leads to the important question of the proper use of\nscientific hypotheses, the connection of which with the subject of the\nexplanation of the phenomena of nature, and of the necessary limits to\nthat explanation, need not be pointed out.\n\n\u00a7 4. An hypothesis is any supposition which we make (either without actual\nevidence, or on evidence avowedly insufficient) in order to endeavor to\ndeduce from it conclusions in accordance with facts which are known to be\nreal; under the idea that if the conclusions to which the hypothesis leads\nare known truths, the hypothesis itself either must be, or at least is\nlikely to be, true. If the hypothesis relates to the cause or mode of\nproduction of a phenomenon, it will serve, if admitted, to explain such\nfacts as are found capable of being deduced from it. And this explanation\nis the purpose of many, if not most hypotheses. Since explaining, in the\nscientific sense, means resolving a uniformity which is not a law of\ncausation, into the laws of causation from which it results, or a complex\nlaw of causation into simpler and more general ones from which it is\ncapable of being deductively inferred, if there do not exist any known\nlaws which fulfill this requirement, we may feign or imagine some which\nwould fulfill it; and this is making an hypothesis.\n\nAn hypothesis being a mere supposition, there are no other limits to\nhypotheses than those of the human imagination; we may, if we please,\nimagine, by way of accounting for an effect, some cause of a kind utterly\nunknown, and acting according to a law altogether fictitious. But as\nhypotheses of this sort would not have any of the plausibility belonging\nto those which ally themselves by analogy with known laws of nature, and\nbesides would not supply the want which arbitrary hypotheses are generally\ninvented to satisfy, by enabling the imagination to represent to itself an\nobscure phenomenon in a familiar light, there is probably no hypothesis in\nthe history of science in which both the agent itself and the law of its\noperation were fictitious. Either the phenomenon assigned as the cause is\nreal, but the law according to which it acts merely supposed; or the cause\nis fictitious, but is supposed to produce its effects according to laws\nsimilar to those of some known class of phenomena. An instance of the\nfirst kind is afforded by the different suppositions made respecting the\nlaw of the planetary central force, anterior to the discovery of the true\nlaw, that the force varies as the inverse square of the distance; which\nalso suggested itself to Newton, in the first instance, as an hypothesis,\nand was verified by proving that it led deductively to Kepler\u2019s laws.\nHypotheses of the second kind are such as the vortices of Descartes, which\nwere fictitious, but were supposed to obey the known laws of rotatory\nmotion; or the two rival hypotheses respecting the nature of light, the\none ascribing the phenomena to a fluid emitted from all luminous bodies,\nthe other (now generally received) attributing them to vibratory motions\namong the particles of an ether pervading all space. Of the existence of\neither fluid there is no evidence, save the explanation they are\ncalculated to afford of some of the phenomena; but they are supposed to\nproduce their effects according to known laws: the ordinary laws of\ncontinued locomotion in the one case, and in the other those of the\npropagation of undulatory movements among the particles of an elastic\nfluid.\n\nAccording to the foregoing remarks, hypotheses are invented to enable the\nDeductive Method to be earlier applied to phenomena. But(161) in order to\ndiscover the cause of any phenomenon by the Deductive Method, the process\nmust consist of three parts: induction, ratiocination, and verification.\nInduction (the place of which, however, may be supplied by a prior\ndeduction), to ascertain the laws of the causes; ratiocination, to compute\nfrom those laws how the causes will operate in the particular combination\nknown to exist in the case in hand; verification, by comparing this\ncalculated effect with the actual phenomenon. No one of these three parts\nof the process can be dispensed with. In the deduction which proves the\nidentity of gravity with the central force of the solar system, all the\nthree are found. First, it is proved from the moon\u2019s motions, that the\nearth attracts her with a force varying as the inverse square of the\ndistance. This (though partly dependent on prior deductions) corresponds\nto the first, or purely inductive, step: the ascertainment of the law of\nthe cause. Secondly, from this law, and from the knowledge previously\nobtained of the moon\u2019s mean distance from the earth, and of the actual\namount of her deflection from the tangent, it is ascertained with what\nrapidity the earth\u2019s attraction would cause the moon to fall, if she were\nno further off, and no more acted upon by extraneous forces, than\nterrestrial bodies are: that is the second step, the ratiocination.\nFinally, this calculated velocity being compared with the observed\nvelocity with which all heavy bodies fall, by mere gravity, toward the\nsurface of the earth (sixteen feet in the first second, forty-eight in the\nsecond, and so forth, in the ratio of the odd numbers, 1, 3, 5, etc.), the\ntwo quantities are found to agree. The order in which the steps are here\npresented was not that of their discovery; but it is their correct logical\norder, as portions of the proof that the same attraction of the earth\nwhich causes the moon\u2019s motion causes also the fall of heavy bodies to the\nearth: a proof which is thus complete in all its parts.\n\nNow, the Hypothetical Method suppresses the first of the three steps, the\ninduction to ascertain the law; and contents itself with the other two\noperations, ratiocination and verification; the law which is reasoned from\nbeing assumed instead of proved.\n\nThis process may evidently be legitimate on one supposition, namely, if\nthe nature of the case be such that the final step, the verification,\nshall amount to, and fulfill the conditions of, a complete induction. We\nwant to be assured that the law we have hypothetically assumed is a true\none; and its leading deductively to true results will afford this\nassurance, provided the case be such that a false law can not lead to a\ntrue result; provided no law, except the very one which we have assumed,\ncan lead deductively to the same conclusions which that leads to. And this\nproviso is often realized. For example, in the very complete specimen of\ndeduction which we just cited, the original major premise of the\nratiocination, the law of the attractive force, was ascertained in this\nmode; by this legitimate employment of the Hypothetical Method. Newton\nbegan by an assumption that the force which at each instant deflects a\nplanet from its rectilineal course, and makes it describe a curve round\nthe sun, is a force tending directly toward the sun. He then proved that\nif this be so, the planet will describe, as we know by Kepler\u2019s first law\nthat it does describe, equal areas in equal times; and, lastly, he proved\nthat if the force acted in any other direction whatever, the planet would\nnot describe equal areas in equal times. It being thus shown that no other\nhypothesis would accord with the facts, the assumption was proved; the\nhypothesis became an inductive truth. Not only did Newton ascertain by\nthis hypothetical process the direction of the deflecting force; he\nproceeded in exactly the same manner to ascertain the law of variation of\nthe quantity of that force. He assumed that the force varied inversely as\nthe square of the distance; showed that from this assumption the remaining\ntwo of Kepler\u2019s laws might be deduced; and, finally, that any other law of\nvariation would give results inconsistent with those laws, and\ninconsistent, therefore, with the real motions of the planets, of which\nKepler\u2019s laws were known to be a correct expression.\n\nI have said that in this case the verification fulfills the conditions of\nan induction; but an induction of what sort? On examination we find that\nit conforms to the canon of the Method of Difference. It affords the two\ninstances, A B C, _a b c_, and B C, _b c_. A represents central force; A B\nC, the planets _plus_ a central force; B C, the planets apart from a\ncentral force. The planets with a central force give _a_, areas\nproportional to the times; the planets without a central force give _b c_\n(a set of motions) without _a_, or with something else instead of _a_.\nThis is the Method of Difference in all its strictness. It is true, the\ntwo instances which the method requires are obtained in this case, not by\nexperiment, but by a prior deduction. But that is of no consequence. It is\nimmaterial what is the nature of the evidence from which we derive the\nassurance that A B C will produce _a b c_, and B C only _b c_; it is\nenough that we have that assurance. In the present case, a process of\nreasoning furnished Newton with the very instances which, if the nature of\nthe case had admitted of it, he would have sought by experiment.\n\nIt is thus perfectly possible, and indeed is a very common occurrence,\nthat what was an hypothesis at the beginning of the inquiry becomes a\nproved law of nature before its close. But in order that this should\nhappen, we must be able, either by deduction or experiment, to obtain\n_both_ the instances which the Method of Difference requires. That we are\nable from the hypothesis to deduce the known facts, gives only the\naffirmative instance, A B C, _a b c_. It is equally necessary that we\nshould be able to obtain, as Newton did, the negative instance B C, _b c_;\nby showing that no antecedent, except the one assumed in the hypothesis,\nwould in conjunction with B C produce _a_.\n\nNow it appears to me that this assurance can not be obtained, when the\ncause assumed in the hypothesis is an unknown cause imagined solely to\naccount for _a_. When we are only seeking to determine the precise law of\na cause already ascertained, or to distinguish the particular agent which\nis in fact the cause, among several agents of the same kind, one or other\nof which it is already known to be, we may then obtain the negative\ninstance. An inquiry which of the bodies of the solar system causes by its\nattraction some particular irregularity in the orbit or periodic time of\nsome satellite or comet, would be a case of the second description.\nNewton\u2019s was a case of the first. If it had not been previously known that\nthe planets were hindered from moving in straight lines by some force\ntending toward the interior of their orbit, though the exact direction was\ndoubtful; or if it had not been known that the force increased in some\nproportion or other as the distance diminished, and diminished as it\nincreased, Newton\u2019s argument would not have proved his conclusion. These\nfacts, however, being already certain, the range of admissible\nsuppositions was limited to the various possible directions of a line, and\nthe various possible numerical relations between the variations of the\ndistance, and the variations of the attractive force. Now among these it\nwas easily shown that different suppositions could not lead to identical\nconsequences.\n\nAccordingly, Newton could not have performed his second great scientific\noperation: that of identifying terrestrial gravity with the central force\nof the solar system by the same hypothetical method. When the law of the\nmoon\u2019s attraction had been proved from the data of the moon itself, then,\non finding the same law to accord with the phenomena of terrestrial\ngravity, he was warranted in adopting it as the law of those phenomena\nlikewise; but it would not have been allowable for him, without any lunar\ndata, to assume that the moon was attracted toward the earth with a force\nas the inverse square of the distance, merely because that ratio would\nenable him to account for terrestrial gravity; for it would have been\nimpossible for him to prove that the observed law of the fall of heavy\nbodies to the earth could not result from any force, save one extending to\nthe moon, and proportional to the inverse square.\n\nIt appears, then, to be a condition of the most genuinely scientific\nhypothesis, that it be not destined always to remain an hypothesis, but be\nof such a nature as to be either proved or disproved by comparison with\nobserved facts. This condition is fulfilled when the effect is already\nknown to depend on the very cause supposed, and the hypothesis relates\nonly to the precise mode of dependence; the law of the variation of the\neffect according to the variations in the quantity or in the relations of\nthe cause. With these may be classed the hypotheses which do not make any\nsupposition with regard to causation, but only with regard to the law of\ncorrespondence between facts which accompany each other in their\nvariations, though there may be no relation of cause and effect between\nthem. Such were the different false hypotheses which Kepler made\nrespecting the law of the refraction of light. It was known that the\ndirection of the line of refraction varied with every variation in the\ndirection of the line of incidence, but it was not known how; that is,\nwhat changes of the one corresponded to the different changes of the\nother. In this case any law different from the true one must have led to\nfalse results. And, lastly, we must add to these all hypothetical modes of\nmerely representing or _describing_ phenomena; such as the hypothesis of\nthe ancient astronomers that the heavenly bodies moved in circles; the\nvarious hypotheses of eccentrics, deferents, and epicycles, which were\nadded to that original hypothesis; the nineteen false hypotheses which\nKepler made and abandoned respecting the form of the planetary orbits; and\neven the doctrine in which he finally rested, that those orbits are\nellipses, which was but an hypothesis like the rest until verified by\nfacts.\n\nIn all these cases, verification is proof; if the supposition accords with\nthe phenomena there needs no other evidence of it. But in order that this\nmay be the case, I conceive it to be necessary, when the hypothesis\nrelates to causation, that the supposed cause should not only be a real\nphenomenon, something actually existing in nature, but should be already\nknown to exercise, or at least to be capable of exercising, an influence\nof some sort over the effect. In any other case, it is no sufficient\nevidence of the truth of the hypothesis that we are able to deduce the\nreal phenomena from it.\n\nIs it, then, never allowable, in a scientific hypothesis, to assume a\ncause, but only to ascribe an assumed law to a known cause? I do not\nassert this. I only say, that in the latter case alone can the hypothesis\nbe received as true merely because it explains the phenomena. In the\nformer case it may be very useful by suggesting a line of investigation\nwhich may possibly terminate in obtaining real proof. But for this\npurpose, as is justly remarked by M. Comte, it is indispensable that the\ncause suggested by the hypothesis should be in its own nature susceptible\nof being proved by other evidence. This seems to be the philosophical\nimport of Newton\u2019s maxim, (so often cited with approbation by subsequent\nwriters), that the cause assigned for any phenomenon must not only be such\nas if admitted would explain the phenomenon, but must also be a _vera\ncausa_. What he meant by a _vera causa_ Newton did not indeed very\nexplicitly define; and Dr. Whewell, who dissents from the propriety of any\nsuch restriction upon the latitude of framing hypotheses, has had little\ndifficulty in showing(162) that his conception of it was neither precise\nnor consistent with itself; accordingly his optical theory was a signal\ninstance of the violation of his own rule. It is certainly not necessary\nthat the cause assigned should be a cause already known; otherwise we\nshould sacrifice our best opportunities of becoming acquainted with new\ncauses. But what is true in the maxim is, that the cause, though not known\npreviously, should be capable of being known thereafter; that its\nexistence should be capable of being detected, and its connection with the\neffect ascribed to it should be susceptible of being proved, by\nindependent evidence. The hypothesis, by suggesting observations and\nexperiments, puts us on the road to that independent evidence, if it be\nreally attainable; and till it be attained, the hypothesis ought only to\ncount for a more or less plausible conjecture.\n\n\u00a7 5. This function, however, of hypotheses, is one which must be reckoned\nabsolutely indispensable in science. When Newton said, \u201cHypotheses non\nfingo,\u201d he did not mean that he deprived himself of the facilities of\ninvestigation afforded by assuming in the first instance what he hoped\nultimately to be able to prove. Without such assumptions, science could\nnever have attained its present state; they are necessary steps in the\nprogress to something more certain; and nearly every thing which is now\ntheory was once hypothesis. Even in purely experimental science, some\ninducement is necessary for trying one experiment rather than another; and\nthough it is abstractedly possible that all the experiments which have\nbeen tried, might have been produced by the mere desire to ascertain what\nwould happen in certain circumstances, without any previous conjecture as\nto the result; yet, in point of fact, those unobvious, delicate, and often\ncumbrous and tedious processes of experiment, which have thrown most light\nupon the general constitution of nature, would hardly ever have been\nundertaken by the persons or at the time they were, unless it had seemed\nto depend on them whether some general doctrine or theory which had been\nsuggested, but not yet proved, should be admitted or not. If this be true\neven of merely experimental inquiry, the conversion of experimental into\ndeductive truths could still less have been effected without large\ntemporary assistance from hypotheses. The process of tracing regularity in\nany complicated, and at first sight confused, set of appearances, is\nnecessarily tentative; we begin by making any supposition, even a false\none, to see what consequences will follow from it; and by observing how\nthese differ from the real phenomena, we learn what corrections to make in\nour assumption. The simplest supposition which accords with the more\nobvious facts is the best to begin with; because its consequences are the\nmost easily traced. This rude hypothesis is then rudely corrected, and the\noperation repeated; and the comparison of the consequences deducible from\nthe corrected hypothesis, with the observed facts, suggests still further\ncorrection, until the deductive results are at last made to tally with the\nphenomena. \u201cSome fact is as yet little understood, or some law is unknown;\nwe frame on the subject an hypothesis as accordant as possible with the\nwhole of the data already possessed; and the science, being thus enabled\nto move forward freely, always ends by leading to new consequences capable\nof observation, which either confirm or refute, unequivocally, the first\nsupposition.\u201d Neither induction nor deduction would enable us to\nunderstand even the simplest phenomena, \u201cif we did not often commence by\nanticipating on the results; by making a provisional supposition, at first\nessentially conjectural, as to some of the very notions which constitute\nthe final object of the inquiry.\u201d(163) Let any one watch the manner in\nwhich he himself unravels a complicated mass of evidence; let him observe\nhow, for instance, he elicits the true history of any occurrence from the\ninvolved statements of one or of many witnesses; he will find that he does\nnot take all the items of evidence into his mind at once, and attempt to\nweave them together; he extemporizes, from a few of the particulars, a\nfirst rude theory of the mode in which the facts took place, and then\nlooks at the other statements one by one, to try whether they can be\nreconciled with that provisional theory, or what alterations or additions\nit requires to make it square with them. In this way, which has been\njustly compared to the Methods of Approximation of mathematicians, we\narrive, by means of hypotheses, at conclusions not hypothetical.(164)\n\n\u00a7 6. It is perfectly consistent with the spirit of the method, to assume\nin this provisional manner not only an hypothesis respecting the law of\nwhat we already know to be the cause, but an hypothesis respecting the\ncause itself. It is allowable, useful, and often even necessary, to begin\nby asking ourselves what cause _may_ have produced the effect, in order\nthat we may know in what direction to look out for evidence to determine\nwhether it actually _did_. The vortices of Descartes would have been a\nperfectly legitimate hypothesis, if it had been possible, by any mode of\nexploration which we could entertain the hope of ever possessing, to bring\nthe reality of the vortices, as a fact in nature, conclusively to the test\nof observation. The vice of the hypothesis was that it could not lead to\nany course of investigation capable of converting it from an hypothesis\ninto a proved fact. It might chance to be _dis_proved, either by some want\nof correspondence with the phenomena it purported to explain, or (as\nactually happened) by some extraneous fact. \u201cThe free passage of comets\nthrough the spaces in which these vortices should have been, convinced men\nthat these vortices did not exist.\u201d(165) But the hypothesis would have\nbeen false, though no such direct evidence of its falsity had been\nprocurable. Direct evidence of its truth there could not be.\n\nThe prevailing hypothesis of a luminiferous ether, in other respects not\nwithout analogy to that of Descartes, is not in its own nature entirely\ncut off from the possibility of direct evidence in its favor. It is well\nknown that the difference between the calculated and the observed times of\nthe periodical return of Encke\u2019s comet, has led to a conjecture that a\nmedium capable of opposing resistance to motion is diffused through space.\nIf this surmise should be confirmed, in the course of ages, by the gradual\naccumulation of a similar variance in the case of the other bodies of the\nsolar system, the luminiferous ether would have made a considerable\nadvance toward the character of a _vera causa_, since the existence would\nhave been ascertained of a great cosmical agent, possessing some of the\nattributes which the hypothesis assumes; though there would still remain\nmany difficulties, and the identification of the ether with the resisting\nmedium would even, I imagine, give rise to new ones. At present, however,\nthis supposition can not be looked upon as more than a conjecture; the\nexistence of the ether still rests on the possibility of deducing from its\nassumed laws a considerable number of actual phenomena; and this evidence\nI can not regard as conclusive, because we can not have, in the case of\nsuch an hypothesis, the assurance that if the hypothesis be false it must\nlead to results at variance with the true facts.\n\nAccordingly, most thinkers of any degree of sobriety allow that an\nhypothesis of this kind is not to be received as probably true because it\naccounts for all the known phenomena; since this is a condition sometimes\nfulfilled tolerably well by two conflicting hypotheses; while there are\nprobably many others which are equally possible, but which, for want of\nany thing analogous in our experience, our minds are unfitted to conceive.\nBut it seems to be thought that an hypothesis of the sort in question is\nentitled to a more favorable reception, if, besides accounting for all the\nfacts previously known, it has led to the anticipation and prediction of\nothers which experience afterward verified; as the undulatory theory of\nlight led to the prediction, subsequently realized by experiment, that two\nluminous rays might meet each other in such a manner as to produce\ndarkness. Such predictions and their fulfillment are, indeed, well\ncalculated to impress the uninformed, whose faith in science rests solely\non similar coincidences between its prophecies and what comes to pass. But\nit is strange that any considerable stress should be laid upon such a\ncoincidence by persons of scientific attainments. If the laws of the\npropagation of light accord with those of the vibrations of an elastic\nfluid in as many respects as is necessary to make the hypothesis afford a\ncorrect expression of all or most of the phenomena known at the time, it\nis nothing strange that they should accord with each other in one respect\nmore. Though twenty such coincidences should occur, they would not prove\nthe reality of the undulatory ether; it would not follow that the\nphenomena of light were results of the laws of elastic fluids, but at most\nthat they are governed by laws partially identical with these; which, we\nmay observe, is already certain, from the fact that the hypothesis in\nquestion could be for a moment tenable.(166) Cases may be cited, even in\nour imperfect acquaintance with nature, where agencies that we have good\nreason to consider as radically distinct produce their effects, or some of\ntheir effects, according to laws which are identical. The law, for\nexample, of the inverse square of the distance, is the measure of the\nintensity not only of gravitation, but (it is believed) of illumination,\nand of heat diffused from a centre. Yet no one looks upon this identity as\nproving similarity in the mechanism by which the three kinds of phenomena\nare produced.\n\nAccording to Dr. Whewell, the coincidence of results predicted from an\nhypothesis with facts afterward observed, amounts to a conclusive proof of\nthe truth of the theory. \u201cIf I copy a long series of letters, of which the\nlast half-dozen are concealed, and if I guess these aright, as is found to\nbe the case when they are afterward uncovered, this must be because I have\nmade out the import of the inscription. To say that because I have copied\nall that I could see, it is nothing strange that I should guess those\nwhich I can not see, would be absurd, without supposing such a ground for\nguessing.\u201d(167) If any one, from examining the greater part of a long\ninscription, can interpret the characters so that the inscription gives a\nrational meaning in a known language, there is a strong presumption that\nhis interpretation is correct; but I do not think the presumption much\nincreased by his being able to guess the few remaining letters without\nseeing them; for we should naturally expect (when the nature of the case\nexcludes chance) that even an erroneous interpretation which accorded with\nall the visible parts of the inscription would accord also with the small\nremainder; as would be the case, for example, if the inscription had been\ndesignedly so contrived as to admit of a double sense. I assume that the\nuncovered characters afford an amount of coincidence too great to be\nmerely casual; otherwise the illustration is not a fair one. No one\nsupposes the agreement of the phenomena of light with the theory of\nundulations to be merely fortuitous. It must arise from the actual\nidentity of some of the laws of undulations with some of those of light;\nand if there be that identity, it is reasonable to suppose that its\nconsequences would not end with the phenomena which first suggested the\nidentification, nor be even confined to such phenomena as were known at\nthe time. But it does not follow, because some of the laws agree with\nthose of undulations, that there are any actual undulations; no more than\nit followed because some (though not so many) of the same laws agreed with\nthose of the projection of particles, that there was actual emission of\nparticles. Even the undulatory hypothesis does not account for all the\nphenomena of light. The natural colors of objects, the compound nature of\nthe solar ray, the absorption of light, and its chemical and vital action,\nthe hypothesis leaves as mysterious as it found them; and some of these\nfacts are, at least apparently, more reconcilable with the emission theory\nthan with that of Young and Fresnel. Who knows but that some third\nhypothesis, including all these phenomena, may in time leave the\nundulatory theory as far behind as that has left the theory of Newton and\nhis successors?\n\nTo the statement, that the condition of accounting for all the known\nphenomena is often fulfilled equally well by two conflicting hypotheses,\nDr. Whewell makes answer that he knows \u201cof no such case in the history of\nscience, where the phenomena are at all numerous and complicated.\u201d(168)\nSuch an affirmation, by a writer of Dr. Whewell\u2019s minute acquaintance with\nthe history of science, would carry great authority, if he had not, a few\npages before, taken pains to refute it,(169) by maintaining that even the\nexploded scientific hypotheses might always, or almost always, have been\nso modified as to make them correct representations of the phenomena. The\nhypothesis of vortices, he tells us, was, by successive modifications,\nbrought to coincide in its results with the Newtonian theory and with the\nfacts. The vortices did not, indeed, explain all the phenomena which the\nNewtonian theory was ultimately found to account for, such as the\nprecession of the equinoxes; but this phenomenon was not, at the time, in\nthe contemplation of either party, as one of the facts to be accounted\nfor. All the facts which they did contemplate, we may believe on Dr.\nWhewell\u2019s authority to have accorded as accurately with the Cartesian\nhypothesis, in its finally improved state, as with Newton\u2019s.\n\nBut it is not, I conceive, a valid reason for accepting any given\nhypothesis, that we are unable to imagine any other which will account for\nthe facts. There is no necessity for supposing that the true explanation\nmust be one which, with only our present experience, we could imagine.\nAmong the natural agents with which we are acquainted, the vibrations of\nan elastic fluid may be the only one whose laws bear a close resemblance\nto those of light; but we can not tell that there does not exist an\nunknown cause, other than an elastic ether diffused through space, yet\nproducing effects identical in some respects with those which would result\nfrom the undulations of such an ether. To assume that no such cause can\nexist, appears to me an extreme case of assumption without evidence. And\nat the risk of being charged with want of modesty, I can not help\nexpressing astonishment that a philosopher of Dr. Whewell\u2019s abilities and\nattainments should have written an elaborate treatise on the philosophy of\ninduction, in which he recognizes absolutely no mode of induction except\nthat of trying hypothesis after hypothesis until one is found which fits\nthe phenomena; which one, when found, is to be assumed as true, with no\nother reservation than that if, on re-examination, it should appear to\nassume more than is needful for explaining the phenomena, the superfluous\npart of the assumption should be cut off. And this without the slightest\ndistinction between the cases in which it may be known beforehand that two\ndifferent hypotheses can not lead to the same result, and those in which,\nfor aught we can ever know, the range of suppositions, all equally\nconsistent with the phenomena, may be infinite.(170)\n\nNevertheless, I do not agree with M. Comte in condemning those who employ\nthemselves in working out into detail the application of these hypotheses\nto the explanation of ascertained facts, provided they bear in mind that\nthe utmost they can prove is, not that the hypothesis is, but that it\n_may_ be true. The ether hypothesis has a very strong claim to be so\nfollowed out, a claim greatly strengthened since it has been shown to\nafford a mechanism which would explain the mode of production, not of\nlight only, but also of heat. Indeed, the speculation has a smaller\nelement of hypothesis in its application to heat, than in the case for\nwhich it was originally framed. We have proof by our senses of the\nexistence of molecular movement among the particles of all heated bodies;\nwhile we have no similar experience in the case of light. When, therefore,\nheat is communicated from the sun to the earth across apparently empty\nspace, the chain of causation has molecular motion both at the beginning\nand end. The hypothesis only makes the motion continuous by extending it\nto the middle. Now, motion in a body is known to be capable of being\nimparted to another body contiguous to it; and the intervention of a\nhypothetical elastic fluid occupying the space between the sun and the\nearth, supplies the contiguity which is the only condition wanting, and\nwhich can be supplied by no supposition but that of an intervening medium.\nThe supposition, notwithstanding, is at best a probable conjecture, not a\nproved truth. For there is no proof that contiguity is absolutely required\nfor the communication of motion from one body to another. Contiguity does\nnot always exist, to our senses at least, in the cases in which motion\nproduces motion. The forces which go under the name of attraction,\nespecially the greatest of all, gravitation, are examples of motion\nproducing motion without apparent contiguity. When a planet moves, its\ndistant satellites accompany its motion. The sun carries the whole solar\nsystem along with it in the progress which it is ascertained to be\nexecuting through space. And even if we were to accept as conclusive the\ngeometrical reasonings (strikingly similar to those by which the\nCartesians defended their vortices) by which it has been attempted to show\nthat the motions of the ether may account for gravitation itself, even\nthen it would only have been proved that the supposed mode of production\nmay be, but not that no other mode can be, the true one.\n\n\u00a7 7. It is necessary, before quitting the subject of hypotheses, to guard\nagainst the appearance of reflecting upon the scientific value of several\nbranches of physical inquiry, which, though only in their infancy, I hold\nto be strictly inductive. There is a great difference between inventing\nagencies to account for classes of phenomena, and endeavoring, in\nconformity with known laws, to conjecture what former collocations of\nknown agents may have given birth to individual facts still in existence.\nThe latter is the legitimate operation of inferring from an observed\neffect the existence, in time past, of a cause similar to that by which we\nknow it to be produced in all cases in which we have actual experience of\nits origin. This, for example, is the scope of the inquiries of geology;\nand they are no more illogical or visionary than judicial inquiries, which\nalso aim at discovering a past event by inference from those of its\neffects which still subsist. As we can ascertain whether a man was\nmurdered or died a natural death, from the indications exhibited by the\ncorpse, the presence or absence of signs of struggling on the ground or on\nthe adjacent objects, the marks of blood, the footsteps of the supposed\nmurderers, and so on, proceeding throughout on uniformities ascertained by\na perfect induction without any mixture of hypothesis; so if we find, on\nand beneath the surface of our planet, masses exactly similar to deposits\nfrom water, or to results of the cooling of matter melted by fire, we may\njustly conclude that such has been their origin; and if the effects,\nthough similar in kind, are on a far larger scale than any which are now\nproduced, we may rationally, and without hypothesis, conclude either that\nthe causes existed formerly with greater intensity, or that they have\noperated during an enormous length of time. Further than this no geologist\nof authority has, since the rise of the present enlightened school of\ngeological speculation, attempted to go.\n\nIn many geological inquiries it doubtless happens that though the laws to\nwhich the phenomena are ascribed are known laws, and the agents known\nagents, those agents are not known to have been present in the particular\ncase. In the speculation respecting the igneous origin of trap or granite,\nthe fact does not admit of direct proof that those substances have been\nactually subjected to intense heat. But the same thing might be said of\nall judicial inquiries which proceed on circumstantial evidence. We can\nconclude that a man was murdered, though it is not proved by the testimony\nof eye-witnesses that some person who had the intention of murdering him\nwas present on the spot. It is enough for most purposes, if no other known\ncause could have generated the effects shown to have been produced.\n\n                  \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\nThe celebrated speculation of Laplace concerning the origin of the earth\nand planets, participates essentially in the inductive character of modern\ngeological theory. The speculation is, that the atmosphere of the sun\noriginally extended to the present limits of the solar system; from which,\nby the process of cooling, it has contracted to its present dimensions;\nand since, by the general principles of mechanics the rotation of the sun\nand of its accompanying atmosphere must increase in rapidity as its volume\ndiminishes, the increased centrifugal force generated by the more rapid\nrotation, overbalancing the action of gravitation, has caused the sun to\nabandon successive rings of vaporous matter, which are supposed to have\ncondensed by cooling, and to have become the planets. There is in this\ntheory no unknown substance introduced on supposition, nor any unknown\nproperty or law ascribed to a known substance. The known laws of matter\nauthorize us to suppose that a body which is constantly giving out so\nlarge an amount of heat as the sun is, must be progressively cooling, and\nthat, by the process of cooling it must contract; if, therefore, we\nendeavor, from the present state of that luminary, to infer its state in a\ntime long past, we must necessarily suppose that its atmosphere extended\nmuch farther than at present, and we are entitled to suppose that it\nextended as far as we can trace effects such as it might naturally leave\nbehind it on retiring; and such the planets are. These suppositions being\nmade, it follows from known laws that successive zones of the solar\natmosphere might be abandoned; that these would continue to revolve round\nthe sun with the same velocity as when they formed part of its substance;\nand that they would cool down, long before the sun itself, to any given\ntemperature, and consequently to that at which the greater part of the\nvaporous matter of which they consisted would become liquid or solid. The\nknown law of gravitation would then cause them to agglomerate in masses,\nwhich would assume the shape our planets actually exhibit; would acquire,\neach about its own axis, a rotatory movement; and would in that state\nrevolve, as the planets actually do, about the sun, in the same direction\nwith the sun\u2019s rotation, but with less velocity, because in the same\nperiodic time which the sun\u2019s rotation occupied when his atmosphere\nextended to that point. There is thus, in Laplace\u2019s theory, nothing,\nstrictly speaking, hypothetical; it is an example of legitimate reasoning\nfrom a present effect to a possible past cause, according to the known\nlaws of that cause. The theory, therefore, is, as I have said, of a\nsimilar character to the theories of geologists; but considerably inferior\nto them in point of evidence. Even if it were proved (which it is not)\nthat the conditions necessary for determining the breaking off of\nsuccessive rings would certainly occur, there would still be a much\ngreater chance of error in assuming that the existing laws of nature are\nthe same which existed at the origin of the solar system, than in merely\npresuming (with geologists) that those laws have lasted through a few\nrevolutions and transformations of a single one among the bodies of which\nthat system is composed.\n\n\n\n\n                               Chapter XV.\n\n\nOf Progressive Effects; And Of The Continued Action Of Causes.\n\n\n\u00a7 1. In the last four chapters we have traced the general outlines of the\ntheory of the generation of derivative laws from ultimate ones. In the\npresent chapter our attention will be directed to a particular case of the\nderivation of laws from other laws, but a case so general, and so\nimportant as not only to repay, but to require, a separate examination.\nThis is the case of a complex phenomenon resulting from one simple law, by\nthe continual addition of an effect to itself.\n\nThere are some phenomena, some bodily sensations, for example, which are\nessentially instantaneous, and whose existence can only be prolonged by\nthe prolongation of the existence of the cause by which they are produced.\nBut most phenomena are in their own nature permanent; having begun to\nexist, they would exist forever unless some cause intervened having a\ntendency to alter or destroy them. Such, for example, are all the facts of\nphenomena which we call bodies. Water, once produced, will not of itself\nrelapse into a state of hydrogen and oxygen; such a change requires some\nagent having the power of decomposing the compound. Such, again, are the\npositions in space and the movements of bodies. No object at rest alters\nits position without the intervention of some conditions extraneous to\nitself; and when once in motion, no object returns to a state of rest, or\nalters either its direction or its velocity, unless some new external\nconditions are superinduced. It, therefore, perpetually happens that a\ntemporary cause gives rise to a permanent effect. The contact of iron with\nmoist air for a few hours, produces a rust which may endure for centuries;\nor a projectile force which launches a cannon-ball into space, produces a\nmotion which would continue forever unless some other force counteracted\nit.\n\nBetween the two examples which we have here given, there is a difference\nworth pointing out. In the former (in which the phenomenon produced is a\nsubstance, and not a motion of a substance), since the rust remains\nforever and unaltered unless some new cause supervenes, we may speak of\nthe contact of air a hundred years ago as even the proximate cause of the\nrust which has existed from that time until now. But when the effect is\nmotion, which is itself a change, we must use a different language. The\npermanency of the effect is now only the permanency of a series of\nchanges. The second foot, or inch, or mile of motion is not the mere\nprolonged duration of the first foot, or inch, or mile, but another fact\nwhich succeeds, and which may in some respects be very unlike the former,\nsince it carries the body through a different region of space. Now, the\noriginal projectile force which set the body moving is the remote cause of\nall its motion, however long continued, but the proximate cause of no\nmotion except that which took place at the first instant. The motion at\nany subsequent instant is proximately caused by the motion which took\nplace at the instant preceding. It is on that, and not on the original\nmoving cause, that the motion at any given moment depends. For, suppose\nthat the body passes through some resisting medium, which partially\ncounteracts the effect of the original impulse, and retards the motion;\nthis counteraction (it need scarcely here be repeated) is as strict an\nexample of obedience to the law of the impulse, as if the body had gone on\nmoving with its original velocity; but the motion which results is\ndifferent, being now a compound of the effects of two causes acting in\ncontrary directions, instead of the single effect of one cause. Now, what\ncause does the body obey in its subsequent motion? The original cause of\nmotion, or the actual motion at the preceding instant? The latter; for\nwhen the object issues from the resisting medium, it continues moving, not\nwith its original, but with its retarded velocity. The motion having once\nbeen diminished, all that which follows is diminished. The effect changes,\nbecause the cause which it really obeys, the proximate cause, the real\ncause in fact, has changed. This principle is recognized by mathematicians\nwhen they enumerate among the causes by which the motion of a body is at\nany instant determined the _force generated_ by the previous motion; an\nexpression which would be absurd if taken to imply that this \u201cforce\u201d was\nan intermediate link between the cause and the effect, but which really\nmeans only the previous motion itself, considered as a cause of further\nmotion. We must, therefore, if we would speak with perfect precision,\nconsider each link in the succession of motions as the effect of the link\npreceding it. But if, for the convenience of discourse, we speak of the\nwhole series as one effect, it must be as an effect produced by the\noriginal impelling force; a permanent effect produced by an instantaneous\ncause, and possessing the property of self-perpetuation.\n\nLet us now suppose that the original agent or cause, instead of being\ninstantaneous, is permanent. Whatever effect has been produced up to a\ngiven time, would (unless prevented by the intervention of some new cause)\nsubsist permanently, even if the cause were to perish. Since, however, the\ncause does not perish, but continues to exist and to operate, it must go\non producing more and more of the effect; and instead of a uniform effect,\nwe have a progressive series of effects, arising from the accumulated\ninfluence of a permanent cause. Thus, the contact of iron with the\natmosphere causes a portion of it to rust; and if the cause ceased, the\neffect already produced would be permanent, but no further effect would be\nadded. If, however, the cause, namely, exposure to moist air, continues,\nmore and more of the iron becomes rusted, until all which is exposed is\nconverted into a red powder, when one of the conditions of the production\nof rust, namely, the presence of unoxidized iron, has ceased, and the\neffect can not any longer be produced. Again, the earth causes bodies to\nfall toward it; that is, the existence of the earth at a given instant\ncauses an unsupported body to move toward it at the succeeding instant;\nand if the earth were annihilated, as much of the effect as is already\nproduced would continue; the object would go on moving in the same\ndirection, with its acquired velocity, until intercepted by some body or\ndeflected by some other force. The earth, however, not being annihilated,\ngoes on producing in the second instant an effect similar and of equal\namount with the first, which two effects being added together, there\nresults an accelerated velocity; and this operation being repeated at each\nsuccessive instant, the mere permanence of the cause, though without\nincrease, gives rise to a constant progressive increase of the effect, so\nlong as all the conditions, negative and positive, of the production of\nthat effect continue to be realized.\n\nIt is obvious that this state of things is merely a case of the\nComposition of Causes. A cause which continues in action must on a strict\nanalysis be considered as a number of causes exactly similar, successively\nintroduced, and producing by their combination the sum of the effects\nwhich they would severally produce if they acted singly. The progressive\nrusting of the iron is in strictness the sum of the effects of many\nparticles of air acting in succession upon corresponding particles of\niron. The continued action of the earth upon a falling body is equivalent\nto a series of forces, applied in successive instants, each tending to\nproduce a certain constant quantity of motion; and the motion at each\ninstant is the sum of the effects of the new force applied at the\npreceding instant, and the motion already acquired. In each instant a\nfresh effect, of which gravity is the proximate cause, is added to the\neffect of which it was the remote cause; or (to express the same thing in\nanother manner), the effect produced by the earth\u2019s influence at the\ninstant last elapsed is added to the sum of the effects of which the\nremote causes were the influences exerted by the earth at all the previous\ninstants since the motion began. The case, therefore, comes under the\nprinciple of a concurrence of causes producing an effect equal to the sum\nof their separate effects. But as the causes come into play not all at\nonce, but successively, and as the effect at each instant is the sum of\nthe effects of those causes only which have come into action up to that\ninstant, the result assumes the form of an ascending series; a succession\nof sums, each greater than that which preceded it; and we have thus a\nprogressive effect from the continued action of a cause.\n\nSince the continuance of the cause influences the effect only by adding to\nits quantity, and since the addition takes place according to a fixed law\n(equal quantities in equal times), the result is capable of being computed\non mathematical principles. In fact, this case, being that of\ninfinitesimal increments, is precisely the case which the differential\ncalculus was invented to meet. The questions, what effect will result from\nthe continual addition of a given cause to itself, and what amount of the\ncause, being continually added to itself, will produce a given amount of\nthe effect, are evidently mathematical questions, and to be treated,\ntherefore, deductively. If, as we have seen, cases of the Composition of\nCauses are seldom adapted for any other than deductive investigation, this\nis especially true in the case now examined, the continual composition of\na cause with its own previous effects; since such a case is peculiarly\namenable to the deductive method, while the undistinguishable manner in\nwhich the effects are blended with one another and with the causes, must\nmake the treatment of such an instance experimentally still more\nchimerical than in any other case.\n\n\u00a7 2. We shall next advert to a rather more intricate operation of the same\nprinciple, namely, when the cause does not merely continue in action, but\nundergoes, during the same time, a progressive change in those of its\ncircumstances which contribute to determine the effect. In this case, as\nin the former, the total effect goes on accumulating by the continual\naddition of a fresh effect to that already produced, but it is no longer\nby the addition of equal quantities in equal times; the quantities added\nare unequal, and even the quality may now be different. If the change in\nthe state of the permanent cause be progressive, the effect will go\nthrough a double series of changes, arising partly from the accumulated\naction of the cause, and partly from the changes in its action. The effect\nis still a progressive effect, produced, however, not by the mere\ncontinuance of a cause, but by its continuance and its progressiveness\ncombined.\n\nA familiar example is afforded by the increase of the temperature as\nsummer advances, that is, as the sun draws nearer to a vertical position,\nand remains a greater number of hours above the horizon. This instance\nexemplifies in a very interesting manner the twofold operation on the\neffect, arising from the continuance of the cause, and from its\nprogressive change. When once the sun has come near enough to the zenith,\nand remains above the horizon long enough, to give more warmth during one\ndiurnal rotation than the counteracting cause, the earth\u2019s radiation, can\ncarry off, the mere continuance of the cause would progressively increase\nthe effect, even if the sun came no nearer and the days grew no longer;\nbut in addition to this, a change takes place in the accidents of the\ncause (its series of diurnal positions), tending to increase the quantity\nof the effect. When the summer solstice has passed, the progressive change\nin the cause begins to take place the reverse way, but, for some time, the\naccumulating effect of the mere continuance of the cause exceeds the\neffect of the changes in it, and the temperature continues to increase.\n\nAgain, the motion of a planet is a progressive effect, produced by causes\nat once permanent and progressive. The orbit of a planet is determined\n(omitting perturbations) by two causes: first, the action of the central\nbody, a permanent cause, which alternately increases and diminishes as the\nplanet draws nearer to or goes farther from its perihelion, and which acts\nat every point in a different direction; and, secondly, the tendency of\nthe planet to continue moving in the direction and with the velocity which\nit has already acquired. This force also grows greater as the planet draws\nnearer to its perihelion, because as it does so its velocity increases,\nand less, as it recedes from its perihelion; and this force as well as the\nother acts at each point in a different direction, because at every point\nthe action of the central force, by deflecting the planet from its\nprevious direction, alters the line in which it tends to continue moving.\nThe motion at each instant is determined by the amount and direction of\nthe motion, and the amount and direction of the sun\u2019s action, at the\nprevious instant; and if we speak of the entire revolution of the planet\nas one phenomenon (which, as it is periodical and similar to itself, we\noften find it convenient to do), that phenomenon is the progressive effect\nof two permanent and progressive causes, the central force and the\nacquired motion. Those causes happening to be progressive in the\nparticular way which is called periodical, the effect necessarily is so\ntoo; because the quantities to be added together returning in a regular\norder, the same sums must also regularly return.\n\nThis example is worthy of consideration also in another respect. Though\nthe causes themselves are permanent, and independent of all conditions\nknown to us, the changes which take place in the quantities and relations\nof the causes are actually caused by the periodical changes in the\neffects. The causes, as they exist at any moment, having produced a\ncertain motion, that motion, becoming itself a cause, reacts upon the\ncauses, and produces a change in them. By altering the distance and\ndirection of the central body relatively to the planet, and the direction\nand quantity of the force in the direction of the tangent, it alters the\nelements which determine the motion at the next succeeding instant. This\nchange renders the next motion somewhat different; and this difference, by\na fresh reaction upon the causes, renders the next motion again different,\nand so on. The original state of the causes might have been such that this\nseries of actions modified by reactions would not have been periodical.\nThe sun\u2019s action, and the original impelling force, might have been in\nsuch a ratio to one another, that the reaction of the effect would have\nbeen such as to alter the causes more and more, without ever bringing them\nback to what they were at any former time. The planet would then have\nmoved in a parabola, or an hyperbola, curves not returning into\nthemselves. The quantities of the two forces were, however, originally\nsuch, that the successive reactions of the effect bring back the causes,\nafter a certain time, to what they were before; and from that time all the\nvariations continued to recur again and again in the same periodical\norder, and must so continue while the causes subsist and are not\ncounteracted.\n\n\u00a7 3. In all cases of progressive effects, whether arising from the\naccumulation of unchanging or of changing elements, there is a uniformity\nof succession not merely between the cause and the effect, but between the\nfirst stages of the effect and its subsequent stages. That a body _in\nvacuo_ falls sixteen feet in the first second, forty-eight in the second,\nand so on in the ratio of the odd numbers, is as much a uniform sequence\nas that when the supports are removed the body falls. The sequence of\nspring and summer is as regular and invariable as that of the approach of\nthe sun and spring; but we do not consider spring to be the cause of\nsummer; it is evident that both are successive effects of the heat\nreceived from the sun, and that, considered merely in itself, spring might\ncontinue forever without having the slightest tendency to produce summer.\nAs we have so often remarked, not the conditional, but the unconditional\ninvariable antecedent is termed the cause. That which would not be\nfollowed by the effect unless something else had preceded, and which if\nthat something else had preceded, would not have been required, is not the\ncause, however invaluable the sequence may in fact be.\n\nIt is in this way that most of those uniformities of succession are\ngenerated, which are not cases of causation. When a phenomenon goes on\nincreasing, or periodically increases and diminishes, or goes through any\ncontinued and unceasing process of variation reducible to a uniform rule\nor law of succession, we do not on this account presume that any two\nsuccessive terms of the series are cause and effect. We presume the\ncontrary; we expect to find that the whole series originates either from\nthe continued action of fixed causes or from causes which go through a\ncorresponding process of continuous change. A tree grows from half an inch\nhigh to a hundred feet; and some trees will generally grow to that height\nunless prevented by some counteracting cause. But we do not call the\nseedling the cause of the full-grown tree; the invariable antecedent it\ncertainly is, and we know very imperfectly on what other antecedents the\nsequence is contingent, but we are convinced that it is contingent on\nsomething; because the homogeneousness of the antecedent with the\nconsequent, the close resemblance of the seedling to the tree in all\nrespects except magnitude, and the graduality of the growth, so exactly\nresembling the progressively accumulating effect produced by the long\naction of some one cause, leave no possibility of doubting that the\nseedling and the tree are two terms in a series of that description, the\nfirst term of which is yet to seek. The conclusion is further confirmed by\nthis, that we are able to prove by strict induction the dependence of the\ngrowth of the tree, and even of the continuance of its existence, upon the\ncontinued repetition of certain processes of nutrition, the rise of the\nsap, the absorptions and exhalations by the leaves, etc.; and the same\nexperiments would probably prove to us that the growth of the tree is the\naccumulated sum of the effects of these continued processes, were we not,\nfor want of sufficiently microscopic eyes, unable to observe correctly and\nin detail what those effects are.\n\nThis supposition by no means requires that the effect should not, during\nits progress, undergo many modifications besides those of quantity, or\nthat it should not sometimes appear to undergo a very marked change of\ncharacter. This may be either because the unknown cause consists of\nseveral component elements or agents, whose effects, accumulating\naccording to different laws, are compounded in different proportions at\ndifferent periods in the existence of the organized being; or because, at\ncertain points in its progress, fresh causes or agencies come in, or are\nevolved, which intermix their laws with those of the prime agent.\n\n\n\n\n                               Chapter XVI.\n\n\nOf Empirical Laws.\n\n\n\u00a7 1. Scientific inquirers give the name of Empirical Laws to those\nuniformities which observation or experiment has shown to exist, but on\nwhich they hesitate to rely in cases varying much from those which have\nbeen actually observed, for want of seeing any reason _why_ such a law\nshould exist. It is implied, therefore, in the notion of an empirical law,\nthat it is not an ultimate law; that if true at all, its truth is capable\nof being, and requires to be, accounted for. It is a derivative law, the\nderivation of which is not yet known. To state the explanation, the _why_,\nof the empirical law, would be to state the laws from which it is\nderived\u2014the ultimate causes on which it is contingent. And if we knew\nthese, we should also know what are its limits; under what conditions it\nwould cease to be fulfilled.\n\nThe periodical return of eclipses, as originally ascertained by the\npersevering observation of the early Eastern astronomers, was an empirical\nlaw, until the general laws of the celestial motions had accounted for it.\nThe following are empirical laws still waiting to be resolved into the\nsimpler laws from which they are derived: the local laws of the flux and\nreflux of the tides in different places; the succession of certain kinds\nof weather to certain appearances of sky; the apparent exceptions to the\nalmost universal truth that bodies expand by increase of temperature; the\nlaw that breeds, both animal and vegetable, are improved by crossing; that\ngases have a strong tendency to permeate animal membranes; that substances\ncontaining a very high proportion of nitrogen (such as hydrocyanic acid\nand morphia) are powerful poisons; that when different metals are fused\ntogether the alloy is harder than the various elements; that the number of\natoms of acid required to neutralize one atom of any base is equal to the\nnumber of atoms of oxygen in the base; that the solubility of substances\nin one another depends,(171) at least in some degree, on the similarity of\ntheir elements.\n\nAn empirical law, then, is an observed uniformity, presumed to be\nresolvable into simpler laws, but not yet resolved into them. The\nascertainment of the empirical laws of phenomena often precedes by a long\ninterval the explanation of those laws by the Deductive Method; and the\nverification of a deduction usually consists in the comparison of its\nresults with empirical laws previously ascertained.\n\n\u00a7 2. From a limited number of ultimate laws of causation, there are\nnecessarily generated a vast number of derivative uniformities, both of\nsuccession and co-existence. Some are laws of succession or of\nco-existence between different effects of the same cause; of these we had\nexamples in the last chapter. Some are laws of succession between effects\nand their remote causes, resolvable into the laws which connect each with\nthe intermediate link. Thirdly, when causes act together and compound\ntheir effects, the laws of those causes generate the fundamental law of\nthe effect, namely, that it depends on the co-existence of those causes.\nAnd, finally, the order of succession or of co-existence which obtains\namong effects necessarily depends on their causes. If they are effects of\nthe same cause, it depends on the laws of that cause; if on different\ncauses, it depends on the laws of those causes severally, and on the\ncircumstances which determine their co-existence. If we inquire further\nwhen and how the causes will co-exist, that, again, depends on _their_\ncauses; and we may thus trace back the phenomena higher and higher, until\nthe different series of effects meet in a point, and the whole is shown to\nhave depended ultimately on some common cause; or until, instead of\nconverging to one point, they terminate in different points, and the order\nof the effects is proved to have arisen from the collocation of some of\nthe primeval causes, or natural agents. For example, the order of\nsuccession and of co-existence among the heavenly motions, which is\nexpressed by Kepler\u2019s laws, is derived from the co-existence of two\nprimeval causes, the sun, and the original impulse or projectile force\nbelonging to each planet.(172) Kepler\u2019s laws are resolved into the laws of\nthese causes and the fact of their co-existence.\n\nDerivative laws, therefore, do not depend solely on the ultimate laws into\nwhich they are resolvable; they mostly depend on those ultimate laws, and\nan ultimate fact; namely, the mode of co-existence of some of the\ncomponent elements of the universe. The ultimate laws of causation might\nbe the same as at present, and yet the derivative laws completely\ndifferent, if the causes co-existed in different proportions, or with any\ndifference in those of their relations by which the effects are\ninfluenced. If, for example, the sun\u2019s attraction, and the original\nprojectile force, had existed in some other ratio to one another than they\ndid (and we know of no reason why this should not have been the case), the\nderivative laws of the heavenly motions might have been quite different\nfrom what they are. The proportions which exist happen to be such as to\nproduce regular elliptical motions; any other proportions would have\nproduced different ellipses, or circular, or parabolic, or hyperbolic\nmotions, but still regular ones; because the effects of each of the agents\naccumulate according to a uniform law; and two regular series of\nquantities, when their corresponding terms are added, must produce a\nregular series of some sort, whatever the quantities themselves are.\n\n\u00a7 3. Now this last-mentioned element in the resolution of a derivative\nlaw, the element which is not a law of causation, but a collocation of\ncauses, can not itself be reduced to any law. There is, as formerly\nremarked,(173) no uniformity, no _norma_, principle, or rule, perceivable\nin the distribution of the primeval natural agents through the universe.\nThe different substances composing the earth, the powers that pervade the\nuniverse, stand in no constant relation to one another. One substance is\nmore abundant than others, one power acts through a larger extent of space\nthan others, without any pervading analogy that we can discover. We not\nonly do not know of any reason why the sun\u2019s attraction and the force in\nthe direction of the tangent co-exist in the exact proportion they do, but\nwe can trace no coincidence between it and the proportions in which any\nother elementary powers in the universe are intermingled. The utmost\ndisorder is apparent in the combination of the causes, which is consistent\nwith the most regular order in their effects; for when each agent carries\non its own operations according to a uniform law, even the most capricious\ncombination of agencies will generate a regularity of some sort; as we see\nin the kaleidoscope, where any casual arrangement of colored bits of glass\nproduces by the laws of reflection a beautiful regularity in the effect.\n\n\u00a7 4. In the above considerations lies the justification of the limited\ndegree of reliance which scientific inquirers are accustomed to place in\nempirical laws.\n\nA derivative law which results wholly from the operation of some one\ncause, will be as universally true as the laws of the cause itself; that\nis, it will always be true except where some one of those effects of the\ncause, on which the derivative law depends, is defeated by a counteracting\ncause. But when the derivative law results not from different effects of\none cause, but from effects of several causes, we can not be certain that\nit will be true under any variation in the mode of co-existence of those\ncauses, or of the primitive natural agents on which the causes ultimately\ndepend. The proposition that coal-beds rest on certain descriptions of\nstrata exclusively, though true on the earth, so far as our observation\nhas reached, can not be extended to the moon or the other planets,\nsupposing coal to exist there; because we can not be assured that the\noriginal constitution of any other planet was such as to produce the\ndifferent depositions in the same order as in our globe. The derivative\nlaw in this case depends not solely on laws, but on a collocation; and\ncollocations can not be reduced to any law.\n\nNow it is the very nature of a derivative law which has not yet been\nresolved into its elements, in other words, an empirical law, that we do\nnot know whether it results from the different effects of one cause, or\nfrom effects of different causes. We can not tell whether it depends\nwholly on laws, or partly on laws and partly on a collocation. If it\ndepends on a collocation, it will be true in all the cases in which that\nparticular collocation exists. But, since we are entirely ignorant, in\ncase of its depending on a collocation, what the collocation is, we are\nnot safe in extending the law beyond the limits of time and place in which\nwe have actual experience of its truth. Since within those limits the law\nhas always been found true, we have evidence that the collocations,\nwhatever they are, on which it depends, do really exist within those\nlimits. But, knowing of no rule or principle to which the collocations\nthemselves conform, we can not conclude that because a collocation is\nproved to exist within certain limits of place or time, it will exist\nbeyond those limits. Empirical laws, therefore, can only be received as\ntrue within the limits of time and place in which they have been found\ntrue by observation; and not merely the limits of time and place, but of\ntime, place, and circumstance; for, since it is the very meaning of an\nempirical law that we do not know the ultimate laws of causation on which\nit is dependent, we can not foresee, without actual trial, in what manner\nor to what extent the introduction of any new circumstance may affect it.\n\n\u00a7 5. But how are we to know that a uniformity ascertained by experience is\nonly an empirical law? Since, by the supposition, we have not been able to\nresolve it into any other laws, how do we know that it is not an ultimate\nlaw of causation?\n\nI answer that no generalization amounts to more than an empirical law when\nthe only proof on which it rests is that of the Method of Agreement. For\nit has been seen that by that method alone we never can arrive at causes.\nThe utmost that the Method of Agreement can do is, to ascertain the whole\nof the circumstances common to all cases in which a phenomenon is\nproduced; and this aggregate includes not only the cause of the\nphenomenon, but all phenomena with which it is connected by any derivative\nuniformity, whether as being collateral effects of the same cause, or\neffects of any other cause which, in all the instances we have been able\nto observe, co-existed with it. The method affords no means of determining\nwhich of these uniformities are laws of causation, and which are merely\nderivative laws, resulting from those laws of causation and from the\ncollocation of the causes. None of them, therefore, can be received in any\nother character than that of derivative laws, the derivation of which has\nnot been traced; in other words, empirical laws: in which light all\nresults obtained by the Method of Agreement (and therefore almost all\ntruths obtained by simple observation without experiment) must be\nconsidered, until either confirmed by the Method of Difference, or\nexplained deductively; in other words, accounted for _a priori_.\n\nThese empirical laws may be of greater or less authority, according as\nthere is reason to presume that they are resolvable into laws only, or\ninto laws and collocations together. The sequences which we observe in the\nproduction and subsequent life of an animal or a vegetable, resting on the\nMethod of Agreement only, are mere empirical laws; but though the\nantecedents in those sequences may not be the causes of the consequents,\nboth the one and the other are doubtless, in the main, successive stages\nof a progressive effect originating in a common cause, and therefore\nindependent of collocations. The uniformities, on the other hand, in the\norder of superposition of strata on the earth, are empirical laws of a\nmuch weaker kind, since they not only are not laws of causation, but there\nis no reason to believe that they depend on any common cause; all\nappearances are in favor of their depending on the particular collocation\nof natural agents which at some time or other existed on our globe, and\nfrom which no inference can be drawn as to the collocation which exists or\nhas existed in any other portion of the universe.\n\n\u00a7 6. Our definition of an empirical law, including not only those\nuniformities which are not known to be laws of causation, but also those\nwhich are, provided there be reason to presume that they are not ultimate\nlaws; this is the proper place to consider by what signs we may judge that\neven if an observed uniformity be a law of causation, it is not an\nultimate, but a derivative law.\n\nThe first sign is, if between the antecedent _a_ and the consequent _b_\nthere be evidence of some intermediate link; some phenomenon of which we\ncan surmise the existence, though from the imperfection of our senses or\nof our instruments we are unable to ascertain its precise nature and laws.\nIf there be such a phenomenon (which may be denoted by the letter _x_), it\nfollows that even if _a_ be the cause of _b_, it is but the remote cause,\nand that the law, _a_ causes _b_, is resolvable into at least two laws,\n_a_ causes _x_, and _x_ causes _b_. This is a very frequent case, since\nthe operations of nature mostly take place on so minute a scale, that many\nof the successive steps are either imperceptible, or very indistinctly\nperceived.\n\nTake, for example, the laws of the chemical composition of substances; as\nthat hydrogen and oxygen being combined, water is produced. All we see of\nthe process is, that the two gases being mixed in certain proportions, and\nheat or electricity being applied, an explosion takes place, the gases\ndisappear, and water remains. There is no doubt about the law, or about\nits being a law of causation. But between the antecedent (the gases in a\nstate of mechanical mixture, heated or electrified), and the consequent\n(the production of water), there must be an intermediate process which we\ndo not see. For if we take any portion whatever of the water, and subject\nit to analysis, we find that it always contains hydrogen and oxygen; nay,\nthe very same proportions of them, namely, two-thirds, in volume, of\nhydrogen, and one-third oxygen. This is true of a single drop; it is true\nof the minutest portion which our instruments are capable of appreciating.\nSince, then, the smallest perceptible portion of the water contains both\nthose substances, portions of hydrogen and oxygen smaller than the\nsmallest perceptible must have come together in every such minute portion\nof space; must have come closer together than when the gases were in a\nstate of mechanical mixture, since (to mention no other reasons) the water\noccupies far less space than the gases. Now, as we can not see this\ncontact or close approach of the minute particles, we can not observe with\nwhat circumstances it is attended, or according to what laws it produces\nits effects. The production of water, that is, of the sensible phenomena\nwhich characterize the compound, may be a very remote effect of those\nlaws. There may be innumerable intervening links; and we are sure that\nthere must be some. Having full proof that corpuscular action of some kind\ntakes place previous to any of the great transformations in the sensible\nproperties of substances, we can have no doubt that the laws of chemical\naction, as at present known, are not ultimate, but derivative laws;\nhowever ignorant we may be, and even though we should forever remain\nignorant, of the nature of the laws of corpuscular action from which they\nare derived.\n\nIn like manner, all the processes of vegetative life, whether in the\nvegetable properly so called or in the animal body, are corpuscular\nprocesses. Nutrition is the addition of particles to one another,\nsometimes merely replacing other particles separated and excreted,\nsometimes occasioning an increase of bulk or weight so gradual that only\nafter a long continuance does it become perceptible. Various organs, by\nmeans of peculiar vessels, secrete from the blood fluids, the component\nparticles of which must have been in the blood, but which differ from it\nmost widely both in mechanical properties and in chemical composition.\nHere, then, are abundance of unknown links to be filled up; and there can\nbe no doubt that the laws of the phenomena of vegetative or organic life\nare derivative laws, dependent on properties of the corpuscles, and of\nthose elementary tissues which are comparatively simple combinations of\ncorpuscles.\n\nThe first sign, then, from which a law of causation, though hitherto\nunresolved, may be inferred to be a derivative law, is any indication of\nthe existence of an intermediate link or links between the antecedent and\nthe consequent. The second is, when the antecedent is an extremely complex\nphenomenon, and its effects, therefore, probably in part at least,\ncompounded of the effects of its different elements; since we know that\nthe case in which the effect of the whole is not made up of the effects of\nits parts is exceptional, the Composition of Causes being by far the more\nordinary case.\n\nWe will illustrate this by two examples, in one of which the antecedent is\nthe sum of many homogeneous, in the other of heterogeneous, parts. The\nweight of a body is made up of the weights of its minute particles; a\ntruth which astronomers express in its most general terms when they say\nthat bodies, at equal distances, gravitate to one another in proportion to\ntheir quantity of matter. All true propositions, therefore, which can be\nmade concerning gravity, are derivative laws; the ultimate law into which\nthey are all resolvable being, that every particle of matter attracts\nevery other. As our second example, we may take any of the sequences\nobserved in meteorology; for instance, a diminution of the pressure of the\natmosphere (indicated by a fall of the barometer) is followed by rain. The\nantecedent is here a complex phenomenon, made up of heterogeneous\nelements; the column of the atmosphere over any particular place\nconsisting of two parts, a column of air, and a column of aqueous vapor\nmixed with it; and the change in the two together manifested by a fall of\nthe barometer, and followed by rain, must be either a change in one of\nthese, or in the other, or in both. We might, then, even in the absence of\nany other evidence, form a reasonable presumption, from the invariable\npresence of both these elements in the antecedent, that the sequence is\nprobably not an ultimate law, but a result of the laws of the two\ndifferent agents; a presumption only to be destroyed when we had made\nourselves so well acquainted with the laws of both, as to be able to\naffirm that those laws could not by themselves produce the observed\nresult.\n\nThere are but few known cases of succession from very complex antecedents\nwhich have not either been actually accounted for from simpler laws, or\ninferred with great probability (from the ascertained existence of\nintermediate links of causation not yet understood) to be capable of being\nso accounted for. It is, therefore, highly probable that all sequences\nfrom complex antecedents are thus resolvable, and that ultimate laws are\nin all cases comparatively simple. If there were not the other reasons\nalready mentioned for believing that the laws of organized nature are\nresolvable into simpler laws, it would be almost a sufficient reason that\nthe antecedents in most of the sequences are so very complex.\n\n\u00a7 7. In the preceding discussion we have recognized two kinds of empirical\nlaws: those known to be laws of causation, but presumed to be resolvable\ninto simpler laws; and those not known to be laws of causation at all.\nBoth these kinds of laws agree in the demand which they make for being\nexplained by deduction, and agree in being the appropriate means of\nverifying such deduction, since they represent the experience with which\nthe result of the deduction must be compared. They agree, further, in\nthis, that until explained, and connected with the ultimate laws from\nwhich they result, they have not attained the highest degree of certainty\nof which laws are susceptible. It has been shown on a former occasion that\nlaws of causation which are derivative, and compounded of simpler laws,\nare not only, as the nature of the case implies, less general, but even\nless certain, than the simpler laws from which they result; not in the\nsame degree to be relied on as universally true. The inferiority of\nevidence, however, which attaches to this class of laws, is trifling,\ncompared with that which is inherent in uniformities not known to be laws\nof causation at all. So long as these are unresolved, we can not tell on\nhow many collocations, as well as laws, their truth may be dependent; we\ncan never, therefore, extend them with any confidence to cases in which we\nhave not assured ourselves, by trial, that the necessary collocation of\ncauses, whatever it may be, exists. It is to this class of laws alone that\nthe property, which philosophers usually consider as characteristic of\nempirical laws, belongs in all its strictness\u2014the property of being unfit\nto be relied on beyond the limits of time, place, and circumstance in\nwhich the observations have been made. These are empirical laws in a more\nemphatic sense; and when I employ that term (except where the context\nmanifestly indicates the reverse) I shall generally mean to designate\nthose uniformities only, whether of succession or of co-existence, which\nare not known to be laws of causation.\n\n\n\n\n                              Chapter XVII.\n\n\nOf Chance And Its Elimination.\n\n\n\u00a7 1. Considering, then, as empirical laws only those observed uniformities\nrespecting which the question whether they are laws of causation must\nremain undecided until they can be explained deductively, or until some\nmeans are found of applying the Method of Difference to the case, it has\nbeen shown in the preceding chapter that until a uniformity can, in one or\nthe other of these modes, be taken out of the class of empirical laws, and\nbrought either into that of laws of causation or of the demonstrated\nresults of laws of causation, it can not with any assurance be pronounced\ntrue beyond the local and other limits within which it has been found so\nby actual observation. It remains to consider how we are to assure\nourselves of its truth even within those limits; after what quantity of\nexperience a generalization which rests solely on the Method of Agreement\ncan be considered sufficiently established, even as an empirical law. In a\nformer chapter, when treating of the Methods of Direct Induction, we\nexpressly reserved this question,(174) and the time is now come for\nendeavoring to solve it.\n\nWe found that the Method of Agreement has the defect of not proving\ncausation, and can, therefore, only be employed for the ascertainment of\nempirical laws. But we also found that besides this deficiency, it labors\nunder a characteristic imperfection, tending to render uncertain even such\nconclusions as it is in itself adapted to prove. This imperfection arises\nfrom Plurality of Causes. Although two or more cases in which the\nphenomenon _a_ has been met with may have no common antecedent except A,\nthis does not prove that there is any connection between _a_ and A, since\n_a_ may have many causes, and may have been produced, in these different\ninstances, not by any thing which the instances had in common, but by some\nof those elements in them which were different. We nevertheless observed,\nthat in proportion to the multiplication of instances pointing to A as the\nantecedent, the characteristic uncertainty of the method diminishes, and\nthe existence of a law of connection between A and _a_ more nearly\napproaches to certainty. It is now to be determined after what amount of\nexperience this certainty may be deemed to be practically attained, and\nthe connection between A and _a_ may be received as an empirical law.\n\nThis question may be otherwise stated in more familiar terms: After how\nmany and what sort of instances may it be concluded that an observed\ncoincidence between two phenomena is not the effect of chance?\n\nIt is of the utmost importance for understanding the logic of induction,\nthat we should form a distinct conception of what is meant by chance, and\nhow the phenomena which common language ascribes to that abstraction are\nreally produced.\n\n\u00a7 2. Chance is usually spoken of in direct antithesis to law; whatever, it\nis supposed, can not be ascribed to any law is attributed to chance. It\nis, however, certain that whatever happens is the result of some law; is\nan effect of causes, and could have been predicted from a knowledge of the\nexistence of those causes, and from their laws. If I turn up a particular\ncard, that is a consequence of its place in the pack. Its place in the\npack was a consequence of the manner in which the cards were shuffled, or\nof the order in which they were played in the last game; which, again,\nwere effects of prior causes. At every stage, if we had possessed an\naccurate knowledge of the causes in existence, it would have been\nabstractedly possible to foretell the effect.\n\nAn event occurring by chance may be better described as a coincidence from\nwhich we have no ground to infer a uniformity\u2014the occurrence of a\nphenomenon in certain circumstances, without our having reason on that\naccount to infer that it will happen again in those circumstances. This,\nhowever, when looked closely into, implies that the enumeration of the\ncircumstances is not complete. Whatever the fact be, since it has occurred\nonce, we may be sure that if _all_ the same circumstances were repeated it\nwould occur again; and not only if all, but there is some particular\nportion of those circumstances on which the phenomenon is invariably\nconsequent. With most of them, however, it is not connected in any\npermanent manner; its conjunction with those is said to be the effect of\nchance, to be merely casual. Facts casually conjoined are separately the\neffects of causes, and therefore of laws; but of different causes, and\ncauses not connected by any law.\n\nIt is incorrect, then, to say that any phenomenon is produced by chance;\nbut we may say that two or more phenomena are conjoined by chance, that\nthey co-exist or succeed one another only by chance; meaning that they are\nin no way related through causation; that they are neither cause and\neffect, nor effects of the same cause, nor effects of causes between which\nthere subsists any law of co-existence, nor even effects of the same\ncollocation of primeval causes.\n\nIf the same casual coincidence never occurred a second time, we should\nhave an easy test for distinguishing such from the coincidences which are\nthe results of a law. As long as the phenomena had been found together\nonly once, so long, unless we knew some more general laws from which the\ncoincidence might have resulted, we could not distinguish it from a casual\none; but if it occurred twice, we should know that the phenomena so\nconjoined must be in some way connected through their causes.\n\nThere is, however, no such test. A coincidence may occur again and again,\nand yet be only casual. Nay, it would be inconsistent with what we know of\nthe order of nature to doubt that every casual coincidence will sooner or\nlater be repeated, as long as the phenomena between which it occurred do\nnot cease to exist, or to be reproduced. The recurrence, therefore, of the\nsame coincidence more than once, or even its frequent recurrence, does not\nprove that it is an instance of any law; does not prove that it is not\ncasual, or, in common language, the effect of chance.\n\nAnd yet, when a coincidence can not be deduced from known laws, nor proved\nby experiment to be itself a case of causation, the frequency of its\noccurrence is the only evidence from which we can infer that it is the\nresult of a law. Not, however, its absolute frequency. The question is not\nwhether the coincidence occurs often or seldom, in the ordinary sense of\nthose terms; but whether it occurs more often than chance will account\nfor; more often than might rationally be expected if the coincidence were\ncasual. We have to decide, therefore, what degree of frequency in a\ncoincidence chance will account for; and to this there can be no general\nanswer. We can only state the principle by which the answer must be\ndetermined; the answer itself will be different in every different case.\n\nSuppose that one of the phenomena, A, exists always, and the other\nphenomenon, B, only occasionally; it follows that every instance of B will\nbe an instance of its coincidence with A, and yet the coincidence will be\nmerely casual, not the result of any connection between them. The fixed\nstars have been constantly in existence since the beginning of human\nexperience, and all phenomena that have come under human observation have,\nin every single instance, co-existed with them; yet this coincidence,\nthough equally invariable with that which exists between any of those\nphenomena and its own cause, does not prove that the stars are its cause,\nnor that they are in anywise connected with it. As strong a case of\ncoincidence, therefore, as can possibly exist, and a much stronger one in\npoint of mere frequency than most of those which prove laws, does not here\nprove a law; why? because, since the stars exist always, they _must_\nco-exist with every other phenomenon, whether connected with them by\ncausation or not. The uniformity, great though it be, is no greater than\nwould occur on the supposition that no such connection exists.\n\nOn the other hand, suppose that we were inquiring whether there be any\nconnection between rain and any particular wind. Rain, we know,\noccasionally occurs with every wind; therefore, the connection, if it\nexists, can not be an actual law; but still rain may be connected with\nsome particular wind through causation; that is, though they can not be\nalways effects of the same cause (for if so they would regularly\nco-exist), there may be some causes common to the two, so that in so far\nas either is produced by those common causes, they will, from the laws of\nthe causes, be found to co-exist. How, then, shall we ascertain this? The\nobvious answer is, by observing whether rain occurs with one wind more\nfrequently than with any other. That, however, is not enough; for perhaps\nthat one wind blows more frequently than any other; so that its blowing\nmore frequently in rainy weather is no more than would happen, although it\nhad no connection with the causes of rain, provided it were not connected\nwith causes adverse to rain. In England, westerly winds blow during about\ntwice as great a portion of the year as easterly. If, therefore, it rains\nonly twice as often with a westerly as with an easterly wind, we have no\nreason to infer that any law of nature is concerned in the coincidence. If\nit rains more than twice as often, we may be sure that some law is\nconcerned; either there is some cause in nature which, in this climate,\ntends to produce both rain and a westerly wind, or a westerly wind has\nitself some tendency to produce rain. But if it rains less than twice as\noften, we may draw a directly opposite inference: the one, instead of\nbeing a cause, or connected with causes of the other, must be connected\nwith causes adverse to it, or with the absence of some cause which\nproduces it; and though it may still rain much oftener with a westerly\nwind than with an easterly, so far would this be from proving any\nconnection between the phenomena, that the connection proved would be\nbetween rain and an easterly wind, to which, in mere frequency of\ncoincidence, it is less allied.\n\nHere, then, are two examples: in one, the greatest possible frequency of\ncoincidence, with no instance whatever to the contrary, does not prove\nthat there is any law; in the other, a much less frequency of\ncoincidence, even when non-coincidence is still more frequent, does\nprove that there is a law. In both cases the principle is the same. In\nboth we consider the positive frequency of the phenomena themselves, and\nhow great frequency of coincidence that must of itself bring about,\nwithout supposing any connection between them, provided there be no\nrepugnance; provided neither be connected with any cause tending to\nfrustrate the other. If we find a greater frequency of coincidence than\nthis, we conclude that there is some connection; if a less frequency,\nthat there is some repugnance. In the former case, we conclude that one\nof the phenomena can under some circumstances cause the other, or that\nthere exists something capable of causing them both; in the latter, that\none of them, or some cause which produces one of them, is capable of\ncounteracting the production of the other. We have thus to deduct from\nthe observed frequency of coincidence as much as may be the effect of\nchance, that is, of the mere frequency of the phenomena themselves; and\nif any thing remains, what does remain is the residual fact which proves\nthe existence of a law.\n\nThe frequency of the phenomena can only be ascertained within definite\nlimits of space and time; depending as it does on the quantity and\ndistribution of the primeval natural agents, of which we can know\nnothing beyond the boundaries of human observation, since no law, no\nregularity, can be traced in it, enabling us to infer the unknown from\nthe known. But for the present purpose this is no disadvantage, the\nquestion being confined within the same limits as the data. The\ncoincidences occurred in certain places and times, and within those we\ncan estimate the frequency with which such coincidences would be\nproduced by chance. If, then, we find from observation that A exists in\none case out of every two, and B in one case out of every three; then,\nif there be neither connection nor repugnance between them, or between\nany of their causes, the instances in which A and B will both exist,\nthat is to say will co-exist, will be one case in every six. For A\nexists in three cases out of six; and B, existing in one case out of\nevery three without regard to the presence or absence of A, will exist\nin one case out of those three. There will therefore be, of the whole\nnumber of cases, two in which A exists without B; one case of B without\nA; two in which neither B nor A exists, and one case out of six in which\nthey both exist. If, then, in point of fact, they are found to co-exist\noftener than in one case out of six; and, consequently, A does not exist\nwithout B so often as twice in three times, nor B without A so often as\nonce in every twice, there is some cause in existence which tends to\nproduce a conjunction between A and B.\n\nGeneralizing the result, we may say that if A occurs in a larger\nproportion of the cases where B is than of the cases where B is not,\nthen will B also occur in a larger proportion of the cases where A is\nthan of the cases where A is not; and there is some connection, through\ncausation, between A and B. If we could ascend to the causes of the two\nphenomena, we should find, at some stage, either proximate or remote,\nsome cause or causes common to both; and if we could ascertain what\nthese are, we could frame a generalization which would be true without\nrestriction of place or time; but until we can do so, the fact of a\nconnection between the two phenomena remains an empirical law.\n\n\u00a7 3. Having considered in what manner it may be determined whether any\ngiven conjunction of phenomena is casual, or the result of some law, to\ncomplete the theory of chance it is necessary that we should now\nconsider those effects which are partly the result of chance and partly\nof law, or, in other words, in which the effects of casual conjunctions\nof causes are habitually blended in one result with the effects of a\nconstant cause.\n\nThis is a case of Composition of Causes; and the peculiarity of it is,\nthat instead of two or more causes intermixing their effects in a\nregular manner with those of one another, we have now one constant\ncause, producing an effect which is successively modified by a series of\nvariable causes. Thus, as summer advances, the approach of the sun to a\nvertical position tends to produce a constant increase of temperature;\nbut with this effect of a constant cause, there are blended the effects\nof many variable causes, winds, clouds, evaporation, electric agencies\nand the like, so that the temperature of any given day depends in part\non these fleeting causes, and only in part on the constant cause. If the\neffect of the constant cause is always accompanied and disguised by\neffects of variable causes, it is impossible to ascertain the law of the\nconstant cause in the ordinary manner by separating it from all other\ncauses and observing it apart. Hence arises the necessity of an\nadditional rule of experimental inquiry.\n\nWhen the action of a cause A is liable to be interfered with, not\nsteadily by the same cause or causes, but by different causes at\ndifferent times, and when these are so frequent, or so indeterminate,\nthat we can not possibly exclude all of them from any experiment, though\nwe may vary them; our resource is, to endeavor to ascertain what is the\neffect of all the variable causes taken together. In order to do this,\nwe make as many trials as possible, preserving A invariable. The results\nof these different trials will naturally be different, since the\nindeterminate modifying causes are different in each; if, then, we do\nnot find these results to be progressive, but, on the contrary, to\noscillate about a certain point, one experiment giving a result a little\ngreater, another a little less, one a result tending a little more in\none direction, another a little more in the contrary direction; while\nthe average or middle point does not vary, but different sets of\nexperiments (taken in as great a variety of circumstances as possible)\nyield the same mean, provided only they be sufficiently numerous; then\nthat mean, or average result, is the part, in each experiment, which is\ndue to the cause A, and is the effect which would have been obtained if\nA could have acted alone; the variable remainder is the effect of\nchance, that is, of causes the co-existence of which with the cause A\nwas merely casual. The test of the sufficiency of the induction in this\ncase is, when any increase of the number of trials from which the\naverage is struck does not materially alter the average.\n\nThis kind of elimination, in which we do not eliminate any one\nassignable cause, but the multitude of floating unassignable ones, may\nbe termed the Elimination of Chance. We afford an example of it when we\nrepeat an experiment, in order, by taking the mean of different results,\nto get rid of the effects of the unavoidable errors of each individual\nexperiment. When there is no permanent cause, such as would produce a\ntendency to error peculiarly in one direction, we are warranted by\nexperience in assuming that the errors on one side will, in a certain\nnumber of experiments, about balance the errors on the contrary side. We\ntherefore repeat the experiment, until any change which is produced in\nthe average of the whole by further repetition, falls within limits of\nerror consistent with the degree of accuracy required by the purpose we\nhave in view.(175)\n\n\u00a7 4. In the supposition hitherto made, the effect of the constant cause\nA has been assumed to form so great and conspicuous a part of the\ngeneral result, that its existence never could be a matter of\nuncertainty, and the object of the eliminating process was only to\nascertain _how much_ is attributable to that cause; what is its exact\nlaw. Cases, however, occur in which the effect of a constant cause is so\nsmall, compared with that of some of the changeable causes with which it\nis liable to be casually conjoined, that of itself it escapes notice,\nand the very existence of any effect arising from a constant cause is\nfirst learned by the process which in general serves only for\nascertaining the quantity of that effect. This case of induction may be\ncharacterized as follows: A given effect is known to be chiefly, and not\nknown not to be wholly, determined by changeable causes. If it be wholly\nso produced, then if the aggregate be taken of a sufficient number of\ninstances, the effects of these different causes will cancel one\nanother. If, therefore, we do not find this to be the case, but, on the\ncontrary, after such a number of trials has been made that no further\nincrease alters the average result, we find that average to be, not\nzero, but some other quantity, about which, though small in comparison\nwith the total effect, the effect nevertheless oscillates, and which is\nthe middle point in its oscillation; we may conclude this to be the\neffect of some constant cause; which cause, by some of the methods\nalready treated of, we may hope to detect. This may be called _the\ndiscovery of a residual phenomenon by eliminating the effects of\nchance_.\n\nIt is in this manner, for example, that loaded dice may be discovered.\nOf course no dice are so clumsily loaded that they must always throw\ncertain numbers; otherwise the fraud would be instantly detected. The\nloading, a constant cause, mingles with the changeable causes which\ndetermine what cast will be thrown in each individual instance. If the\ndice were not loaded, and the throw were left to depend entirely on the\nchangeable causes, these in a sufficient number of instances would\nbalance one another, and there would be no preponderant number of throws\nof any one kind. If, therefore, after such a number of trials that no\nfurther increase of their number has any material effect upon the\naverage, we find a preponderance in favor of a particular throw; we may\nconclude with assurance that there is some constant cause acting in\nfavor of that throw, or, in other words, that the dice are not fair; and\nthe exact amount of the unfairness. In a similar manner, what is called\nthe diurnal variation of the barometer, which is very small compared\nwith the variations arising from the irregular changes in the state of\nthe atmosphere, was discovered by comparing the average height of the\nbarometer at different hours of the day. When this comparison was made,\nit was found that there was a small difference, which on the average was\nconstant, however the absolute quantities might vary, and which\ndifference, therefore, must be the effect of a constant cause. This\ncause was afterward ascertained, deductively, to be the rarefaction of\nthe air, occasioned by the increase of temperature as the day advances.\n\n\u00a7 5. After these general remarks on the nature of chance, we are\nprepared to consider in what manner assurance may be obtained that a\nconjunction between two phenomena, which has been observed a certain\nnumber of times, is not casual, but a result of causation, and to be\nreceived, therefore, as one of the uniformities of nature, though (until\naccounted for _a priori_) only as an empirical law.\n\nWe will suppose the strongest case, namely, that the phenomenon B has\nnever been observed except in conjunction with A. Even then, the\nprobability that they are connected is not measured by the total number\nof instances in which they have been found together, but by the excess\nof that number above the number due to the absolutely frequency of A.\nIf, for example, A exists always, and therefore co-exists with every\nthing, no number of instances of its co-existence with B would prove a\nconnection; as in our example of the fixed stars. If A be a fact of such\ncommon occurrence that it may be presumed to be present in half of all\nthe cases that occur, and therefore in half the cases in which B occurs,\nit is only the proportional excess above half that is to be reckoned as\nevidence toward proving a connection between A and B.\n\nIn addition to the question, What is the number of coincidences which,\non an average of a great multitude of trials, may be expected to arise\nfrom chance alone? there is also another question, namely, Of what\nextent of deviation from that average is the occurrence credible, from\nchance alone, in some number of instances smaller than that required for\nstriking a fair average? It is not only to be considered what is the\ngeneral result of the chances in the long run, but also what are the\nextreme limits of variation from the general result, which may\noccasionally be expected as the result of some smaller number of\ninstances.\n\nThe consideration of the latter question, and any consideration of the\nformer beyond that already given to it, belong to what mathematicians\nterm the doctrine of chances, or, in a phrase of greater pretension, the\nTheory of Probabilities.\n\n\n\n\n                              Chapter XVIII.\n\n\nOf The Calculation Of Chances.\n\n\n\u00a7 1. \u201cProbability,\u201d says Laplace,(176) \u201chas reference partly to our\nignorance, partly to our knowledge. We know that among three or more\nevents, one, and only one, must happen; but there is nothing leading us\nto believe that any one of them will happen rather than the others. In\nthis state of indecision, it is impossible for us to pronounce with\ncertainty on their occurrence. It is, however, probable that any one of\nthese events, selected at pleasure, will not take place; because we\nperceive several cases, all equally possible, which exclude its\noccurrence, and only one which favors it.\n\n\u201cThe theory of chances consists in reducing all events of the same kind\nto a certain number of cases equally possible, that is, such that we are\n_equally undecided_ as to their existence; and in determining the number\nof these cases which are favorable to the event of which the probability\nis sought. The ratio of that number to the number of all the possible\ncases is the measure of the probability; which is thus a fraction,\nhaving for its numerator the number of cases favorable to the event, and\nfor its denominator the number of all the cases which are possible.\u201d\n\nTo a calculation of chances, then, according to Laplace, two things are\nnecessary; we must know that of several events some one will certainly\nhappen, and no more than one; and we must not know, nor have any reason\nto expect, that it will be one of these events rather than another. It\nhas been contended that these are not the only requisites, and that\nLaplace has overlooked, in the general theoretical statement, a\nnecessary part of the foundation of the doctrine of chances. To be able\n(it has been said) to pronounce two events equally probable, it is not\nenough that we should know that one or the other must happen, and should\nhave no grounds for conjecturing which. Experience must have shown that\nthe two events are of equally frequent occurrence. Why, in tossing up a\nhalf-penny, do we reckon it equally probable that we shall throw cross\nor pile? Because we know that in any great number of throws, cross and\npile are thrown about equally often; and that the more throws we make,\nthe more nearly the equality is perfect. We may know this if we please\nby actual experiment, or by the daily experience which life affords of\nevents of the same general character, or, deductively, from the effect\nof mechanical laws on a symmetrical body acted upon by forces varying\nindefinitely in quantity and direction. We may know it, in short, either\nby specific experience, or on the evidence of our general knowledge of\nnature. But, in one way or the other, we must know it, to justify us in\ncalling the two events equally probable; and if we knew it not, we\nshould proceed as much at hap-hazard in staking equal sums on the\nresult, as in laying odds.\n\nThis view of the subject was taken in the first edition of the present\nwork; but I have since become convinced that the theory of chances, as\nconceived by Laplace and by mathematicians generally, has not the\nfundamental fallacy which I had ascribed to it.\n\nWe must remember that the probability of an event is not a quality of\nthe event itself, but a mere name for the degree of ground which we, or\nsome one else, have for expecting it. The probability of an event to one\nperson is a different thing from the probability of the same event to\nanother, or to the same person after he has acquired additional\nevidence. The probability to me, that an individual of whom I know\nnothing but his name will die within the year, is totally altered by my\nbeing told the next minute that he is in the last stage of a\nconsumption. Yet this makes no difference in the event itself, nor in\nany of the causes on which it depends. Every event is in itself certain,\nnot probable; if we knew all, we should either know positively that it\nwill happen, or positively that it will not. But its probability to us\nmeans the degree of expectation of its occurrence, which we are\nwarranted in entertaining by our present evidence.\n\nBearing this in mind, I think it must be admitted, that even when we\nhave no knowledge whatever to guide our expectations, except the\nknowledge that what happens must be some one of a certain number of\npossibilities, we may still reasonably judge, that one supposition is\nmore probable _to us_ than another supposition; and if we have any\ninterest at stake, we shall best provide for it by acting conformably to\nthat judgment.\n\n\u00a7 2. Suppose that we are required to take a ball from a box, of which we\nonly know that it contains balls both black and white, and none of any\nother color. We know that the ball we select will be either a black or a\nwhite ball; but we have no ground for expecting black rather than white,\nor white rather than black. In that case, if we are obliged to make a\nchoice, and to stake something on one or the other supposition, it will,\nas a question of prudence, be perfectly indifferent which; and we shall\nact precisely as we should have acted if we had known beforehand that\nthe box contained an equal number of black and white balls. But though\nour conduct would be the same, it would not be founded on any surmise\nthat the balls were in fact thus equally divided; for we might, on the\ncontrary, know by authentic information that the box contained\nninety-nine balls of one color, and only one of the other; still, if we\nare not told which color has only one, and which has ninety-nine, the\ndrawing of a white and of a black ball will be equally probable to us.\nWe shall have no reason for staking any thing on the one event rather\nthan on the other; the option between the two will be a matter of\nindifference; in other words, it will be an even chance.\n\nBut let it now be supposed that instead of two there are three\ncolors\u2014white, black, and red; and that we are entirely ignorant of the\nproportion in which they are mingled. We should then have no reason for\nexpecting one more than another, and if obliged to bet, should venture\nour stake on red, white, or black with equal indifference. But should we\nbe indifferent whether we betted for or against some one color, as, for\ninstance, white? Surely not. From the very fact that black and red are\neach of them separately equally probable to us with white, the two\ntogether must be twice as probable. We should in this case expect not\nwhite rather than white, and so much rather that we would lay two to one\nupon it. It is true, there might, for aught we knew, be more white balls\nthan black and red together; and if so, our bet would, if we knew more,\nbe seen to be a disadvantageous one. But so also, for aught we knew,\nmight there be more red balls than black and white, or more black balls\nthan white and red, and in such case the effect of additional knowledge\nwould be to prove to us that our bet was more advantageous than we had\nsupposed it to be. There is in the existing state of our knowledge a\nrational probability of two to one against white; a probability fit to\nbe made a basis of conduct. No reasonable person would lay an even wager\nin favor of white against black and red; though against black alone or\nred alone he might do so without imprudence.\n\nThe common theory, therefore, of the calculation of chances, appears to\nbe tenable. Even when we know nothing except the number of the possible\nand mutually excluding contingencies, and are entirely ignorant of their\ncomparative frequency, we may have grounds, and grounds numerically\nappreciable, for acting on one supposition rather than on another; and\nthis is the meaning of Probability.\n\n\u00a7 3. The principle, however, on which the reasoning proceeds, is\nsufficiently evident. It is the obvious one that when the cases which\nexist are shared among several kinds, it is impossible that _each_ of\nthose kinds should be a majority of the whole: on the contrary, there\nmust be a majority against each kind, except one at most; and if any\nkind has more than its share in proportion to the total number, the\nothers collectively must have less. Granting this axiom, and assuming\nthat we have no ground for selecting any one kind as more likely than\nthe rest to surpass the average proportion, it follows that we can not\nrationally presume this of any, which we should do if we were to bet in\nfavor of it, receiving less odds than in the ratio of the number of the\nother kinds. Even, therefore, in this extreme case of the calculation of\nprobabilities, which does not rest on special experience at all, the\nlogical ground of the process is our knowledge\u2014such knowledge as we then\nhave\u2014of the laws governing the frequency of occurrence of the different\ncases; but in this case the knowledge is limited to that which, being\nuniversal and axiomatic, does not require reference to specific\nexperience, or to any considerations arising out of the special nature\nof the problem under discussion.\n\nExcept, however, in such cases as games of chance, where the very\npurpose in view requires ignorance instead of knowledge, I can conceive\nno case in which we ought to be satisfied with such an estimate of\nchances as this\u2014an estimate founded on the absolute minimum of knowledge\nrespecting the subject. It is plain that, in the case of the colored\nballs, a very slight ground of surmise that the white balls were really\nmore numerous than either of the other colors, would suffice to vitiate\nthe whole of the calculations made in our previous state of\nindifference. It would place us in that position of more advanced\nknowledge, in which the probabilities, to us, would be different from\nwhat they were before; and in estimating these new probabilities we\nshould have to proceed on a totally different set of data, furnished no\nlonger by mere counting of possible suppositions, but by specific\nknowledge of facts. Such data it should always be our endeavor to\nobtain; and in all inquiries, unless on subjects equally beyond the\nrange of our means of knowledge and our practical uses, they may be\nobtained, if not good, at least better than none at all.(177)\n\nIt is obvious, too, that even when the probabilities are derived from\nobservation and experiment, a very slight improvement in the data, by\nbetter observations, or by taking into fuller consideration the special\ncircumstances of the case, is of more use than the most elaborate\napplication of the calculus to probabilities founded on the data in\ntheir previous state of inferiority. The neglect of this obvious\nreflection has given rise to misapplications of the calculus of\nprobabilities which have made it the real opprobrium of mathematics. It\nis sufficient to refer to the applications made of it to the credibility\nof witnesses, and to the correctness of the verdicts of juries. In\nregard to the first, common sense would dictate that it is impossible to\nstrike a general average of the veracity and other qualifications for\ntrue testimony of mankind, or of any class of them; and even if it were\npossible, the employment of it for such a purpose implies a\nmisapprehension of the use of averages, which serve, indeed, to protect\nthose whose interest is at stake, against mistaking the general result\nof large masses of instances, but are of extremely small value as\ngrounds of expectation in any one individual instance, unless the case\nbe one of those in which the great majority of individual instances do\nnot differ much from the average. In the case of a witness, persons of\ncommon sense would draw their conclusions from the degree of consistency\nof his statements, his conduct under cross-examination, and the relation\nof the case itself to his interests, his partialities, and his mental\ncapacity, instead of applying so rude a standard (even if it were\ncapable of being verified) as the ratio between the number of true and\nthe number of erroneous statements which he may be supposed to make in\nthe course of his life.\n\nAgain, on the subject of juries or other tribunals, some mathematicians\nhave set out from the proposition that the judgment of any one judge or\njuryman is, at least in some small degree, more likely to be right than\nwrong, and have concluded that the chance of a number of persons\nconcurring in a wrong verdict is diminished the more the number is\nincreased; so that if the judges are only made sufficiently numerous,\nthe correctness of the judgment may be reduced almost to certainty. I\nsay nothing of the disregard shown to the effect produced on the moral\nposition of the judges by multiplying their numbers, the virtual\ndestruction of their individual responsibility, and weakening of the\napplication of their minds to the subject. I remark only the fallacy of\nreasoning from a wide average to cases necessarily differing greatly\nfrom any average. It may be true that, taking all causes one with\nanother, the opinion of any one of the judges would be oftener right\nthan wrong; but the argument forgets that in all but the more simple\ncases, in all cases in which it is really of much consequence what the\ntribunal is, the proposition might probably be reversed; besides which,\nthe cause of error, whether arising from the intricacy of the case or\nfrom some common prejudice or mental infirmity, if it acted upon one\njudge, would be extremely likely to affect all the others in the same\nmanner, or at least a majority, and thus render a wrong instead of a\nright decision more probable the more the number was increased.\n\nThese are but samples of the errors frequently committed by men who,\nhaving made themselves familiar with the difficult formul\u00e6 which algebra\naffords for the estimation of chances under suppositions of a complex\ncharacter, like better to employ those formul\u00e6 in computing what are the\nprobabilities to a person half informed about a case than to look out\nfor means of being better informed. Before applying the doctrine of\nchances to any scientific purpose, the foundation must be laid for an\nevaluation of the chances, by possessing ourselves of the utmost\nattainable amount of positive knowledge. The knowledge required is that\nof the comparative frequency with which the different events in fact\noccur. For the purposes, therefore, of the present work, it is allowable\nto suppose that conclusions respecting the probability of a fact of a\nparticular kind rest on our knowledge of the proportion between the\ncases in which facts of that kind occur, and those in which they do not\noccur; this knowledge being either derived from specific experiment, or\ndeduced from our knowledge of the causes in operation which tend to\nproduce, compared with those which tend to prevent, the fact in\nquestion.\n\nSuch calculation of chances is grounded on an induction; and to render\nthe calculation legitimate, the induction must be a valid one. It is not\nless an induction, though it does not prove that the event occurs in all\ncases of a given description, but only that out of a given number of\nsuch cases it occurs in about so many. The fraction which mathematicians\nuse to designate the probability of an event is the ratio of these two\nnumbers; the ascertained proportion between the number of cases in which\nthe event occurs and the sum of all the cases, those in which it occurs\nand in which it does not occur, taken together. In playing at cross and\npile, the description of cases concerned are throws, and the probability\nof cross is one-half, because if we throw often enough cross is thrown\nabout once in every two throws. In the cast of a die, the probability of\nace is one-sixth; not simply because there are six possible throws, of\nwhich ace is one, and because we do not know any reason why one should\nturn up rather than another\u2014though I have admitted the validity of this\nground in default of a better\u2014but because we do actually know, either by\nreasoning or by experience, that in a hundred or a million of throws ace\nis thrown in about one-sixth of that number, or once in six times.\n\n\u00a7 4. I say, \u201ceither by reasoning or by experience,\u201d meaning specific\nexperience. But in estimating probabilities, it is not a matter of\nindifference from which of these two sources we derive our assurance.\nThe probability of events, as calculated from their mere frequency in\npast experience, affords a less secure basis for practical guidance than\ntheir probability as deduced from an equally accurate knowledge of the\nfrequency of occurrence of their causes.\n\nThe generalization that an event occurs in ten out of every hundred\ncases of a given description, is as real an induction as if the\ngeneralization were that it occurs in all cases. But when we arrive at\nthe conclusion by merely counting instances in actual experience, and\ncomparing the number of cases in which A has been present with the\nnumber in which it has been absent, the evidence is only that of the\nMethod of Agreement, and the conclusion amounts only to an empirical\nlaw. We can make a step beyond this when we can ascend to the causes on\nwhich the occurrence of A or its non-occurrence will depend, and form an\nestimate of the comparative frequency of the causes favorable and of\nthose unfavorable to the occurrence. These are data of a higher order,\nby which the empirical law derived from a mere numerical comparison of\naffirmative and negative instances will be either corrected or\nconfirmed, and in either case we shall obtain a more correct measure of\nprobability than is given by that numerical comparison. It has been well\nremarked that in the kind of examples by which the doctrine of chances\nis usually illustrated, that of balls in a box, the estimate of\nprobabilities is supported by reasons of causation, stronger than\nspecific experience. \u201cWhat is the reason that in a box where there are\nnine black balls and one white, we expect to draw a black ball nine\ntimes as much (in other words, nine times as often, frequency being the\ngauge of intensity in expectation) as a white? Obviously because the\nlocal conditions are nine times as favorable; because the hand may\nalight in nine places and get a black ball, while it can only alight in\none place and find a white ball; just for the same reason that we do not\nexpect to succeed in finding a friend in a crowd, the conditions in\norder that we and he should come together being many and difficult. This\nof course would not hold to the same extent were the white balls of\nsmaller size than the black, neither would the probability remain the\nsame; the larger ball would be much more likely to meet the hand.\u201d(178)\n\nIt is, in fact, evident that when once causation is admitted as a\nuniversal law, our expectation of events can only be rationally grounded\non that law. To a person who recognizes that every event depends on\ncauses, a thing\u2019s having happened once is a reason for expecting it to\nhappen again, only because proving that there exists, or is liable to\nexist, a cause adequate to produce it.(179) The frequency of the\nparticular event, apart from all surmise respecting its cause, can give\nrise to no other induction than that _per enumerationem simplicem_; and\nthe precarious inferences derived from this are superseded, and\ndisappear from the field as soon as the principle of causation makes its\nappearance there.\n\nNotwithstanding, however, the abstract superiority of an estimate of\nprobability grounded on causes, it is a fact that in almost all cases in\nwhich chances admit of estimation sufficiently precise to render their\nnumerical appreciation of any practical value, the numerical data are\nnot drawn from knowledge of the causes, but from experience of the\nevents themselves. The probabilities of life at different ages or in\ndifferent climates; the probabilities of recovery from a particular\ndisease; the chances of the birth of male or female offspring; the\nchances of the destruction of houses or other property by fire; the\nchances of the loss of a ship in a particular voyage, are deduced from\nbills of mortality, returns from hospitals, registers of births, of\nshipwrecks, etc., that is, from the observed frequency not of the\ncauses, but of the effects. The reason is, that in all these classes of\nfacts the causes are either not amenable to direct observation at all,\nor not with the requisite precision, and we have no means of judging of\ntheir frequency except from the empirical law afforded by the frequency\nof the effects. The inference does not the less depend on causation\nalone. We reason from an effect to a similar effect by passing through\nthe cause. If the actuary of an insurance office infers from his tables\nthat among a hundred persons now living of a particular age, five on the\naverage will attain the age of seventy, his inference is legitimate, not\nfor the simple reason that this is the proportion who have lived till\nseventy in times past, but because the fact of their having so lived\nshows that this is the proportion existing, at that place and time,\nbetween the causes which prolong life to the age of seventy and those\ntending to bring it to an earlier close.(180)\n\n\u00a7 5. From the preceding principles it is easy to deduce the\ndemonstration of that theorem of the doctrine of probabilities which is\nthe foundation of its application to inquiries for ascertaining the\noccurrence of a given event, or the reality of an individual fact. The\nsigns or evidences by which a fact is usually proved are some of its\nconsequences; and the inquiry hinges upon determining what cause is most\nlikely to have produced a given effect. The theorem applicable to such\ninvestigations is the Sixth Principle in Laplace\u2019s \u201c_Essai Philosophique\nsur les Probabilit\u00e9s_,\u201d which is described by him as the \u201cfundamental\nprinciple of that branch of the Analysis of Chances which consists in\nascending from events to their causes.\u201d(181)\n\nGiven an effect to be accounted for, and there being several causes\nwhich might have produced it, but of the presence of which in the\nparticular case nothing is known; the probability that the effect was\nproduced by any one of these causes _is as the antecedent probability of\nthe cause, multiplied by the probability that the cause, if it existed,\nwould have produced the given effect_.\n\nLet M be the effect, and A, B, two causes, by either of which it might\nhave been produced. To find the probability that it was produced by the\none and not by the other, ascertain which of the two is most likely to\nhave existed, and which of them, if it did exist, was most likely to\nproduce the effect M: the probability sought is a compound of these two\nprobabilities.\n\nCASE I. Let the causes be both alike in the second respect: either A or\nB, when it exists, being supposed equally likely (or equally certain) to\nproduce M; but let A be in itself twice as likely as B to exist, that\nis, twice as frequent a phenomenon. Then it is twice as likely to have\nexisted in this case, and to have been the cause which produced M.\n\nFor, since A exists in nature twice as often as B, in any 300 cases in\nwhich one or other existed, A has existed 200 times and B 100. But\neither A or B must have existed wherever M is produced; therefore, in\n300 times that M is produced, A was the producing cause 200 times, B\nonly 100, that is, in the ratio of 2 to 1. Thus, then, if the causes are\nalike in their capacity of producing the effect, the probability as to\nwhich actually produced it is in the ratio of their antecedent\nprobabilities.\n\nCASE II. Reversing the last hypothesis, let us suppose that the causes\nare equally frequent, equally likely to have existed, but not equally\nlikely, if they did exist, to produce M; that in three times in which A\noccurs, it produces that effect twice, while B, in three times, produces\nit only once. Since the two causes are equally frequent in their\noccurrence; in every six times that either one or the other exists, A\nexists three times and B three times. A, of its three times, produces M\nin two; B, of its three times, produces M in one. Thus, in the whole six\ntimes, M is only produced thrice; but of that thrice it is produced\ntwice by A, once only by B. Consequently, when the antecedent\nprobabilities of the causes are equal, the chances that the effect was\nproduced by them are in the ratio of the probabilities that if they did\nexist they would produce the effect.\n\nCASE III. The third case, that in which the causes are unlike in both\nrespects, is solved by what has preceded. For, when a quantity depends\non two other quantities, in such a manner that while either of them\nremains constant it is proportional to the other, it must necessarily be\nproportional to the product of the two quantities, the product being the\nonly function of the two which obeys that law of variation. Therefore,\nthe probability that M was produced by either cause, is as the\nantecedent probability of the cause, multiplied by the probability that\nif it existed it would produce M. Which was to be demonstrated.\n\nOr we may prove the third case as we proved the first and second. Let A\nbe twice as frequent as B, and let them also be unequally likely, when\nthey exist, to produce M; let A produce it twice in four times, B thrice\nin four times. The antecedent probability of A is to that of B as 2 to\n1; the probabilities of their producing M are as 2 to 3; the product of\nthese ratios is the ratio of 4 to 3; and this will be the ratio of the\nprobabilities that A or B was the producing cause in the given instance.\nFor, since A is twice as frequent as B, out of twelve cases in which one\nor other exists, A exists in 8 and B in 4. But of its eight cases, A, by\nthe supposition, produces M in only 4, while B of its four cases\nproduces M in 3. M, therefore, is only produced at all in seven of the\ntwelve cases; but in four of these it is produced by A, in three by B;\nhence the probabilities of its being produced by A and by B are as 4 to\n3, and are expressed by the fractions \u2074\u2044\u2087 and \u00b3\u2044\u2087. Which was to be\ndemonstrated.\n\n\u00a7 6. It remains to examine the bearing of the doctrine of chances on the\npeculiar problem which occupied us in the preceding chapter, namely, how\nto distinguish coincidences which are casual from those which are the\nresult of law; from those in which the facts which accompany or follow\none another are somehow connected through causation.\n\nThe doctrine of chances affords means by which, if we knew the _average_\nnumber of coincidences to be looked for between two phenomena connected\nonly casually, we could determine how often any given deviation from\nthat average will occur by chance. If the probability of any casual\ncoincidence, considered in itself, be 1/_m_, the probability that the\nsame coincidence will be repeated _n_ times in succession is 1/_m_n. For\nexample, in one throw of a die the probability of ace being \u2159; the\nprobability of throwing ace twice in succession will be 1 divided by the\nsquare of 6, or \u00b9\u2044\u2083\u2086. For ace is thrown at the first throw once in six,\nor six in thirty-six times, and of those six, the die being cast again,\nace will be thrown but once; being altogether once in thirty-six times.\nThe chance of the same cast three times successively is, by a similar\nreasoning, \u00b9\u2044\u2086\u2083 or \u00b9\u2044\u2082\u2081\u2086; that is, the event will happen, on a large\naverage, only once in two hundred and sixteen throws.\n\nWe have thus a rule by which to estimate the probability that any given\nseries of coincidences arises from chance, provided we can measure\ncorrectly the probability of a single coincidence. If we can obtain an\nequally precise expression for the probability that the same series of\ncoincidences arises from causation, we should only have to compare the\nnumbers. This, however, can rarely be done. Let us see what degree of\napproximation can practically be made to the necessary precision.\n\nThe question falls within Laplace\u2019s sixth principle, just demonstrated.\nThe given fact, that is to say, the series of coincidences, may have\noriginated either in a casual conjunction of causes or in a law of\nnature. The probabilities, therefore, that the fact originated in these\ntwo modes, are as their antecedent probabilities, multiplied by the\nprobabilities that if they existed they would produce the effect. But\nthe particular combination of chances, if it occurred, or the law of\nnature if real, would certainly produce the series of coincidences. The\nprobabilities, therefore, that the coincidences are produced by the two\ncauses in question are as the antecedent probabilities of the causes.\nOne of these, the antecedent probability of the combination of mere\nchances which would produce the given result, is an appreciable\nquantity. The antecedent probability of the other supposition may be\nsusceptible of a more or less exact estimation, according to the nature\nof the case.\n\nIn some cases, the coincidence, supposing it to be the result of\ncausation at all, must be the result of a known cause; as the succession\nof aces, if not accidental, must arise from the loading of the die. In\nsuch cases we may be able to form a conjecture as to the antecedent\nprobability of such a circumstance from the characters of the parties\nconcerned, or other such evidence; but it would be impossible to\nestimate that probability with any thing like numerical precision. The\ncounter-probability, however, that of the accidental origin of the\ncoincidence, dwindling so rapidly as it does at each new trial, the\nstage is soon reached at which the chance of unfairness in the die,\nhowever small in itself, must be greater than that of a casual\ncoincidence; and on this ground, a practical decision can generally be\ncome to without much hesitation, if there be the power of repeating the\nexperiment.\n\nWhen, however, the coincidence is one which can not be accounted for by\nany known cause, and the connection between the two phenomena, if\nproduced by causation, must be the result of some law of nature hitherto\nunknown; which is the case we had in view in the last chapter; then,\nthough the probability of a casual coincidence may be capable of\nappreciation, that of the counter-supposition, the existence of an\nundiscovered law of nature, is clearly unsusceptible of even an\napproximate valuation. In order to have the data which such a case would\nrequire, it would be necessary to know what proportion of all the\nindividual sequences or co-existences occurring in nature are the result\nof law, and what proportion are mere casual coincidences. It being\nevident that we can not form any plausible conjecture as to this\nproportion, much less appreciate it numerically, we can not attempt any\nprecise estimation of the comparative probabilities. But of this we are\nsure, that the detection of an unknown law of nature\u2014of some previously\nunrecognized constancy of conjunction among phenomena\u2014is no uncommon\nevent. If, therefore, the number of instances in which a coincidence is\nobserved, over and above that which would arise on the average from the\nmere concurrence of chances, be such that so great an amount of\ncoincidences from accident alone would be an extremely uncommon event;\nwe have reason to conclude that the coincidence is the effect of\ncausation, and may be received (subject to correction from further\nexperience) as an empirical law. Further than this, in point of\nprecision, we can not go; nor, in most cases, is greater precision\nrequired, for the solution of any practical doubt.(182)\n\n\n\n\n                               Chapter XIX.\n\n\nOf The Extension Of Derivative Laws To Adjacent Cases.\n\n\n\u00a7 1. We have had frequent occasion to notice the inferior generality of\nderivative laws, compared with the ultimate laws from which they are\nderived. This inferiority, which affects not only the extent of the\npropositions themselves, but their degree of certainty within that\nextent, is most conspicuous in the uniformities of co-existence and\nsequence obtaining between effects which depend ultimately on different\nprimeval causes. Such uniformities will only obtain where there exists\nthe same collocation of those primeval causes. If the collocation\nvaries, though the laws themselves remain the same, a totally different\nset of derivative uniformities may, and generally will, be the result.\n\nEven where the derivative uniformity is between different effects of the\nsame cause, it will by no means obtain as universally as the law of the\ncause itself. If _a_ and _b_ accompany or succeed one another as effects\nof the cause A, it by no means follows that A is the only cause which\ncan produce them, or that if there be another cause, as B, capable of\nproducing _a_, it must produce _b_ likewise. The conjunction, therefore,\nof _a_ and _b_ perhaps does not hold universally, but only in the\ninstances in which _a_ arises from A. When it is produced by _a_ cause\nother than A, _a_ and _b_ may be dissevered. Day (for example) is always\nin our experience followed by night; but day is not the cause of night;\nboth are successive effects of _a_ common cause, the periodical passage\nof the spectator into and out of the earth\u2019s shadow, consequent on the\nearth\u2019s rotation, and on the illuminating property of the sun. If,\ntherefore, day is ever produced by a different cause or set of causes\nfrom this, day will not, or at least may not, be followed by night. On\nthe sun\u2019s own surface, for instance, this may be the case.\n\nFinally, even when the derivative uniformity is itself a law of\ncausation (resulting from the combination of several causes), it is not\naltogether independent of collocations. If a cause supervenes, capable\nof wholly or partially counteracting the effect of any one of the\nconjoined causes, the effect will no longer conform to the derivative\nlaw. While, therefore, each ultimate law is only liable to frustration\nfrom one set of counteracting causes, the derivative law is liable to it\nfrom several. Now, the possibility of the occurrence of counteracting\ncauses which do not arise from any of the conditions involved in the law\nitself depends on the original collocations.\n\nIt is true that, as we formerly remarked, laws of causation, whether\nultimate or derivative, are, in most cases, fulfilled even when\ncounteracted; the cause produces its effect, though that effect is\ndestroyed by something else. That the effect may be frustrated, is,\ntherefore, no objection to the universality of laws of causation. But it\nis fatal to the universality of the sequences or co-existences of\neffects, which compose the greater part of the derivative laws flowing\nfrom laws of causation. When, from the law of a certain combination of\ncauses, there results a certain order in the effects; as from the\ncombination of a single sun with the rotation of an opaque body round\nits axis, there results, on the whole surface of that opaque body, an\nalternation of day and night; then, if we suppose one of the combined\ncauses counteracted, the rotation stopped, the sun extinguished, or a\nsecond sun superadded, the truth of that particular law of causation is\nin no way affected; it is still true that one sun shining on an opaque\nrevolving body will alternately produce day and night; but since the sun\nno longer does shine on such a body, the derivative uniformity, the\nsuccession of day and night on the given planet, is no longer true.\nThose derivative uniformities, therefore, which are not laws of\ncausation, are (except in the rare case of their depending on one cause\nalone, not on a combination of causes) always more or less contingent on\ncollocations; and are hence subject to the characteristic infirmity of\nempirical laws\u2014that of being admissible only where the collocations are\nknown by experience to be such as are requisite for the truth of the\nlaw; that is, only within the conditions of time and place confirmed by\nactual observation.\n\n\u00a7 2. This principle, when stated in general terms, seems clear and\nindisputable; yet many of the ordinary judgments of mankind, the\npropriety of which is not questioned, have at least the semblance of\nbeing inconsistent with it. On what grounds, it may be asked, do we\nexpect that the sun will rise to-morrow? To-morrow is beyond the limits\nof time comprehended in our observations. They have extended over some\nthousands of years past, but they do not include the future. Yet we\ninfer with confidence that the sun will rise to-morrow; and nobody\ndoubts that we are entitled to do so. Let us consider what is the\nwarrant for this confidence.\n\nIn the example in question, we know the causes on which the derivative\nuniformity depends. They are: the sun giving out light, the earth in a\nstate of rotation and intercepting light. The induction which shows\nthese to be the real causes, and not merely prior effects of a common\ncause, being complete, the only circumstances which could defeat the\nderivative law are such as would destroy or counteract one or other of\nthe combined causes. While the causes exist and are not counteracted,\nthe effect will continue. If they exist and are not counteracted\nto-morrow, the sun will rise to-morrow.\n\nSince the causes, namely, the sun and the earth, the one in the state of\ngiving out light, the other in a state of rotation, will exist until\nsomething destroys them, all depends on the probabilities of their\ndestruction, or of their counteraction. We know by observation (omitting\nthe inferential proofs of an existence for thousands of ages anterior)\nthat these phenomena have continued for (say) five thousand years.\nWithin that time there has existed no cause sufficient to diminish them\nappreciably, nor which has counteracted their effect in any appreciable\ndegree. The chance, therefore, that the sun may not rise to-morrow\namounts to the chance that some cause, which has not manifested itself\nin the smallest degree during five thousand years, will exist to-morrow\nin such intensity as to destroy the sun or the earth, the sun\u2019s light or\nthe earth\u2019s rotation, or to produce an immense disturbance in the effect\nresulting from those causes.\n\nNow, if such a cause will exist to-morrow, or at any future time, some\ncause, proximate or remote, of that cause must exist now, and must have\nexisted during the whole of the five thousand years. If, therefore, the\nsun do not rise to-morrow, it will be because some cause has existed,\nthe effects of which, though during five thousand years they have not\namounted to a perceptible quantity, will in one day become overwhelming.\nSince this cause has not been recognized during such an interval of time\nby observers stationed on our earth, it must, if it be a single agent,\nbe either one whose effects develop themselves gradually and very\nslowly, or one which existed in regions beyond our observation, and is\nnow on the point of arriving in our part of the universe. Now all causes\nwhich we have experience of act according to laws incompatible with the\nsupposition that their effects, after accumulating so slowly as to be\nimperceptible for five thousand years, should start into immensity in a\nsingle day. No mathematical law of proportion between an effect and the\nquantity or relations of its cause could produce such contradictory\nresults. The sudden development of an effect of which there was no\nprevious trace always arises from the coming together of several\ndistinct causes, not previously conjoined; but if such sudden\nconjunction is destined to take place, the causes, or _their_ causes,\nmust have existed during the entire five thousand years; and their not\nhaving once come together during that period shows how rare that\nparticular combination is. We have, therefore, the warrant of a rigid\ninduction for considering it probable, in a degree undistinguishable\nfrom certainty, that the known conditions requisite for the sun\u2019s rising\nwill exist to-morrow.\n\n\u00a7 3. But this extension of derivative laws, not causative, beyond the\nlimits of observation can only be to _adjacent_ cases. If, instead of\nto-morrow, we had said this day twenty thousand years, the inductions\nwould have been any thing but conclusive. That a cause which, in\nopposition to very powerful causes, produced no perceptible effect\nduring five thousand years, should produce a very considerable one by\nthe end of twenty thousand, has nothing in it which is not in conformity\nwith our experience of causes. We know many agents, the effect of which\nin a short period does not amount to a perceptible quantity, but by\naccumulating for a much longer period becomes considerable. Besides,\nlooking at the immense multitude of the heavenly bodies, their vast\ndistances, and the rapidity of the motion of such of them as are known\nto move, it is a supposition not at all contradictory to experience that\nsome body may be in motion toward us, or we toward it, within the limits\nof whose influence we have not come during five thousand years, but\nwhich in twenty thousand more may be producing effects upon us of the\nmost extraordinary kind. Or the fact which is capable of preventing\nsunrise may be, not the cumulative effect of one cause, but some new\ncombination of causes; and the chances favorable to that combination,\nthough they have not produced it once in five thousand years, may\nproduce it once in twenty thousand. So that the inductions which\nauthorize us to expect future events, grow weaker and weaker the further\nwe look into the future, and at length become inappreciable.\n\nWe have considered the probabilities of the sun\u2019s rising to-morrow, as\nderived from the real laws; that is, from the laws of the causes on\nwhich that uniformity is dependent. Let us now consider how the matter\nwould have stood if the uniformity had been known only as an empirical\nlaw; if we had not been aware that the sun\u2019s light and the earth\u2019s\nrotation (or the sun\u2019s motion) were the causes on which the periodical\noccurrence of daylight depends. We could have extended this empirical\nlaw to cases adjacent in time, though not to so great a distance of time\nas we can now. Having evidence that the effects had remained unaltered\nand been punctually conjoined for five thousand years, we could infer\nthat the unknown causes on which the conjunction is dependent had\nexisted undiminished and uncounteracted during the same period. The same\nconclusions, therefore, would follow as in the preceding case, except\nthat we should only know that during five thousand years nothing had\noccurred to defeat perceptibly this particular effect; while, when we\nknow the causes, we have the additional assurance that during that\ninterval no such change has been noticeable in the causes themselves as\nby any degree of multiplication or length of continuance could defeat\nthe effect.\n\nTo this must be added, that when we know the causes, we may be able to\njudge whether there exists any known cause capable of counteracting\nthem, while as long as they are unknown, we can not be sure but that if\nwe did know them, we could predict their destruction from causes\nactually in existence. A bed-ridden savage, who had never seen the\ncataract of Niagara, but who lived within hearing of it, might imagine\nthat the sound he heard would endure forever; but if he knew it to be\nthe effect of a rush of waters over a barrier of rock which is\nprogressively wearing away, he would know that within a number of ages\nwhich may be calculated it will be heard no more. In proportion,\ntherefore, to our ignorance of the causes on which the empirical law\ndepends, we can be less assured that it will continue to hold good; and\nthe further we look into futurity, the less improbable is it that some\none of the causes, whose co-existence gives rise to the derivative\nuniformity, may be destroyed or counteracted. With every prolongation of\ntime the chances multiply of such an event; that is to say, its\nnon-occurrence hitherto becomes a less guarantee of its not occurring\nwithin the given time. If, then, it is only to cases which in point of\ntime are adjacent (or nearly adjacent) to those which we have actually\nobserved, that _any_ derivative law, not of causation, can be extended\nwith an assurance equivalent to certainty, much more is this true of a\nmerely empirical law. Happily, for the purposes of life it is to such\ncases alone that we can almost ever have occasion to extend them.\n\nIn respect of place, it might seem that a merely empirical law could not\nbe extended even to adjacent cases; that we could have no assurance of\nits being true in any place where it has not been specially observed.\nThe past duration of a cause is a guarantee for its future existence,\nunless something occurs to destroy it; but the existence of a cause in\none or any number of places is no guarantee for its existence in any\nother place, since there is no uniformity in the collocations of\nprimeval causes. When, therefore, an empirical law is extended beyond\nthe local limits within which it has been found true by observation, the\ncases to which it is thus extended must be such as are presumably within\nthe influence of the same individual agents. If we discover a new planet\nwithin the known bounds of the solar system (or even beyond those\nbounds, but indicating its connection with the system by revolving round\nthe sun), we may conclude, with great probability, that it revolves on\nits axis. For all the known planets do so; and this uniformity points to\nsome common cause, antecedent to the first records of astronomical\nobservation; and though the nature of this cause can only be matter of\nconjecture, yet if it be, as is not unlikely, and as Laplace\u2019s theory\nsupposes, not merely the same kind of cause, but the same individual\ncause (such as an impulse given to all the bodies at once), that cause,\nacting at the extreme points of the space occupied by the sun and\nplanets, is likely, unless defeated by some counteracting cause, to have\nacted at every intermediate point, and probably somewhat beyond; and\ntherefore acted, in all probability, upon the supposed newly-discovered\nplanet.\n\nWhen, therefore, effects which are always found conjoined can be traced\nwith any probability to an identical (and not merely a similar) origin,\nwe may with the same probability extend the empirical law of their\nconjunction to all places within the extreme local boundaries within\nwhich the fact has been observed, subject to the possibility of\ncounteracting causes in some portion of the field. Still more\nconfidently may we do so when the law is not merely empirical; when the\nphenomena which we find conjoined are effects of ascertained causes,\nfrom the laws of which the conjunction of their effects is deducible. In\nthat case, we may both extend the derivative uniformity over a larger\nspace, and with less abatement for the chance of counteracting causes.\nThe first, because instead of the local boundaries of our observation of\nthe fact itself, we may include the extreme boundaries of the\nascertained influence of its causes. Thus the succession of day and\nnight, we know, holds true of all the bodies of the solar system except\nthe sun itself; but we know this only because we are acquainted with the\ncauses. If we were not, we could not extend the proposition beyond the\norbits of the earth and moon, at both extremities of which we have the\nevidence of observation for its truth. With respect to the probability\nof counteracting causes, it has been seen that this calls for a greater\nabatement of confidence, in proportion to our ignorance of the causes on\nwhich the phenomena depend. On both accounts, therefore, a derivative\nlaw which we know how to resolve, is susceptible of a greater extension\nto cases adjacent in place, than a merely empirical law.\n\n\n\n\n                               Chapter XX.\n\n\nOf Analogy.\n\n\n\u00a7 1. The word Analogy, as the name of a mode of reasoning, is generally\ntaken for some kind of argument supposed to be of an inductive nature, but\nnot amounting to a complete induction. There is no word, however, which is\nused more loosely, or in a greater variety of senses, than Analogy. It\nsometimes stands for arguments which may be examples of the most rigorous\ninduction. Archbishop Whately, for instance, following Ferguson and other\nwriters, defines Analogy conformably to its primitive acceptation, that\nwhich was given to it by mathematicians: Resemblance of Relations. In this\nsense, when a country which has sent out colonies is termed the mother\ncountry, the expression is analogical, signifying that the colonies of a\ncountry stand in the same _relation_ to her in which children stand to\ntheir parents. And if any inference be drawn from this resemblance of\nrelations, as, for instance, that obedience or affection is due from\ncolonies to the mother country, this is called reasoning by analogy. Or,\nif it be argued that a nation is most beneficially governed by an assembly\nelected by the people, from the admitted fact that other associations for\na common purpose, such as joint-stock companies, are best managed by a\ncommittee chosen by the parties interested; this, too, is an argument from\nanalogy in the preceding sense, because its foundation is, not that a\nnation is like a joint-stock company, or Parliament like a board of\ndirectors, but that Parliament stands in the same _relation_ to the nation\nin which a board of directors stands to a joint-stock company. Now, in an\nargument of this nature, there is no inherent inferiority of\nconclusiveness. Like other arguments from resemblance, it may amount to\nnothing, or it may be a perfect and conclusive induction. The circumstance\nin which the two cases resemble, may be capable of being shown to be the\n_material_ circumstance; to be that on which all the consequences,\nnecessary to be taken into account in the particular discussion, depend.\nIn the example last given, the resemblance is one of relation; the\n_fundamentum relationis_ being the management, by a few persons, of\naffairs in which a much greater number are interested along with them.\nNow, some may contend that this circumstance which is common to the two\ncases, and the various consequences which follow from it, have the chief\nshare in determining all the effects which make up what we term good or\nbad administration. If they can establish this, their argument has the\nforce of a rigorous induction; if they can not, they are said to have\nfailed in proving the analogy between the two cases; a mode of speech\nwhich implies that when the analogy can be proved, the argument founded on\nit can not be resisted.\n\n\u00a7 2. It is on the whole more usual, however, to extend the name of\nanalogical evidence to arguments from any sort of resemblance, provided\nthey do not amount to a complete induction; without peculiarly\ndistinguishing resemblance of relations. Analogical reasoning, in this\nsense, may be reduced to the following formula: Two things resemble each\nother in one or more respects; a certain proposition is true of the one;\ntherefore it is true of the other. But we have nothing here by which to\ndiscriminate analogy from induction, since this type will serve for all\nreasoning from experience. In the strictest induction, equally with the\nfaintest analogy, we conclude because A resembles B in one or more\nproperties, that it does so in a certain other property. The difference\nis, that in the case of a complete induction it has been previously shown,\nby due comparison of instances, that there is an invariable conjunction\nbetween the former property or properties and the latter property; but in\nwhat is called analogical reasoning, no such conjunction has been made\nout. There have been no opportunities of putting in practice the Method of\nDifference, or even the Method of Agreement; but we conclude (and that is\nall which the argument of analogy amounts to) that a fact _m_, known to be\ntrue of A, is more likely to be true of B if B agrees with A in some of\nits properties (even though no connection is known to exist between _m_\nand those properties), than if no resemblance at all could be traced\nbetween B and any other thing known to possess the attribute _m_.\n\nTo this argument it is of course requisite that the properties common to A\nwith B shall be merely not known to be connected with _m_; they must not\nbe properties known to be unconnected with it. If, either by processes of\nelimination, or by deduction from previous knowledge of the laws of the\nproperties in question, it can be concluded that they have nothing to do\nwith _m_, the argument of analogy is put out of court. The supposition\nmust be that _m_ is an effect really dependent on some property of A, but\nwe know not on which. We can not point out any of the properties of A,\nwhich is the cause of _m_, or united with it by any law. After rejecting\nall which we know to have nothing to do with it, there remain several\nbetween which we are unable to decide; of which remaining properties, B\npossesses one or more. This, accordingly, we consider as affording\ngrounds, of more or less strength, for concluding by analogy that B\npossesses the attribute _m_.\n\nThere can be no doubt that every such resemblance which can be pointed out\nbetween B and A, affords some degree of probability, beyond what would\notherwise exist, in favor of the conclusion drawn from it. If B resembled\nA in all its ultimate properties, its possessing the attribute _m_ would\nbe a certainty, not a probability; and every resemblance which can be\nshown to exist between them, places it by so much the nearer to that\npoint. If the resemblance be in an ultimate property, there will be\nresemblance in all the derivative properties dependent on that ultimate\nproperty, and of these _m_ may be one. If the resemblance be in a\nderivative property, there is reason to expect resemblance in the ultimate\nproperty on which it depends, and in the other derivative properties\ndependent on the same ultimate property. Every resemblance which can be\nshown to exist, affords ground for expecting an indefinite number of other\nresemblances; the particular resemblance sought will, therefore, be\noftener found among things thus known to resemble, than among things\nbetween which we know of no resemblance.\n\nFor example, I might infer that there are probably inhabitants in the\nmoon, because there are inhabitants on the earth, in the sea, and in the\nair: and this is the evidence of analogy. The circumstance of having\ninhabitants is here assumed not to be an ultimate property, but (as is\nreasonable to suppose) a consequence of other properties; and depending,\ntherefore, in the case of the earth, on some of its properties as a\nportion of the universe, but on which of those properties we know not. Now\nthe moon resembles the earth in being a solid, opaque, nearly spherical\nsubstance, appearing to contain, or to have contained, active volcanoes;\nreceiving heat and light from the sun, in about the same quantity as our\nearth; revolving on its axis; composed of materials which gravitate, and\nobeying all the various laws resulting from that property. And I think no\none will deny that if this were all that was known of the moon, the\nexistence of inhabitants in that luminary would derive from these various\nresemblances to the earth, a greater degree of probability than it would\notherwise have; though the amount of the augmentation it would be useless\nto attempt to estimate.\n\nIf, however, every resemblance proved between B and A, in any point not\nknown to be immaterial with respect to _m_, forms some additional reason\nfor presuming that B has the attribute _m_; it is clear, _\u00e8 contra_, that\nevery dissimilarity which can be proved between them furnishes a\ncounter-probability of the same nature on the other side. It is not,\nindeed, unusual that different ultimate properties should, in some\nparticular instances, produce the same derivative property; but on the\nwhole it is certain that things which differ in their ultimate properties,\nwill differ at least as much in the aggregate of their derivative\nproperties, and that the differences which are unknown will, on the\naverage of cases, bear some proportion to those which are known. There\nwill, therefore, be a competition between the known points of agreement\nand the known points of difference in A and B; and according as the one or\nthe other may be deemed to preponderate, the probability derived from\nanalogy will be for or against B\u2019s having the property _m_. The moon, for\ninstance, agrees with the earth in the circumstances already mentioned;\nbut differs in being smaller, in having its surface more unequal, and\napparently volcanic throughout, in having, at least on the side next the\nearth, no atmosphere sufficient to refract light, no clouds, and (it is\ntherefore concluded) no water. These differences, considered merely as\nsuch, might perhaps balance the resemblances, so that analogy would afford\nno presumption either way. But considering that some of the circumstances\nwhich are wanting on the moon are among those which, on the earth, are\nfound to be indispensable conditions of animal life, we may conclude that\nif that phenomenon does exist in the moon (or at all events on the nearer\nside), it must be as an effect of causes totally different from those on\nwhich it depends here; as a consequence, therefore, of the moon\u2019s\ndifferences from the earth, not of the points of agreement. Viewed in this\nlight, all the resemblances which exist become presumptions against, not\nin favor of, the moon\u2019s being inhabited. Since life can not exist there in\nthe manner in which it exists here, the greater the resemblance of the\nlunar world to the terrestrial in other respects, the less reason we have\nto believe that it can contain life.\n\nThere are, however, other bodies in our system, between which and the\nearth there is a much closer resemblance; which possess an atmosphere,\nclouds, consequently water (or some fluid analogous to it), and even give\nstrong indications of snow in their polar regions; while the cold, or\nheat, though differing greatly on the average from ours, is, in some parts\nat least of those planets, possibly not more extreme than in some regions\nof our own which are habitable. To balance these agreements, the\nascertained differences are chiefly in the average light and heat,\nvelocity of rotation, density of material, intensity of gravity, and\nsimilar circumstances of a secondary kind. With regard to these planets,\ntherefore, the argument of analogy gives a decided preponderance in favor\nof their resembling the earth in any of its derivative properties, such as\nthat of having inhabitants; though when we consider how immeasurably\nmultitudinous are those of their properties which we are entirely ignorant\nof, compared with the few which we know, we can attach but trifling weight\nto any considerations of resemblance in which the known elements bear so\ninconsiderable a proportion to the unknown.\n\nBesides the competition between analogy and diversity, there may be a\ncompetition of conflicting analogies. The new case may be similar in\nsome of its circumstances to cases in which the fact _m_ exists, but in\nothers to cases in which it is known not to exist. Amber has some\nproperties in common with vegetable, others with mineral products. A\npainting of unknown origin may resemble, in certain of its characters,\nknown works of a particular master, but in others it may as strikingly\nresemble those of some other painter. A vase may bear some analogy to\nworks of Grecian, and some to those of Etruscan, or Egyptian art. We are\nof course supposing that it does not possess any quality which has been\nascertained, by a sufficient induction, to be a conclusive mark either\nof the one or of the other.\n\n\u00a7 3. Since the value of an analogical argument inferring one resemblance\nfrom other resemblances without any antecedent evidence of a connection\nbetween them, depends on the extent of ascertained resemblance, compared\nfirst with the amount of ascertained difference, and next with the\nextent of the unexplored region of unascertained properties; it follows\nthat where the resemblance is very great, the ascertained difference\nvery small, and our knowledge of the subject-matter tolerably extensive,\nthe argument from analogy may approach in strength very near to a valid\ninduction. If, after much observation of B, we find that it agrees with\nA in nine out of ten of its known properties, we may conclude with a\nprobability of nine to one, that it will possess any given derivative\nproperty of A. If we discover, for example, an unknown animal or plant,\nresembling closely some known one in the greater number of the\nproperties we observe in it, but differing in some few, we may\nreasonably expect to find in the unobserved remainder of its properties,\na general agreement with those of the former; but also a difference\ncorresponding proportionately to the amount of observed diversity.\n\nIt thus appears that the conclusions derived from analogy are only of\nany considerable value, when the case to which we reason is an adjacent\ncase; adjacent, not as before, in place or time, but in circumstances.\nIn the case of effects of which the causes are imperfectly or not at all\nknown, when consequently the observed order of their occurrence amounts\nonly to an empirical law, it often happens that the conditions which\nhave co-existed whenever the effect was observed, have been very\nnumerous. Now if a new case presents itself, in which all these\nconditions do not exist, but the far greater part of them do, some one\nor a few only being wanting, the inference that the effect will occur,\nnotwithstanding this deficiency of complete resemblance to the cases in\nwhich it has been observed, may, though of the nature of analogy,\npossess a high degree of probability. It is hardly necessary to add\nthat, however considerable this probability may be, no competent\ninquirer into nature will rest satisfied with it when a complete\ninduction is attainable; but will consider the analogy as a mere\nguide-post, pointing out the direction in which more rigorous\ninvestigations should be prosecuted.\n\nIt is in this last respect that considerations of analogy have the\nhighest scientific value. The cases in which analogical evidence affords\nin itself any very high degree of probability, are, as we have observed,\nonly those in which the resemblance is very close and extensive; but\nthere is no analogy, however faint, which may not be of the utmost value\nin suggesting experiments or observations that may lead to more positive\nconclusions. When the agents and their effects are out of the reach of\nfurther observation and experiment, as in the speculations already\nalluded to respecting the moon and planets, such slight probabilities\nare no more than an interesting theme for the pleasant exercise of\nimagination; but any suspicion, however slight, that sets an ingenious\nperson at work to contrive an experiment, or affords a reason for trying\none experiment rather than another, may be of the greatest benefit to\nscience.\n\nOn this ground, though I can not accept as positive truths any of those\nscientific hypotheses which are unsusceptible of being ultimately\nbrought to the test of actual induction, such, for instance, as the two\ntheories of light, the emission theory of the last century, and the\nundulatory theory which predominates in the present, I am yet unable to\nagree with those who consider such hypotheses to be worthy of entire\ndisregard. As is well said by Hartley (and concurred in by a thinker in\ngeneral so diametrically opposed to Hartley\u2019s opinions as Dugald\nStewart), \u201cany hypothesis which has so much plausibility as to explain a\nconsiderable number of facts, helps us to digest these facts in proper\norder, to bring new ones to light, and make _experimenta crucis_ for the\nsake of future inquirers.\u201d(183) If an hypothesis both explains known\nfacts, and has led to the prediction of others previously unknown, and\nsince verified by experience, the laws of the phenomenon which is the\nsubject of inquiry must bear at least a great similarity to those of the\nclass of phenomena to which the hypothesis assimilates it; and since the\nanalogy which extends so far may probably extend further, nothing is\nmore likely to suggest experiments tending to throw light upon the real\nproperties of the phenomenon, than the following out such an hypothesis.\nBut to this end it is by no means necessary that the hypothesis be\nmistaken for a scientific truth. On the contrary, that illusion is in\nthis respect, as in every other, an impediment to the progress of real\nknowledge, by leading inquirers to restrict themselves arbitrarily to\nthe particular hypothesis which is most accredited at the time, instead\nof looking out for every class of phenomena between the laws of which\nand those of the given phenomenon any analogy exists, and trying all\nsuch experiments as may tend to the discovery of ulterior analogies\npointing in the same direction.\n\n\n\n\n                               Chapter XXI.\n\n\nOf The Evidence Of The Law Of Universal Causation.\n\n\n\u00a7 1. We have now completed our review of the logical processes by which\nthe laws, or uniformities, of the sequence of phenomena, and those\nuniformities in their co-existence which depend on the laws of their\nsequence, are ascertained or tested. As we recognized in the\ncommencement, and have been enabled to see more clearly in the progress\nof the investigation, the basis of all these logical operations is the\nlaw of causation.\n\nThe validity of all the Inductive Methods depends on the assumption that\nevery event, or the beginning of every phenomenon, must have some cause;\nsome antecedent, on the existence of which it is invariably and\nunconditionally consequent. In the Method of Agreement this is obvious;\nthat method avowedly proceeding on the supposition that we have found\nthe true cause as soon as we have negatived every other. The assertion\nis equally true of the Method of Difference. That method authorizes us\nto infer a general law from two instances; one, in which A exists\ntogether with a multitude of other circumstances, and B follows;\nanother, in which, A being removed, and all other circumstances\nremaining the same, B is prevented. What, however, does this prove? It\nproves that B, in the particular instance, can not have had any other\ncause than A; but to conclude from this that A was the cause, or that A\nwill on other occasions be followed by B, is only allowable on the\nassumption that B must have some cause; that among its antecedents in\nany single instance in which it occurs, there must be one which has the\ncapacity of producing it at other times. This being admitted, it is seen\nthat in the case in question that antecedent can be no other than A; but\nthat if it be no other than A it must be A, is not proved, by these\ninstances at least, but taken for granted. There is no need to spend\ntime in proving that the same thing is true of the other Inductive\nMethods. The universality of the law of causation is assumed in them\nall.\n\nBut is this assumption warranted? Doubtless (it may be said) _most_\nphenomena are connected as effects with some antecedent or cause, that\nis, are never produced unless some assignable fact has preceded them;\nbut the very circumstance that complicated processes of induction are\nsometimes necessary, shows that cases exist in which this regular order\nof succession is not apparent to our unaided apprehension. If, then, the\nprocesses which bring these cases within the same category with the\nrest, require that we should assume the universality of the very law\nwhich they do not at first sight appear to exemplify, is not this a\n_petitio principii_? Can we prove a proposition, by an argument which\ntakes it for granted? And if not so proved, on what evidence does it\nrest?\n\nFor this difficulty, which I have purposely stated in the strongest\nterms it will admit of, the school of metaphysicians who have long\npredominated in this country find a ready salvo. They affirm, that the\nuniversality of causation is a truth which we can not help believing;\nthat the belief in it is an instinct, one of the laws of our believing\nfaculty. As the proof of this, they say, and they have nothing else to\nsay, that every body does believe it; and they number it among the\npropositions, rather numerous in their catalogue, which may be logically\nargued against, and perhaps can not be logically proved, but which are\nof higher authority than logic, and so essentially inherent in the human\nmind, that even he who denies them in speculation, shows by his habitual\npractice that his arguments make no impression upon himself.\n\nInto the merits of this question, considered as one of psychology, it\nwould be foreign to my purpose to enter here; but I must protest against\nadducing, as evidence of the truth of a fact in external nature, the\ndisposition, however strong or however general, of the human mind to\nbelieve it. Belief is not proof, and does not dispense with the\nnecessity of proof. I am aware, that to ask for evidence of a\nproposition which we are supposed to believe instinctively, is to expose\none\u2019s self to the charge of rejecting the authority of the human\nfaculties; which of course no one can consistently do, since the human\nfaculties are all which any one has to judge by; and inasmuch as the\nmeaning of the word evidence is supposed to be, something which when\nlaid before the mind, induces it to believe; to demand evidence when the\nbelief is insured by the mind\u2019s own laws, is supposed to be appealing to\nthe intellect against the intellect. But this, I apprehend, is a\nmisunderstanding of the nature of evidence. By evidence is not meant any\nthing and every thing which produces belief. There are many things which\ngenerate belief besides evidence. A mere strong association of ideas\noften causes a belief so intense as to be unshakable by experience or\nargument. Evidence is not that which the mind does or must yield to, but\nthat which it ought to yield to, namely, that, by yielding to which its\nbelief is kept conformable to fact. There is no appeal from the human\nfaculties generally, but there is an appeal from one human faculty to\nanother; from the judging faculty, to those which take cognizance of\nfact, the faculties of sense and consciousness. The legitimacy of this\nappeal is admitted whenever it is allowed that our judgments ought to be\nconformable to fact. To say that belief suffices for its own\njustification is making opinion the test of opinion; it is denying the\nexistence of any outward standard, the conformity of an opinion to which\nconstitutes its truth. We call one mode of forming opinions right and\nanother wrong, because the one does, and the other does not, tend to\nmake the opinion agree with the fact\u2014to make people believe what really\nis, and expect what really will be. Now a mere disposition to believe,\neven if supposed instinctive, is no guarantee for the truth of the thing\nbelieved. If, indeed, the belief ever amounted to an irresistible\nnecessity, there would then be no _use_ in appealing from it, because\nthere would be no possibility of altering it. But even then the truth of\nthe belief would not follow; it would only follow that mankind were\nunder a permanent necessity of believing what might possibly not be\ntrue; in other words, that a case might occur in which our senses or\nconsciousness, if they could be appealed to, might testify one thing,\nand our reason believe another. But in fact there is no such permanent\nnecessity. There is no proposition of which it can be asserted that\nevery human mind must eternally and irrevocably believe it. Many of the\npropositions of which this is most confidently stated, great numbers of\nhuman beings have disbelieved. The things which it has been supposed\nthat nobody could possibly help believing, are innumerable; but no two\ngenerations would make out the same catalogue of them. One age or nation\nbelieves implicitly what to another seems incredible and inconceivable;\none individual has not a vestige of a belief which another deems to be\nabsolutely inherent in humanity. There is not one of these supposed\ninstinctive beliefs which is really inevitable. It is in the power of\nevery one to cultivate habits of thought which make him independent of\nthem. The habit of philosophical analysis (of which it is the surest\neffect to enable the mind to command, instead of being commanded by, the\nlaws of the merely passive part of its own nature), by showing to us\nthat things are not necessarily connected in fact because their ideas\nare connected in our minds, is able to loosen innumerable associations\nwhich reign despotically over the undisciplined or early-prejudiced\nmind. And this habit is not without power even over those associations\nwhich the school of which I have been speaking regard as connate and\ninstinctive. I am convinced that any one accustomed to abstraction and\nanalysis, who will fairly exert his faculties for the purpose, will,\nwhen his imagination has once learned to entertain the notion, find no\ndifficulty in conceiving that in some one, for instance, of the many\nfirmaments into which sidereal astronomy now divides the universe,\nevents may succeed one another at random, without any fixed law; nor can\nany thing in our experience, or in our mental nature, constitute a\nsufficient, or indeed any, reason for believing that this is nowhere the\ncase.\n\nWere we to suppose (what it is perfectly possible to imagine) that the\npresent order of the universe were brought to an end, and that a chaos\nsucceeded in which there was no fixed succession of events, and the past\ngave no assurance of the future; if a human being were miraculously kept\nalive to witness this change, he surely would soon cease to believe in\nany uniformity, the uniformity itself no longer existing. If this be\nadmitted, the belief in uniformity either is not an instinct, or it is\nan instinct conquerable, like all other instincts, by acquired\nknowledge.\n\nBut there is no need to speculate on what might be, when we have\npositive and certain knowledge of what has been. It is not true, as a\nmatter of fact, that mankind have always believed that all the\nsuccessions of events were uniform and according to fixed laws. The\nGreek philosophers, not even excepting Aristotle, recognized Chance and\nSpontaneity (\u03c4\u03cd\u03c7\u03b7 and \u03c4\u1f78 \u03b1\u1f50\u03c4\u03bf\u03bc\u03ac\u03c4\u03bf\u03bd) as among the agents in nature; in\nother words, they believed that to that extent there was no guarantee\nthat the past had been similar to itself, or that the future would\nresemble the past. Even now a full half of the philosophical world,\nincluding the very same metaphysicians who contend most for the\ninstinctive character of the belief in uniformity, consider one\nimportant class of phenomena, volitions, to be an exception to the\nuniformity, and not governed by a fixed law.(184)\n\n\u00a7 2. As was observed in a former place,(185) the belief we entertain in\nthe universality, throughout nature, of the law of cause and effect, is\nitself an instance of induction; and by no means one of the earliest\nwhich any of us, or which mankind in general, can have made. We arrive\nat this universal law, by generalization from many laws of inferior\ngenerality. We should never have had the notion of causation (in the\nphilosophical meaning of the term) as a condition of all phenomena,\nunless many cases of causation, or in other words, many partial\nuniformities of sequence, had previously become familiar. The more\nobvious of the particular uniformities suggest, and give evidence of,\nthe general uniformity, and the general uniformity, once established,\nenables us to prove the remainder of the particular uniformities of\nwhich it is made up. As, however, all rigorous processes of induction\npresuppose the general uniformity, our knowledge of the particular\nuniformities from which it was first inferred was not, of course,\nderived from rigorous induction, but from the loose and uncertain mode\nof induction _per enumerationem simplicem_; and the law of universal\ncausation, being collected from results so obtained, can not itself rest\non any better foundation.\n\nIt would seem, therefore, that induction _per enumerationem simplicem_\nnot only is not necessarily an illicit logical process, but is in\nreality the only kind of induction possible; since the more elaborate\nprocess depends for its validity on a law, itself obtained in that\ninartificial mode. Is there not then an inconsistency in contrasting the\nlooseness of one method with the rigidity of another, when that other is\nindebted to the looser method for its own foundation?\n\nThe inconsistency, however, is only apparent. Assuredly, if induction by\nsimple enumeration were an invalid process, no process grounded on it\ncould be valid; just as no reliance could be placed on telescopes, if we\ncould not trust our eyes. But though a valid process, it is a fallible\none, and fallible in very different degrees: if, therefore, we can\nsubstitute for the more fallible forms of the process, an operation\ngrounded on the same process in a less fallible form, we shall have\neffected a very material improvement. And this is what scientific\ninduction does.\n\nA mode of concluding from experience must be pronounced untrustworthy\nwhen subsequent experience refuses to confirm it. According to this\ncriterion, induction by simple enumeration\u2014in other words,\ngeneralization of an observed fact from the mere absence of any known\ninstance to the contrary\u2014affords in general a precarious and unsafe\nground of assurance; for such generalizations are incessantly\ndiscovered, on further experience, to be false. Still, however, it\naffords some assurance, sufficient, in many cases, for the ordinary\nguidance of conduct. It would be absurd to say, that the generalizations\narrived at by mankind in the outset of their experience, such as\nthese\u2014food nourishes, fire burns, water drowns\u2014were unworthy of\nreliance.(186) There is a scale of trustworthiness in the results of the\noriginal unscientific induction; and on this diversity (as observed in\nthe fourth chapter of the present book) depend the rules for the\nimprovement of the process. The improvement consists in correcting one\nof these inartificial generalizations by means of another. As has been\nalready pointed out, this is all that art can do. To test a\ngeneralization, by showing that it either follows from, or conflicts\nwith, some stronger induction, some generalization resting on a broader\nfoundation of experience, is the beginning and end of the logic of\ninduction.\n\n\u00a7 3. Now the precariousness of the method of simple enumeration is in an\ninverse ratio to the largeness of the generalization. The process is\ndelusive and insufficient, exactly in proportion as the subject-matter\nof the observation is special and limited in extent. As the sphere\nwidens, this unscientific method becomes less and less liable to\nmislead; and the most universal class of truths, the law of causation,\nfor instance, and the principles of number and of geometry, are duly and\nsatisfactorily proved by that method alone, nor are they susceptible of\nany other proof.\n\nWith respect to the whole class of generalizations of which we have\nrecently treated, the uniformities which depend on causation, the truth\nof the remark just made follows by obvious inference from the principles\nlaid down in the preceding chapters. When a fact has been observed a\ncertain number of times to be true, and is not in any instance known to\nbe false, if we at once affirm that fact as a universal truth or law of\nnature, without either testing it by any of the four methods of\ninduction, or deducing it from other known laws, we shall in general err\ngrossly; but we are perfectly justified in affirming it as an empirical\nlaw, true within certain limits of time, place, and circumstance,\nprovided the number of coincidences be greater than can with any\nprobability be ascribed to chance. The reason for not extending it\nbeyond those limits is, that the fact of its holding true within them\nmay be a consequence of collocations, which can not be concluded to\nexist in one place because they exist in another; or may be dependent on\nthe accidental absence of counteracting agencies, which any variation of\ntime, or the smallest change of circumstances, may possibly bring into\nplay. If we suppose, then, the subject-matter of any generalization to\nbe so widely diffused that there is no time, no place, and no\ncombination of circumstances, but must afford an example either of its\ntruth or of its falsity, and if it be never found otherwise than true,\nits truth can not be contingent on any collocations, unless such as\nexist at all times and places; nor can it be frustrated by any\ncounteracting agencies, unless by such as never actually occur. It is,\ntherefore, an empirical law co-extensive with all human experience; at\nwhich point the distinction between empirical laws and laws of nature\nvanishes, and the proposition takes its place among the most firmly\nestablished as well as largest truths accessible to science.\n\nNow, the most extensive in its subject-matter of all generalizations\nwhich experience warrants, respecting the sequences and co-existences of\nphenomena, is the law of causation. It stands at the head of all\nobserved uniformities, in point of universality, and therefore (if the\npreceding observations are correct) in point of certainty. And if we\nconsider, not what mankind would have been justified in believing in the\ninfancy of their knowledge, but what may rationally be believed in its\npresent more advanced state, we shall find ourselves warranted in\nconsidering this fundamental law, though itself obtained by induction\nfrom particular laws of causation, as not less certain, but on the\ncontrary, more so, than any of those from which it was drawn. It adds to\nthem as much proof as it receives from them. For there is probably no\none even of the best established laws of causation which is not\nsometimes counteracted, and to which, therefore, apparent exceptions do\nnot present themselves, which would have necessarily and justly shaken\nthe confidence of mankind in the universality of those laws, if\ninductive processes founded on the universal law had not enabled us to\nrefer those exceptions to the agency of counteracting causes, and\nthereby reconcile them with the law with which they apparently conflict.\nErrors, moreover, may have slipped into the statement of any one of the\nspecial laws, through inattention to some material circumstance: and\ninstead of the true proposition, another may have been enunciated, false\nas a universal law, though leading, in all cases hitherto observed, to\nthe same result. To the law of causation, on the contrary, we not only\ndo not know of any exception, but the exceptions which limit or\napparently invalidate the special laws, are so far from contradicting\nthe universal one, that they confirm it; since in all cases which are\nsufficiently open to our observation, we are able to trace the\ndifference of result, either to the absence of a cause which had been\npresent in ordinary cases, or to the presence of one which had been\nabsent.\n\nThe law of cause and effect, being thus certain, is capable of imparting\nits certainty to all other inductive propositions which can be deduced\nfrom it; and the narrower inductions may be regarded as receiving their\nultimate sanction from that law, since there is no one of them which is\nnot rendered more certain than it was before, when we are able to\nconnect it with that larger induction, and to show that it can not be\ndenied, consistently with the law that every thing which begins to exist\nhas a cause. And hence we are justified in the seeming inconsistency, of\nholding induction by simple enumeration to be good for proving this\ngeneral truth, the foundation of scientific induction, and yet refusing\nto rely on it for any of the narrower inductions. I fully admit that if\nthe law of causation were unknown, generalization in the more obvious\ncases of uniformity in phenomena would nevertheless be possible, and\nthough in all cases more or less precarious, and in some extremely so,\nwould suffice to constitute a certain measure of probability; but what\nthe amount of this probability might be, we are dispensed from\nestimating, since it never could amount to the degree of assurance which\nthe proposition acquires, when, by the application to it of the Four\nMethods, the supposition of its falsity is shown to be inconsistent with\nthe Law of Causation. We are therefore logically entitled, and, by the\nnecessities of scientific induction, required, to disregard the\nprobabilities derived from the early rude method of generalizing, and to\nconsider no minor generalization as proved except so far as the law of\ncausation confirms it, nor probable except so far as it may reasonably\nbe expected to be so confirmed.\n\n\u00a7 4. The assertion, that our inductive processes assume the law of\ncausation, while the law of causation is itself a case of induction, is\na paradox, only on the old theory of reasoning, which supposes the\nuniversal truth, or major premise, in a ratiocination, to be the real\nproof of the particular truths which are ostensibly inferred from it.\nAccording to the doctrine maintained in the present treatise,(187) the\nmajor premise is not the proof of the conclusion, but is itself proved,\nalong with the conclusion from the same evidence. \u201cAll men are mortal\u201d\nis not the proof that Lord Palmerston is mortal; but our past experience\nof mortality authorizes us to infer _both_ the general truth and the\nparticular fact, and the one with exactly the same degree of assurance\nas the other. The mortality of Lord Palmerston is not an inference from\nthe mortality of all men, but from the experience which proves the\nmortality of all men; and is a correct inference from experience, if\nthat general truth is so too. This relation between our general beliefs\nand their particular applications holds equally true in the more\ncomprehensive case which we are now discussing. Any new fact of\ncausation inferred by induction, is rightly inferred, if no other\nobjection can be made to the inference than can be made to the general\ntruth that every event has a cause. The utmost certainty which can be\ngiven to a conclusion arrived at in the way of inference, stops at this\npoint. When we have ascertained that the particular conclusion must\nstand or fall with the general uniformity of the laws of nature\u2014that it\nis liable to no doubt except the doubt whether every event has a\ncause\u2014we have done all that can be done for it. The strongest assurance\nwe can obtain of any theory respecting the cause of a given phenomenon,\nis that the phenomenon has either that cause or none.\n\nThe latter supposition might have been an admissible one in a very early\nperiod of our study of nature. But we have been able to perceive that in\nthe stage which mankind have now reached, the generalization which gives\nthe Law of Universal Causation has grown into a stronger and better\ninduction, one deserving of greater reliance, than any of the\nsubordinate generalizations. We may even, I think, go a step further\nthan this, and regard the certainty of that great induction as not\nmerely comparative, but, for all practical purposes, complete.\n\nThe considerations, which, as I apprehend, give, at the present day, to\nthe proof of the law of uniformity of succession as true of all\nphenomena without exception, this character of completeness and\nconclusiveness, are the following: First, that we now know it directly\nto be true of far the greatest number of phenomena; that there are none\nof which we know it not to be true, the utmost that can be said being,\nthat of some we can not positively from direct evidence affirm its\ntruth; while phenomenon after phenomenon, as they become better known to\nus, are constantly passing from the latter class into the former; and in\nall cases in which that transition has not yet taken place, the absence\nof direct proof is accounted for by the rarity or the obscurity of the\nphenomena, our deficient means of observing them, or the logical\ndifficulties arising from the complication of the circumstances in which\nthey occur; insomuch that, notwithstanding as rigid a dependence on\ngiven conditions as exists in the case of any other phenomenon, it was\nnot likely that we should be better acquainted with those conditions\nthan we are. Besides this first class of considerations, there is a\nsecond, which still further corroborates the conclusion. Although there\nare phenomena the production and changes of which elude all our attempts\nto reduce them universally to any ascertained law; yet in every such\ncase, the phenomenon, or the objects concerned in it, are found in some\ninstances to obey the known laws of nature. The wind, for example, is\nthe type of uncertainty and caprice, yet we find it in some cases\nobeying with as much constancy as any phenomenon in nature the law of\nthe tendency of fluids to distribute themselves so as to equalize the\npressure on every side of each of their particles; as in the case of the\ntrade-winds and the monsoons.\n\nLightning might once have been supposed to obey no laws; but since it\nhas been ascertained to be identical with electricity, we know that the\nvery same phenomenon in some of its manifestations is implicitly\nobedient to the action of fixed causes. I do not believe that there is\nnow one object or event in all our experience of nature, within the\nbounds of the solar system at least, which has not either been\nascertained by direct observation to follow laws of its own, or been\nproved to be closely similar to objects and events which, in more\nfamiliar manifestations, or on a more limited scale, follow strict laws;\nour inability to trace the same laws on a larger scale and in the more\nrecondite instances, being accounted for by the number and complication\nof the modifying causes, or by their inaccessibility to observation.\n\nThe progress of experience, therefore, has dissipated the doubt which\nmust have rested on the universality of the law of causation while there\nwere phenomena which seemed to be _sui generis_, not subject to the same\nlaws with any other class of phenomena, and not as yet ascertained to\nhave peculiar laws of their own. This great generalization, however,\nmight reasonably have been, as it in fact was, acted on as a probability\nof the highest order, before there were sufficient grounds for receiving\nit as a certainty. In matters of evidence, as in all other human things,\nwe neither require, nor can attain, the absolute. We must hold even our\nstrongest convictions with an opening left in our minds for the\nreception of facts which contradict them; and only when we have taken\nthis precaution, have we earned the right to act upon our convictions\nwith complete confidence when no such contradiction appears. Whatever\nhas been found true in innumerable instances, and never found to be\nfalse after due examination in any, we are safe in acting on as\nuniversal provisionally, until an undoubted exception appears; provided\nthe nature of the case be such that a real exception could scarcely have\nescaped notice. When every phenomenon that we ever knew sufficiently\nwell to be able to answer the question, had a cause on which it was\ninvariably consequent, it was more rational to suppose that our\ninability to assign the causes of other phenomena arose from our\nignorance, than that there were phenomena which were uncaused, and which\nhappened to be exactly those which we had hitherto had no sufficient\nopportunity of studying.\n\nIt must, at the same time, be remarked, that the reasons for this\nreliance do not hold in circumstances unknown to us, and beyond the\npossible range of our experience. In distant parts of the stellar\nregions, where the phenomena may be entirely unlike those with which we\nare acquainted, it would be folly to affirm confidently that this\ngeneral law prevails, any more than those special ones which we have\nfound to hold universally on our own planet. The uniformity in the\nsuccession of events, otherwise called the law of causation, must be\nreceived not as a law of the universe, but of that portion of it only\nwhich is within the range of our means of sure observation, with a\nreasonable degree of extension to adjacent cases. To extend it further\nis to make a supposition without evidence, and to which, in the absence\nof any ground from experience for estimating its degree of probability,\nit would be idle to attempt to assign any.(188)\n\n\n\n\n                              Chapter XXII.\n\n\nOf Uniformities Of Co-Existence Not Dependent On Causation.\n\n\n\u00a7 1. The order of the occurrence of phenomena in time, is either\nsuccessive or simultaneous; the uniformities, therefore, which obtain in\ntheir occurrence, are either uniformities of succession or of\nco-existence. Uniformities of succession are all comprehended under the\nlaw of causation and its consequences. Every phenomenon has a cause, which\nit invariably follows; and from this are derived other invariable\nsequences among the successive stages of the same effect, as well as\nbetween the effects resulting from causes which invariably succeed one\nanother.\n\nIn the same manner with these derivative uniformities of succession, a\ngreat variety of uniformities of co-existence also take their rise.\nCo-ordinate effects of the same cause naturally co-exist with one another.\nHigh water at any point on the earth\u2019s surface, and high water at the\npoint diametrically opposite to it, are effects uniformly simultaneous,\nresulting from the direction in which the combined attractions of the sun\nand moon act upon the waters of the ocean. An eclipse of the sun to us,\nand an eclipse of the earth to a spectator situated in the moon, are in\nlike manner phenomena invariably co-existent; and their co-existence can\nequally be deduced from the laws of their production.\n\nIt is an obvious question, therefore, whether all the uniformities of\nco-existence among phenomena may not be accounted for in this manner. And\nit can not be doubted that between phenomena which are themselves effects,\nthe co-existences must necessarily depend on the causes of those\nphenomena. If they are effects immediately or remotely of the same cause,\nthey can not co-exist except by virtue of some laws or properties of that\ncause; if they are effects of different causes, they can not co-exist\nunless it be because their causes co-exist; and the uniformity of\nco-existence, if such there be, between the effects, proves that those\nparticular causes, within the limits of our observation, have uniformly\nbeen co-existent.\n\n\u00a7 2. But these same considerations compel us to recognize that there must\nbe one class of co-existences which can not depend on causation: the\nco-existences between the ultimate properties of things\u2014those properties\nwhich are the causes of all phenomena, but are not themselves caused by\nany phenomenon, and a cause for which could only be sought by ascending to\nthe origin of all things. Yet among these ultimate properties there are\nnot only co-existences, but uniformities of co-existence. General\npropositions may be, and are, formed, which assert that whenever certain\nproperties are found, certain others are found along with them. We\nperceive an object; say, for instance, water. We recognize it to be water,\nof course by certain of its properties. Having recognized it, we are able\nto affirm of it innumerable other properties; which we could not do unless\nit were a general truth, a law or uniformity in nature, that the set of\nproperties by which we identify the substance as water always have those\nother properties conjoined with them.\n\nIn a former place(189) it has been explained, in some detail, what is\nmeant by the Kinds of objects; those classes which differ from one another\nnot by a limited and definite, but by an indefinite and unknown, number of\ndistinctions. To this we have now to add, that every proposition by which\nany thing is asserted of a Kind, affirms a uniformity of co-existence.\nSince we know nothing of Kinds but their properties, the Kind, to us, _is_\nthe set of properties by which it is identified, and which must of course\nbe sufficient to distinguish it from every other kind.(190) In affirming\nany thing, therefore, of a Kind, we are affirming something to be\nuniformly co-existent with the properties by which the kind is recognized;\nand that is the sole meaning of the assertion.\n\nAmong the uniformities of co-existence which exist in nature, may hence be\nnumbered all the properties of Kinds. The whole of these, however, are not\nindependent of causation, but only a portion of them. Some are ultimate\nproperties, others derivative: of some, no cause can be assigned, but\nothers are manifestly dependent on causes. Thus, pure oxygen gas is a\nKind, and one of its most unequivocal properties is its gaseous form; this\nproperty, however, has for its cause the presence of a certain quantity of\nlatent heat; and if that heat could be taken away (as has been done from\nso many gases in Faraday\u2019s experiments), the gaseous form would doubtless\ndisappear, together with numerous other properties which depend on, or are\ncaused by, that property.\n\nIn regard to all substances which are chemical compounds, and which\ntherefore may be regarded as products of the juxtaposition of substances\ndifferent in Kind from themselves, there is considerable reason to presume\nthat the specific properties of the compound are consequent, as effects,\non some of the properties of the elements, though little progress has yet\nbeen made in tracing any invariable relation between the latter and the\nformer. Still more strongly will a similar presumption exist, when the\nobject itself, as in the case of organized beings, is no primeval agent,\nbut an effect, which depends on a cause or causes for its very existence.\nThe Kinds, therefore, which are called in chemistry simple substances, or\nelementary natural agents, are the only ones, any of whose properties can\nwith certainty be considered ultimate; and of these the ultimate\nproperties are probably much more numerous than we at present recognize,\nsince every successful instance of the resolution of the properties of\ntheir compounds into simpler laws, generally leads to the recognition of\nproperties in the elements distinct from any previously known. The\nresolution of the laws of the heavenly motions established the previously\nunknown ultimate property of a mutual attraction between all bodies; the\nresolution, so far as it has yet proceeded, of the laws of\ncrystallization, of chemical composition, electricity, magnetism, etc.,\npoints to various polarities, ultimately inherent in the particles of\nwhich bodies are composed; the comparative atomic weights of different\nkinds of bodies were ascertained by resolving into more general laws the\nuniformities observed in the proportions in which substances combine with\none another, and so forth. Thus, although every resolution of a complex\nuniformity into simpler and more elementary laws has an apparent tendency\nto diminish the number of the ultimate properties, and really does remove\nmany properties from the list; yet (since the result of this simplifying\nprocess is to trace up an ever greater variety of different effects to the\nsame agents) the further we advance in this direction, the greater number\nof distinct properties we are forced to recognize in one and the same\nobject; the co-existences of which properties must accordingly be ranked\namong the ultimate generalities of nature.\n\n\u00a7 3. There are, therefore, only two kinds of propositions which assert\nuniformity of co-existence between properties. Either the properties\ndepend on causes or they do not. If they do, the proposition which affirms\nthem to be co-existent is a derivative law of co-existence between\neffects, and, until resolved into the laws of causation on which it\ndepends, is an empirical law, and to be tried by the principles of\ninduction to which such laws are amenable. If, on the other hand, the\nproperties do not depend on causes, but are ultimate properties, then, if\nit be true that they invariably co-exist, they must all be ultimate\nproperties of one and the same Kind; and it is of these only that the\nco-existences can be classed as a peculiar sort of laws of nature.\n\nWhen we affirm that all crows are black, or that all negroes have woolly\nhair, we assert a uniformity of co-existence. We assert that the property\nof blackness or of having woolly hair invariably co-exists with the\nproperties which, in common language, or in the scientific classification\nthat we adopt, are taken to constitute the class crow, or the class negro.\nNow, supposing blackness to be an ultimate property of black objects, or\nwoolly hair an ultimate property of the animals which possess it;\nsupposing that these properties are not results of causation, are not\nconnected with antecedent phenomena by any law; then if all crows are\nblack, and all negroes have woolly hair, these must be ultimate properties\nof the kind _crow_, or _negro_, or of some kind which includes them. If,\non the contrary, blackness or woolly hair be an effect depending on\ncauses, these general propositions are manifestly empirical laws; and all\nthat has already been said respecting that class of generalizations may be\napplied without modification to these.\n\nNow, we have seen that in the case of all compounds\u2014of all things, in\nshort, except the elementary substances and primary powers of nature\u2014the\npresumption is, that the properties do really depend upon causes; and it\nis impossible in any case whatever to be certain that they do not. We\ntherefore should not be safe in claiming for any generalization respecting\nthe co-existence of properties, a degree of certainty to which, if the\nproperties should happen to be the result of causes, it would have no\nclaim. A generalization respecting co-existence, or, in other words,\nrespecting the properties of kinds, may be an ultimate truth, but it may\nalso be merely a derivative one; and since, if so, it is one of those\nderivative laws which are neither laws of causation nor have been resolved\ninto the laws of causation on which they depend, it can possess no higher\ndegree of evidence than belongs to an empirical law.\n\n\u00a7 4. This conclusion will be confirmed by the consideration of one great\ndeficiency, which precludes the application to the ultimate uniformities\nof co-existence, of a system of rigorous scientific induction, such as the\nuniformities in the succession of phenomena have been found to admit of.\nThe basis of such a system is wanting; there is no general axiom standing\nin the same relation to the uniformities of co-existence as the law of\ncausation does to those of succession. The Methods of Induction applicable\nto the ascertainment of causes and effects are grounded on the principle\nthat every thing which has a beginning must have some cause or other; that\namong the circumstances which actually existed at the time of its\ncommencement, there is certainly some one combination, on which the effect\nin question is unconditionally consequent, and on the repetition of which\nit would certainly again recur. But in an inquiry whether some kind (as\ncrow) universally possesses a certain property (as blackness), there is no\nroom for any assumption analogous to this. We have no previous certainty\nthat the property must have something which constantly co-exists with it;\nmust have an invariable co-existent, in the same manner as an event must\nhave an invariable antecedent. When we feel pain, we must be in some\ncircumstances under which, if exactly repeated, we should always feel\npain. But when we are conscious of blackness, it does not follow that\nthere is something else present of which blackness is a constant\naccompaniment. There is, therefore, no room for elimination; no method of\nAgreement or Difference, or of Concomitant Variations (which is but a\nmodification either of the Method of Agreement or of the Method of\nDifference). We can not conclude that the blackness we see in crows must\nbe an invariable property of crows merely because there is nothing else\npresent of which it can be an invariable property. We therefore inquire\ninto the truth of a proposition like \u201cAll crows are black,\u201d under the same\ndisadvantage as if, in our inquiries into causation, we were compelled to\nlet in, as one of the possibilities, that the effect may in that\nparticular instance have arisen without any cause at all.\n\nTo overlook this grand distinction was, as it seems to me, the capital\nerror in Bacon\u2019s view of inductive philosophy. The principle of\nelimination, that great logical instrument which he had the immense merit\nof first bringing into general use, he deemed applicable in the same\nsense, and in as unqualified a manner, to the investigation of the\nco-existences, as to that of the successions of phenomena. He seems to\nhave thought that as every event has a cause, or invariable antecedent, so\nevery property of an object has an invariable co-existent, which he called\nits form; and the examples he chiefly selected for the application and\nillustration of his method, were inquiries into such forms; attempts to\ndetermine in what else all those objects resembled, which agreed in some\none general property, as hardness or softness, dryness or moistness, heat\nor coldness. Such inquiries could lead to no result. The objects seldom\nhave any such circumstances in common. They usually agree in the one point\ninquired into, and in nothing else. A great proportion of the properties\nwhich, so far as we can conjecture, are the likeliest to be really\nultimate, would seem to be inherently properties of many different kinds\nof things not allied in any other respect. And as for the properties\nwhich, being effects of causes, we are able to give some account of, they\nhave generally nothing to do with the ultimate resemblances or diversities\nin the objects themselves, but depend on some outward circumstances, under\nthe influence of which any objects whatever are capable of manifesting\nthose properties; as is emphatically the case with those favorite subjects\nof Bacon\u2019s scientific inquiries, hotness and coldness, as well as with\nhardness and softness, solidity and fluidity, and many other conspicuous\nqualities.\n\nIn the absence, then, of any universal law of co-existence similar to the\nuniversal law of causation which regulates sequence, we are thrown back\nupon the unscientific induction of the ancients, _per enumerationem\nsimplicem, ubi non reperitur instantia contradictoria_. The reason we have\nfor believing that all crows are black, is simply that we have seen and\nheard of many black crows, and never one of any other color. It remains to\nbe considered how far this evidence can reach, and how we are to measure\nits strength in any given case.\n\n\u00a7 5. It sometimes happens that a mere change in the mode of verbally\nenunciating a question, though nothing is really added to the meaning\nexpressed, is of itself a considerable step toward its solution. This, I\nthink, happens in the present instance. The degree of certainty of any\ngeneralization which rests on no other evidence than the agreement, so far\nas it goes, of all past observation, is but another phrase for the degree\nof improbability that an exception, if any existed, could have hitherto\nremained unobserved. The reason for believing that all crows are black, is\nmeasured by the improbability that crows of any other color should have\nexisted to the present time without our being aware of it. Let us state\nthe question in this last mode, and consider what is implied in the\nsupposition that there may be crows which are not black, and under what\nconditions we can be justified in regarding this as incredible.\n\nIf there really exist crows which are not black, one of two things must be\nthe fact. Either the circumstance of blackness, in all crows hitherto\nobserved, must be, as it were, an accident, not connected with any\ndistinction of Kind; or if it be a property of Kind, the crows which are\nnot black must be a new Kind, a Kind hitherto overlooked, though coming\nunder the same general description by which crows have hitherto been\ncharacterized. The first supposition would be proved true if we were to\ndiscover casually a white crow among black ones, or if it were found that\nblack crows sometimes turn white. The second would be shown to be the fact\nif in Australia or Central Africa a species or a race of white or gray\ncrows were found to exist.\n\n\u00a7 6. The former of these suppositions necessarily implies that the color\nis an effect of causation. If blackness, in the crows in which it has been\nobserved, be not a property of Kind, but can be present or absent without\nany difference generally in the properties of the object, then it is not\nan ultimate fact in the individuals themselves, but is certainly dependent\non a cause. There are, no doubt, many properties which vary from\nindividual to individual of the same Kind, even the same _infima species_,\nor lowest Kind. Some flowers may be either white or red, without differing\nin any other respect. But these properties are not ultimate; they depend\non causes. So far as the properties of a thing belong to its own nature,\nand do not arise from some cause extrinsic to it, they are always the same\nin the same Kind. Take, for instance, all simple substances and elementary\npowers; the only things of which we are certain that some at least of\ntheir properties are really ultimate. Color is generally esteemed the most\nvariable of all properties: yet we do not find that sulphur is sometimes\nyellow and sometimes white, or that it varies in color at all, except so\nfar as color is the effect of some extrinsic cause, as of the sort of\nlight thrown upon it, the mechanical arrangement of the particles (as\nafter fusion), etc. We do not find that iron is sometimes fluid and\nsometimes solid at the same temperature; gold sometimes malleable and\nsometimes brittle; that hydrogen will sometimes combine with oxygen and\nsometimes not; or the like. If from simple substances we pass to any of\ntheir definite compounds, as water, lime, or sulphuric acid, there is the\nsame constancy in their properties. When properties vary from individual\nto individual, it is either in the case of miscellaneous aggregations,\nsuch as atmospheric air or rock, composed of heterogeneous substances, and\nnot constituting or belonging to any real Kind,(191) or it is in the case\nof organic beings. In them, indeed, there is variability in a high degree.\nAnimals of the same species and race, human beings of the same age, sex,\nand country, will be most different, for example, in face and figure. But\norganized beings (from the extreme complication of the laws by which they\nare regulated) being more eminently modifiable, that is, liable to be\ninfluenced by a greater number and variety of causes, than any other\nphenomena whatever; having also themselves had a beginning, and therefore\na cause; there is reason to believe that none of their properties are\nultimate, but all of them derivative, and produced by causation. And the\npresumption is confirmed, by the fact that the properties which vary from\none individual to another, also generally vary more or less at different\ntimes in the same individual; which variation, like any other event,\nsupposes a cause, and implies, consequently, that the properties are not\nindependent of causation.\n\nIf, therefore, blackness be merely accidental in crows, and capable of\nvarying while the Kind remains the same, its presence or absence is\ndoubtless no ultimate fact, but the effect of some unknown cause: and in\nthat case the universality of the experience that all crows are black is\nsufficient proof of a common cause, and establishes the generalization as\nan empirical law. Since there are innumerable instances in the\naffirmative, and hitherto none at all in the negative, the causes on which\nthe property depends must exist everywhere in the limits of the\nobservations which have been made; and the proposition may be received as\nuniversal within those limits, and with the allowable degree of extension\nto adjacent cases.\n\n\u00a7 7. If, in the second place, the property, in the instances in which it\nhas been observed, is not an effect of causation, it is a property of\nKind; and in that case the generalization can only be set aside by the\ndiscovery of a new Kind of crow. That, however, a peculiar Kind not\nhitherto discovered should exist in nature, is a supposition so often\nrealized that it can not be considered at all improbable. We have nothing\nto authorize us in attempting to limit the Kinds of things which exist in\nnature. The only unlikelihood would be that a new Kind should be\ndiscovered in localities which there was previously reason to believe had\nbeen thoroughly explored; and even this improbability depends on the\ndegree of conspicuousness of the difference between the newly-discovered\nKind and all others, since new kinds of minerals, plants, and even\nanimals, previously overlooked or confounded with known species, are still\ncontinually detected in the most frequented situations. On this second\nground, therefore, as well as on the first, the observed uniformity of\nco-existence can only hold good as an empirical law, within the limits not\nonly of actual observation, but of an observation as accurate as the\nnature of the case required. And hence it is that (as remarked in an early\nchapter of the present book) we so often give up generalizations of this\nclass at the first summons. If any credible witness stated that he had\nseen a white crow, under circumstances which made it not incredible that\nit should have escaped notice previously, we should give full credence to\nthe statement.\n\nIt appears, then, that the uniformities which obtain in the co-existence\nof phenomena\u2014those which we have reason to consider as ultimate, no less\nthan those which arise from the laws of causes yet undetected\u2014are entitled\nto reception only as empirical laws; are not to be presumed true except\nwithin the limits of time, place, and circumstance, in which the\nobservations were made, or except in cases strictly adjacent.\n\n\u00a7 8. We have seen in the last chapter that there is a point of generality\nat which empirical laws become as certain as laws of nature, or, rather,\nat which there is no longer any distinction between empirical laws and\nlaws of nature. As empirical laws approach this point, in other words, as\nthey rise in their degree of generality, they become more certain; their\nuniversality may be more strongly relied on. For, in the first place, if\nthey are results of causation (which, even in the class of uniformities\ntreated of in the present chapter, we never can be certain that they are\nnot) the more general they are, the greater is proved to be the space over\nwhich the necessary collocations prevail, and within which no causes exist\ncapable of counteracting the unknown causes on which the empirical law\ndepends. To say that any thing is an invariable property of some very\nlimited class of objects, is to say that it invariably accompanies some\nvery numerous and complex group of distinguishing properties; which, if\ncausation be at all concerned in the matter, argues a combination of many\ncauses, and therefore a great liability to counteraction; while the\ncomparatively narrow range of the observations renders it impossible to\npredict to what extent unknown counteracting causes may be distributed\nthroughout nature. But when a generalization has been found to hold good\nof a very large proportion of all things whatever, it is already proved\nthat nearly all the causes which exist in nature have no power over it;\nthat very few changes in the combination of causes can affect it; since\nthe greater number of possible combinations must have already existed in\nsome one or other of the instances in which it has been found true. If,\ntherefore, any empirical law is a result of causation, the more general it\nis, the more it may be depended on. And even if it be no result of\ncausation, but an ultimate co-existence, the more general it is, the\ngreater amount of experience it is derived from, and the greater therefore\nis the probability that if exceptions had existed, some would already have\npresented themselves.\n\nFor these reasons, it requires much more evidence to establish an\nexception to one of the more general empirical laws than to the more\nspecial ones. We should not have any difficulty in believing that there\nmight be a new Kind of crow; or a new kind of bird resembling a crow in\nthe properties hitherto considered distinctive of that Kind. But it would\nrequire stronger proof to convince us of the existence of a Kind of crow\nhaving properties at variance with any generally recognized universal\nproperty of birds; and a still higher degree if the properties conflict\nwith any recognized universal property of animals. And this is conformable\nto the mode of judgment recommended by the common sense and general\npractice of mankind, who are more incredulous as to any novelties in\nnature, according to the degree of generality of the experience which\nthese novelties seem to contradict.\n\n\u00a7 9. It is conceivable that the alleged properties might conflict with\nsome recognized universal property of all matter. In that case their\nimprobability would be at the highest, but would not even then amount to\nincredibility. There are only two known properties common to all matter;\nin other words, there is but one known uniformity of co-existence of\nproperties co-extensive with all physical nature, namely, that whatever\nopposes resistance to movement gravitates, or, as Professor Bain expresses\nit, Inertia and Gravity are co-existent through all matter, and\nproportionate in their amount. These properties, as he truly says, are not\nmutually implicated; from neither of them could we, on grounds of\ncausation, presume the other. But, for this very reason, we are never\ncertain that a Kind may not be discovered possessing one of the properties\nwithout the other. The hypothetical ether, if it exists, may be such a\nKind. Our senses can not recognize in it either resistance or gravity; but\nif the reality of a resisting medium should eventually be proved (by\nalteration, for example, in the times of revolution of periodic comets,\ncombined with the evidences afforded by the phenomena of light and heat),\nit would be rash to conclude from this alone, without other proofs, that\nit must gravitate.\n\nFor even the greater generalizations, which embrace comprehensive Kinds\ncontaining under them a great number and variety of _infim\u00e6 species_, are\nonly empirical laws, resting on induction by simple enumeration merely,\nand not on any process of elimination\u2014a process wholly inapplicable to\nthis sort of case. Such generalizations, therefore, ought to be grounded\non an examination of all the _infim\u00e6 species_ comprehended in them, and\nnot of a portion only. We can not conclude (where causation is not\nconcerned), because a proposition is true of a number of things resembling\none another only in being animals, that it is therefore true of all\nanimals. If, indeed, any thing be true of species which differ more from\none another than either differs from a third, especially if that third\nspecies occupies in most of its known properties a position between the\ntwo former, there is some probability that the same thing will also be\ntrue of that intermediate species; for it is often, though by no means\nuniversally, found, that there is a sort of parallelism in the properties\nof different Kinds, and that their degree of unlikeness in one respect\nbears some proportion to their unlikeness in others. We see this\nparallelism in the properties of the different metals; in those of\nsulphur, phosphorus, and carbon; of chlorine, iodine, and bromine; in the\nnatural orders of plants and animals, etc. But there are innumerable\nanomalies and exceptions to this sort of conformity; if indeed the\nconformity itself be any thing but an anomaly and an exception in nature.\n\nUniversal propositions, therefore, respecting the properties of superior\nKinds, unless grounded on proved or presumed connection by causation,\nought not to be hazarded except after separately examining every known\nsub-kind included in the larger Kind. And even then such generalizations\nmust be held in readiness to be given up on the occurrence of some new\nanomaly, which, when the uniformity is not derived from causation, can\nnever, even in the case of the most general of these empirical laws, be\nconsidered very improbable. Thus, all the universal propositions which it\nhas been attempted to lay down respecting simple substances, or concerning\nany of the classes which have been formed among simple substances (and the\nattempt has been often made), have, with the progress of experience,\neither faded into inanity, or been proved to be erroneous; and each Kind\nof simple substance remains, with its own collection of properties apart\nfrom the rest, saving a certain parallelism with a few other Kinds, the\nmost similar to itself. In organized beings, indeed, there are abundance\nof propositions ascertained to be universally true of superior genera, to\nmany of which the discovery hereafter of any exceptions must be regarded\nas extremely improbable. But these, as already observed, are, we have\nevery reason to believe, properties dependent on causation.(192)\n\nUniformities of co-existence, then, not only when they are consequences of\nlaws of succession, but also when they are ultimate truths, must be\nranked, for the purpose of logic, among empirical laws; and are amenable\nin every respect to the same rules with those unresolved uniformities\nwhich are known to be dependent on causation.(193)\n\n\n\n\n                              Chapter XXIII.\n\n\nOf Approximate Generalizations, And Probable Evidence.\n\n\n\u00a7 1. In our inquiries into the nature of the inductive process, we must\nnot confine our notice to such generalizations from experience as profess\nto be universally true. There is a class of inductive truths avowedly not\nuniversal; in which it is not pretended that the predicate is always true\nof the subject; but the value of which, as generalizations, is\nnevertheless extremely great. An important portion of the field of\ninductive knowledge does not consist of universal truths, but of\napproximations to such truths; and when a conclusion is said to rest on\nprobable evidence, the premises it is drawn from are usually\ngeneralizations of this sort.\n\nAs every certain inference respecting a particular case implies that there\nis ground for a general proposition of the form, every A is B; so does\nevery probable inference suppose that there is ground for a proposition of\nthe form, Most A are B; and the degree of probability of the inference in\nan average case will depend on the proportion between the number of\ninstances existing in nature which accord with the generalization, and the\nnumber of those which conflict with it.\n\n\u00a7 2. Propositions in the form, Most A are B, are of a very different\ndegree of importance in science, and in the practice of life. To the\nscientific inquirer they are valuable chiefly as materials for, and steps\ntoward universal truths. The discovery of these is the proper end of\nscience; its work is not done if it stops at the proposition that a\nmajority of A are B, without circumscribing that majority by some common\ncharacter, fitted to distinguish them from the minority. Independently of\nthe inferior precision of such imperfect generalizations, and the inferior\nassurance with which they can be applied to individual cases, it is plain\nthat, compared with exact generalizations, they are almost useless as\nmeans of discovering ulterior truths by way of deduction. We may, it is\ntrue, by combining the proposition Most A are B, with a universal\nproposition, Every B is C, arrive at the conclusion that Most A are C. But\nwhen a second proposition of the approximate kind is introduced\u2014or even\nwhen there is but one, if that one be the major premise\u2014nothing can, in\ngeneral, be positively concluded. When the major is Most B are D, then,\neven if the minor be Every A is B, we can not infer that most A are D, or\nwith any certainty that even some A are D. Though the majority of the\nclass B have the attribute signified by D, the whole of the sub-class A\nmay belong to the minority.(194)\n\nThough so little use can be made, in science, of approximate\ngeneralizations, except as a stage on the road to something better, for\npractical guidance they are often all we have to rely on. Even when\nscience has really determined the universal laws of any phenomenon, not\nonly are those laws generally too much encumbered with conditions to be\nadapted for everyday use, but the cases which present themselves in life\nare too complicated, and our decisions require to be taken too rapidly, to\nadmit of waiting till the existence of a phenomenon can be proved by what\nhave been scientifically ascertained to be universal marks of it. To be\nindecisive and reluctant to act, because we have not evidence of a\nperfectly conclusive character to act on, is a defect sometimes incident\nto scientific minds, but which, wherever it exists, renders them unfit for\npractical emergencies. If we would succeed in action, we must judge by\nindications which, though they do not generally mislead us, sometimes do,\nand must make up, as far as possible, for the incomplete conclusiveness of\nany one indication, by obtaining others to corroborate it. The principles\nof induction applicable to approximate generalization are therefore a not\nless important subject of inquiry than the rules for the investigation of\nuniversal truths; and might reasonably be expected to detain us almost as\nlong, were it not that these principles are mere corollaries from those\nwhich have been already treated of.\n\n\u00a7 3. There are two sorts of cases in which we are forced to guide\nourselves by generalizations of the imperfect form, Most A are B. The\nfirst is, when we have no others; when we have not been able to carry our\ninvestigation of the laws of the phenomena any further; as in the\nfollowing propositions\u2014Most dark-eyed persons have dark hair; Most springs\ncontain mineral substances; Most stratified formations contain fossils.\nThe importance of this class of generalizations is not very great; for,\nthough it frequently happens that we see no reason why that which is true\nof most individuals of a class is not true of the remainder, nor are able\nto bring the former under any general description which can distinguish\nthem from the latter, yet if we are willing to be satisfied with\npropositions of a less degree of generality, and to break down the class A\ninto sub-classes, we may generally obtain a collection of propositions\nexactly true. We do not know why most wood is lighter than water, nor can\nwe point out any general property which discriminates wood that is lighter\nthan water from that which is heavier. But we know exactly what species\nare the one and what the other. And if we meet with a specimen not\nconformable to any known species (the only case in which our previous\nknowledge affords no other guidance than the approximate generalization),\nwe can generally make a specific experiment, which is a surer resource.\n\nIt often happens, however, that the proposition, Most A are B, is not the\nultimatum of our scientific attainments, though the knowledge we possess\nbeyond it can not conveniently be brought to bear upon the particular\ninstance. We may know well enough what circumstances distinguish the\nportion of A which has the attribute B from the portion which has it not,\nbut may have no means, or may not have time, to examine whether those\ncharacteristic circumstances exist or not in the individual case. This is\nthe situation we are generally in when the inquiry is of the kind called\nmoral, that is, of the kind which has in view to predict human actions. To\nenable us to affirm any thing universally concerning the actions of\nclasses of human beings, the classification must be grounded on the\ncircumstances of their mental culture and habits, which in an individual\ncase are seldom exactly known; and classes grounded on these distinctions\nwould never precisely accord with those into which mankind are divided for\nsocial purposes. All propositions which can be framed respecting the\nactions of human beings as ordinarily classified, or as classified\naccording to any kind of outward indications, are merely approximate. We\ncan only say, Most persons of a particular age, profession, country, or\nrank in society, have such and such qualities; or, Most persons, when\nplaced in certain circumstances, act in such and such a way. Not that we\ndo not often know well enough on what causes the qualities depend, or what\nsort of persons they are who act in that particular way; but we have\nseldom the means of knowing whether any individual person has been under\nthe influence of those causes, or is a person of that particular sort. We\ncould replace the approximate generalizations by propositions universally\ntrue; but these would hardly ever be capable of being applied to practice.\nWe should be sure of our majors, but we should not be able to get minors\nto fit; we are forced, therefore, to draw our conclusions from coarser and\nmore fallible indications.\n\n\u00a7 4. Proceeding now to consider what is to be regarded as sufficient\nevidence of an approximate generalization, we can have no difficulty in at\nonce recognizing that, when admissible at all, it is admissible only as an\nempirical law. Propositions of the form, Every A is B, are not necessarily\nlaws of causation, or ultimate uniformities of co-existence; propositions\nlike Most A are B, _can not_ be so. Propositions hitherto found true in\nevery observed instance may yet be no necessary consequence of laws of\ncausation, or of ultimate uniformities, and unless they are so, may, for\naught we know, be false beyond the limits of actual observation; still\nmore evidently must this be the case with propositions which are only true\nin a mere majority of the observed instances.\n\nThere is some difference, however, in the degree of certainty of the\nproposition, Most A are B, according as that approximate generalization\ncomposes the whole of our knowledge of the subject, or not. Suppose,\nfirst, that the former is the case. We know only that most A are B, not\nwhy they are so, nor in what respect those which are differ from those\nwhich are not. How, then, did we learn that most A are B? Precisely in the\nmanner in which we should have learned, had such happened to be the fact\nthat all A are B. We collected a number of instances sufficient to\neliminate chance, and, having done so, compared the number of instances in\nthe affirmative with the number in the negative. The result, like other\nunresolved derivative laws, can be relied on solely within the limits not\nonly of place and time, but also of circumstance, under which its truth\nhas been actually observed; for, as we are supposed to be ignorant of the\ncauses which make the proposition true, we can not tell in what manner any\nnew circumstance might perhaps affect it. The proposition, Most judges are\ninaccessible to bribes, would probably be found true of Englishmen,\nFrenchmen, Germans, North Americans, and so forth; but if on this evidence\nalone we extended the assertion to Orientals, we should step beyond the\nlimits, not only of place but of circumstance, within which the fact had\nbeen observed, and should let in possibilities of the absence of the\ndetermining causes, or the presence of counteracting ones, which might be\nfatal to the approximate generalization.\n\nIn the case where the approximate proposition is not the ultimatum of our\nscientific knowledge, but only the most available form of it for practical\nguidance; where we know, not only that most A have the attribute B, but\nalso the causes of B, or some properties by which the portion of A which\nhas that attribute is distinguished from the portion which has it not, we\nare rather more favorably situated than in the preceding case. For we have\nnow a double mode of ascertaining whether it be true that most A are B;\nthe direct mode, as before, and an indirect one, that of examining whether\nthe proposition admits of being deduced from the known cause, or from any\nknown criterion, of B. Let the question, for example, be whether most\nScotchmen can read? We may not have observed, or received the testimony of\nothers respecting, a sufficient number and variety of Scotchmen to\nascertain this fact; but when we consider that the cause of being able to\nread is the having been taught it, another mode of determining the\nquestion presents itself, namely, by inquiring whether most Scotchmen have\nbeen sent to schools where reading is effectually taught. Of these two\nmodes, sometimes one and sometimes the other is the more available. In\nsome cases, the frequency of the effect is the more accessible to that\nextensive and varied observation which is indispensable to the\nestablishment of an empirical law; at other times, the frequency of the\ncauses, or of some collateral indications. It commonly happens that\nneither is susceptible of so satisfactory an induction as could be\ndesired, and that the grounds on which the conclusion is received are\ncompounded of both. Thus a person may believe that most Scotchmen can\nread, because, so far as his information extends, most Scotchmen have been\nsent to school, and most Scotch schools teach reading effectually; and\nalso because most of the Scotchmen whom he has known or heard of could\nread; though neither of these two sets of observations may by itself\nfulfill the necessary conditions of extent and variety.\n\nAlthough the approximate generalization may in most cases be indispensable\nfor our guidance, even when we know the cause, or some certain mark, of\nthe attribute predicated, it needs hardly be observed that we may always\nreplace the uncertain indication by a certain one, in any case in which we\ncan actually recognize the existence of the cause or mark. For example, an\nassertion is made by a witness, and the question is whether to believe it.\nIf we do not look to any of the individual circumstances of the case, we\nhave nothing to direct us but the approximate generalization, that truth\nis more common than falsehood, or, in other words, that most persons, on\nmost occasions, speak truth. But if we consider in what circumstances the\ncases where truth is spoken differ from those in which it is not, we find,\nfor instance, the following: the witness\u2019s being an honest person or not;\nhis being an accurate observer or not; his having an interest to serve in\nthe matter or not. Now, not only may we be able to obtain other\napproximate generalizations respecting the degree of frequency of these\nvarious possibilities, but we may know which of them is positively\nrealized in the individual case. That the witness has or has not an\ninterest to serve, we perhaps know directly; and the other two points\nindirectly, by means of marks; as, for example, from his conduct on some\nformer occasion; or from his reputation, which, though a very uncertain\nmark, affords an approximate generalization (as, for instance, Most\npersons who are believed to be honest by those with whom they have had\nfrequent dealings, are really so), which approaches nearer to a universal\ntruth than the approximate general proposition with which we set out,\nviz., Most persons on most occasions speak truth.\n\nAs it seems unnecessary to dwell further on the question of the evidence\nof approximate generalizations, we shall proceed to a not less important\ntopic, that of the cautions to be observed in arguing from these\nincompletely universal propositions to particular cases.\n\n\u00a7 5. So far as regards the direct application of an approximate\ngeneralization to an individual instance, this question presents no\ndifficulty. If the proposition, Most A are B, has been established, by a\nsufficient induction, as an empirical law, we may conclude that any\nparticular A is B with a probability proportioned to the preponderance of\nthe number of affirmative instances over the number of exceptions. If it\nhas been found practicable to attain numerical precision in the data, a\ncorresponding degree of precision may be given to the evaluation of the\nchances of error in the conclusion. If it can be established as an\nempirical law that nine out of every ten A are B, there will be one chance\nin ten of error in assuming that any A, not individually known to us, is a\nB: but this of course holds only within the limits of time, place, and\ncircumstance, embraced in the observations, and therefore can not be\ncounted on for any sub-class or variety of A (or for A in any set of\nexternal circumstances) which were not included in the average. It must be\nadded, that we can guide ourselves by the proposition, Nine out of every\nten A are B, only in cases of which we know nothing except that they fall\nwithin the class A. For if we know, of any particular instances _i_, not\nonly that it falls under A, but to what species or variety of A it\nbelongs, we shall generally err in applying to _i_ the average struck for\nthe whole genus, from which the average corresponding to that species\nalone would, in all probability, materially differ. And so if _i_, instead\nof being a particular sort of instance, is an instance known to be under\nthe influence of a particular set of circumstances, the presumption drawn\nfrom the numerical proportions in the whole genus would probably, in such\na case, only mislead. A general average should only be applied to cases\nwhich are neither known, nor can be presumed, to be other than average\ncases. Such averages, therefore, are commonly of little use for the\npractical guidance of any affairs but those which concern large numbers.\nTables of the chances of life are useful to insurance offices, but they go\na very little way toward informing any one of the chances of his own life,\nor any other life in which he is interested, since almost every life is\neither better or worse than the average. Such averages can only be\nconsidered as supplying the first term in a series of approximations; the\nsubsequent terms proceeding on an appreciation of the circumstances\nbelonging to the particular case.\n\n\u00a7 6. From the application of a single approximate generalization to\nindividual cases, we proceed to the application of two or more of them\ntogether to the same case.\n\nWhen a judgment applied to an individual instance is grounded on two\napproximate generalizations taken in conjunction, the propositions may\ncooperate toward the result in two different ways. In the one, each\nproposition is separately applicable to the case in hand, and our object\nin combining them is to give to the conclusion in that particular case the\ndouble probability arising from the two propositions separately. This may\nbe called joining two probabilities by way of Addition; and the result is\na probability greater than either. The other mode is, when only one of the\npropositions is directly applicable to the case, the second being only\napplicable to it by virtue of the application of the first. This is\njoining two probabilities by way of Ratiocination or Deduction; the result\nof which is a less probability than either. The type of the first argument\nis, Most A are B; most C are B; this thing is both an A and a C; therefore\nit is probably a B. The type of the second is, Most A are B; most C are A;\nthis is a C; therefore it is probably an A, therefore it is probably a B.\nThe first is exemplified when we prove a fact by the testimony of two\nunconnected witnesses; the second, when we adduce only the testimony of\none witness that he has heard the thing asserted by another. Or again, in\nthe first mode it may be argued that the accused committed the crime,\nbecause he concealed himself, and because his clothes were stained with\nblood; in the second, that he committed it because he washed or destroyed\nhis clothes, which is supposed to render it probable that they were\nstained with blood. Instead of only two links, as in these instances, we\nmay suppose chains of any length. A chain of the former kind was termed by\nBentham(195) a self-corroborative chain of evidence; the second, a\nself-infirmative chain.\n\nWhen approximate generalizations are joined by way of addition, we may\ndeduce from the theory of probabilities laid down in a former chapter, in\nwhat manner each of them adds to the probability of a conclusion which has\nthe warrant of them all.\n\nIf, on an average, two of every three As are Bs, and three of every four\nCs are Bs, the probability that something which is both an A and a C is a\nB, will be more than two in three, or than three in four. Of every twelve\nthings which are As, all except four are Bs by the supposition; and if the\nwhole twelve, and consequently those four, have the characters of C\nlikewise, three of these will be Bs on that ground. Therefore, out of\ntwelve which are both As and Cs, eleven are Bs. To state the argument in\nanother way; a thing which is both an A and a C, but which is not a B, is\nfound in only one of three sections of the class A, and in only one of\nfour sections of the class C; but this fourth of C being spread over the\nwhole of A indiscriminately, only one-third part of it (or one-twelfth of\nthe whole number) belongs to the third section of A; therefore a thing\nwhich is not a B occurs only once, among twelve things which are both As\nand Cs. The argument would, in the language of the doctrine of chances, be\nthus expressed: the chance that an A is not a B is \u2153, the chance that a\nC is not a B is \u00bc; hence if the thing be both an A and a C, the chance\nis \u2153 of \u00bc = \u00b9\u2044\u2081\u2082.(196)\n\nIn this computation it is of course supposed that the probabilities\narising from A and C are independent of each other. There must not be any\nsuch connection between A and C, that when a thing belongs to the one\nclass it will therefore belong to the other, or even have a greater chance\nof doing so. Otherwise the not-Bs which are Cs may be, most or even all of\nthem, identical with the not-Bs which are As; in which last case the\nprobability arising from A and C together will be no greater than that\narising from A alone.\n\nWhen approximate generalizations are joined together in the other mode,\nthat of deduction, the degree of probability of the inference, instead of\nincreasing, diminishes at each step. From two such premises as Most A are\nB, Most B are C, we can not with certainty conclude that even a single A\nis C; for the whole of the portion of A which in any way falls under B,\nmay perhaps be comprised in the exceptional part of it. Still, the two\npropositions in question afford an appreciable probability that any given\nA is C, provided the average on which the second proposition is grounded\nwas taken fairly with reference to the first; provided the proposition,\nMost B are C, was arrived at in a manner leaving no suspicion that the\nprobability arising from it is otherwise than fairly distributed over the\nsection of B which belongs to A. For though the instances which are A\n_may_ be all in the minority, they may, also, be all in the majority; and\nthe one possibility is to be set against the other. On the whole, the\nprobability arising from the two propositions taken together, will be\ncorrectly measured by the probability arising from the one, abated in the\nratio of that arising from the other. If nine out of ten Swedes have light\nhair, and eight out of nine inhabitants of Stockholm are Swedes, the\nprobability arising from these two propositions, that any given inhabitant\nof Stockholm is light-haired, will amount to eight in ten; though it is\nrigorously possible that the whole Swedish population of Stockholm might\nbelong to that tenth section of the people of Sweden who are an exception\nto the rest.\n\nIf the premises are known to be true not of a bare majority, but of nearly\nthe whole, of their respective subjects, we may go on joining one such\nproposition to another for several steps, before we reach a conclusion not\npresumably true even of a majority. The error of the conclusion will\namount to the aggregate of the errors of all the premises. Let the\nproposition, most A are B, be true of nine in ten; Most B are C, of eight\nin nine; then not only will one A in ten not be C, because not B, but even\nof the nine-tenths which are B, only eight-ninths will be C; that is, the\ncases of A which are C will be only \u2078\u2044\u2089 of \u2079\u2044\u2081\u2080, or four-fifths. Let us\nnow add Most C are D, and suppose this to be true of seven cases out of\neight; the proportion of A which is D will be only \u215e of \u2078\u2044\u2089 of \u2079\u2044\u2081\u2080, or\n\u2077\u2044\u2081\u2080. Thus the probability progressively dwindles. The experience,\nhowever, on which our approximate generalizations are grounded, has so\nrarely been subjected to, or admits of, accurate numerical estimation,\nthat we can not in general apply any measurement to the diminution of\nprobability which takes place at each illation; but must be content with\nremembering that it does diminish at every step, and that unless the\npremises approach very nearly indeed to being universally true, the\nconclusion after a very few steps is worth nothing. A hearsay of a\nhearsay, or an argument from presumptive evidence depending not on\nimmediate marks but on marks of marks, is worthless at a very few removes\nfrom the first stage.\n\n\u00a7 7. There are, however, two cases in which reasonings depending on\napproximate generalizations may be carried to any length we please with as\nmuch assurance, and are as strictly scientific, as if they were composed\nof universal laws of nature. But these cases are exceptions of the sort\nwhich are currently said to prove the rule. The approximate\ngeneralizations are as suitable, in the cases in question, for purposes of\nratiocination, as if they were complete generalizations, because they are\ncapable of being transformed into complete generalizations exactly\nequivalent.\n\nFirst: If the approximate generalization is of the class in which our\nreason for stopping at the approximation is not the impossibility, but\nonly the inconvenience, of going further; if we are cognizant of the\ncharacter which distinguishes the cases that accord with the\ngeneralization from those which are exceptions to it; we may then\nsubstitute for the approximate proposition, a universal proposition with a\nproviso. The proposition, Most persons who have uncontrolled power employ\nit ill, is a generalization of this class, and may be transformed into the\nfollowing: All persons who have uncontrolled power employ it ill, provided\nthey are not persons of unusual strength of judgment and rectitude of\npurpose. The proposition, carrying the hypothesis or proviso with it, may\nthen be dealt with no longer as an approximate, but as a universal\nproposition; and to whatever number of steps the reasoning may reach, the\nhypothesis, being carried forward to the conclusion, will exactly indicate\nhow far that conclusion is from being applicable universally. If in the\ncourse of the argument other approximate generalizations are introduced,\neach of them being in like manner expressed as a universal proposition\nwith a condition annexed, the sum of all the conditions will appear at the\nend as the sum of all the errors which affect the conclusion. Thus, to the\nproposition last cited, let us add the following: All absolute monarchs\nhave uncontrolled power, unless their position is such that they need the\nactive support of their subjects (as was the case with Queen Elizabeth,\nFrederick of Prussia, and others). Combining these two propositions, we\ncan deduce from them a universal conclusion, which will be subject to both\nthe hypotheses in the premises; All absolute monarchs employ their power\nill, unless their position makes them need the active support of their\nsubjects, or unless they are persons of unusual strength of judgment and\nrectitude of purpose. It is of no consequence how rapidly the errors in\nour premises accumulate, if we are able in this manner to record each\nerror, and keep an account of the aggregate as it swells up.\n\nSecondly: there is a case in which approximate propositions, even without\nour taking note of the conditions under which they are not true of\nindividual cases, are yet, for the purposes of science, universal ones;\nnamely, in the inquiries which relate to the properties not of\nindividuals, but of multitudes. The principal of these is the science of\npolitics, or of human society. This science is principally concerned with\nthe actions not of solitary individuals, but of masses; with the fortunes\nnot of single persons, but of communities. For the statesman, therefore,\nit is generally enough to know that _most_ persons act or are acted upon\nin a particular way; since his speculations and his practical arrangements\nrefer almost exclusively to cases in which the whole community, or some\nlarge portion of it, is acted upon at once, and in which, therefore, what\nis done or felt by _most_ persons determines the result produced by or\nupon the body at large. He can get on well enough with approximate\ngeneralizations on human nature, since what is true approximately of all\nindividuals is true absolutely of all masses. And even when the operations\nof individual men have a part to play in his deductions, as when he is\nreasoning of kings, or other single rulers, still, as he is providing for\nindefinite duration, involving an indefinite succession of such\nindividuals, he must in general both reason and act as if what is true of\nmost persons were true of all.\n\nThe two kinds of considerations above adduced are a sufficient refutation\nof the popular error, that speculations on society and government, as\nresting on merely probable evidence, must be inferior in certainty and\nscientific accuracy to the conclusions of what are called the exact\nsciences, and less to be relied on in practice. There are reasons enough\nwhy the moral sciences must remain inferior to at least the more perfect\nof the physical; why the laws of their more complicated phenomena can not\nbe so completely deciphered, nor the phenomena predicted with the same\ndegree of assurance. But though we can not attain to so many truths, there\nis no reason that those we can attain should deserve less reliance, or\nhave less of a scientific character. Of this topic, however, I shall treat\nmore systematically in the concluding Book, to which place any further\nconsideration of it must be deferred.\n\n\n\n\n                              Chapter XXIV.\n\n\nOf The Remaining Laws Of Nature.\n\n\n\u00a7 1. In the First Book we found that all the assertions which can be\nconveyed by language, express some one or more of five different things:\nExistence; Order in Place; Order in Time; Causation; and Resemblance.(197)\nOf these, Causation, in our view of the subject, not being fundamentally\ndifferent from Order in Time, the five species of possible assertions are\nreduced to four. The propositions which affirm Order in Time in either of\nits two modes, Co-existence and Succession, have formed, thus far, the\nsubject of the present Book. And we have now concluded the exposition, so\nfar as it falls within the limits assigned to this work, of the nature of\nthe evidence on which these propositions rest, and the processes of\ninvestigation by which they are ascertained and proved. There remain three\nclasses of facts: Existence, Order in Place, and Resemblance; in regard to\nwhich the same questions are now to be resolved.\n\nRegarding the first of these, very little needs be said. Existence in\ngeneral, is a subject not for our science, but for metaphysics. To\ndetermine what things can be recognized as really existing, independently\nof our own sensible or other impressions, and in what meaning the term is,\nin that case, predicated of them, belongs to the consideration of \u201cThings\nin themselves,\u201d from which, throughout this work, we have as much as\npossible kept aloof. Existence, so far as Logic is concerned about it, has\nreference only to phenomena; to actual, or possible, states of external or\ninternal consciousness, in ourselves or others. Feelings of sensitive\nbeings, or possibilities of having such feelings, are the only things the\nexistence of which can be a subject of logical induction, because the only\nthings of which the existence in individual cases can be a subject of\nexperience.\n\nIt is true that a thing is said by us to exist, even when it is absent,\nand therefore is not and can not be perceived. But even then, its\nexistence is to us only another word for our conviction that we should\nperceive it on a certain supposition; namely, if we were in the needful\ncircumstances of time and place, and endowed with the needful perfection\nof organs. My belief that the Emperor of China exists, is simply my belief\nthat if I were transported to the imperial palace or some other locality\nin Pekin, I should see him. My belief that Julius C\u00e6sar existed, is my\nbelief that I should have seen him if I had been present in the field of\nPharsalia, or in the senate-house at Rome. When I believe that stars exist\nbeyond the utmost range of my vision, though assisted by the most powerful\ntelescopes yet invented, my belief, philosophically expressed, is, that\nwith still better telescopes, if such existed, I could see them, or that\nthey may be perceived by beings less remote from them in space, or whose\ncapacities of perception are superior to mine.\n\nThe existence, therefore, of a phenomenon, is but another word for its\nbeing perceived, or for the inferred possibility of perceiving it. When\nthe phenomenon is within the range of present observation, by present\nobservation we assure ourselves of its existence; when it is beyond that\nrange, and is therefore said to be absent, we infer its existence from\nmarks or evidences. But what can these evidences be? Other phenomena;\nascertained by induction to be connected with the given phenomenon, either\nin the way of succession or of co-existence. The simple existence,\ntherefore, of an individual phenomenon, when not directly perceived, is\ninferred from some inductive law of succession or co-existence; and is\nconsequently not amenable to any peculiar inductive principles. We prove\nthe existence of a thing, by proving that it is connected by succession or\nco-existence with some known thing.\n\nWith respect to _general_ propositions of this class, that is, which\naffirm the bare fact of existence, they have a peculiarity which renders\nthe logical treatment of them a very easy matter; they are generalizations\nwhich are sufficiently proved by a single instance. That ghosts, or\nunicorns, or sea-serpents exist, would be fully established if it could be\nascertained positively that such things had been even once seen. Whatever\nhas once happened, is capable of happening again; the only question\nrelates to the conditions under which it happens.\n\nSo far, therefore, as relates to simple existence, the Inductive Logic has\nno knots to untie. And we may proceed to the remaining two of the great\nclasses into which facts have been divided; Resemblance, and Order in\nPlace.\n\n\u00a7 2. Resemblance and its opposite, except in the case in which they assume\nthe names of Equality and Inequality, are seldom regarded as subjects of\nscience; they are supposed to be perceived by simple apprehension; by\nmerely applying our senses or directing our attention to the two objects\nat once, or in immediate succession. And this simultaneous, or virtually\nsimultaneous, application of our faculties to the two things which are to\nbe compared, does necessarily constitute the ultimate appeal, wherever\nsuch application is practicable. But, in most cases, it is not\npracticable: the objects can not be brought so close together that the\nfeeling of their resemblance (at least a complete feeling of it) directly\narises in the mind. We can only compare each of them with some third\nobject, capable of being transported from one to the other. And besides,\neven when the objects can be brought into immediate juxtaposition, their\nresemblance or difference is but imperfectly known to us, unless we have\ncompared them minutely, part by part. Until this has been done, things in\nreality very dissimilar often appear undistinguishably alike. Two lines of\nvery unequal length will appear about equal when lying in different\ndirections; but place them parallel with their farther extremities even,\nand if we look at the nearer extremities, their inequality becomes a\nmatter of direct perception.\n\nTo ascertain whether, and in what, two phenomena resemble or differ, is\nnot always, therefore, so easy a thing as it might at first appear. When\nthe two can not be brought into juxtaposition, or not so that the observer\nis able to compare their several parts in detail, he must employ the\nindirect means of reasoning and general propositions. When we can not\nbring two straight lines together, to determine whether they are equal, we\ndo it by the physical aid of a foot-rule applied first to one and then to\nthe other, and the logical aid of the general proposition or formula,\n\u201cThings which are equal to the same thing are equal to one another.\u201d The\ncomparison of two things through the intervention of a third thing, when\ntheir direct comparison is impossible, is the appropriate scientific\nprocess for ascertaining resemblances and dissimilarities, and is the sum\ntotal of what Logic has to teach on the subject.\n\nAn undue extension of this remark induced Locke to consider reasoning\nitself as nothing but the comparison of two ideas through the medium of a\nthird, and knowledge as the perception of the agreement or disagreement of\ntwo ideas; doctrines which the Condillac school blindly adopted, without\nthe qualifications and distinctions with which they were studiously\nguarded by their illustrious author. Where, indeed, the agreement or\ndisagreement (otherwise called resemblance or dissimilarity) of any two\nthings is the very matter to be determined, as is the case particularly in\nthe sciences of quantity and extension; there, the process by which a\nsolution, if not attainable by direct perception, must be indirectly\nsought, consists in comparing these two things through the medium of a\nthird. But this is far from being true of all inquiries. The knowledge\nthat bodies fall to the ground is not a perception of agreement or\ndisagreement, but of a series of physical occurrences, a succession of\nsensations. Locke\u2019s definitions of knowledge and of reasoning required to\nbe limited to our knowledge of, and reasoning about, resemblances. Nor,\neven when thus restricted, are the propositions strictly correct; since\nthe comparison is not made, as he represents, between the ideas of the two\nphenomena, but between the phenomena themselves. This mistake has been\npointed out in an earlier part of our inquiry,(198) and we traced it to an\nimperfect conception of what takes place in mathematics, where very often\nthe comparison is really made between the ideas, without any appeal to the\noutward senses; only, however, because in mathematics a comparison of the\nideas is strictly equivalent to a comparison of the phenomena themselves.\nWhere, as in the case of numbers, lines, and figures, our idea of an\nobject is a complete picture of the object, so far as respects the matter\nin hand; we can, of course, learn from the picture, whatever could be\nlearned from the object itself by mere contemplation of it as it exists at\nthe particular instant when the picture is taken. No mere contemplation of\ngunpowder would ever teach us that a spark would make it explode, nor,\nconsequently, would the contemplation of the idea of gunpowder do so; but\nthe mere contemplation of a straight line shows that it can not inclose a\nspace; accordingly the contemplation of the idea of it will show the same.\nWhat takes place in mathematics is thus no argument that the comparison is\nbetween the ideas only. It is always, either indirectly or directly, a\ncomparison of the phenomena.\n\nIn cases in which we can not bring the phenomena to the test of direct\ninspection at all, or not in a manner sufficiently precise, but must judge\nof their resemblance by inference from other resemblances or\ndissimilarities more accessible to observation, we of course require, as\nin all cases of ratiocination, generalizations or formul\u00e6 applicable to\nthe subject. We must reason from laws of nature; from the uniformities\nwhich are observable in the fact of likeness or unlikeness.\n\n\u00a7 3. Of these laws or uniformities, the most comprehensive are those\nsupplied by mathematics; the axioms relating to equality, inequality, and\nproportionality, and the various theorems thereon founded. And these are\nthe only Laws of Resemblance which require to be, or which can be, treated\napart. It is true there are innumerable other theorems which affirm\nresemblances among phenomena; as that the angle of the reflection of light\nis _equal_ to its angle of incidence (equality being merely exact\nresemblance in magnitude). Again, that the heavenly bodies describe\n_equal_ areas in equal times; and that their periods of revolution are\n_proportional_ (another species of resemblance) to the sesquiplicate\npowers of their distances from the centre of force. These and similar\npropositions affirm resemblances, of the same nature with those asserted\nin the theorems of mathematics; but the distinction is, that the\npropositions of mathematics are true of all phenomena whatever, or at\nleast without distinction of origin; while the truths in question are\naffirmed only of special phenomena, which originate in a certain way; and\nthe equalities, proportionalities, or other resemblances, which exist\nbetween such phenomena, must necessarily be either derived from, or\nidentical with, the law of their origin\u2014the law of causation on which they\ndepend. The equality of the areas described in equal times by the planets,\nis _derived_ from the laws of the causes; and, until its derivation was\nshown, it was an empirical law. The equality of the angles of reflection\nand incidence is _identical_ with the law of the cause; for the cause is\nthe incidence of a ray of light upon a reflecting surface, and the\nequality in question is the very law according to which that cause\nproduces its effects. This class, therefore, of the uniformities of\nresemblance between phenomena, are inseparable, in fact and in thought,\nfrom the laws of the production of those phenomena; and the principles of\ninduction applicable to them are no other than those of which we have\ntreated in the preceding chapters of this Book.\n\nIt is otherwise with the truths of mathematics. The laws of equality and\ninequality between spaces, or between numbers, have no connection with\nlaws of causation. That the angle of reflection is equal to the angle of\nincidence, is a statement of the mode of action of a particular cause; but\nthat when two straight lines intersect each other the opposite angles are\nequal, is true of all such lines and angles, by whatever cause produced.\nThat the squares of the periodic times of the planets are proportional to\nthe cubes of their distances from the sun, is a uniformity derived from\nthe laws of the causes (or forces) which produce the planetary motions;\nbut that the square of any number is four times the square of half the\nnumber, is true independently of any cause. The only laws of resemblance,\ntherefore, which we are called upon to consider independently of\ncausation, belong to the province of mathematics.\n\n\u00a7 4. The same thing is evident with respect to the only one remaining of\nour five categories, Order in Place. The order in place, of the effects of\na cause, is (like every thing else belonging to the effects) a consequence\nof the laws of that cause. The order in place, or, as we have termed it,\nthe collocation, of the primeval causes, is (as well as their resemblance)\nin each instance an ultimate fact, in which no laws or uniformities are\ntraceable. The only remaining general propositions respecting order in\nplace, and the only ones which have nothing to do with causation, are some\nof the truths of geometry; laws through which we are able, from the order\nin place of certain points, lines, or spaces, to infer the order in place\nof others which are connected with the former in some known mode; quite\nindependently of the particular nature of those points, lines, or spaces,\nin any other respect than position or magnitude, as well as independently\nof the physical cause from which in any particular case they happen to\nderive their origin.\n\nIt thus appears that mathematics is the only department of science into\nthe methods of which it still remains to inquire. And there is the less\nnecessity that this inquiry should occupy us long, as we have already, in\nthe Second Book, made considerable progress in it. We there remarked, that\nthe directly inductive truths of mathematics are few in number; consisting\nof the axioms, together with certain propositions concerning existence,\ntacitly involved in most of the so-called definitions. And we gave what\nappeared conclusive reasons for affirming that these original premises,\nfrom which the remaining truths of the science are deduced, are,\nnotwithstanding all appearances to the contrary, results of observation\nand experience; founded, in short, on the evidence of the senses. That\nthings equal to the same thing are equal to one another, and that two\nstraight lines which have once intersected one another continue to\ndiverge, are inductive truths; resting, indeed, like the law of universal\ncausation, only on induction _per enumerationem simplicem_; on the fact\nthat they have been perpetually perceived to be true, and never once found\nto be false. But, as we have seen in a recent chapter that this evidence,\nin the case of a law so completely universal as the law of causation,\namounts to the fullest proof, so is this even more evidently true of the\ngeneral propositions to which we are now adverting; because, as a\nperception of their truth in any individual case whatever, requires only\nthe simple act of looking at the objects in a proper position, there never\ncould have been in their case (what, for a long period, there were in the\ncase of the law of causation) instances which were apparently, though not\nreally, exceptions to them. Their infallible truth was recognized from the\nvery dawn of speculation; and as their extreme familiarity made it\nimpossible for the mind to conceive the objects under any other law, they\nwere, and still are, generally considered as truths recognized by their\nown evidence, or by instinct.\n\n\u00a7 5. There is something which seems to require explanation, in the fact\nthat the immense multitude of truths (a multitude still as far from being\nexhausted as ever) comprised in the mathematical sciences, can be elicited\nfrom so small a number of elementary laws. One sees not, at first, how it\nis that there can be room for such an infinite variety of true\npropositions, on subjects apparently so limited.\n\nTo begin with the science of number. The elementary or ultimate truths of\nthis science are the common axioms concerning equality, namely, \u201cThings\nwhich are equal to the same thing are equal to one another,\u201d and \u201cEquals\nadded to equals make equal sums\u201d (no other axioms are required),(199)\ntogether with the definitions of the various numbers. Like other so-called\ndefinitions, these are composed of two things, the explanation of a name,\nand the assertion of a fact; of which the latter alone can form a first\nprinciple or premise of a science. The fact asserted in the definition of\na number is a physical fact. Each of the numbers two, three, four, etc.,\ndenotes physical phenomena, and connotes a physical property of those\nphenomena. Two, for instance, denotes all pairs of things, and twelve all\ndozens of things, connoting what makes them pairs, or dozens; and that\nwhich makes them so is something physical; since it can not be denied that\ntwo apples are physically distinguishable from three apples, two horses\nfrom one horse, and so forth; that they are a different visible and\ntangible phenomenon. I am not undertaking to say what the difference is;\nit is enough that there is a difference of which the senses can take\ncognizance. And although a hundred and two horses are not so easily\ndistinguished from a hundred and three, as two horses are from\nthree\u2014though in most positions the senses do not perceive any\ndifference\u2014yet they may be so placed that a difference will be\nperceptible, or else we should never have distinguished them, and given\nthem different names. Weight is confessedly a physical property of things;\nyet small differences between great weights are as imperceptible to the\nsenses in most situations, as small differences between great numbers; and\nare only put in evidence by placing the two objects in a peculiar\nposition\u2014namely, in the opposite scales of a delicate balance.\n\nWhat, then, is that which is connoted by a name of number? Of course, some\nproperty belonging to the agglomeration of things which we call by the\nname; and that property is, the characteristic manner in which the\nagglomeration is made up of, and may be separated into, parts. I will\nendeavor to make this more intelligible by a few explanations.\n\nWhen we call a collection of objects _two_, _three_, or _four_, they are\nnot two, three, or four in the abstract; they are two, three, or four\nthings of some particular kind; pebbles, horses, inches, pounds\u2019 weight.\nWhat the name of number connotes is, the manner in which single objects of\nthe given kind must be put together, in order to produce that particular\naggregate. If the aggregate be of pebbles, and we call it _two_, the name\nimplies that, to compose the aggregate, one pebble must be joined to one\npebble. If we call it _three_, one and one and one pebble must be brought\ntogether to produce it, or else one pebble must be joined to an aggregate\nof the kind called _two_, already existing. The aggregate which we call\n_four_, has a still greater number of characteristic modes of formation.\nOne and one and one and one pebble may be brought together; or two\naggregates of the kind called _two_ may be united; or one pebble may be\nadded to an aggregate of the kind called _three_. Every succeeding number\nin the ascending series, may be formed by the junction of smaller numbers\nin a progressively greater variety of ways. Even limiting the parts to\ntwo, the number may be formed, and consequently may be divided, in as many\ndifferent ways as there are numbers smaller than itself; and, if we admit\nof threes, fours, etc., in a still greater variety. Other modes of\narriving at the same aggregate present themselves, not by the union of\nsmaller, but by the dismemberment of larger aggregates. Thus, _three\npebbles_ may be formed by taking away one pebble from an aggregate of\nfour; _two pebbles_, by an equal division of a similar aggregate; and so\non.\n\nEvery arithmetical proposition; every statement of the result of an\narithmetical operation; is a statement of one of the modes of formation of\na given number. It affirms that a certain aggregate might have been formed\nby putting together certain other aggregates, or by withdrawing certain\nportions of some aggregate; and that, by consequence, we might reproduce\nthose aggregates from it, by reversing the process.\n\nThus, when we say that the cube of 12 is 1728, what we affirm is this:\nthat if, having a sufficient number of pebbles or of any other objects, we\nput them together into the particular sort of parcels or aggregates called\ntwelves; and put together these twelves again into similar collections;\nand, finally, make up twelve of these largest parcels; the aggregate thus\nformed will be such a one as we call 1728; namely, that which (to take the\nmost familiar of its modes of formation) may be made by joining the parcel\ncalled a thousand pebbles, the parcel called seven hundred pebbles, the\nparcel called twenty pebbles, and the parcel called eight pebbles.\n\nThe converse proposition that the cube root of 1728 is 12, asserts that\nthis large aggregate may again be decomposed into the twelve twelves of\ntwelves of pebbles which it consists of.\n\nThe modes of formation of any number are innumerable; but when we know one\nmode of formation of each, all the rest may be determined deductively. If\nwe know that _a_ is formed from _b_ and _c_, _b_ from _a_ and _e_, _c_\nfrom _d_ and _f_, and so forth, until we have included all the numbers of\nany scale we choose to select (taking care that for each number the mode\nof formation be really a distinct one, not bringing us round again to the\nformer numbers, but introducing a new number), we have a set of\npropositions from which we may reason to all the other modes of formation\nof those numbers from one another. Having established a chain of inductive\ntruths connecting together all the numbers of the scale, we can ascertain\nthe formation of any one of those numbers from any other by merely\ntraveling from one to the other along the chain. Suppose that we know only\nthe following modes of formation: 6=4+2, 4=7\u20133, 7=5+2, 5=9\u20134. We could\ndetermine how 6 may be formed from 9. For 6=4+2=7\u20133+2=5+2\u20133+2=9\u20134+2\u20133+2.\nIt may therefore be formed by taking away 4 and 3, and adding 2 and 2. If\nwe know besides that 2+2=4, we obtain 6 from 9 in a simpler mode, by\nmerely taking away 3.\n\nIt is sufficient, therefore, to select one of the various modes of\nformation of each number, as a means of ascertaining all the rest. And\nsince things which are uniform, and therefore simple, are most easily\nreceived and retained by the understanding, there is an obvious advantage\nin selecting a mode of formation which shall be alike for all; in fixing\nthe connotation of names of number on one uniform principle. The mode in\nwhich our existing numerical nomenclature is contrived possesses this\nadvantage, with the additional one, that it happily conveys to the mind\ntwo of the modes of formation of every number. Each number is considered\nas formed by the addition of a unit to the number next below it in\nmagnitude, and this mode of formation is conveyed by the place which it\noccupies in the series. And each is also considered as formed by the\naddition of a number of units less than ten, and a number of aggregates\neach equal to one of the successive powers of ten; and this mode of its\nformation is expressed by its spoken name, and by its numerical character.\n\nWhat renders arithmetic the type of a deductive science, is the fortunate\napplicability to it of a law so comprehensive as \u201cThe sums of equals are\nequals:\u201d or (to express the same principle in less familiar but more\ncharacteristic language), Whatever is made up of parts, is made up of the\nparts of those parts. This truth, obvious to the senses in all cases which\ncan be fairly referred to their decision, and so general as to be\nco-extensive with nature itself, being true of all sorts of phenomena (for\nall admit of being numbered), must be considered an inductive truth, or\nlaw of nature, of the highest order. And every arithmetical operation is\nan application of this law, or of other laws capable of being deduced from\nit. This is our warrant for all calculations. We believe that five and two\nare equal to seven, on the evidence of this inductive law, combined with\nthe definitions of those numbers. We arrive at that conclusion (as all\nknow who remember how they first learned it) by adding a single unit at a\ntime: 5 + 1=6, therefore 5+1+1=6+1=7; and again 2=1+1, therefore\n5+2=5+1+1=7.\n\n\u00a7 6. Innumerable as are the true propositions which can be formed\nconcerning particular numbers, no adequate conception could be gained,\nfrom these alone, of the extent of the truths composing the science of\nnumber. Such propositions as we have spoken of are the least general of\nall numerical truths. It is true that even these are co-extensive with all\nnature; the properties of the number four are true of all objects that are\ndivisible into four equal parts, and all objects are either actually or\nideally so divisible. But the propositions which compose the science of\nalgebra are true, not of a particular number, but of all numbers; not of\nall things under the condition of being divided in a particular way, but\nof all things under the condition of being divided in any way\u2014of being\ndesignated by a number at all.\n\nSince it is impossible for different numbers to have any of their modes of\nformation completely in common, it is a kind of paradox to say, that all\npropositions which can be made concerning numbers relate to their modes of\nformation from other numbers, and yet that there are propositions which\nare true of all numbers. But this very paradox leads to the real principle\nof generalization concerning the properties of numbers. Two different\nnumbers can not be formed in the same manner from the same numbers; but\nthey may be formed in the same manner from different numbers; as nine is\nformed from three by multiplying it into itself, and sixteen is formed\nfrom four by the same process. Thus there arises a classification of modes\nof formation, or in the language commonly used by mathematicians, a\nclassification of Functions. Any number, considered as formed from any\nother number, is called a function of it; and there are as many kinds of\nfunctions as there are modes of formation. The simple functions are by no\nmeans numerous, most functions being formed by the combination of several\nof the operations which form simple functions, or by successive\nrepetitions of some one of those operations. The simple functions of any\nnumber _x_ are all reducible to the following forms: _x_+_a_, _x_\u2013_a_,\n_ax_, _x_/_a_, log. _x_ (to the base _a_), and the same expressions varied\nby putting _x_ for _a_ and _a_ for _x_, wherever that substitution would\nalter the value: to which, perhaps, ought to be added sin _x_, and arc\n(sin=_x_). All other functions of _x_ are formed by putting some one or\nmore of the simple functions in the place of _x_ or _a_, and subjecting\nthem to the same elementary operations.\n\nIn order to carry on general reasonings on the subject of Functions, we\nrequire a nomenclature enabling us to express any two numbers by names\nwhich, without specifying what particular numbers they are, shall show\nwhat function each is of the other; or, in other words, shall put in\nevidence their mode of formation from one another. The system of general\nlanguage called algebraical notation does this. The expressions _a_ and\na2+3a denote, the one any number, the other the number formed from it in a\nparticular manner. The expressions _a_, _b_, _n_, and (_a+b_)n, denote any\nthree numbers, and a fourth which is formed from them in a certain mode.\n\nThe following may be stated as the general problem of the algebraical\ncalculus: F being a certain function of a given number, to find what\nfunction F will be of any function of that number. For example, a binomial\n_a + b_ is a function of its two parts _a_ and _b_, and the parts are, in\ntheir turn, functions of _a + b_: now (_a + b_)n is a certain function of\nthe binomial; what function will this be of _a_ and _b_, the two parts?\nThe answer to this question is the binomial theorem. The formula _(a +\nb)__n__ = a__n__ + n/1 a__n\u20131__ b + n.n\u20131/1.2 a__n\u20132__ b__2_, etc., shows\nin what manner the number which is formed by multiplying _a + b_ into\nitself _n_ times, might be formed without that process, directly from _a,\nb_, and _n_. And of this nature are all the theorems of the science of\nnumber. They assert the identity of the result of different modes of\nformation. They affirm that some mode of formation from _x_, and some mode\nof formation from a certain function of _x_, produce the same number.\n\nSuch, as above described, is the aim and end of the calculus. As for its\nprocesses, every one knows that they are simply deductive. In\ndemonstrating an algebraical theorem, or in resolving an equation, we\ntravel from the _datum_ to the _qu\u00e6situm_ by pure ratiocination; in which\nthe only premises introduced, besides the original hypotheses, are the\nfundamental axioms already mentioned\u2014that things equal to the same thing\nare equal to one another, and that the sums of equal things are equal. At\neach step in the demonstration or in the calculation, we apply one or\nother of these truths, or truths deducible from them, as, that the\ndifferences, products, etc., of equal numbers are equal.\n\nIt would be inconsistent with the scale of this work, and not necessary to\nits design, to carry the analysis of the truths and processes of algebra\nany further; which is also the less needful, as the task has been, to a\nvery great extent, performed by other writers. Peacock\u2019s Algebra, and Dr.\nWhewell\u2019s _Doctrine of Limits_, are full of instruction on the subject.\nThe profound treatises of a truly philosophical mathematician, Professor\nDe Morgan, should be studied by every one who desires to comprehend the\nevidence of mathematical truths, and the meaning of the obscurer processes\nof the calculus, and the speculations of M. Comte, in his _Cours de\nPhilosophie Positive_, on the philosophy of the higher branches of\nmathematics, are among the many valuable gifts for which philosophy is\nindebted to that eminent thinker.\n\n\u00a7 7. If the extreme generality, and remoteness not so much from sense as\nfrom the visual and tactual imagination, of the laws of number, renders it\na somewhat difficult effort of abstraction to conceive those laws as being\nin reality physical truths obtained by observation; the same difficulty\ndoes not exist with regard to the laws of extension. The facts of which\nthose laws are expressions, are of a kind peculiarly accessible to the\nsenses, and suggesting eminently distinct images to the fancy. That\ngeometry is a strictly physical science would doubtless have been\nrecognized in all ages, had it not been for the illusions produced by two\ncircumstances. One of these is the characteristic property, already\nnoticed, of the facts of geometry, that they may be collected from our\nideas or mental pictures of objects as effectually as from the objects\nthemselves. The other is, the demonstrative character of geometrical\ntruths; which was at one time supposed to constitute a radical distinction\nbetween them and physical truths; the latter, as resting on merely\nprobable evidence, being deemed essentially uncertain and unprecise. The\nadvance of knowledge has, however, made it manifest that physical science,\nin its better understood branches, is quite as demonstrative as geometry.\nThe task of deducing its details from a few comparatively simple\nprinciples is found to be any thing but the impossibility it was once\nsupposed to be; and the notion of the superior certainty of geometry is an\nillusion, arising from the ancient prejudice which, in that science,\nmistakes the ideal data from which we reason, for a peculiar class of\nrealities, while the corresponding ideal data of any deductive physical\nscience are recognized as what they really are, hypotheses.\n\nEvery theorem in geometry is a law of external nature, and might have been\nascertained by generalizing from observation and experiment, which in this\ncase resolve themselves into comparison and measurement. But it was found\npracticable, and, being practicable, was desirable, to deduce these truths\nby ratiocination from a small number of general laws of nature, the\ncertainty and universality of which are obvious to the most careless\nobserver, and which compose the first principles and ultimate premises of\nthe science. Among these general laws must be included the same two which\nwe have noticed as ultimate principles of the Science of Number also, and\nwhich are applicable to every description of quantity; viz., The sums of\nequals are equal, and Things which are equal to the same thing are equal\nto one another; the latter of which may be expressed in a manner more\nsuggestive of the inexhaustible multitude of its consequences, by the\nfollowing terms: Whatever is equal to any one of a number of equal\nmagnitudes, is equal to any other of them. To these two must be added, in\ngeometry, a third law of equality, namely, that lines, surfaces, or solid\nspaces, which can be so applied to one another as to coincide, are equal.\nSome writers have asserted that this law of nature is a mere verbal\ndefinition; that the expression \u201cequal magnitudes\u201d _means_ nothing but\nmagnitudes which can be so applied to one another as to coincide. But in\nthis opinion I can not agree. The equality of two geometrical magnitudes\ncan not differ fundamentally in its nature from the equality of two\nweights, two degrees of heat, or two portions of duration, to none of\nwhich would this definition of equality be suitable. None of these things\ncan be so applied to one another as to coincide, yet we perfectly\nunderstand what we mean when we call them equal. Things are equal in\nmagnitude, as things are equal in weight, when they are felt to be exactly\nsimilar in respect of the attribute in which we compare them: and the\napplication of the objects to each other in the one case, like the\nbalancing them with a pair of scales in the other, is but a mode of\nbringing them into a position in which our senses can recognize\ndeficiencies of exact resemblance that would otherwise escape our notice.\n\nAlong with these three general principles or axioms, the remainder of the\npremises of geometry consists of the so-called definitions: that is to\nsay, propositions asserting the real existence of the various objects\ntherein designated, together with some one property of each. In some cases\nmore than one property is commonly assumed, but in no case is more than\none necessary. It is assumed that there are such things in nature as\nstraight lines, and that any two of them setting out from the same point,\ndiverge more and more without limit. This assumption (which includes and\ngoes beyond Euclid\u2019s axiom that two straight lines can not inclose a\nspace) is as indispensable in geometry, and as evident, resting on as\nsimple, familiar, and universal observation, as any of the other axioms.\nIt is also assumed that straight lines diverge from one another in\ndifferent degrees; in other words, that there are such things as angles,\nand that they are capable of being equal or unequal. It is assumed that\nthere is such a thing as a circle, and that all its radii are equal; such\nthings as ellipses, and that the sums of the focal distances are equal for\nevery point in an ellipse; such things as parallel lines, and that those\nlines are everywhere equally distant.(200)\n\n\u00a7 8. It is a matter of more than curiosity to consider, to what\npeculiarity of the physical truths which are the subject of geometry, it\nis owing that they can all be deduced from so small a number of original\npremises; why it is that we can set out from only one characteristic\nproperty of each kind of phenomenon, and with that and two or three\ngeneral truths relating to equality, can travel from mark to mark until we\nobtain a vast body of derivative truths, to all appearance extremely\nunlike those elementary ones.\n\nThe explanation of this remarkable fact seems to lie in the following\ncircumstances. In the first place, all questions of position and figure\nmay be resolved into questions of magnitude. The position and figure of\nany object are determined by determining the position of a sufficient\nnumber of points in it; and the position of any point may be determined by\nthe magnitude of three rectangular co-ordinates, that is, of the\nperpendiculars drawn from the point to three planes at right angles to one\nanother, arbitrarily selected. By this transformation of all questions of\nquality into questions only of quantity, geometry is reduced to the single\nproblem of the measurement of magnitudes, that is, the ascertainment of\nthe equalities which exist between them. Now when we consider that by one\nof the general axioms, any equality, when ascertained, is proof of as many\nother equalities as there are other things equal to either of the two\nequals; and that by another of those axioms, any ascertained equality is\nproof of the equality of as many pairs of magnitudes as can be formed by\nthe numerous operations which resolve themselves into the addition of the\nequals to themselves or to other equals; we cease to wonder that in\nproportion as a science is conversant about equality, it should afford a\nmore copious supply of marks of marks; and that the sciences of number and\nextension, which are conversant with little else than equality, should be\nthe most deductive of all the sciences.\n\nThere are also two or three of the principal laws of space or extension\nwhich are unusually fitted for rendering one position or magnitude a mark\nof another, and thereby contributing to render the science largely\ndeductive. First, the magnitudes of inclosed spaces, whether superficial\nor solid, are completely determined by the magnitudes of the lines and\nangles which bound them. Secondly, the length of any line, whether\nstraight or curve, is measured (certain other things being given) by the\nangle which it subtends, and _vic\u00e8 versa_. Lastly, the angle which any two\nstraight lines make with each other at an inaccessible point, is measured\nby the angles they severally make with any third line we choose to select.\nBy means of these general laws, the measurement of all lines, angles, and\nspaces whatsoever might be accomplished by measuring a single straight\nline and a sufficient number of angles; which is the plan actually pursued\nin the trigonometrical survey of a country; and fortunate it is that this\nis practicable, the exact measurement of long straight lines being always\ndifficult, and often impossible, but that of angles very easy. Three such\ngeneralizations as the foregoing afford such facilities for the indirect\nmeasurement of magnitudes (by supplying us with known lines or angles\nwhich are marks of the magnitude of unknown ones, and thereby of the\nspaces which they inclose), that it is easily intelligible how from a few\ndata we can go on to ascertain the magnitude of an indefinite multitude of\nlines, angles, and spaces, which we could not easily, or could not at all,\nmeasure by any more direct process.\n\n\u00a7 9. Such are the remarks which it seems necessary to make in this place,\nrespecting the laws of nature which are the peculiar subject of the\nsciences of number and extension. The immense part which those laws take\nin giving a deductive character to the other departments of physical\nscience, is well known; and is not surprising, when we consider that all\ncauses operate according to mathematical laws. The effect is always\ndependent on, or is a function of, the quantity of the agent; and\ngenerally of its position also. We can not, therefore, reason respecting\ncausation, without introducing considerations of quantity and extension at\nevery step; and if the nature of the phenomena admits of our obtaining\nnumerical data of sufficient accuracy, the laws of quantity become the\ngrand instrument for calculating forward to an effect, or backward to a\ncause. That in all other sciences, as well as in geometry, questions of\nquality are scarcely ever independent of questions of quantity, may be\nseen from the most familiar phenomena. Even when several colors are mixed\non a painter\u2019s palette, the comparative quantity of each entirely\ndetermines the color of the mixture.\n\nWith this mere suggestion of the general causes which render mathematical\nprinciples and processes so predominant in those deductive sciences which\nafford precise numerical data, I must, on the present occasion, content\nmyself; referring the reader who desires a more thorough acquaintance with\nthe subject, to the first two volumes of M. Comte\u2019s systematic work.\n\nIn the same work, and more particularly in the third volume, are also\nfully discussed the limits of the applicability of mathematical principles\nto the improvement of other sciences. Such principles are manifestly\ninapplicable, where the causes on which any class of phenomena depend are\nso imperfectly accessible to our observation, that we can not ascertain,\nby a proper induction, their numerical laws; or where the causes are so\nnumerous, and intermixed in so complex a manner with one another, that\neven supposing their laws known, the computation of the aggregate effect\ntranscends the powers of the calculus as it is, or is likely to be; or,\nlastly, where the causes themselves are in a state of perpetual\nfluctuation; as in physiology, and still more, if possible, in the social\nscience. The mathematical solutions of physical questions become\nprogressively more difficult and imperfect, in proportion as the questions\ndivest themselves of their abstract and hypothetical character, and\napproach nearer to the degree of complication actually existing in nature;\ninsomuch that beyond the limits of astronomical phenomena, and of those\nmost nearly analogous to them, mathematical accuracy is generally obtained\n\u201cat the expense of the reality of the inquiry:\u201d while even in astronomical\nquestions, \u201cnotwithstanding the admirable simplicity of their mathematical\nelements, our feeble intelligence becomes incapable of following out\neffectually the logical combinations of the laws on which the phenomena\nare dependent, as soon as we attempt to take into simultaneous\nconsideration more than two or three essential influences.\u201d(201) Of this,\nthe problem of the Three Bodies has already been cited, more than once, as\na remarkable instance; the complete solution of so comparatively simple a\nquestion having vainly tried the skill of the most profound\nmathematicians. We may conceive, then, how chimerical would be the hope\nthat mathematical principles could be advantageously applied to phenomena\ndependent on the mutual action of the innumerable minute particles of\nbodies, as those of chemistry, and still more, of physiology; and for\nsimilar reasons those principles remain inapplicable to the still more\ncomplex inquiries, the subjects of which are phenomena of society and\ngovernment.\n\nThe value of mathematical instruction as a preparation for those more\ndifficult investigations, consists in the applicability not of its\ndoctrines, but of its method. Mathematics will ever remain the most\nperfect type of the Deductive Method in general; and the applications of\nmathematics to the deductive branches of physics, furnish the only school\nin which philosophers can effectually learn the most difficult and\nimportant portion of their art, the employment of the laws of simpler\nphenomena for explaining and predicting those of the more complex. These\ngrounds are quite sufficient for deeming mathematical training an\nindispensable basis of real scientific education, and regarding (according\nto the _dictum_ which an old but unauthentic tradition ascribes to Plato)\none who is \u1f00\u03b3\u03b5\u03c9\u03bc\u03ad\u03c4\u03c1\u03b7\u03c4\u03bf\u03c2, as wanting in one of the most essential\nqualifications for the successful cultivation of the higher branches of\nphilosophy.\n\n\n\n\n                               Chapter XXV.\n\n\nOf The Grounds Of Disbelief.\n\n\n\u00a7 1. The method of arriving at general truths, or general propositions fit\nto be believed, and the nature of the evidence on which they are grounded,\nhave been discussed, as far as space and the writer\u2019s faculties permitted,\nin the twenty-four preceding chapters. But the result of the examination\nof evidence is not always belief, nor even suspension of judgment; it is\nsometimes disbelief. The philosophy, therefore, of induction and\nexperimental inquiry is incomplete, unless the grounds not only of belief,\nbut of disbelief, are treated of; and to this topic we shall devote one,\nand the final, chapter.\n\nBy disbelief is not here to be understood the mere absence of belief. The\nground for abstaining from belief is simply the absence or insufficiency\nof proof; and in considering what is sufficient evidence to support any\ngiven conclusion, we have already, by implication, considered what\nevidence is not sufficient for the same purpose. By disbelief is here\nmeant, not the state of mind in which we form no opinion concerning a\nsubject, but that in which we are fully persuaded that some opinion is not\ntrue; insomuch that if evidence, even of great apparent strength (whether\ngrounded on the testimony of others or on our own supposed perceptions),\nwere produced in favor of the opinion, we should believe that the\nwitnesses spoke falsely, or that they, or we ourselves if we were the\ndirect percipients, were mistaken.\n\nThat there are such cases, no one is likely to dispute. Assertions for\nwhich there is abundant positive evidence are often disbelieved, on\naccount of what is called their improbability, or impossibility. And the\nquestion for consideration is what, in the present case, these words mean,\nand how far and in what circumstances the properties which they express\nare sufficient grounds for disbelief.\n\n\u00a7 2. It is to be remarked, in the first place, that the positive evidence\nproduced in support of an assertion which is nevertheless rejected on the\nscore of impossibility or improbability, is never such as amounts to full\nproof. It is always grounded on some approximate generalization. The fact\nmay have been asserted by a hundred witnesses; but there are many\nexceptions to the universality of the generalization that what a hundred\nwitnesses affirm is true. We may seem to ourselves to have actually seen\nthe fact; but that we really see what we think we see, is by no means a\nuniversal truth; our organs may have been in a morbid state; or we may\nhave inferred something, and imagined that we perceived it. The evidence,\nthen, in the affirmative being never more than an approximate\ngeneralization, all will depend on what the evidence in the negative is.\nIf that also rests on an approximate generalization, it is a case for\ncomparison of probabilities. If the approximate generalizations leading to\nthe affirmative are, when added together, less strong, or, in other words,\nfarther from being universal, than the approximate generalizations which\nsupport the negative side of the question, the proposition is said to be\nimprobable, and is to be disbelieved provisionally. If, however, an\nalleged fact be in contradiction, not to any number of approximate\ngeneralizations, but to a completed generalization grounded on a rigorous\ninduction, it is said to be impossible, and is to be disbelieved totally.\n\nThis last principle, simple and evident as it appears, is the doctrine\nwhich, on the occasion of an attempt to apply it to the question of the\ncredibility of miracles, excited so violent a controversy. Hume\u2019s\ncelebrated doctrine, that nothing is credible which is contradictory to\nexperience, or at variance with laws of nature, is merely this very plain\nand harmless proposition, that whatever is contradictory to a complete\ninduction is incredible. That such a maxim as this should either be\naccounted a dangerous heresy, or mistaken for a great and recondite truth,\nspeaks ill for the state of philosophical speculation on such subjects.\n\nBut does not (it may be asked) the very statement of the proposition imply\na contradiction? An alleged fact, according to this theory, is not to be\nbelieved if it contradict a complete induction. But it is essential to the\ncompleteness of an induction that it shall not contradict any known fact.\nIs it not, then, a _petitio principii_ to say, that the fact ought to be\ndisbelieved because the induction opposed to it is complete? How can we\nhave a right to declare the induction complete, while facts, supported by\ncredible evidence, present themselves in opposition to it?\n\nI answer, we have that right whenever the scientific canons of induction\ngive it to us; that is, whenever the induction _can_ be complete. We have\nit, for example, in a case of causation in which there has been an\n_experimentum crucis_. If an antecedent A, superadded to a set of\nantecedents in all other respects unaltered, is followed by an effect B\nwhich did not exist before, A is, in that instance at least, the cause of\nB, or an indispensable part of its cause; and if A be tried again with\nmany totally different sets of antecedents and B still follows, then it is\nthe whole cause. If these observations or experiments have been repeated\nso often, and by so many persons, as to exclude all supposition of error\nin the observer, a law of nature is established; and so long as this law\nis received as such, the assertion that on any particular occasion A took\nplace, and yet B did not follow, _without any counteracting cause_, must\nbe disbelieved. Such an assertion is not to be credited on any less\nevidence than what would suffice to overturn the law. The general truths,\nthat whatever has a beginning has a cause, and that when none but the same\ncauses exist, the same effects follow, rest on the strongest inductive\nevidence possible; the proposition that things affirmed by even a crowd of\nrespectable witnesses are true, is but an approximate generalization;\nand\u2014even if we fancy we actually saw or felt the fact which is in\ncontradiction to the law\u2014what a human being can see is no more than a set\nof appearances; from which the real nature of the phenomenon is merely an\ninference, and in this inference approximate generalizations usually have\na large share. If, therefore, we make our election to hold by the law, no\nquantity of evidence whatever ought to persuade us that there has occurred\nany thing in contradiction to it. If, indeed, the evidence produced is\nsuch that it is more likely that the set of observations and experiments\non which the law rests should have been inaccurately performed or\nincorrectly interpreted, than that the evidence in question should be\nfalse, we may believe the evidence; but then we must abandon the law. And\nsince the law was received on what seemed a complete induction, it can\nonly be rejected on evidence equivalent; namely, as being inconsistent not\nwith any number of approximate generalizations, but with some other and\nbetter established law of nature. This extreme case, of a conflict between\ntwo supposed laws of nature, has probably never actually occurred where,\nin the process of investigating both the laws, the true canons of\nscientific induction had been kept in view; but if it did occur, it must\nterminate in the total rejection of one of the supposed laws. It would\nprove that there must be a flaw in the logical process by which either one\nor the other was established; and if there be so, that supposed general\ntruth is no truth at all. We can not admit a proposition as a law of\nnature, and yet believe a fact in real contradiction to it. We must\ndisbelieve the alleged fact, or believe that we were mistaken in admitting\nthe supposed law.\n\nBut in order that any alleged fact should be contradictory to a law of\ncausation, the allegation must be, not simply that the cause existed\nwithout being followed by the effect, for that would be no uncommon\noccurrence; but that this happened in the absence of any adequate\ncounteracting cause. Now in the case of an alleged miracle, the assertion\nis the exact opposite of this. It is, that the effect was defeated, not in\nthe absence, but in consequence of a counteracting cause, namely, a direct\ninterposition of an act of the will of some being who has power over\nnature; and in particular of a Being, whose will being assumed to have\nendowed all the causes with the powers by which they produce their\neffects, may well be supposed able to counteract them. A miracle (as was\njustly remarked by Brown)(202) is no contradiction to the law of cause and\neffect; it is a new effect, supposed to be produced by the introduction of\na new cause. Of the adequacy of that cause, if present, there can be no\ndoubt; and the only antecedent improbability which can be ascribed to the\nmiracle, is the improbability that any such cause existed.\n\nAll, therefore, which Hume has made out, and this he must be considered to\nhave made out, is, that (at least in the imperfect state of our knowledge\nof natural agencies, which leaves it always possible that some of the\nphysical antecedents may have been hidden from us) no evidence can prove a\nmiracle to any one who did not previously believe the existence of a being\nor beings with supernatural power; or who believes himself to have full\nproof that the character of the Being whom he recognizes is inconsistent\nwith his having seen fit to interfere on the occasion in question.\n\nIf we do not already believe in supernatural agencies, no miracle can\nprove to us their existence. The miracle itself, considered merely as an\nextraordinary fact, may be satisfactorily certified by our senses or by\ntestimony; but nothing can ever prove that it is a miracle; there is still\nanother possible hypothesis, that of its being the result of some unknown\nnatural cause; and this possibility can not be so completely shut out, as\nto leave no alternative but that of admitting the existence and\nintervention of a being superior to nature. Those, however, who already\nbelieve in such a being have two hypotheses to choose from, a supernatural\nand an unknown natural agency; and they have to judge which of the two is\nthe most probable in the particular case. In forming this judgment, an\nimportant element of the question will be the conformity of the result to\nthe laws of the supposed agent, that is, to the character of the Deity as\nthey conceive it. But with the knowledge which we now possess of the\ngeneral uniformity of the course of nature, religion, following in the\nwake of science, has been compelled to acknowledge the government of the\nuniverse as being on the whole carried on by general laws, and not by\nspecial interpositions. To whoever holds this belief, there is a general\npresumption against any supposition of divine agency not operating through\ngeneral laws, or, in other words, there is an antecedent improbability in\nevery miracle, which, in order to outweigh it, requires an extraordinary\nstrength of antecedent probability derived from the special circumstances\nof the case.\n\n\u00a7 3. It appears from what has been said, that the assertion that a cause\nhas been defeated of an effect which is connected with it by a completely\nascertained law of causation, is to be disbelieved or not, according to\nthe probability or improbability that there existed in the particular\ninstance an adequate counteracting cause. To form an estimate of this, is\nnot more difficult than of other probabilities. With regard to all _known_\ncauses capable of counteracting the given causes, we have generally some\nprevious knowledge of the frequency or rarity of their occurrence, from\nwhich we may draw an inference as to the antecedent improbability of their\nhaving been present in any particular case. And neither in respect to\nknown nor unknown causes are we required to pronounce on the probability\nof their existing in nature, but only of their having existed at the time\nand place at which the transaction is alleged to have happened. We are\nseldom, therefore, without the means (when the circumstances of the case\nare at all known to us) of judging how far it is likely that such a cause\nshould have existed at that time and place without manifesting its\npresence by some other marks, and (in the case of an unknown cause)\nwithout having hitherto manifested its existence in any other instance.\nAccording as this circumstance, or the falsity of the testimony, appears\nmore improbable\u2014that is, conflicts with an approximate generalization of a\nhigher order\u2014we believe the testimony, or disbelieve it; with a stronger\nor a weaker degree of conviction, according to the preponderance; at least\nuntil we have sifted the matter further.\n\nSo much, then, for the case in which the alleged fact conflicts, or\nappears to conflict, with a real law of causation. But a more common case,\nperhaps, is that of its conflicting with uniformities of mere\nco-existence, not proved to be dependent on causation; in other words,\nwith the properties of Kinds. It is with these uniformities principally\nthat the marvelous stories related by travelers are apt to be at variance;\nas of men with tails, or with wings, and (until confirmed by experience)\nof flying fish; or of ice, in the celebrated anecdote of the Dutch\ntravelers and the King of Siam. Facts of this description, facts\npreviously unheard of, but which could not from any known law of causation\nbe pronounced impossible, are what Hume characterizes as not contrary to\nexperience, but merely unconformable to it; and Bentham, in his treatise\non Evidence, denominates them facts disconformable _in specie_, as\ndistinguished from such as are disconformable _in toto_ or in _degree_\n\nIn a case of this description, the fact asserted is the existence of a new\nKind; which in itself is not in the slightest degree incredible, and only\nto be rejected if the improbability that any variety of object existing at\nthe particular place and time should not have been discovered sooner, be\ngreater than that of error or mendacity in the witnesses. Accordingly,\nsuch assertions, when made by credible persons, and of unexplored places,\nare not disbelieved, but at most regarded as requiring confirmation from\nsubsequent observers; unless the alleged properties of the supposed new\nKind are at variance with known properties of some larger kind which\nincludes it; or, in other words, unless, in the new Kind which is asserted\nto exist, some properties are said to have been found disjoined from\nothers which have always been known to accompany them; as in the case of\nPliny\u2019s men, or any other kind of animal of a structure different from\nthat which has always been found to co-exist with animal life. On the mode\nof dealing with any such case, little needs be added to what has been said\non the same topic in the twenty-second chapter.(203) When the uniformities\nof co-existence which the alleged fact would violate, are such as to raise\na strong presumption of their being the result of causation, the fact\nwhich conflicts with them is to be disbelieved; at least provisionally,\nand subject to further investigation. When the presumption amounts to a\nvirtual certainty, as in the case of the general structure of organized\nbeings, the only question requiring consideration is whether, in phenomena\nso little understood, there may not be liabilities to counteraction from\ncauses hitherto unknown; or whether the phenomena may not be capable of\noriginating in some other way, which would produce a different set of\nderivative uniformities. Where (as in the case of the flying fish, or the\nornithorhynchus) the generalization to which the alleged fact would be an\nexception is very special and of limited range, neither of the above\nsuppositions can be deemed very improbable; and it is generally, in the\ncase of such alleged anomalies, wise to suspend our judgment, pending the\nsubsequent inquiries which will not fail to confirm the assertion if it be\ntrue. But when the generalization is very comprehensive, embracing a vast\nnumber and variety of observations, and covering a considerable province\nof the domain of nature; then, for reasons which have been fully\nexplained, such an empirical law comes near to the certainty of an\nascertained law of causation; and any alleged exception to it can not be\nadmitted, unless on the evidence of some law of causation proved by a\nstill more complete induction.\n\nSuch uniformities in the course of nature as do not bear marks of being\nthe results of causation are, as we have already seen, admissible as\nuniversal truths with a degree of credence proportioned to their\ngenerality. Those which are true of all things whatever, or at least which\nare totally independent of the varieties of Kinds, namely, the laws of\nnumber and extension, to which we may add the law of causation itself, are\nprobably the only ones, an exception to which is absolutely and\npermanently incredible. Accordingly, it is to assertions supposed to be\ncontradictory to these laws, or to some others coming near to them in\ngenerality, that the word impossibility (at least _total_ impossibility)\nseems to be generally confined. Violations of other laws, of special laws\nof causation, for instance, are said, by persons studious of accuracy in\nexpression, to be impossible _in the circumstances of the case_; or\nimpossible unless some cause had existed which did not exist in the\nparticular case.(204) Of no assertion, not in contradiction to some of\nthese very general laws, will more than improbability be asserted by any\ncautious person; and improbability not of the highest degree, unless the\ntime and place in which the fact is said to have occurred, render it\nalmost certain that the anomaly, if real, could not have been overlooked\nby other observers. Suspension of judgment is in all other cases the\nresource of the judicious inquirer; provided the testimony in favor of the\nanomaly presents, when well sifted, no suspicious circumstances.\n\nBut the testimony is scarcely ever found to stand that test, in cases in\nwhich the anomaly is not real. In the instances on record in which a great\nnumber of witnesses, of good reputation and scientific acquirements, have\ntestified to the truth of something which has turned out untrue, there\nhave almost always been circumstances which, to a keen observer who had\ntaken due pains to sift the matter, would have rendered the testimony\nuntrustworthy. There have generally been means of accounting for the\nimpression on the senses or minds of the alleged percipients, by\nfallacious appearances; or some epidemic delusion, propagated by the\ncontagious influence of popular feeling, has been concerned in the case;\nor some strong interest has been implicated\u2014religious zeal, party feeling,\nvanity, or at least the passion for the marvelous, in persons strongly\nsusceptible of it. When none of these or similar circumstances exist to\naccount for the apparent strength of the testimony; and where the\nassertion is not in contradiction either to those universal laws which\nknow no counteraction or anomaly, or to the generalizations next in\ncomprehensiveness to them, but would only amount, if admitted, to the\nexistence of an unknown cause or an anomalous Kind, in circumstances not\nso thoroughly explored but that it is credible that things hitherto\nunknown may still come to light; a cautious person will neither admit nor\nreject the testimony, but will wait for confirmation at other times and\nfrom other unconnected sources. Such ought to have been the conduct of the\nKing of Siam when the Dutch travelers affirmed to him the existence of\nice. But an ignorant person is as obstinate in his contemptuous\nincredulity as he is unreasonably credulous. Any thing unlike his own\nnarrow experience he disbelieves, if it flatters no propensity; any\nnursery tale is swallowed implicitly by him if it does.\n\n\u00a7 4. I shall now advert to a very serious misapprehension of the\nprinciples of the subject, which has been committed by some of the writers\nagainst Hume\u2019s Essay on Miracles, and by Bishop Butler before them, in\ntheir anxiety to destroy what appeared to them a formidable weapon of\nassault against the Christian religion; and the effect of which is\nentirely to confound the doctrine of the Grounds of Disbelief. The mistake\nconsists in overlooking the distinction between (what may be called)\nimprobability before the fact and improbability after it; or (since, as\nMr. Venn remarks, the distinction of past and future is not the material\ncircumstance) between the improbability of a mere guess being right, and\nthe improbability of an alleged fact being true.\n\nMany events are altogether improbable to us, before they have happened, or\nbefore we are informed of their happening, which are not in the least\nincredible when we are informed of them, because not contrary to any, even\napproximate, induction. In the cast of a perfectly fair die, the chances\nare five to one against throwing ace, that is, ace will be thrown on an\naverage only once in six throws. But this is no reason against believing\nthat ace was thrown on a given occasion, if any credible witness asserts\nit; since though ace is only thrown once in six times, _some_ number which\nis only thrown once in six times must have been thrown if the die was\nthrown at all. The improbability, then, or, in other words, the\nunusualness, of any fact, is no reason for disbelieving it, if the nature\nof the case renders it certain that either that or something equally\nimprobable, that is, equally unusual, did happen. Nor is this all; for\neven if the other five sides of the die were all twos, or all threes, yet\nas ace would still, on the average, come up once in every six throws, its\ncoming up in a given throw would be not in any way contradictory to\nexperience. If we disbelieved all facts which had the chances against them\nbeforehand, we should believe hardly any thing. We are told that A. B.\ndied yesterday; the moment before we were so told, the chances against his\nhaving died on that day may have been ten thousand to one; but since he\nwas certain to die at some time or other, and when he died must\nnecessarily die on some particular day, while the preponderance of chances\nis very great against every day in particular, experience affords no\nground for discrediting any testimony which may be produced to the event\u2019s\nhaving taken place on a given day.\n\nYet it has been considered by Dr. Campbell and others, as a complete\nanswer to Hume\u2019s doctrine (that things are incredible which are _contrary_\nto the uniform course of experience), that we do not disbelieve, merely\nbecause the chances were against them, things in strict _conformity_ to\nthe uniform course of experience; that we do not disbelieve an alleged\nfact merely because the combination of causes on which it depends occurs\nonly once in a certain number of times. It is evident that whatever is\nshown by observation, or can be proved from laws of nature, to occur in a\ncertain proportion (however small) of the whole number of possible cases,\nis not contrary to experience; though we are right in disbelieving it, if\nsome other supposition respecting the matter in question involves, on the\nwhole, a less departure from the ordinary course of events. Yet on such\ngrounds as this have able writers been led to the extraordinary\nconclusion, that nothing supported by credible testimony ought ever to be\ndisbelieved.\n\n\u00a7 5. We have considered two species of events, commonly said to be\nimprobable; one kind which are in no way extraordinary, but which, having\nan immense preponderance of chances against them, are improbable until\nthey are affirmed, but no longer; another kind which, being contrary to\nsome recognized law of nature, are incredible on any amount of testimony\nexcept such as would be sufficient to shake our belief in the law itself.\nBut between these two classes of events, there is an intermediate class,\nconsisting of what are commonly termed Coincidences: in other words, those\ncombinations of chances which present some peculiar and unexpected\nregularity, assimilating them, in so far, to the results of law. As if,\nfor example, in a lottery of a thousand tickets, the numbers should be\ndrawn in the exact order of what are called the natural numbers, 1, 2, 3,\netc. We have still to consider the principles of evidence applicable to\nthis case: whether there is any difference between coincidences and\nordinary events, in the amount of testimony or other evidence necessary to\nrender them credible.\n\nIt is certain that on every rational principle of expectation, a\ncombination of this peculiar sort may be expected quite as often as any\nother given series of a thousand numbers; that with perfectly fair dice,\nsixes will be thrown twice, thrice, or any number of times in succession,\nquite as often in a thousand or a million throws, as any other succession\nof numbers fixed upon beforehand; and that no judicious player would give\ngreater odds against the one series than against the other.\nNotwithstanding this, there is a general disposition to regard the one as\nmuch more improbable than the other, and as requiring much stronger\nevidence to make it credible. Such is the force of this impression, that\nit has led some thinkers to the conclusion, that nature has greater\ndifficulty in producing regular combinations than irregular ones; or in\nother words, that there is some general tendency of things, some law,\nwhich prevents regular combinations from occurring, or at least from\noccurring so often as others. Among these thinkers may be numbered\nD\u2019Alembert; who, in an Essay on Probabilities to be found in the fifth\nvolume of his _M\u00e9langes_, contends that regular combinations, though\nequally probable according to the mathematical theory with any others, are\nphysically less probable. He appeals to common sense, or, in other words,\nto common impressions; saying, if dice thrown repeatedly in our presence\ngave sixes every time, should we not, before the number of throws had\nreached ten (not to speak of thousands of millions), be ready to affirm,\nwith the most positive conviction, that the dice were false?\n\nThe common and natural impression is in favor of D\u2019Alembert: the regular\nseries would be thought much more unlikely than an irregular. But this\ncommon impression is, I apprehend, merely grounded on the fact, that\nscarcely any body remembers to have ever seen one of these peculiar\ncoincidences: the reason of which is simply that no one\u2019s experience\nextends to any thing like the number of trials, within which that or any\nother given combination of events can be expected to happen. The chance of\nsixes on a single throw of two dice being \u00b9\u2044\u2083\u2086, the chance of sixes ten\ntimes in succession is 1 divided by the tenth power of 36; in other words,\nsuch a concurrence is only likely to happen once in 3,656,158,440,062,976\ntrials, a number which no dice-player\u2019s experience comes up to a millionth\npart of. But if, instead of sixes ten times, any other given succession of\nten throws had been fixed upon, it would have been exactly as unlikely\nthat in any individual\u2019s experience that particular succession had ever\noccurred; although this does not _seem_ equally improbable, because no one\nwould be likely to have remembered whether it had occurred or not, and\nbecause the comparison is tacitly made, not between sixes ten times and\nany one particular series of throws, but between all regular and all\nirregular successions taken together.\n\nThat (as D\u2019Alembert says) if the succession of sixes was actually thrown\nbefore our eyes, we should ascribe it not to chance, but to unfairness in\nthe dice, is unquestionably true. But this arises from a totally different\nprinciple. We should then be considering, not the probability of the fact\nin itself, but the comparative probability with which, when it is known to\nhave happened, it may be referred to one or to another cause. The regular\nseries is not at all less likely than the irregular one to be brought\nabout by chance, but it is much more likely than the irregular one to be\nproduced by design; or by some general cause operating through the\nstructure of the dice. It is the nature of casual combinations to produce\na repetition of the same event, as often and no oftener than any other\nseries of events. But it is the nature of general causes to reproduce, in\nthe same circumstances, always the same event. Common sense and science\nalike dictate that, all other things being the same, we should rather\nattribute the effect to a cause which if real would be very likely to\nproduce it, than to a cause which would be very unlikely to produce it.\nAccording to Laplace\u2019s sixth theorem, which we demonstrated in a former\nchapter, the difference of probability arising from the superior\n_efficacy_ of the constant cause, unfairness in the dice, would after a\nvery few throws far outweigh any antecedent probability which there could\nbe against its existence.\n\nD\u2019Alembert should have put the question in another manner. He should have\nsupposed that we had ourselves previously tried the dice, and knew by\nample experience that they were fair. Another person then tries them in\nour absence, and assures us that he threw sixes ten times in succession.\nIs the assertion credible or not? Here the effect to be accounted for is\nnot the occurrence itself, but the fact of the witness\u2019s asserting it.\nThis may arise either from its having really happened, or from some other\ncause. What we have to estimate is the comparative probability of these\ntwo suppositions.\n\nIf the witness affirmed that he had thrown any other series of numbers,\nsupposing him to be a person of veracity, and tolerable accuracy, and to\nprofess that he took particular notice, we should believe him. But the ten\nsixes are exactly as likely to have been really thrown as the other\nseries. If, therefore, this assertion is less credible than the other, the\nreason must be, not that it is less likely than the other to be made\ntruly, but that it is more likely than the other to be made falsely.\n\nOne reason obviously presents itself why what is called a coincidence,\nshould be oftener asserted falsely than an ordinary combination. It\nexcites wonder. It gratifies the love of the marvelous. The motives,\ntherefore, to falsehood, one of the most frequent of which is the desire\nto astonish, operate more strongly in favor of this kind of assertion than\nof the other kind. Thus far there is evidently more reason for\ndiscrediting an alleged coincidence, than a statement in itself not more\nprobable, but which if made would not be thought remarkable. There are\ncases, however, in which the presumption on this ground would be the other\nway. There are some witnesses who, the more extraordinary an occurrence\nmight appear, would be the more anxious to verify it by the utmost\ncarefulness of observation before they would venture to believe it, and\nstill more before they would assert it to others.\n\n\u00a7 6. Independently, however, of any peculiar chances of mendacity arising\nfrom the nature of the assertion, Laplace contends, that merely on the\ngeneral ground of the fallibility of testimony, a coincidence is not\ncredible on the same amount of testimony on which we should be warranted\nin believing an ordinary combination of events. In order to do justice to\nhis argument, it is necessary to illustrate it by the example chosen by\nhimself.\n\nIf, says Laplace, there were one thousand tickets in a box, and one only\nhas been drawn out, then if an eye-witness affirms that the number drawn\nwas 79, this, though the chances were 999 in 1000 against it, is not on\nthat account the less credible; its credibility is equal to the antecedent\nprobability of the witness\u2019s veracity. But if there were in the box 999\nblack balls and only one white, and the witness affirms that the white\nball was drawn, the case according to Laplace is very different: the\ncredibility of his assertion is but a small fraction of what it was in the\nformer case; the reason of the difference being as follows:\n\nThe witnesses of whom we are speaking must, from the nature of the case,\nbe of a kind whose credibility falls materially short of certainty; let us\nsuppose, then, the credibility of the witness in the case in question to\nbe \u2079\u2044\u2081\u2080; that is, let us suppose that in every ten statements which the\nwitness makes, nine on an average are correct, and one incorrect. Let us\nnow suppose that there have taken place a sufficient number of drawings to\nexhaust all the possible combinations, the witness deposing in every one.\nIn one case out of every ten in all these drawings he will actually have\nmade a false announcement. But in the case of the thousand tickets these\nfalse announcements will have been distributed impartially over all the\nnumbers, and of the 999 cases in which No. 79 was not drawn, there will\nhave been only one case in which it was announced. On the contrary, in the\ncase of the thousand balls (the announcement being always either \u201cblack\u201d\nor \u201cwhite\u201d), if white was not drawn, and there was a false announcement,\nthat false announcement _must_ have been white; and since by the\nsupposition there was a false announcement once in every ten times, white\nwill have been announced falsely in one-tenth part of all the cases in\nwhich it was not drawn, that is, in one-tenth part of 999 cases out of\nevery thousand. White, then, is drawn, on an average, exactly as often as\nNo. 79, but it is announced, without having been really drawn, 999 times\nas often as No. 79; the announcement, therefore, requires a much greater\namount of testimony to render it credible.(205)\n\nTo make this argument valid it must of course be supposed, that the\nannouncements made by the witness are average specimens of his general\nveracity and accuracy; or, at least, that they are neither more nor less\nso in the case of the black and white balls, than in the case of the\nthousand tickets. This assumption, however, is not warranted. A person is\nfar less likely to mistake, who has only one form of error to guard\nagainst, than if he had 999 different errors to avoid. For instance, in\nthe example chosen, a messenger who might make a mistake once in ten times\nin reporting the number drawn in a lottery, might not err once in a\nthousand times if sent simply to observe whether a ball was black or\nwhite. Laplace\u2019s argument, therefore, is faulty even as applied to his own\ncase. Still less can that case be received as completely representing all\ncases of coincidence. Laplace has so contrived his example, that though\nblack answers to 999 distinct possibilities, and white only to one, the\nwitness has nevertheless no bias which can make him prefer black to white.\nThe witness did not know that there were 999 black balls in the box and\nonly one white; or if he did, Laplace has taken care to make all the 999\ncases so undistinguishably alike, that there is hardly a possibility of\nany cause of falsehood or error operating in favor of any of them, which\nwould not operate in the same manner if there were only one. Alter this\nsupposition, and the whole argument falls to the ground. Let the balls,\nfor instance, be numbered, and let the white ball be No. 79. Considered in\nrespect of their color, there are but two things which the witness can be\ninterested in asserting, or can have dreamed or hallucinated, or has to\nchoose from if he answers at random, viz., black and white; but considered\nin respect of the numbers attached to them, there are a thousand; and if\nhis interest or error happens to be connected with the numbers, though the\nonly assertion he makes is about the color, the case becomes precisely\nassimilated to that of the thousand tickets. Or instead of the balls\nsuppose a lottery, with 1000 tickets and but one prize, and that I hold\nNo. 79, and being interested only in that, ask the witness not what was\nthe number drawn, but whether it was 79 or some other. There are now only\ntwo cases, as in Laplace\u2019s example; yet he surely would not say that if\nthe witness answered 79, the assertion would be in an enormous proportion\nless credible, than if he made the same answer to the same question asked\nin the other way. If, for instance (to put a case supposed by Laplace\nhimself), he has staked a large sum on one of the chances, and thinks that\nby announcing its occurrence he shall increase his credit; he is equally\nlikely to have betted on any one of the 999 numbers which are attached to\nblack balls, and so far as the chances of mendacity from this cause are\nconcerned, there will be 999 times as many chances of his announcing black\nfalsely as white.\n\nOr suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and\nthat of these one man has been killed, and it is not known which. I ask\nthe question, and the witness answers, the Frenchman. This was not only as\nimprobable _a priori_, but is in itself as singular a circumstance, as\nremarkable a coincidence, as the drawing of the white ball; yet we should\nbelieve the statement as readily, as if the answer had been John Thompson.\nBecause, though the 999 Englishmen were all alike in the point in which\nthey differed from the Frenchman, they were not, like the 999 black balls,\nundistinguishable in every other respect; but being all different, they\nadmitted as many chances of interest or error, as if each man had been of\na different nation; and if a lie was told or a mistake made, the\nmisstatement was as likely to fall on any Jones or Thompson of the set, as\non the Frenchman.\n\nThe example of a coincidence selected by D\u2019Alembert, that of sixes thrown\non a pair of dice ten times in succession, belongs to this sort of cases\nrather than to such as Laplace\u2019s. The coincidence is here far more\nremarkable, because of far rarer occurrence, than the drawing of the white\nball. But though the improbability of its really occurring is greater, the\nsuperior probability of its being announced falsely can not be established\nwith the same evidence. The announcement \u201cblack\u201d represented 999 cases,\nbut the witness may not have known this, and if he did, the 999 cases are\nso exactly alike, that there is really only one set of possible causes of\nmendacity corresponding to the whole. The announcement \u201csixes _not_ drawn\nten times,\u201d represents, and is known by the witness to represent, a great\nmultitude of contingencies, every one of which being unlike every other,\nthere may be a different and a fresh set of causes of mendacity\ncorresponding to each.\n\nIt appears to me, therefore, that Laplace\u2019s doctrine is not strictly true\nof any coincidences, and is wholly inapplicable to most; and that to know\nwhether a coincidence does or does not require more evidence to render it\ncredible than an ordinary event, we must refer, in every instance, to\nfirst principles, and estimate afresh what is the probability that the\ngiven testimony would have been delivered in that instance, supposing the\nfact which it asserts not to be true.\n\nWith these remarks we close the discussion of the Grounds of Disbelief;\nand along with it, such exposition as space admits, and as the writer has\nit in his power to furnish, of the Logic of Induction.\n\n\n\n\n                                 Book IV.\n\n\nOF OPERATIONS SUBSIDIARY TO INDUCTION.\n\n\n    \u201cClear and distinct ideas are terms which, though familiar and\n    frequent in men\u2019s mouths, I have reason to think every one who\n    uses does not perfectly understand. And possibly it is but here\n    and there one who gives himself the trouble to consider them so\n    far as to know what he himself or others precisely mean by them; I\n    have, therefore, in most places, chose to put determinate or\n    determined, instead of clear and distinct, as more likely to\n    direct men\u2019s thoughts to my meaning in this matter.\u201d\u2014LOCKE\u2019S\n    _Essay on the Human Understanding_; Epistle to the Reader.\n\n    \u201cIl ne peut y avoir qu\u2019une m\u00e9thode parfaite, qui est la _m\u00e9thode\n    naturelle_; on nomme ainsi un arrangement dans lequel les \u00eatres du\n    m\u00eame genre seraient plus voisins entre eux que ceux de tous les\n    autres genres; les genres du m\u00eame ordre, plus que ceux de tous les\n    autres ordres; et ainsi de suite. Cette m\u00e9thode est l\u2019id\u00e9al auquel\n    l\u2019histoire naturelle doit tendre; car il est \u00e9vident que si l\u2019on y\n    parvenait, l\u2019on aurait l\u2019expression exacte et compl\u00e8te de la\n    nature enti\u00e8re.\u201d\u2014CUVIER, _R\u00e8gne Animal_, Introduction.\n\n    \u201cDeux grandes notions philosophiques dominent la th\u00e9orie\n    fondamentale de la m\u00e9thode naturelle proprement dite, savoir la\n    formation des groupes naturels, et ensuite leur succession\n    hi\u00e9rarchique.\u201d\u2014COMTE, _Cours de Philosophie Positive_, 42me le\u00e7on.\n\n\n\n\n                                Chapter I.\n\n\nOf Observation And Description.\n\n\n\u00a7 1. The inquiry which occupied us in the two preceding Books, has\nconducted us to what appears a satisfactory solution of the principal\nproblem of Logic, according to the conception I have formed of the\nscience. We have found, that the mental process with which Logic is\nconversant, the operation of ascertaining truths by means of evidence, is\nalways, even when appearances point to a different theory of it, a process\nof induction. And we have particularized the various modes of induction,\nand obtained a clear view of the principles to which it must conform, in\norder to lead to results which can be relied on.\n\nThe consideration of Induction, however, does not end with the direct\nrules for its performance. Something must be said of those other\noperations of the mind, which are either necessarily presupposed in all\ninduction, or are instrumental to the more difficult and complicated\ninductive processes. The present Book will be devoted to the consideration\nof these subsidiary operations; among which our attention must first be\ngiven to those, which are indispensable preliminaries to all induction\nwhatsoever.\n\nInduction being merely the extension to a class of cases, of something\nwhich has been observed to be true in certain individual instances of the\nclass; the first place among the operations subsidiary to induction, is\nclaimed by Observation. This is not, however, the place to lay down rules\nfor making good observers; nor is it within the competence of Logic to do\nso, but of the art of intellectual Education. Our business with\nobservation is only in its connection with the appropriate problem of\nlogic, the estimation of evidence. We have to consider, not how or what to\nobserve, but under what conditions observation is to be relied on; what is\nneedful, in order that the fact, supposed to be observed, may safely be\nreceived as true.\n\n\u00a7 2. The answer to this question is very simple, at least in its first\naspect. The sole condition is, that what is supposed to have been observed\nshall really have been observed; that it be an observation, not an\ninference. For in almost every act of our perceiving faculties,\nobservation and inference are intimately blended. What we are said to\nobserve is usually a compound result, of which one-tenth may be\nobservation, and the remaining nine-tenths inference.\n\nI affirm, for example, that I hear a man\u2019s voice. This would pass, in\ncommon language, for a direct perception. All, however, which is really\nperception, is that I hear a sound. That the sound is a voice, and that\nvoice the voice of a man, are not perceptions but inferences. I affirm,\nagain, that I saw my brother at a certain hour this morning. If any\nproposition concerning a matter of fact would commonly be said to be known\nby the direct testimony of the senses, this surely would be so. The truth,\nhowever, is far otherwise. I only saw a certain colored surface; or rather\nI had the kind of visual sensations which are usually produced by a\ncolored surface; and from these as marks, known to be such by previous\nexperience, I concluded that I saw my brother. I might have had sensations\nprecisely similar, when my brother was not there. I might have seen some\nother person so nearly resembling him in appearance, as, at the distance,\nand, with the degree of attention which I bestowed, to be mistaken for\nhim. I might have been asleep, and have dreamed that I saw him; or in a\nstate of nervous disorder, which brought his image before me in a waking\nhallucination. In all these modes, many have been led to believe that they\nsaw persons well known to them, who were dead or far distant. If any of\nthese suppositions had been true, the affirmation that I saw my brother\nwould have been erroneous; but whatever was matter of direct perception,\nnamely the visual sensations, would have been real. The inference only\nwould have been ill grounded; I should have ascribed those sensations to a\nwrong cause.\n\nInnumerable instances might be given, and analyzed in the same manner, of\nwhat are vulgarly called errors of sense. There are none of them properly\nerrors of sense; they are erroneous inferences from sense. When I look at\na candle through a multiplying glass, I see what seems a dozen candles\ninstead of one; and if the real circumstances of the case were skillfully\ndisguised, I might suppose that there were really that number; there would\nbe what is called an optical deception. In the kaleidoscope there really\nis that deception; when I look through the instrument, instead of what is\nactually there, namely a casual arrangement of colored fragments, the\nappearance presented is that of the same combination several times\nrepeated in symmetrical arrangement round a point. The delusion is of\ncourse effected by giving me the same sensations which I should have had\nif such a symmetrical combination had really been presented to me. If I\ncross two of my fingers, and bring any small object, a marble for\ninstance, into contact with both, at points not usually touched\nsimultaneously by one object, I can hardly, if my eyes are shut, help\nbelieving that there are two marbles instead of one. But it is not my\ntouch in this case, nor my sight in the other, which is deceived; the\ndeception, whether durable or only momentary, is in my judgment. From my\nsenses I have only the sensations, and those are genuine. Being accustomed\nto have those or similar sensations when, and only when, a certain\narrangement of outward objects is present to my organs, I have the habit\nof instantly, when I experience the sensations, inferring the existence of\nthat state of outward things. This habit has become so powerful, that the\ninference, performed with the speed and certainty of an instinct, is\nconfounded with intuitive perceptions. When it is correct, I am\nunconscious that it ever needed proof; even when I know it to be\nincorrect, I can not without considerable effort abstain from making it.\nIn order to be aware that it is not made by instinct but by an acquired\nhabit, I am obliged to reflect on the slow process through which I learned\nto judge by the eye of many things which I now appear to perceive directly\nby sight; and on the reverse operation performed by persons learning to\ndraw, who with difficulty and labor divest themselves of their acquired\nperceptions, and learn afresh to see things as they appear to the eye.\n\nIt would be easy to prolong these illustrations, were there any need to\nexpatiate on a topic so copiously exemplified in various popular works.\nFrom the examples already given, it is seen sufficiently, that the\nindividual facts from which we collect our inductive generalizations are\nscarcely ever obtained by observation alone. Observation extends only to\nthe sensations by which we recognize objects; but the propositions which\nwe make use of, either in science or in common life, relate mostly to the\nobjects themselves. In every act of what is called observation, there is\nat least one inference\u2014from the sensations to the presence of the object;\nfrom the marks or diagnostics, to the entire phenomenon. And hence, among\nother consequences, follows the seeming paradox, that a general\nproposition collected from particulars is often more certainly true than\nany one of the particular propositions from which, by an act of induction,\nit was inferred. For, each of those particular (or rather singular)\npropositions involved an inference, from the impression on the senses to\nthe fact which caused that impression; and this inference may have been\nerroneous in any one of the instances, but can not well have been\nerroneous in all of them, provided their number was sufficient to\neliminate chance. The conclusion, therefore, that is, the general\nproposition, may deserve more complete reliance than it would be safe to\nrepose in any one of the inductive premises.\n\nThe logic of observation, then, consists solely in a correct\ndiscrimination between that, in a result of observation, which has really\nbeen perceived, and that which is an inference from the perception.\nWhatever portion is inference, is amenable to the rules of induction\nalready treated of, and requires no further notice here; the question for\nus in this place is, when all which is inference is taken away what\nremains? There remains, in the first place, the mind\u2019s own feelings or\nstates of consciousness, namely, its outward feelings or sensations, and\nits inward feelings\u2014its thoughts, emotions, and volitions. Whether any\nthing else remains, or all else is inference from this; whether the mind\nis capable of directly perceiving or apprehending any thing except states\nof its own consciousness\u2014is a problem of metaphysics not to be discussed\nin this place. But after excluding all questions on which metaphysicians\ndiffer, it remains true, that for most purposes the discrimination we are\ncalled upon practically to exercise is that between sensations or other\nfeelings, of our own or of other people, and inferences drawn from them.\nAnd on the theory of Observation this is all which seems necessary to be\nsaid for the purposes of the present work.\n\n\u00a7 3. If, in the simplest observation, or in what passes for such, there is\na large part which is not observation but something else; so in the\nsimplest description of an observation, there is, and must always be, much\nmore asserted than is contained in the perception itself. We can not\ndescribe a fact, without implying more than the fact. The perception is\nonly of one individual thing; but to describe it is to affirm a connection\nbetween it and every other thing which is either denoted or connoted by\nany of the terms used. To begin with an example, than which none can be\nconceived more elementary: I have a sensation of sight, and I endeavor to\ndescribe it by saying that I see something white. In saying this, I do not\nsolely affirm my sensation; I also class it. I assert a resemblance\nbetween the thing I see, and all things which I and others are accustomed\nto call white. I assert that it resembles them in the circumstance in\nwhich they all resemble one another, in that which is the ground of their\nbeing called by the name. This is not merely one way of describing an\nobservation, but the only way. If I would either register my observation\nfor my own future use, or make it known for the benefit of others, I must\nassert a resemblance between the fact which I have observed and something\nelse. It is inherent in a description, to be the statement of a\nresemblance, or resemblances.\n\nWe thus see that it is impossible to express in words any result of\nobservation, without performing an act possessing what Dr. Whewell\nconsiders to be characteristic of Induction. There is always something\nintroduced which was not included in the observation itself; some\nconception common to the phenomenon with other phenomena to which it is\ncompared. An observation can not be spoken of in language at all without\ndeclaring more than that one observation; without assimilating it to other\nphenomena already observed and classified. But this identification of an\nobject\u2014this recognition of it as possessing certain known\ncharacteristics\u2014has never been confounded with Induction. It is an\noperation which precedes all induction, and supplies it with its\nmaterials. It is a perception of resemblances, obtained by comparison.\n\nThese resemblances are not always apprehended directly, by merely\ncomparing the object observed with some other present object, or with our\nrecollection of an object which is absent. They are often ascertained\nthrough intermediate marks, that is, deductively. In describing some new\nkind of animal, suppose me to say that it measures ten feet in length,\nfrom the forehead to the extremity of the tail. I did not ascertain this\nby the unassisted eye. I had a two-foot rule which I applied to the\nobject, and, as we commonly say, measured it; an operation which was not\nwholly manual, but partly also mathematical, involving the two\npropositions, Five times two is ten, and Things which are equal to the\nsame thing are equal to one another. Hence, the fact that the animal is\nten feet long is not an immediate perception, but a conclusion from\nreasoning; the minor premises alone being furnished by observation of the\nobject. Nevertheless, this is called an observation, or a description of\nthe animal, not an induction respecting it.\n\nTo pass at once from a very simple to a very complex example: I affirm\nthat the earth is globular. The assertion is not grounded on direct\nperception; for the figure of the earth can not, by us, be directly\nperceived, though the assertion would not be true unless circumstances\ncould be supposed under which its truth could be so perceived. That the\nform of the earth is globular is inferred from certain marks, as for\ninstance from this, that its shadow thrown upon the moon is circular; or\nthis, that on the sea, or any extensive plain, our horizon is always a\ncircle; either of which marks is incompatible with any other than a\nglobular form. I assert further, that the earth is that particular kind of\na globe which is termed an oblate spheroid; because it is found by\nmeasurement in the direction of the meridian, that the length on the\nsurface of the earth which subtends a given angle at its centre,\ndiminishes as we recede from the equator and approach the poles. But these\npropositions, that the earth is globular, and that it is an oblate\nspheroid, assert, each of them, an individual fact; in its own nature\ncapable of being perceived by the senses when the requisite organs and the\nnecessary position are supposed, and only not actually perceived because\nthose organs and that position are wanting. This identification of the\nearth, first as a globe, and next as an oblate spheroid, which, if the\nfact could have been seen, would have been called a description of the\nfigure of the earth, may without impropriety be so called when, instead of\nbeing seen, it is inferred. But we could not without impropriety call\neither of these assertions an induction from facts respecting the earth.\nThey are not general propositions collected from particular facts, but\nparticular facts deduced from general propositions. They are conclusions\nobtained deductively, from premises originating in induction: but of these\npremises some were not obtained by observation of the earth, nor had any\npeculiar reference to it.\n\nIf, then, the truth respecting the figure of the earth is not an\ninduction, why should the truth respecting the figure of the earth\u2019s orbit\nbe so? The two cases only differ in this, that the form of the orbit was\nnot, like the form of the earth itself, deduced by ratiocination from\nfacts which were marks of ellipticity, but was got at by boldly guessing\nthat the path was an ellipse, and finding afterward, on examination, that\nthe observations were in harmony with the hypothesis. According to Dr.\nWhewell, however, this process of guessing and verifying our guesses is\nnot only induction, but the whole of induction: no other exposition can be\ngiven of that logical operation. That he is wrong in the latter assertion,\nthe whole of the preceding book has, I hope, sufficiently proved; and that\nthe process by which the ellipticity of the planetary orbits was\nascertained, is not induction at all, was attempted to be shown in the\nsecond chapter of the same Book.(206) We are now, however, prepared to go\nmore into the heart of the matter than at that earlier period of our\ninquiry, and to show, not merely what the operation in question is not,\nbut what it is.\n\n\u00a7 4. We observed, in the second chapter, that the proposition \u201cthe earth\nmoves in an ellipse,\u201d so far as it only serves for the colligation or\nconnecting together of actual observations (that is, as it only affirms\nthat the observed positions of the earth may be correctly represented by\nas many points in the circumference of an imaginary ellipse), is not an\ninduction, but a description: it is an induction, only when it affirms\nthat the intermediate positions, of which there has been no direct\nobservation, would be found to correspond to the remaining points of the\nsame elliptic circumference. Now, though this real induction is one thing,\nand the description another, we are in a very different condition for\nmaking the induction before we have obtained the description, and after\nit. For inasmuch as the description, like all other descriptions, contains\nthe assertion of a resemblance between the phenomenon described and\nsomething else; in pointing out something which the series of observed\nplaces of a planet resembles, it points out something in which the several\nplaces themselves agree. If the series of places correspond to as many\npoints of an ellipse, the places themselves agree in being situated in\nthat ellipse. We have, therefore, by the same process which gave us the\ndescription, obtained the requisites for an induction by the Method of\nAgreement. The successive observed places of the earth being considered as\neffects, and its motion as the cause which produces them, we find that\nthose effects, that is, those places, agree in the circumstance of being\nin an ellipse. We conclude that the remaining effects, the places which\nhave not been observed, agree in the same circumstance, and that the _law_\nof the motion of the earth is motion in an ellipse.\n\nThe Colligation of Facts, therefore, by means of hypotheses, or, as Dr.\nWhewell prefers to say, by means of Conceptions, instead of being, as he\nsupposes, Induction itself, takes its proper place among operations\nsubsidiary to Induction. All Induction supposes that we have previously\ncompared the requisite number of individual instances, and ascertained in\nwhat circumstances they agree. The Colligation of Facts is no other than\nthis preliminary operation. When Kepler, after vainly endeavoring to\nconnect the observed places of a planet by various hypotheses of circular\nmotion, at last tried the hypotheses of an ellipse and found it answer to\nthe phenomena; what he really attempted, first unsuccessfully and at last\nsuccessfully, was to discover the circumstance in which all the observed\npositions of the planet agreed. And when he in like manner connected\nanother set of observed facts, the periodic times of the different\nplanets, by the proposition that the squares of the times are proportional\nto the cubes of the distances, what he did was simply to ascertain the\nproperty in which the periodic times of all the different planets agreed.\n\nSince, therefore, all that is true and to the purpose in Dr. Whewell\u2019s\ndoctrine of Conceptions might be fully expressed by the more familiar term\nHypothesis; and since his Colligation of Facts by means of appropriate\nConceptions, is but the ordinary process of finding by a comparison of\nphenomena, in what consists their agreement or resemblance; I would\nwillingly have confined myself to those better understood expressions, and\npersevered to the end in the same abstinence which I have hitherto\nobserved from ideological discussions; considering the mechanism of our\nthoughts to be a topic distinct from and irrelevant to the principles and\nrules by which the trustworthiness of the results of thinking is to be\nestimated. Since, however, a work of such high pretensions, and, it must\nalso be said, of so much real merit, has rested the whole theory of\nInduction upon such ideological considerations, it seems necessary for\nothers who follow to claim for themselves and their doctrines whatever\nposition may properly belong to them on the same metaphysical ground. And\nthis is the object of the succeeding chapter.\n\n\n\n\n                               Chapter II.\n\n\nOf Abstraction, Or The Formation Of Conceptions.\n\n\n\u00a7 1. The metaphysical inquiry into the nature and composition of what have\nbeen called Abstract Ideas, or, in other words, of the notions which\nanswer in the mind to classes and to general names, belongs not to Logic,\nbut to a different science, and our purpose does not require that we\nshould enter upon it here. We are only concerned with the universally\nacknowledged fact, that such notions or conceptions do exist. The mind can\nconceive a multitude of individual things as one assemblage or class; and\ngeneral names do really suggest to us certain ideas or mental\nrepresentations, otherwise we could not use the names with consciousness\nof a meaning. Whether the idea called up by a general name is composed of\nthe various circumstances in which all the individuals denoted by the name\nagree, and of no others (which is the doctrine of Locke, Brown, and the\nConceptualists); or whether it be the idea of some one of those\nindividuals, clothed in its individualizing peculiarities, but with the\naccompanying knowledge that those peculiarities are not properties of the\nclass (which is the doctrine of Berkeley, Mr. Bailey,(207) and the modern\nNominalists); or whether (as held by Mr. James Mill) the idea of the class\nis that of a miscellaneous assemblage of individuals belonging to the\nclass; or whether, finally, it be any one or any other of all these,\naccording to the accidental circumstances of the case; certain it is, that\n_some_ idea or mental conception is suggested by a general name, whenever\nwe either hear it or employ it with consciousness of a meaning. And this,\nwhich we may call, if we please, a general idea, _represents_ in our minds\nthe whole class of things to which the name is applied. Whenever we think\nor reason concerning the class, we do so by means of this idea. And the\nvoluntary power which the mind has, of attending to one part of what is\npresent to it at any moment, and neglecting another part, enables us to\nkeep our reasonings and conclusions respecting the class unaffected by any\nthing in the idea or mental image which is not really, or at least which\nwe do not really believe to be common, to the whole class.(208)\n\nThere are, then, such things as general conceptions, or conceptions by\nmeans of which we can think generally; and when we form a set of phenomena\ninto a class, that is, when we compare them with one another to ascertain\nin what they agree, some general conception is implied in this mental\noperation. And inasmuch as such a comparison is a necessary preliminary to\nInduction, it is most true that Induction could not go on without general\nconceptions.\n\n\u00a7 2. But it does not therefore follow that these general conceptions must\nhave existed in the mind previously to the comparison. It is not a law of\nour intellect, that in comparing things with each other and taking note of\ntheir agreement we merely recognize as realized in the outward world\nsomething that we already had in our minds. The conception originally\nfound its way to us as the _result_ of such a comparison. It was obtained\n(in metaphysical phrase) by _abstraction_ from individual things. These\nthings may be things which we perceived or thought of on former occasions,\nbut they may also be the things which we are perceiving or thinking of on\nthe very occasion. When Kepler compared the observed places of the planet\nMars, and found that they agreed in being points of an elliptic\ncircumference, he applied a general conception which was already in his\nmind, having been derived from his former experience. But this is by no\nmeans universally the case. When we compare several objects and find them\nto agree in being white, or when we compare the various species of\nruminating animals and find them to agree in being cloven-footed, we have\njust as much a general conception in our minds as Kepler had in his: we\nhave the conception of \u201ca white thing,\u201d or the conception of \u201ca\ncloven-footed animal.\u201d But no one supposes that we necessarily bring these\nconceptions with us, and _superinduce_ them (to adopt Dr. Whewell\u2019s\nexpression) upon the facts: because in these simple cases every body sees\nthat the very act of comparison which ends in our connecting the facts by\nmeans of the conception, may be the source from which we derive the\nconception itself. If we had never seen any white object or had never seen\nany cloven-footed animal before, we should at the same time and by the\nsame mental act acquire the idea, and employ it for the colligation of the\nobserved phenomena. Kepler, on the contrary, really had to bring the idea\nwith him, and superinduce it upon the facts; he could not evolve it out of\nthem: if he had not already had the idea, he would not have been able to\nacquire it by a comparison of the planet\u2019s positions. But this inability\nwas a mere accident; the idea of an ellipse could have been acquired from\nthe paths of the planets as effectually as from any thing else, if the\npaths had not happened to be invisible. If the planet had left a visible\ntrack, and we had been so placed that we could see it at the proper angle,\nwe might have abstracted our original idea of an ellipse from the\nplanetary orbit. Indeed, every conception which can be made the instrument\nfor connecting a set of facts, might have been originally evolved from\nthose very facts. The conception is a conception _of_ something; and that\nwhich it is a conception of, is really _in_ the facts, and might, under\nsome supposable circumstances, or by some supposable extension of the\nfaculties which we actually possess, have been detected in them. And not\nonly is this always in itself possible, but it actually happens in almost\nall cases in which the obtaining of the right conception is a matter of\nany considerable difficulty. For if there be no new conception required;\nif one of those already familiar to mankind will serve the purpose, the\naccident of being the first to whom the right one occurs, may happen to\nalmost any body; at least in the case of a set of phenomena which the\nwhole scientific world are engaged in attempting to connect. The honor, in\nKepler\u2019s case, was that of the accurate, patient, and toilsome\ncalculations by which he compared the results that followed from his\ndifferent guesses, with the observations of Tycho Brahe; but the merit was\nvery small of guessing an ellipse; the only wonder is that men had not\nguessed it before, nor could they have failed to do so if there had not\nexisted an obstinate _a priori_ prejudice that the heavenly bodies must\nmove, if not in a circle, in some combination of circles.\n\nThe really difficult cases are those in which the conception destined to\ncreate light and order out of darkness and confusion has to be sought for\namong the very phenomena which it afterward serves to arrange. Why,\naccording to Dr. Whewell himself, did the ancients fail in discovering the\nlaws of mechanics, that is, of equilibrium and of the communication of\nmotion? Because they had not, or at least had not clearly, the ideas or\nconceptions of pressure and resistance, momentum, and uniform and\naccelerating force. And whence could they have obtained these ideas except\nfrom the very facts of equilibrium and motion? The tardy development of\nseveral of the physical sciences, for example, of optics, electricity,\nmagnetism, and the higher generalizations of chemistry, he ascribes to the\nfact that mankind had not yet possessed themselves of the Idea of\nPolarity, that is, the idea of opposite properties in opposite directions.\nBut what was there to suggest such an idea, until, by a separate\nexamination of several of these different branches of knowledge, it was\nshown that the facts of each of them did present, in some instances at\nleast, the curious phenomenon of opposite properties in opposite\ndirections? The thing was superficially manifest only in two cases, those\nof the magnet and of electrified bodies; and there the conception was\nencumbered with the circumstance of material poles, or fixed points in the\nbody itself, in which points this opposition of properties seemed to be\ninherent. The first comparison and abstraction had led only to this\nconception of poles; and if any thing corresponding to that conception had\nexisted in the phenomena of chemistry or optics, the difficulty now justly\nconsidered so great, would have been extremely small. The obscurity arose\nfrom the fact, that the polarities in chemistry and optics were distinct\nspecies, though of the same genus, with the polarities in electricity and\nmagnetism; and that in order to assimilate the phenomena to one another,\nit was necessary to compare a polarity without poles, such for instance as\nis exemplified in the polarization of light, and the polarity with\n(apparent) poles, which we see in the magnet; and to recognize that these\npolarities, while different in many other respects, agree in the one\ncharacter which is expressed by the phrase, opposite properties in\nopposite directions. From the result of such a comparison it was that the\nminds of scientific men formed this new general conception; between which,\nand the first confused feeling of an analogy between some of the phenomena\nof light and those of electricity and magnetism, there is a long interval,\nfilled up by the labors and more or less sagacious suggestions of many\nsuperior minds.\n\nThe conceptions, then, which we employ for the colligation and\nmethodization of facts, do not develop themselves from within, but are\nimpressed upon the mind from without; they are never obtained otherwise\nthan by way of comparison and abstraction, and, in the most important and\nthe most numerous cases, are evolved by abstraction from the very\nphenomena which it is their office to colligate. I am far, however, from\nwishing to imply that it is not often a very difficult thing to perform\nthis process of abstraction well, or that the success of an inductive\noperation does not, in many cases, principally depend on the skill with\nwhich we perform it. Bacon was quite justified in designating as one of\nthe principal obstacles to good induction, general conceptions wrongly\nformed, \u201cnotiones temer\u00e8 \u00e0 rebus abstract\u00e6;\u201d to which Dr. Whewell adds,\nthat not only does bad abstraction make bad induction, but that, in order\nto perform induction well, we must have abstracted well; our general\nconceptions must be \u201cclear\u201d and \u201cappropriate\u201d to the matter in hand.\n\n\u00a7 3. In attempting to show what the difficulty in this matter really is,\nand how it is surmounted, I must beg the reader, once for all, to bear\nthis in mind; that although, in discussing the opinions of a different\nschool of philosophy, I am willing to adopt their language, and to speak,\ntherefore, of connecting facts through the instrumentality of a\nconception, this technical phraseology means neither more nor less than\nwhat is commonly called comparing the facts with one another and\ndetermining in what they agree. Nor has the technical expression even the\nadvantage of being metaphysically correct. The facts are not _connected_,\nexcept in a merely metaphorical acceptation of the term. The _ideas_ of\nthe facts may become connected, that is, we may be led to think of them\ntogether; but this consequence is no more than what may be produced by any\ncasual association. What really takes place, is, I conceive, more\nphilosophically expressed by the common word Comparison, than by the\nphrases \u201cto connect\u201d or \u201cto superinduce.\u201d For, as the general conception\nis itself obtained by a comparison of particular phenomena, so, when\nobtained, the mode in which we apply it to other phenomena is again by\ncomparison. We compare phenomena with each other to get the conception,\nand we then compare those and other phenomena _with_ the conception. We\nget the conception of an animal (for instance) by comparing different\nanimals, and when we afterward see a creature resembling an animal, we\ncompare it with our general conception of an animal; and if it agrees with\nthat general conception, we include it in the class. The conception\nbecomes the type of comparison.\n\nAnd we need only consider what comparison is, to see that where the\nobjects are more than two, and still more when they are an indefinite\nnumber, a type of some sort is an indispensable condition of the\ncomparison. When we have to arrange and classify a great number of objects\naccording to their agreements and differences, we do not make a confused\nattempt to compare all with all. We know that two things are as much as\nthe mind can easily attend to at a time, and we therefore fix upon one of\nthe objects, either at hazard or because it offers in a peculiarly\nstriking manner some important character, and, taking this as our\nstandard, compare it with one object after another. If we find a second\nobject which presents a remarkable agreement with the first, inducing us\nto class them together, the question instantly arises, in what particular\ncircumstances do they agree? and to take notice of these circumstances is\nalready a first stage of abstraction, giving rise to a general conception.\nHaving advanced thus far, when we now take in hand a third object we\nnaturally ask ourselves the question, not merely whether this third object\nagrees with the first, but whether it agrees with it in the same\ncircumstances in which the second did? in other words, whether it agrees\nwith the general conception which has been obtained by abstraction from\nthe first and second? Thus we see the tendency of general conceptions, as\nsoon as formed, to substitute themselves as types, for whatever individual\nobjects previously answered that purpose in our comparisons. We may,\nperhaps, find that no considerable number of other objects agree with this\nfirst general conception; and that we must drop the conception, and\nbeginning again with a different individual case, proceed by fresh\ncomparisons to a different general conception. Sometimes, again, we find\nthat the same conception will serve, by merely leaving out some of its\ncircumstances; and by this higher effort of abstraction, we obtain a still\nmore general conception; as in the case formerly referred to, the\nscientific world rose from the conception of poles to the general\nconception of opposite properties in opposite directions; or as those\nSouth-Sea islanders, whose conception of a quadruped had been abstracted\nfrom hogs (the only animals of that description which they had seen), when\nthey afterward compared that conception with other quadrupeds, dropped\nsome of the circumstances, and arrived at the more general conception\nwhich Europeans associate with the term.\n\nThese brief remarks contain, I believe, all that is well grounded in the\ndoctrine, that the conception by which the mind arranges and gives unity\nto phenomena must be furnished by the mind itself, and that we find the\nright conception by a tentative process, trying first one and then another\nuntil we hit the mark. The conception is not furnished _by_ the mind until\nit has been furnished _to_ the mind; and the facts which supply it are\nsometimes extraneous facts, but more often the very facts which we are\nattempting to arrange by it. It is quite true, however, that in\nendeavoring to arrange the facts, at whatever point we begin, we never\nadvance three steps without forming a general conception, more or less\ndistinct and precise; and that this general conception becomes the clue\nwhich we instantly endeavor to trace through the rest of the facts, or\nrather, becomes the standard with which we thenceforth compare them. If we\nare not satisfied with the agreements which we discover among the\nphenomena by comparing them with this type, or with some still more\ngeneral conception which by an additional stage of abstraction we can form\nfrom the type; we change our path, and look out for other agreements; we\nrecommence the comparison from a different starting-point, and so generate\na different set of general conceptions. This is the tentative process\nwhich Dr. Whewell speaks of; and which has not unnaturally suggested the\ntheory, that the conception is supplied by the mind itself; since the\ndifferent conceptions which the mind successively tries, it either already\npossessed from its previous experience, or they were supplied to it in the\nfirst stage of the corresponding act of comparison; so that, in the\nsubsequent part of the process, the conception manifested itself as\nsomething compared with the phenomena, not evolved from them.\n\n\u00a7 4. If this be a correct account of the instrumentality of general\nconceptions in the comparison which necessarily precedes Induction, we are\nnow able to translate into our own language what Dr. Whewell means by\nsaying that conceptions, to be subservient to Induction, must be \u201cclear\u201d\nand \u201cappropriate.\u201d\n\nIf the conception corresponds to a real agreement among the phenomena; if\nthe comparison which we have made of a set of objects has led us to class\nthem according to real resemblances and differences; the conception which\ndoes this can not fail to be appropriate, for some purpose or other. The\nquestion of appropriateness is relative to the particular object we have\nin view. As soon as, by our comparison, we have ascertained some\nagreement, something which can be predicated in common of a number of\nobjects; we have obtained a basis on which an inductive process is capable\nof being founded. But the agreements, or the ulterior consequences to\nwhich those agreements lead, may be of very different degrees of\nimportance. If, for instance, we only compare animals according to their\ncolor, and class those together which are colored alike, we form the\ngeneral conceptions of a white animal, a black animal, etc., which are\nconceptions legitimately formed; and if an induction were to be attempted\nconcerning the causes of the colors of animals, this comparison would be\nthe proper and necessary preparation for such an induction, but would not\nhelp us toward a knowledge of the laws of any other of the properties of\nanimals; while if, with Cuvier, we compare and class them according to the\nstructure of the skeleton, or, with Blainville, according to the nature of\ntheir outward integuments, the agreements and differences which are\nobservable in these respects are not only of much greater importance in\nthemselves, but are marks of agreements and differences in many other\nimportant particulars of the structure and mode of life of the animals.\nIf, therefore, the study of their structure and habits be our object, the\nconceptions generated by these last comparisons are far more \u201cappropriate\u201d\nthan those generated by the former. Nothing, other than this, can be meant\nby the appropriateness of a conception.\n\nWhen Dr. Whewell says that the ancients, or the school-men, or any modern\ninquirers, missed discovering the real law of a phenomenon because they\napplied to it an inappropriate instead of an appropriate conception; he\ncan only mean that in comparing various instances of the phenomenon, to\nascertain in what those instances agreed, they missed the important points\nof agreement; and fastened upon such as were either imaginary, and not\nagreements at all, or, if real agreements, were comparatively trifling,\nand had no connection with the phenomenon, the law of which was sought.\n\nAristotle, philosophizing on the subject of motion, remarked that certain\nmotions apparently take place spontaneously; bodies fall to the ground,\nflame ascends, bubbles of air rise in water, etc.; and these he called\nnatural motions; while others not only never take place without external\nincitement, but even when such incitement is applied, tend spontaneously\nto cease; which, to distinguish them from the former, he called violent\nmotions. Now, in comparing the so-called natural motions with one another,\nit appeared to Aristotle that they agreed in one circumstance, namely,\nthat the body which moved (or seemed to move) spontaneously, was moving\n_toward its own place_; meaning thereby the place from whence it\noriginally came, or the place where a great quantity of matter similar to\nitself was assembled. In the other class of motions, as when bodies are\nthrown up in the air, they are, on the contrary, moving _from_ their own\nplace. Now, this conception of a body moving toward its own place may\njustly be considered inappropriate; because, though it expresses a\ncircumstance really found in some of the most familiar instances of motion\napparently spontaneous, yet, first, there are many other cases of such\nmotion, in which that circumstance is absent; the motion, for instance, of\nthe earth and planets. Secondly, even when it is present, the motion, on\ncloser examination, would often be seen not to be spontaneous; as, when\nair rises in water, it does not rise by its own nature, but is pushed up\nby the superior weight of the water which presses upon it. Finally, there\nare many cases in which the spontaneous motion takes place in the contrary\ndirection to what the theory considers as the body\u2019s own place; for\ninstance, when a fog rises from a lake, or when water dries up. The\nagreement, therefore, which Aristotle selected as his principle of\nclassification, did not extend to all cases of the phenomenon he wanted to\nstudy, spontaneous motion; while it did include cases of the absence of\nthe phenomenon, cases of motion not spontaneous. The conception was hence\n\u201cinappropriate.\u201d We may add that, in the case in question, no conception\nwould be appropriate; there is no agreement which runs through all the\ncases of spontaneous or apparently spontaneous motion and no others; they\ncan not be brought under one law; it is a case of Plurality of\nCauses.(209)\n\n\u00a7 5. So much for the first of Dr. Whewell\u2019s conditions, that conceptions\nmust be appropriate. The second is, that they shall be \u201cclear:\u201d and let us\nconsider what this implies. Unless the conception corresponds to a real\nagreement, it has a worse defect than that of not being clear: it is not\napplicable to the case at all. Among the phenomena, therefore, which we\nare attempting to connect by means of the conception, we must suppose that\nthere really is an agreement, and that the conception is a conception of\nthat agreement. In order, then, that it may be clear, the only requisite\nis, that we shall know exactly in what the agreement consists; that it\nshall have been carefully observed, and accurately remembered. We are said\nnot to have a clear conception of the resemblance among a set of objects,\nwhen we have only a general feeling that they resemble, without having\nanalyzed their resemblance, or perceived in what points it consists, and\nfixed in our memory an exact recollection of those points. This want of\nclearness, or, as it may be otherwise called, this vagueness in the\ngeneral conception, may be owing either to our having no accurate\nknowledge of the objects themselves, or merely to our not having carefully\ncompared them. Thus a person may have no clear idea of a ship because he\nhas never seen one, or because he remembers but little, and that faintly,\nof what he has seen. Or he may have a perfect knowledge and remembrance of\nmany ships of various kinds, frigates among the rest, but he may have no\nclear but only a confused idea of a frigate, because he has never been\ntold, and has not compared them sufficiently to have remarked and\nremembered, in what particular points a frigate differs from some other\nkind of ship.\n\nIt is not, however, necessary, in order to have clear ideas, that we\nshould know all the common properties of the things which we class\ntogether. That would be to have our conception of the class complete as\nwell as clear. It is sufficient if we never class things together without\nknowing exactly why we do so\u2014without having ascertained exactly what\nagreements we are about to include in our conception; and if, after having\nthus fixed our conception, we never vary from it, never include in the\nclass any thing which has not those common properties, nor exclude from it\nany thing which has. A clear conception means a determinate conception;\none which does not fluctuate, which is not one thing to-day and another\nto-morrow, but remains fixed and invariable, except when, from the\nprogress of our knowledge, or the correction of some error, we consciously\nadd to it or alter it. A person of clear ideas is a person who always\nknows in virtue of what properties his classes are constituted; what\nattributes are connoted by his general names.\n\nThe principal requisites, therefore, of clear conceptions, are habits of\nattentive observation, an extensive experience, and a memory which\nreceives and retains an exact image of what is observed. And in proportion\nas any one has the habit of observing minutely and comparing carefully a\nparticular class of phenomena, and an accurate memory for the results of\nthe observation and comparison, so will his conceptions of that class of\nphenomena be clear; provided he has the indispensable habit (naturally,\nhowever, resulting from those other endowments), of never using general\nnames without a precise connotation.\n\nAs the clearness of our conceptions chiefly depends on the _carefulness_\nand _accuracy_ of our observing and comparing faculties, so their\nappropriateness, or rather the chance we have of hitting upon the\nappropriate conception in any case, mainly depends on the _activity_ of\nthe same faculties. He who by habit, grounded on sufficient natural\naptitude, has acquired a readiness in accurately observing and comparing\nphenomena, will perceive so many more agreements, and will perceive them\nso much more rapidly than other people, that the chances are much greater\nof his perceiving, in any instance, the agreement on which the important\nconsequences depend.\n\n\u00a7 6. It is of so much importance that the part of the process of\ninvestigating truth, discussed in this chapter, should be rightly\nunderstood, that I think it is desirable to restate the results we have\narrived at, in a somewhat different mode of expression.\n\nWe can not ascertain general truths, that is, truths applicable to\nclasses, unless we have formed the classes in such a manner that general\ntruths can be affirmed of them. In the formation of any class, there is\ninvolved a conception of it as a class, that is, a conception of certain\ncircumstances as being those which characterize the class, and distinguish\nthe objects composing it from all other things. When we know exactly what\nthese circumstances are, we have a clear idea (or conception) of the\nclass, and of the meaning of the general name which designates it. The\nprimary condition implied in having this clear idea, is that the class be\nreally a class; that it correspond to a real distinction; that the things\nit includes really do agree with one another in certain particulars, and\ndiffer, in those same particulars, from all other things. A person without\nclear ideas is one who habitually classes together, under the same general\nnames, things which have no common properties, or none which are not\npossessed also by other things; or who, if the usage of other people\nprevents him from actually misclassing things, is unable to state to\nhimself the common properties in virtue of which he classes them rightly.\n\nBut is it not the sole requisite of classification that the classes should\nbe real classes, framed by a legitimate mental process? Some modes of\nclassing things are more valuable than others for human uses, whether of\nspeculation or of practice; and our classifications are not well made,\nunless the things which they bring together not only agree with each other\nin something which distinguishes them from all other things, but agree\nwith each other and differ from other things in the very circumstances\nwhich are of primary importance for the purpose (theoretical or practical)\nwhich we have in view, and which constitutes the problem before us. In\nother words, our conceptions, though they may be clear, are not\n_appropriate_ for our purpose, unless the properties we comprise in them\nare those which will help us toward what we wish to understand\u2014_i.e._,\neither those which go deepest into the nature of the things, if our object\nbe to understand that, or those which are most closely connected with the\nparticular property which we are endeavoring to investigate.\n\nWe can not, therefore, frame good general conceptions beforehand. That the\nconception we have obtained is the one we want, can only be known when we\nhave done the work for the sake of which we wanted it; when we completely\nunderstand the general character of the phenomena, or the conditions of\nthe particular property with which we concern ourselves. General\nconceptions formed without this thorough knowledge, are Bacon\u2019s \u201cnotiones\ntemer\u00e8 \u00e0 rebus abstract\u00e6.\u201d Yet such premature conceptions we must be\ncontinually making up, in our progress to something better. They are an\nimpediment to the progress of knowledge, only when they are permanently\nacquiesced in. When it has become our habit to group things in wrong\nclasses\u2014in groups which either are not really classes, having no\ndistinctive points of agreement (absence of _clear_ ideas), or which are\nnot classes of which any thing important to our purpose can be predicated\n(absence of _appropriate_ ideas); and when, in the belief that these badly\nmade classes are those sanctioned by nature, we refuse to exchange them\nfor others, and can not or will not make up our general conceptions from\nany other elements; in that case all the evils which Bacon ascribes to his\n\u201cnotiones temer\u00e8 abstract\u00e6\u201d really occur. This was what the ancients did\nin physics, and what the world in general does in morals and politics to\nthe present day.\n\nIt would thus, in my view of the matter, be an inaccurate mode of\nexpression to say, that obtaining appropriate conceptions is a condition\nprecedent to generalization. Throughout the whole process of comparing\nphenomena with one another for the purpose of generalization, the mind is\ntrying to make up a conception; but the conception which it is trying to\nmake up is that of the really important point of agreement in the\nphenomena. As we obtain more knowledge of the phenomena themselves, and of\nthe conditions on which their important properties depend, our views on\nthis subject naturally alter; and thus we advance from a less to a more\n\u201cappropriate\u201d general conception, in the progress of our investigations.\n\nWe ought not, at the same time, to forget that the really important\nagreement can not always be discovered by mere comparison of the very\nphenomena in question, without the aid of a conception acquired elsewhere;\nas in the case, so often referred to, of the planetary orbits.\n\nThe search for the agreement of a set of phenomena is in truth very\nsimilar to the search for a lost or hidden object. At first we place\nourselves in a sufficiently commanding position, and cast our eyes round\nus, and if we can see the object it is well; if not, we ask ourselves\nmentally what are the places in which it may be hid, in order that we may\nthere search for it: and so on, until we imagine the place where it really\nis. And here too we require to have had a previous conception, or\nknowledge, of those different places. As in this familiar process, so in\nthe philosophical operation which it illustrates, we first endeavor to\nfind the lost object or recognize the common attribute, without\nconjecturally invoking the aid of any previously acquired conception, or,\nin other words, of any hypothesis. Having failed in this, we call upon our\nimagination for some hypothesis of a possible place, or a possible point\nof resemblance, and then look to see whether the facts agree with the\nconjecture.\n\nFor such cases something more is required than a mind accustomed to\naccurate observation and comparison. It must be a mind stored with general\nconceptions, previously acquired, of the sorts which bear affinity to the\nsubject of the particular inquiry. And much will also depend on the\nnatural strength and acquired culture of what has been termed the\nscientific imagination; on the faculty possessed of mentally arranging\nknown elements into new combinations, such as have not yet been observed\nin nature, though not contradictory to any known laws.\n\nBut the variety of intellectual habits, the purposes which they serve, and\nthe modes in which they may be fostered and cultivated, are considerations\nbelonging to the Art of Education: a subject far wider than Logic, and\nwhich this treatise does not profess to discuss. Here, therefore, the\npresent chapter may properly close.\n\n\n\n\n                               Chapter III.\n\n\nOf Naming, As Subsidiary To Induction.\n\n\n\u00a7 1. It does not belong to the present undertaking to dwell on the\nimportance of language as a medium of human intercourse, whether for\npurposes of sympathy or of information. Nor does our design admit of more\nthan a passing allusion to that great property of names, on which their\nfunctions as an intellectual instrument are, in reality, ultimately\ndependent; their potency as a means of forming, and of riveting,\nassociations among our other ideas; a subject on which an able\nthinker(210) has thus written:\n\n\u201cNames are impressions of sense, and as such take the strongest hold on\nthe mind, and of all other impressions can be most easily recalled and\nretained in view. They therefore serve to give a point of attachment to\nall the more volatile objects of thought and feeling. Impressions that\nwhen passed might be dissipated forever, are, by their connection with\nlanguage, always within reach. Thoughts, of themselves, are perpetually\nslipping out of the field of immediate mental vision; but the name abides\nwith us, and the utterance of it restores them in a moment. Words are the\ncustodiers of every product of mind less impressive than themselves. All\nextensions of human knowledge, all new generalizations, are fixed and\nspread, even unintentionally, by the use of words. The child growing up\nlearns, along with the vocables of his mother-tongue, that things which he\nwould have believed to be different are, in important points, the same.\nWithout any formal instruction, the language in which we grow up teaches\nus all the common philosophy of the age. It directs us to observe and know\nthings which we should have overlooked; it supplies us with\nclassifications ready made, by which things are arranged (as far as the\nlight of by-gone generations admits) with the objects to which they bear\nthe greatest total resemblance. The number of general names in a language,\nand the degree of generality of those names, afford a test of the\nknowledge of the era, and of the intellectual insight which is the\nbirthright of any one born into it.\u201d\n\nIt is not, however, of the functions of Names, considered generally, that\nwe have here to treat, but only of the manner and degree in which they are\ndirectly instrumental to the investigation of truth; in other words, to\nthe process of induction.\n\n\u00a7 2. Observation and Abstraction, the operations which formed the subject\nof the two foregoing chapters, are conditions indispensable to induction;\nthere can be no induction where they are not. It has been imagined that\nNaming is also a condition equally indispensable. There are thinkers who\nhave held that language is not solely, according to a phrase generally\ncurrent, _an_ instrument of thought, but _the_ instrument; that names, or\nsomething equivalent to them, some species of artificial signs, are\nnecessary to reasoning; that there could be no inference, and consequently\nno induction, without them. But if the nature of reasoning was correctly\nexplained in the earlier part of the present work, this opinion must be\nheld to be an exaggeration, though of an important truth. If reasoning be\nfrom particulars to particulars, and if it consist in recognizing one fact\nas a mark of another, or a mark of a mark of another, nothing is required\nto render reasoning possible, except senses and association; senses to\nperceive that two facts are conjoined; association, as the law by which\none of those two facts raises up the idea of the other.(211) For these\nmental phenomena, as well as for the belief or expectation which follows,\nand by which we recognize as having taken place, or as about to take\nplace, that of which we have perceived a mark, there is evidently no need\nof language. And this inference of one particular fact from another is a\ncase of induction. It is of this sort of induction that brutes are\ncapable; it is in this shape that uncultivated minds make almost all their\ninductions, and that we all do so in the cases in which familiar\nexperience forces our conclusions upon us without any active process of\ninquiry on our part, and in which the belief or expectation follows the\nsuggestion of the evidence with the promptitude and certainty of an\ninstinct.(212)\n\n\u00a7 3. But though inference of an inductive character is possible without\nthe use of signs, it could never, without them, be carried much beyond the\nvery simple cases which we have just described, and which form, in all\nprobability, the limit of the reasonings of those animals to whom\nconventional language is unknown. Without language, or something\nequivalent to it, there could only be as much reasoning from experience as\ncan take place without the aid of general propositions. Now, though in\nstrictness we may reason from past experience to a fresh individual case\nwithout the intermediate stage of a general proposition, yet without\ngeneral propositions we should seldom remember what past experience we\nhave had, and scarcely ever what conclusions that experience will warrant.\nThe division of the inductive process into two parts, the first\nascertaining what is a mark of the given fact, the second whether in the\nnew case that mark exists, is natural, and scientifically indispensable.\nIt is, indeed, in a majority of cases, rendered necessary by mere distance\nof time. The experience by which we are to guide our judgments may be\nother people\u2019s experience, little of which can be communicated to us\notherwise than by language; when it is our own, it is generally experience\nlong past; unless, therefore, it were recorded by means of artificial\nsigns, little of it (except in cases involving our intenser sensations or\nemotions, or the subjects of our daily and hourly contemplation) would be\nretained in the memory. It is hardly necessary to add, that when the\ninductive inference is of any but the most direct and obvious nature\u2014when\nit requires several observations or experiments, in varying circumstances,\nand the comparison of one of these with another\u2014it is impossible to\nproceed a step, without the artificial memory which words bestow. Without\nwords, we should, if we had often seen A and B in immediate and obvious\nconjunction, expect B whenever we saw A; but to discover their conjunction\nwhen not obvious, or to determine whether it is really constant or only\ncasual, and whether there is reason to expect it under any given change of\ncircumstances, is a process far too complex to be performed without some\ncontrivance to make our remembrance of our own mental operations accurate.\nNow, language is such a contrivance. When that instrument is called to our\naid, the difficulty is reduced to that of making our remembrance of the\nmeaning of words accurate. This being secured, whatever passes through our\nminds may be remembered accurately, by putting it carefully into words,\nand committing the words either to writing or to memory.\n\nThe function of Naming, and particularly of General Names, in Induction,\nmay be recapitulated as follows. Every inductive inference which is good\nat all, is good for a whole class of cases; and, that the inference may\nhave any better warrant of its correctness than the mere clinging together\nof two ideas, a process of experimentation and comparison is necessary; in\nwhich the whole class of cases must be brought to view, and some\nuniformity in the course of nature evolved and ascertained, since the\nexistence of such a uniformity is required as a justification for drawing\nthe inference in even a single case. This uniformity, therefore, may be\nascertained once for all; and if, being ascertained, it can be remembered,\nit will serve as a formula for making, in particular cases, all such\ninferences as the previous experience will warrant. But we can only secure\nits being remembered, or give ourselves even a chance of carrying in our\nmemory any considerable number of such uniformities, by registering them\nthrough the medium of permanent signs; which (being, from the nature of\nthe case, signs not of an individual fact, but of a uniformity, that is,\nof an indefinite number of facts similar to one another) are general\nsigns; universals; general names, and general propositions.\n\n\u00a7 4. And here I can not omit to notice an oversight committed by some\neminent thinkers; who have said that the cause of our using general names\nis the infinite multitude of individual objects, which, making it\nimpossible to have a name for each, compels us to make one name serve for\nmany.\n\nThis is a very limited view of the function of general names. Even if\nthere were a name for every individual object, we should require general\nnames as much as we now do. Without them we could not express the result\nof a single comparison, nor record any one of the uniformities existing in\nnature; and should be hardly better off in respect to Induction than if we\nhad no names at all. With none but names of individuals (or, in other\nwords, proper names), we might, by pronouncing the name, suggest the idea\nof the object, but we could not assert any proposition; except the\nunmeaning ones formed by predicating two proper names one of another. It\nis only by means of general names that we can convey any information,\npredicate any attribute, even of an individual, much more of a class.\nRigorously speaking, we could get on without any other general names than\nthe abstract names of attributes; all our propositions might be of the\nform \u201csuch an individual object possesses such an attribute,\u201d or \u201csuch an\nattribute is always (or never) conjoined with such another attribute.\u201d In\nfact, however, mankind have always given general names to objects as well\nas attributes, and indeed before attributes: but the general names given\nto objects imply attributes, derive their whole meaning from attributes;\nand are chiefly useful as the language by means of which we predicate the\nattributes which they connote.\n\nIt remains to be considered what principles are to be adhered to in giving\ngeneral names, so that these names, and the general propositions in which\nthey fill a place, may conduce most to the purposes of Induction.\n\n\n\n\n                               Chapter IV.\n\n\nOf The Requisites Of A Philosophical Language, And The Principles Of\nDefinition.\n\n\n\u00a7 1. In order that we may possess a language perfectly suitable for the\ninvestigation and expression of general truths, there are two principal,\nand several minor requisites. The first is, that every general name should\nhave a meaning, steadily fixed, and precisely determined. When, by the\nfulfillment of this condition, such names as we possess are fitted for the\ndue performance of their functions, the next requisite, and the second in\norder of importance, is that we should possess a name wherever one is\nneeded; wherever there is any thing to be designated by it, which it is of\nimportance to express.\n\nThe former of these requisites is that to which our attention will be\nexclusively directed in the present chapter.\n\n\u00a7 2. Every general name, then, must have a certain and knowable meaning.\nNow the meaning (as has so often been explained) of a general connotative\nname, resides in the connotation; in the attribute on account of which,\nand to express which, the name is given. Thus, the name animal being given\nto all things which possess the attributes of sensation and voluntary\nmotion, the word connotes those attributes exclusively, and they\nconstitute the whole of its meaning. If the name be abstract, its\ndenotation is the same with the connotation of the corresponding concrete;\nit designates directly the attribute, which the concrete term implies. To\ngive a precise meaning to general names is, then, to fix with steadiness\nthe attribute or attributes connoted by each concrete general name, and\ndenoted by the corresponding abstract. Since abstract names, in the order\nof their creation, do not precede but follow concrete ones, as is proved\nby the etymological fact that they are almost always derived from them; we\nmay consider their meaning as determined by, and dependent on, the meaning\nof their concrete; and thus the problem of giving a distinct meaning to\ngeneral language, is all included in that of giving a precise connotation\nto all concrete general names.\n\nThis is not difficult in the case of new names; of the technical terms\ncreated by scientific inquirers for the purposes of science or art. But\nwhen a name is in common use, the difficulty is greater; the problem in\nthis case not being that of choosing a convenient connotation for the\nname, but of ascertaining and fixing the connotation with which it is\nalready used. That this can ever be a matter of doubt, is a sort of\nparadox. But the vulgar (including in that term all who have not accurate\nhabits of thought) seldom know exactly what assertion they intend to make,\nwhat common property they mean to express, when they apply the same name\nto a number of different things. All which the name expresses with them,\nwhen they predicate it of an object, is a confused feeling of resemblance\nbetween that object and some of the other things which they have been\naccustomed to denote by the name. They have applied the name Stone to\nvarious objects previously seen; they see a new object, which appears to\nthem somewhat like the former, and they call it a stone, without asking\nthemselves in what respect it is like, or what mode or degree of\nresemblance the best authorities, or even they themselves, require as a\nwarrant for using the name. This rough general impression of resemblance\nis, however, made up of particular circumstances of resemblance; and into\nthese it is the business of the logician to analyze it; to ascertain what\npoints of resemblance among the different things commonly called by the\nname, have produced in the common mind this vague feeling of likeness;\nhave given to the things the similarity of aspect, which has made them a\nclass, and has caused the same name to be bestowed upon them.\n\nBut though general names are imposed by the vulgar without any more\ndefinite connotation than that of a vague resemblance; general\npropositions come in time to be made, in which predicates are applied to\nthose names, that is, general assertions are made concerning the _whole_\nof the things which are denoted by the name. And since by each of these\npropositions some attribute, more or less precisely conceived, is of\ncourse predicated, the ideas of these various attributes thus become\nassociated with the name, and in a sort of uncertain way it comes to\nconnote them; there is a hesitation to apply the name in any new case in\nwhich any of the attributes familiarly predicated of the class do not\nexist. And thus, to common minds, the propositions which they are in the\nhabit of hearing or uttering concerning a class make up in a loose way a\nsort of connotation for the class name. Let us take, for instance, the\nword Civilized. How few could be found, even among the most educated\npersons, who would undertake to say exactly what the term Civilized\nconnotes. Yet there is a feeling in the minds of all who use it, that they\nare using it with a meaning; and this meaning is made up, in a confused\nmanner, of every thing which they have heard or read that civilized men or\ncivilized communities are, or may be expected to be.\n\nIt is at this stage, probably, in the progress of a concrete name, that\nthe corresponding abstract name generally comes into use. Under the notion\nthat the concrete name must of course convey a meaning, or, in other\nwords, that there is some property common to all things which it denotes,\npeople give a name to this common property; from the concrete Civilized,\nthey form the abstract Civilization. But since most people have never\ncompared the different things which are called by the concrete name, in\nsuch a manner as to ascertain what properties these things have in common,\nor whether they have any; each is thrown back upon the marks by which he\nhimself has been accustomed to be guided in his application of the term;\nand these, being merely vague hearsays and current phrases, are not the\nsame in any two persons, nor in the same person at different times. Hence\nthe word (as Civilization, for example) which professes to be the\ndesignation of the unknown common property, conveys scarcely to any two\nminds the same idea. No two persons agree in the things they predicate of\nit; and when it is itself predicated of any thing, no other person knows,\nnor does the speaker himself know with precision, what he means to assert.\nMany other words which could be named, as the word _honor_, or the word\n_gentleman_, exemplify this uncertainty still more strikingly.\n\nIt needs scarcely be observed, that general propositions of which no one\ncan tell exactly what they assert, can not possibly have been brought to\nthe test of a correct induction. Whether a name is to be used as an\ninstrument of thinking, or as a means of communicating the result of\nthought, it is imperative to determine exactly the attribute or attributes\nwhich it is to express; to give it, in short, a fixed and ascertained\nconnotation.\n\n\u00a7 3. It would, however, be a complete misunderstanding of the proper\noffice of a logician in dealing with terms already in use, if we were to\nthink that because a name has not at present an ascertained connotation,\nit is competent to any one to give it such a connotation at his own\nchoice. The meaning of a term actually in use is not an arbitrary quantity\nto be fixed, but an unknown quantity to be sought.\n\nIn the first place, it is obviously desirable to avail ourselves, as far\nas possible, of the associations already connected with the name; not\nenjoining the employment of it in a manner which conflicts with all\nprevious habits, and especially not so as to require the rupture of those\nstrongest of all associations between names, which are created by\nfamiliarity with propositions in which they are predicated of one another.\nA philosopher would have little chance of having his example followed, if\nhe were to give such a meaning to his terms as should require us to call\nthe North American Indians a civilized people, or the higher classes in\nEurope savages; or to say that civilized people live by hunting, and\nsavages by agriculture. Were there no other reason, the extreme difficulty\nof effecting so complete a revolution in speech would be more than a\nsufficient one. The endeavor should be, that all generally received\npropositions into which the term enters, should be at least as true after\nits meaning is fixed, as they were before; and that the concrete name,\ntherefore, should not receive such a connotation as shall prevent it from\ndenoting things which, in common language, it is currently affirmed of.\nThe fixed and precise connotation which it receives should not be in\ndeviation from, but in agreement (as far as it goes) with, the vague and\nfluctuating connotation which the term already had.\n\nTo fix the connotation of a concrete name, or the denotation of the\ncorresponding abstract, is to define the name. When this can be done\nwithout rendering any received assertions inadmissible, the name can be\ndefined in accordance with its received use, which is vulgarly called\ndefining not the name but the thing. What is meant by the improper\nexpression of defining a thing (or rather a class of things\u2014for nobody\ntalks of defining an individual), is to define the name, subject to the\ncondition that it shall denote those things. This, of course, supposes a\ncomparison of the things, feature by feature and property by property, to\nascertain what attributes they agree in; and not unfrequently an operation\nstrictly inductive, for the purpose of ascertaining some unobvious\nagreement, which is the cause of the obvious agreements.\n\nFor, in order to give a connotation to a name, consistently with its\ndenoting certain objects, we have to make our selection from among the\nvarious attributes in which those objects agree. To ascertain in what they\ndo agree is, therefore, the first logical operation requisite. When this\nhas been done as far as is necessary or practicable, the question arises,\nwhich of these common attributes shall be selected to be associated with\nthe name. For if the class which the name denotes be a Kind, the common\nproperties are innumerable; and even if not, they are often extremely\nnumerous. Our choice is first limited by the preference to be given to\nproperties which are well known, and familiarly predicated of the class;\nbut even these are often too numerous to be all included in the\ndefinition, and, besides, the properties most generally known may not be\nthose which serve best to mark out the class from all others. We should\ntherefore select from among the common properties (if among them any such\nare to be found) those on which it has been ascertained by experience, or\nproved by deduction, that many others depend; or at least which are sure\nmarks of them, and from whence, therefore, many others will follow by\ninference. We thus see that to frame a good definition of a name already\nin use, is not a matter of choice but of discussion, and discussion not\nmerely respecting the usage of language, but respecting the properties of\nthings, and even the origin of those properties. And hence every\nenlargement of our knowledge of the objects to which the name is applied,\nis liable to suggest an improvement in the definition. It is impossible to\nframe a perfect set of definitions on any subject, until the theory of the\nsubject is perfect; and as science makes progress, its definitions are\nalso progressive.\n\n\u00a7 4. The discussion of Definitions, in so far as it does not turn on the\nuse of words but on the properties of things, Dr. Whewell calls the\nExplication of Conceptions. The act of ascertaining, better than before,\nin what particulars any phenomena which are classed together agree, he\ncalls in his technical phraseology, unfolding the general conception in\nvirtue of which they are so classed. Making allowance for what appears to\nme the darkening and misleading tendency of this mode of expression,\nseveral of his remarks are so much to the purpose, that I shall take the\nliberty of transcribing them.\n\nHe observes,(213) that many of the controversies which have had an\nimportant share in the formation of the existing body of science, have\n\u201cassumed the form of a battle of Definitions. For example, the inquiry\nconcerning the laws of falling bodies led to the question whether the\nproper definition of a _uniform force_ is that it generates a velocity\nproportional to the _space_ from rest, or to the _time_. The controversy\nof the _vis viva_ was what was the proper definition of the _measure of\nforce_. A principal question in the classification of minerals is, what is\nthe definition of a _mineral species_. Physiologists have endeavored to\nthrow light on their subject by defining _organization_, or some similar\nterm.\u201d Questions of the same nature were long open and are not yet\ncompletely closed, respecting the definitions of Specific Heat, Latent\nHeat, Chemical Combination, and Solution.\n\n\u201cIt is very important for us to observe, that these controversies have\nnever been questions of insulated and _arbitrary_ definitions, as men seem\noften tempted to imagine them to have been. In all cases there is a tacit\nassumption of some proposition which is to be expressed by means of the\ndefinition, and which gives it its importance. The dispute concerning the\ndefinition thus acquires a real value, and becomes a question concerning\ntrue and false. Thus, in the discussion of the question, What is a uniform\nforce? it was taken for granted that gravity is a uniform force. In the\ndebate of the _vis viva_, it was assumed that in the mutual action of\nbodies the whole effect of the force is unchanged. In the zoological\ndefinition of species (that it consists of individuals which have, or may\nhave, sprung from the same parents), it is presumed that individuals so\nrelated resemble each other more than those which are excluded by such a\ndefinition; or, perhaps, that species so defined have permanent and\ndefinite differences. A definition of organization, or of some other term\nwhich was not employed to express some principle, would be of no value.\n\n\u201cThe establishment, therefore, of a right definition of a term, may be a\nuseful step in the explication of our conceptions; but this will be the\ncase then only when we have under our consideration some proposition in\nwhich the term is employed. For then the question really is, how the\nconception shall be understood and defined in order that the proposition\nmay be true.\n\n\u201cTo unfold our conceptions by means of definitions has never been\nserviceable to science, except when it has been associated with an\nimmediate use of the definitions. The endeavor to define a Uniform Force\nwas combined with the assertion that gravity is a uniform force; the\nattempt to define Accelerating Force was immediately followed by the\ndoctrine that accelerating forces may be compounded; the process of\ndefining Momentum was connected with the principle that momenta gained and\nlost are equal; naturalists would have given in vain the definition of\nSpecies which we have quoted, if they had not also given the characters of\nspecies so separated.... Definition may be the best mode of explaining our\nconception, but that which alone makes it worth while to explain it in any\nmode, is the opportunity of using it in the expression of truth. When a\ndefinition is propounded to us as a useful step in knowledge, we are\nalways entitled to ask what principle it serves to enunciate.\u201d\n\nIn giving, then, an exact connotation to the phrase, \u201ca uniform force,\u201d\nthe condition was understood, that the phrase should continue to denote\ngravity. The discussion, therefore, respecting the definition, resolved\nitself into this question, What is there of a uniform nature in the\nmotions produced by gravity? By observations and comparisons, it was found\nthat what was uniform in those motions was the ratio of the velocity\nacquired to the time elapsed; equal velocities being added in equal times.\nA uniform force, therefore, was defined a force which adds equal\nvelocities in equal times. So, again, in defining momentum. It was already\na received doctrine that, when two objects impinge upon one another, the\nmomentum lost by the one is equal to that gained by the other. This\nproposition it was deemed necessary to preserve, not from the motive\n(which operates in many other cases) that it was firmly fixed in popular\nbelief; for the proposition in question had never been heard of by any but\nthe scientifically instructed. But it was felt to contain a truth; even a\nsuperficial observation of the phenomena left no doubt that in the\npropagation of motion from one body to another, there was something of\nwhich the one body gained precisely what the other lost; and the word\nmomentum had been invented to express this unknown something. The\nsettlement, therefore, of the definition of momentum, involved the\ndetermination of the question, What is that of which a body, when it sets\nanother body in motion, loses exactly as much as it communicates? And when\nexperiment had shown that this _something_ was the product of the velocity\nof the body by its mass, or quantity of matter, this became the definition\nof momentum.\n\nThe following remarks,(214) therefore, are perfectly just: \u201cThe business\nof definition is part of the business of discovery.... To define, so that\nour definition shall have any scientific value, requires no small portion\nof that sagacity by which truth is detected.... When it has been clearly\nseen what ought to be our definition, it must be pretty well known what\ntruth we have to state. The definition, as well as the discovery, supposes\na decided step in our knowledge to have been made. The writers on Logic,\nin the Middle Ages, made Definition the last stage in the progress of\nknowledge; and in this arrangement at least, the history of science, and\nthe philosophy derived from the history, confirm their speculative views.\u201d\nFor in order to judge finally how the name which denotes a class may best\nbe defined, we must know all the properties common to the class, and all\nthe relations of causation or dependence among those properties.\n\nIf the properties which are fittest to be selected as marks of other\ncommon properties are also obvious and familiar, and especially if they\nbear a great part in producing that general air of resemblance which was\nthe original inducement to the formation of the class, the definition will\nthen be most felicitous. But it is often necessary to define the class by\nsome property not familiarly known, provided that property be the best\nmark of those which are known. M. De Blainville, for instance, founded his\ndefinition of life on the process of decomposition and recomposition which\nincessantly takes place in every living body, so that the particles\ncomposing it are never for two instants the same. This is by no means one\nof the most obvious properties of living bodies; it might escape\naltogether the notice of an unscientific observer. Yet great authorities\n(independently of M. De Blainville, who is himself a first-rate authority)\nhave thought that no other property so well answers the conditions\nrequired for the definition.\n\n\u00a7 5. Having laid down the principles which ought for the most part to be\nobserved in attempting to give a precise connotation to a term in use, I\nmust now add, that it is not always practicable to adhere to those\nprinciples, and that even when practicable, it is occasionally not\ndesirable.\n\nCases in which it is impossible to comply with all the conditions of a\nprecise definition of a name in agreement with usage, occur very\nfrequently. There is often no one connotation capable of being given to a\nword, so that it shall still denote every thing it is accustomed to\ndenote; or that all the propositions into which it is accustomed to enter,\nand which have any foundation in truth, shall remain true. Independently\nof accidental ambiguities, in which the different meanings have no\nconnection with one another; it continually happens that a word is used in\ntwo or more senses derived from each other, but yet radically distinct. So\nlong as a term is vague, that is, so long as its connotation is not\nascertained and permanently fixed, it is constantly liable to be applied\nby _extension_ from one thing to another, until it reaches things which\nhave little, or even no, resemblance to those which were first designated\nby it.\n\n\u201cSuppose,\u201d says Dugald Stewart, in his _Philosophical Essays_,(215) \u201cthat\nthe letters A, B, C, D, E, denote a series of objects; that A possesses\nsome one quality in common with B; B a quality in common with C; C a\nquality in common with D; D a quality in common with E; while at the same\ntime, no quality can be found which belongs in common to any _three_\nobjects in the series. Is it not conceivable, that the affinity between A\nand B may produce a transference of the name of the first to the second;\nand that, in consequence of the other affinities which connect the\nremaining objects together, the same name may pass in succession from B to\nC; from C to D; and from D to E? In this manner, a common appellation will\narise between A and E, although the two objects may, in their nature and\nproperties, be so widely distant from each other, that no stretch of\nimagination can conceive how the thoughts were led from the former to the\nlatter. The transitions, nevertheless, may have been all so easy and\ngradual, that, were they successfully detected by the fortunate ingenuity\nof a theorist, we should instantly recognize, not only the verisimilitude,\nbut the truth of the conjecture: in the same way as we admit, with the\nconfidence of intuitive conviction, the certainty of the well-known\netymological process which connects the Latin preposition _e_ or _ex_ with\nthe English substantive _stranger_, the moment that the intermediate links\nof the chain are submitted to our examination.\u201d(216)\n\nThe applications which a word acquires by this gradual extension of it\nfrom one set of objects to another, Stewart, adopting an expression from\nMr. Payne Knight, calls its _transitive_ applications; and after briefly\nillustrating such of them as are the result of local or casual\nassociations, he proceeds as follows:(217)\n\n\u201cBut although by far the greater part of the transitive or derivative\napplications of words depend on casual and unaccountable caprices of the\nfeelings or the fancy, there are certain cases in which they open a very\ninteresting field of philosophical speculation. Such are those, in which\nan analogous transference of the corresponding term may be remarked\nuniversally, or very generally, in other languages; and in which, of\ncourse, the uniformity of the result must be ascribed to the essential\nprinciples of the human frame. Even in such cases, however, it will by no\nmeans be always found, on examination, that the various applications of\nthe same term have arisen from any common quality or qualities in the\nobjects to which they relate. In the greater number of instances, they may\nbe traced to some natural and universal associations of ideas, founded in\nthe common faculties, common organs, and common condition of the human\nrace.... According to the different degrees of intimacy and strength in\nthe associations on which the _transitions_ of language are founded, very\ndifferent effects may be expected to arise. Where the association is\nslight and casual, the several meanings will remain distinct from each\nother, and will often, in process of time, assume the appearance of\ncapricious varieties in the use of the same arbitrary sign. _Where the\nassociation is so natural and habitual as to become virtually\nindissoluble, the transitive meanings will coalesce in one complex\nconception; and every new transition will become a more comprehensive\ngeneralization of the term in question._\u201d\n\nI solicit particular attention to the law of mind expressed in the last\nsentence, and which is the source of the perplexity so often experienced\nin detecting these transitions of meaning. Ignorance of that law is the\nshoal on which some of the most powerful intellects which have adorned the\nhuman race have been stranded. The inquiries of Plato into the definitions\nof some of the most general terms of moral speculation are characterized\nby Bacon as a far nearer approach to a true inductive method than is\nelsewhere to be found among the ancients, and are, indeed, almost perfect\nexamples of the preparatory process of comparison and abstraction; but,\nfrom being unaware of the law just mentioned, he often wasted the powers\nof this great logical instrument on inquiries in which it could realize no\nresult, since the phenomena, whose common properties he so elaborately\nendeavored to detect, had not really any common properties. Bacon himself\nfell into the same error in his speculations on the nature of heat, in\nwhich he evidently confounded under the name hot, classes of phenomena\nwhich have no property in common. Stewart certainly overstates the matter\nwhen he speaks of \u201ca prejudice which has descended to modern times from\nthe scholastic ages, that when a word admits of a variety of\nsignifications, these different significations must all be species of the\nsame genus, and must consequently include some essential idea common to\nevery individual to which the generic term can be applied;\u201d(218) for both\nAristotle and his followers were well aware that there are such things as\nambiguities of language, and delighted in distinguishing them. But they\nnever suspected ambiguity in the cases where (as Stewart remarks) the\nassociation on which the transition of meaning was founded is so natural\nand habitual, that the two meanings blend together in the mind, and a real\ntransition becomes an apparent generalization. Accordingly they wasted\ninfinite pains in endeavoring to find a definition which would serve for\nseveral distinct meanings at once; as in an instance noticed by Stewart\nhimself, that of \u201ccausation; the ambiguity of the word which, in the Greek\nlanguage corresponds to the English word _cause_, having suggested to them\nthe vain attempt of tracing the common idea which, in the case of any\n_effect_, belongs to the _efficient_, to the _matter_, to the _form_, and\nto the _end_. The idle generalities\u201d (he adds) \u201cwe meet with in other\nphilosophers, about the ideas of the _good_, the _fit_, and the\n_becoming_, have taken their rise from the same undue influence of popular\nepithets on the speculations of the learned.\u201d(219)\n\nAmong the words which have undergone so many successive transitions of\nmeaning that every trace of a property common to all the things they are\napplied to, or at least common and also peculiar to those things, has been\nlost, Stewart considers the word Beautiful to be one. And (without\nattempting to decide a question which in no respect belongs to logic) I\ncan not but feel, with him, considerable doubt whether the word beautiful\nconnotes the same property when we speak of a beautiful color, a beautiful\nface, a beautiful scene, a beautiful character, and a beautiful poem. The\nword was doubtless extended from one of these objects to another on\naccount of a resemblance between them, or, more probably, between the\nemotions they excited; and, by this progressive extension, it has at last\nreached things very remote from those objects of sight to which there is\nno doubt that it was first appropriated; and it is at least questionable\nwhether there is now any property common to all the things which,\nconsistently with usage, may be called beautiful, except the property of\nagreeableness, which the term certainly does connote, but which can not be\nall that people usually intend to express by it, since there are many\nagreeable things which are never called beautiful. If such be the case, it\nis impossible to give to the word Beautiful any fixed connotation, such\nthat it shall denote all the objects which in common use it now denotes,\nbut no others. A fixed connotation, however, it ought to have; for, so\nlong as it has not, it is unfit to be used as a scientific term, and is a\nperpetual source of false analogies and erroneous generalizations.\n\nThis, then, constitutes a case in exemplification of our remark, that even\nwhen there is a property common to all the things denoted by a name, to\nerect that property into the definition and exclusive connotation of the\nname is not always desirable. The various things called beautiful\nunquestionably resemble one another in being agreeable; but to make this\nthe definition of beauty, and so extend the word Beautiful to all\nagreeable things, would be to drop altogether a portion of meaning which\nthe word really, though indistinctly, conveys, and to do what depends on\nus toward causing those qualities of the objects which the word\npreviously, though vaguely, pointed at, to be overlooked and forgotten. It\nis better, in such a case, to give a fixed connotation to the term by\nrestricting, than by extending its use; rather excluding from the epithet\nBeautiful some things to which it is commonly considered applicable, than\nleaving out of its connotation any of the qualities by which, though\noccasionally lost sight of, the general mind may have been habitually\nguided in the commonest and most interesting applications of the term. For\nthere is no question that when people call any thing beautiful, they think\nthey are asserting more than that it is merely agreeable. They think they\nare ascribing a peculiar _sort_ of agreeableness, analogous to that which\nthey find in some other of the things to which they are accustomed to\napply the same name. If, therefore, there be any peculiar sort of\nagreeableness which is common though not to all, yet to the principal\nthings which are called beautiful, it is better to limit the denotation of\nthe term to those things, than to leave that kind of quality without a\nterm to connote it, and thereby divert attention from its peculiarities.\n\n\u00a7 6. The last remark exemplifies a rule of terminology, which is of great\nimportance, and which has hardly yet been recognized as a rule, but by a\nfew thinkers of the present century. In attempting to rectify the use of a\nvague term by giving it a fixed connotation, we must take care not to\ndiscard (unless advisedly, and on the ground of a deeper knowledge of the\nsubject) any portion of the connotation which the word, in however\nindistinct a manner, previously carried with it. For otherwise language\nloses one of its inherent and most valuable properties, that of being the\nconservator of ancient experience; the keeper-alive of those thoughts and\nobservations of former ages, which may be alien to the tendencies of the\npassing time. This function of language is so often overlooked or\nundervalued, that a few observations on it appear to be extremely\nrequired.\n\nEven when the connotation of a term has been accurately fixed, and still\nmore if it has been left in the state of a vague unanalyzed feeling of\nresemblance; there is a constant tendency in the word, through familiar\nuse, to part with a portion of its connotation. It is a well-known law of\nthe mind, that a word originally associated with a very complex cluster of\nideas, is far from calling up all those ideas in the mind, every time the\nword is used; it calls up only one or two, from which the mind runs on by\nfresh associations to another set of ideas, without waiting for the\nsuggestion of the remainder of the complex cluster. If this were not the\ncase, processes of thought could not take place with any thing like the\nrapidity which we know they possess. Very often, indeed, when we are\nemploying a word in our mental operations, we are so far from waiting\nuntil the complex idea which corresponds to the meaning of the word is\nconsciously brought before us in all its parts, that we run on to new\ntrains of ideas by the other associations which the mere word excites,\nwithout having realized in our imagination any part whatever of the\nmeaning; thus using the word, and even using it well and accurately, and\ncarrying on important processes of reasoning by means of it, in an almost\nmechanical manner; so much so, that some metaphysicians, generalizing from\nan extreme case, have fancied that all reasoning is but the mechanical use\nof a set of terms according to a certain form. We may discuss and settle\nthe most important interests of towns or nations, by the application of\ngeneral theorems or practical maxims previously laid down, without having\nhad consciously suggested to us, once in the whole process, the houses and\ngreen fields, the thronged market-places and domestic hearths, of which\nnot only those towns and nations consist, but which the words town and\nnation confessedly mean.\n\nSince, then, general names come in this manner to be used (and even to do\na portion of their work well) without suggesting to the mind the whole of\ntheir meaning, and often with the suggestion of a very small, or no part\nat all of that meaning; we can not wonder that words so used come in time\nto be no longer capable of suggesting any other of the ideas appropriated\nto them, than those with which the association is most immediate and\nstrongest, or most kept up by the incidents of life; the remainder being\nlost altogether; unless the mind, by often consciously dwelling on them,\nkeeps up the association. Words naturally retain much more of their\nmeaning to persons of active imagination, who habitually represent to\nthemselves things in the concrete, with the detail which belongs to them\nin the actual world. To minds of a different description, the only\nantidote to this corruption of language is predication. The habit of\npredicating of the name, all the various properties which it originally\nconnoted, keeps up the association between the name and those properties.\n\nBut in order that it may do so, it is necessary that the predicates should\nthemselves retain their association with the properties which they\nseverally connote. For the propositions can not keep the meaning of the\nwords alive, if the meaning of the propositions themselves should die. And\nnothing is more common than for propositions to be mechanically repeated,\nmechanically retained in the memory, and their truth undoubtingly assented\nto and relied on, while yet they carry no meaning distinctly home to the\nmind; and while the matter of fact or law of nature which they originally\nexpressed is as much lost sight of, and practically disregarded, as if it\nnever had been heard of at all. In those subjects which are at the same\ntime familiar and complicated, and especially in those which are so in as\ngreat a degree as moral and social subjects are, it is a matter of common\nremark how many important propositions are believed and repeated from\nhabit, while no account could be given, and no sense is practically\nmanifested, of the truths which they convey. Hence it is, that the\ntraditional maxims of old experience, though seldom questioned, have often\nso little effect on the conduct of life; because their meaning is never,\nby most persons, really felt, until personal experience has brought it\nhome. And thus also it is that so many doctrines of religion, ethics, and\neven politics, so full of meaning and reality to first converts, have\nmanifested (after the association of that meaning with the verbal formulas\nhas ceased to be kept up by the controversies which accompanied their\nfirst introduction) a tendency to degenerate rapidly into lifeless dogmas;\nwhich tendency, all the efforts of an education expressly and skillfully\ndirected to keeping the meaning alive, are barely sufficient to\ncounteract.\n\nConsidering, then, that the human mind, in different generations, occupies\nitself with different things, and in one age is led by the circumstances\nwhich surround it to fix more of its attention upon one of the properties\nof a thing, in another age upon another; it is natural and inevitable that\nin every age a certain portion of our recorded and traditional knowledge,\nnot being continually suggested by the pursuits and inquiries with which\nmankind are at that time engrossed, should fall asleep, as it were, and\nfade from the memory. It would be in danger of being totally lost, if the\npropositions or formulas, the results of the previous experience, did not\nremain, as forms of words it may be, but of words that once really\nconveyed, and are still supposed to convey, a meaning: which meaning,\nthough suspended, may be historically traced, and when suggested, may be\nrecognized by minds of the necessary endowments as being still matter of\nfact, or truth. While the formulas remain, the meaning may at any time\nrevive; and as, on the one hand, the formulas progressively lose the\nmeaning they were intended to convey, so, on the other, when this\nforgetfulness has reached its height and begun to produce obvious\nconsequences, minds arise which from the contemplation of the formulas\nrediscover the truth, when truth it was, which was contained in them, and\nannounce it again to mankind, not as a discovery, but as the meaning of\nthat which they have been taught, and still profess to believe.\n\nThus there is a perpetual oscillation in spiritual truths, and in\nspiritual doctrines of any significance, even when not truths. Their\nmeaning is almost always in a process either of being lost or of being\nrecovered. Whoever has attended to the history of the more serious\nconvictions of mankind\u2014of the opinions by which the general conduct of\ntheir lives is, or as they conceive ought to be, more especially\nregulated\u2014is aware that even when recognizing verbally the same doctrines,\nthey attach to them at different periods a greater or a less quantity, and\neven a different kind of meaning. The words in their original acceptation\nconnoted, and the propositions expressed, a complication of outward facts\nand inward feelings, to different portions of which the general mind is\nmore particularly alive in different generations of mankind. To common\nminds, only that portion of the meaning is in each generation suggested,\nof which that generation possesses the counterpart in its own habitual\nexperience. But the words and propositions lie ready to suggest to any\nmind duly prepared the remainder of the meaning. Such individual minds are\nalmost always to be found; and the lost meaning, revived by them, again by\ndegrees works its way into the general mind.\n\nThe arrival of this salutary reaction may, however, be materially retarded\nby the shallow conceptions and incautious proceedings of mere logicians.\nIt sometimes happens that toward the close of the downward period, when\nthe words have lost part of their significance, and have not yet begun to\nrecover it, persons arise whose leading and favorite idea is the\nimportance of clear conceptions and precise thought, and the necessity,\ntherefore, of definite language. These persons, in examining the old\nformulas, easily perceive that words are used in them without a meaning;\nand if they are not the sort of persons who are capable of rediscovering\nthe lost signification, they naturally enough dismiss the formula, and\ndefine the name without reference to it. In so doing they fasten down the\nname to what it connotes in common use at the time when it conveys the\nsmallest quantity of meaning; and introduce the practice of employing it,\nconsistently and uniformly, according to that connotation. The word in\nthis way acquires an extent of denotation far beyond what it had before;\nit becomes extended to many things to which it was previously, in\nappearance capriciously, refused. Of the propositions in which it was\nformerly used, those which were true in virtue of the forgotten part of\nits meaning are now, by the clearer light which the definition diffuses,\nseen not to be true according to the definition; which, however, is the\nrecognized and sufficiently correct expression of all that is perceived to\nbe in the mind of any one by whom the term is used at the present day. The\nancient formulas are consequently treated as prejudices; and people are no\nlonger taught as before, though not to understand them, yet to believe\nthat there is truth in them. They no longer remain in the general mind\nsurrounded by respect, and ready at any time to suggest their original\nmeaning. Whatever truths they contain are not only, in these\ncircumstances, rediscovered far more slowly, but, when rediscovered, the\nprejudice with which novelties are regarded is now, in some degree at\nleast, against them, instead of being on their side.\n\nAn example may make these remarks more intelligible. In all ages, except\nwhere moral speculation has been silenced by outward compulsion, or where\nthe feelings which prompt to it still continue to be satisfied by the\ntraditional doctrines of an established faith, one of the subjects which\nhave most occupied the minds of thinking persons is the inquiry, What is\nvirtue? or, What is a virtuous character? Among the different theories on\nthe subject which have, at different times, grown up and obtained partial\ncurrency, every one of which reflected as in the clearest mirror the\nexpress image of the age which gave it birth; there was one, according to\nwhich virtue consists in a correct calculation of our own personal\ninterests, either in this world only, or also in another. To make this\ntheory plausible, it was of course necessary that the only beneficial\nactions which people in general were accustomed to see, or were therefore\naccustomed to praise, should be such as were, or at least might without\ncontradicting obvious facts be supposed to be, the result of a prudential\nregard to self-interest; so that the words really connoted no more, in\ncommon acceptation, than was set down in the definition.\n\nSuppose, now, that the partisans of this theory had contrived to introduce\na consistent and undeviating use of the term according to this definition.\nSuppose that they had seriously endeavored, and had succeeded in the\nendeavor, to banish the word disinterestedness from the language; had\nobtained the disuse of all expressions attaching odium to selfishness or\ncommendation to self-sacrifice, or which implied generosity or kindness to\nbe any thing but doing a benefit in order to receive a greater personal\nadvantage in return. Need we say that this abrogation of the old formulas\nfor the sake of preserving clear ideas and consistency of thought, would\nhave been a great evil? while the very inconsistency incurred by the\nco-existence of the formulas with philosophical opinions which seemed to\ncondemn them as absurdities, operated as a stimulus to the re-examination\nof the subject and thus the very doctrines originating in the oblivion\ninto which a part of the truth had fallen, were rendered indirectly, but\npowerfully, instrumental to its revival.\n\nThe doctrine of the Coleridge school, that the language of any people\namong whom culture is of old date, is a sacred deposit, the property of\nall ages, and which no one age should consider itself empowered to\nalter\u2014borders indeed, as thus expressed, on an extravagance; but it is\ngrounded on a truth, frequently overlooked by that class of logicians who\nthink more of having a clear than of having a comprehensive meaning; and\nwho perceive that every age is adding to the truths which it has received\nfrom its predecessors, but fail to see that a counter process of losing\ntruths already possessed, is also constantly going on, and requiring the\nmost sedulous attention to counteract it. Language is the depository of\nthe accumulated body of experience to which all former ages have\ncontributed their part, and which is the inheritance of all yet to come.\nWe have no right to prevent ourselves from transmitting to posterity a\nlarger portion of this inheritance than we may ourselves have profited by.\nHowever much we may be able to improve on the conclusions of our\nforefathers, we ought to be careful not inadvertently to let any of their\npremises slip through our fingers. It may be good to alter the meaning of\na word, but it is bad to let any part of the meaning drop. Whoever seeks\nto introduce a more correct use of a term with which important\nassociations are connected, should be required to possess an accurate\nacquaintance with the history of the particular word, and of the opinions\nwhich in different stages of its progress it served to express. To be\nqualified to define the name, we must know all that has ever been known of\nthe properties of the class of objects which are, or originally were,\ndenoted by it. For if we give it a meaning according to which any\nproposition will be false which has ever been generally held to be true,\nit is incumbent on us to be sure that we know and have considered all\nwhich those who believed the proposition understood by it.\n\n\n\n\n                                Chapter V.\n\n\nOn The Natural History Of The Variations In The Meaning Of Terms.\n\n\n\u00a7 1. It is not only in the mode which has now been pointed out, namely by\ngradual inattention to a portion of the ideas conveyed, that words in\ncommon use are liable to shift their connotation. The truth is, that the\nconnotation of such words is perpetually varying; as might be expected\nfrom the manner in which words in common use acquire their connotation. A\ntechnical term, invented for purposes of art or science, has, from the\nfirst, the connotation given to it by its inventor; but a name which is in\nevery one\u2019s mouth before any one thinks of defining it, derives its\nconnotation only from the circumstances which are habitually brought to\nmind when it is pronounced. Among these circumstances, the properties\ncommon to the things denoted by the name, have naturally a principal\nplace; and would have the sole place, if language were regulated by\nconvention rather than by custom and accident. But besides these common\nproperties, which if they exist are _certainly_ present whenever the name\nis employed, any other circumstance may _casually_ be found along with it,\nso frequently as to become associated with it in the same manner, and as\nstrongly, as the common properties themselves. In proportion as this\nassociation forms itself, people give up using the name in cases in which\nthose casual circumstances do not exist. They prefer using some other\nname, or the same name with some adjunct, rather than employ an expression\nwhich will call up an idea they do not want to excite. The circumstance\noriginally casual, thus becomes regularly a part of the connotation of the\nword.\n\nIt is this continual incorporation of circumstances originally accidental,\ninto the permanent signification of words, which is the cause that there\nare so few exact synonyms. It is this also which renders the dictionary\nmeaning of a word, by universal remark so imperfect an exponent of its\nreal meaning. The dictionary meaning is marked out in a broad, blunt way,\nand probably includes all that was originally necessary for the correct\nemployment of the term; but in process of time so many collateral\nassociations adhere to words, that whoever should attempt to use them with\nno other guide than the dictionary, would confound a thousand nice\ndistinctions and subtle shades of meaning which dictionaries take no\naccount of; as we notice in the use of a language in conversation or\nwriting by a foreigner not thoroughly master of it. The history of a word,\nby showing the causes which determine its use, is in these cases a better\nguide to its employment than any definition; for definitions can only show\nits meaning at the particular time, or at most the series of its\nsuccessive meanings, but its history may show the law by which the\nsuccession was produced. The word _gentleman_, for instance, to the\ncorrect employment of which a dictionary would be no guide, originally\nmeant simply a man born in a certain rank. From this it came by degrees to\nconnote all such qualities or adventitious circumstances as were usually\nfound to belong to persons of that rank. This consideration at once\nexplains why in one of its vulgar acceptations it means any one who lives\nwithout labor, in another without manual labor, and in its more elevated\nsignification it has in every age signified the conduct, character,\nhabits, and outward appearance, in whomsoever found, which, according to\nthe ideas of that age, belonged or were expected to belong to persons born\nand educated in a high social position.\n\nIt continually happens that of two words, whose dictionary meanings are\neither the same or very slightly different, one will be the proper word to\nuse in one set of circumstances, another in another, without its being\npossible to show how the custom of so employing them originally grew up.\nThe accident that one of the words was used and not the other on a\nparticular occasion or in a particular social circle, will be sufficient\nto produce so strong an association between the word and some specialty of\ncircumstances, that mankind abandon the use of it in any other case, and\nthe specialty becomes part of its signification. The tide of custom first\ndrifts the word on the shore of a particular meaning, then retires and\nleaves it there.\n\nAn instance in point is the remarkable change which, in the English\nlanguage at least, has taken place in the signification of the word\n_loyalty_. That word originally meant in English, as it still means in the\nlanguage from whence it came, fair, open dealing, and fidelity to\nengagements; in that sense the quality it expressed was part of the ideal\nchivalrous or knightly character. By what process, in England, the term\nbecame restricted to the single case of fidelity to the throne, I am not\nsufficiently versed in the history of courtly language to be able to\npronounce. The interval between a _loyal chevalier_ and a loyal subject is\ncertainly great. I can only suppose that the word was, at some period, the\nfavorite term at court to express fidelity to the oath of allegiance;\nuntil at length those who wished to speak of any other, and as it was\nprobably deemed, inferior sort of fidelity, either did not venture to use\nso dignified a term, or found it convenient to employ some other in order\nto avoid being misunderstood.\n\n\u00a7 2. Cases are not unfrequent in which a circumstance, at first casually\nincorporated into the connotation of a word which originally had no\nreference to it, in time wholly supersedes the original meaning, and\nbecomes not merely a part of the connotation, but the whole of it. This is\nexemplified in the word pagan, _paganus_; which originally, as its\netymology imports, was equivalent to _villager_; the inhabitant of a\n_pagus_, or village. At a particular era in the extension of Christianity\nover the Roman empire, the adherents of the old religion, and the\nvillagers or country people, were nearly the same body of individuals, the\ninhabitants of the towns having been earliest converted; as in our own\nday, and at all times, the greater activity of social intercourse renders\nthem the earliest recipients of new opinions and modes, while old habits\nand prejudices linger longest among the country people; not to mention\nthat the towns were more immediately under the direct influence of the\nGovernment, which at that time had embraced Christianity. From this casual\ncoincidence, the word _paganus_ carried with it, and began more and more\nsteadily to suggest, the idea of a worshiper of the ancient divinities;\nuntil at length it suggested that idea so forcibly that people who did not\ndesire to suggest the idea avoided using the word. But when _paganus_ had\ncome to connote heathenism, the very unimportant circumstance, with\nreference to that fact, of the place of residence, was soon disregarded in\nthe employment of the word. As there was seldom any occasion for making\nseparate assertions respecting heathens who lived in the country, there\nwas no need for a separate word to denote them; and pagan came not only to\nmean heathen, but to mean that exclusively.\n\nA case still more familiar to most readers is that of the word _villain_\nor _villein_. This term, as every body knows, had in the Middle Ages a\nconnotation as strictly defined as a word could have, being the proper\nlegal designation for those persons who were the subjects of the less\nonerous forms of feudal bondage. The scorn of the semi-barbarous military\naristocracy for these their abject dependants, rendered the act of\nlikening any person to this class of people a mark of the greatest\ncontumely; the same scorn led them to ascribe to the same people all\nmanner of hateful qualities, which doubtless also, in the degrading\nsituation in which they were held, were often not unjustly imputed to\nthem. These circumstances combined to attach to the term villain ideas of\ncrime and guilt, in so forcible a manner that the application of the\nepithet even to those to whom it legally belonged became an affront, and\nwas abstained from whenever no affront was intended. From that time guilt\nwas part of the connotation; and soon became the whole of it, since\nmankind were not prompted by any urgent motive to continue making a\ndistinction in their language between bad men of servile station and bad\nmen of any other rank in life.\n\nThese and similar instances in which the original signification of a term\nis totally lost\u2014another and an entirely distinct meaning being first\ningrafted upon the former, and finally substituted for it\u2014afford examples\nof the double movement which is always taking place in language: two\ncounter-movements, one of Generalization, by which words are perpetually\nlosing portions of their connotation, and becoming of less meaning and\nmore general acceptation; the other of Specialization, by which other, or\neven these same words, are continually taking on fresh connotation;\nacquiring additional meaning by being restricted in their employment to a\npart only of the occasions on which they might properly be used before.\nThis double movement is of sufficient importance in the natural history of\nlanguage (to which natural history the artificial modifications ought\nalways to have some degree of reference), to justify our dwelling a little\nlonger on the nature of the twofold phenomenon, and the causes to which it\nowes its existence.\n\n\u00a7 3. To begin with the movement of generalization. It might seem\nunnecessary to dwell on the changes in the meaning of names which take\nplace merely from their being used ignorantly, by persons who, not having\nproperly mastered the received connotation of a word, apply it in a looser\nand wider sense than belongs to it. This, however, is a real source of\nalterations in the language; for when a word, from being often employed in\ncases where one of the qualities which it connotes does not exist, ceases\nto suggest that quality with certainty, then even those who are under no\nmistake as to the proper meaning of the word, prefer expressing that\nmeaning in some other way, and leave the original word to its fate. The\nword \u2019Squire, as standing for an owner of a landed estate; Parson, as\ndenoting not the rector of the parish, but clergymen in general; Artist,\nto denote only a painter or sculptor; are cases in point. Such cases give\na clear insight into the process of the degeneration of languages in\nperiods of history when literary culture was suspended; and we are now in\ndanger of experiencing a similar evil through the superficial extension of\nthe same culture. So many persons without any thing deserving the name of\neducation have become writers by profession, that written language may\nalmost be said to be principally wielded by persons ignorant of the proper\nuse of the instrument, and who are spoiling it more and more for those who\nunderstand it. Vulgarisms, which creep in nobody knows how, are daily\ndepriving the English language of valuable modes of expressing thought. To\ntake a present instance: the verb _transpire_ formerly conveyed very\nexpressively its correct meaning, viz., to _become known_ through\nunnoticed channels\u2014to exhale, as it were, into publicity through invisible\npores, like a vapor or gas disengaging itself. But of late a practice has\ncommenced of employing this word, for the sake of finery, as a mere\nsynonym of _to happen_: \u201cthe events which have _transpired_ in the\nCrimea,\u201d meaning the incidents of the war. This vile specimen of bad\nEnglish is already seen in the dispatches of noblemen and viceroys; and\nthe time is apparently not far distant when nobody will understand the\nword if used in its proper sense. In other cases it is not the love of\nfinery, but simple want of education, which makes writers employ words in\nsenses unknown to genuine English. The use of \u201caggravating\u201d for\n\u201cprovoking,\u201d in my boyhood a vulgarism of the nursery, has crept into\nalmost all newspapers, and into many books; and when the word is used in\nits proper sense, as when writers on criminal law speak of aggravating and\nextenuating circumstances, their meaning, it is probable, is already\nmisunderstood. It is a great error to think that these corruptions of\nlanguage do no harm. Those who are struggling with the difficulty (and who\nknow by experience how great it already is) of expressing one\u2019s self\nclearly with precision, find their resources continually narrowed by\nilliterate writers, who seize and twist from its purpose some form of\nspeech which once served to convey briefly and compactly an unambiguous\nmeaning. It would hardly be believed how often a writer is compelled to a\ncircumlocution by the single vulgarism, introduced during the last few\nyears, of using the word _alone_ as an adverb, _only_ not being fine\nenough for the rhetoric of ambitious ignorance. A man will say \u201cto which I\nam not alone bound by honor but also by law,\u201d unaware that what he has\nunintentionally said is, that he is _not alone_ bound, some other person\nbeing bound with him. Formerly, if any one said, \u201cI am not alone\nresponsible for this,\u201d he was understood to mean (what alone his words\nmean in correct English), that he is not the sole person responsible; but\nif he now used such an expression, the reader would be confused between\nthat and two other meanings: that he is not _only responsible_ but\nsomething more; or that he is responsible _not only for this_ but for\nsomething besides. The time is coming when Tennyson\u2019s \u0152none could not say,\n\u201cI will not die alone,\u201d lest she should be supposed to mean that she would\nnot only die but do something else.\n\nThe blunder of writing _predicate_ for _predict_ has become so widely\ndiffused that it bids fair to render one of the most useful terms in the\nscientific vocabulary of Logic unintelligible. The mathematical and\nlogical term \u201cto eliminate\u201d is undergoing a similar destruction. All who\nare acquainted either with the proper use of the word or with its\netymology know that to eliminate a thing is to thrust it out: but those\nwho know nothing about it, except that it is a fine-looking phrase, use it\nin a sense precisely the reverse, to denote, not turning any thing out,\nbut bringing it in. They talk of _eliminating_ some truth, or other useful\nresult, from a mass of details.(220) A similar permanent deterioration in\nthe language is in danger of being produced by the blunders of\ntranslators. The writers of telegrams, and the foreign correspondents of\nnewspapers, have gone on so long translating _demander_ by \u201cto demand,\u201d\nwithout a suspicion that it means only to ask, that (the context generally\nshowing that nothing else is meant) English readers are gradually\nassociating the English word demand with simple asking, thus leaving the\nlanguage without a term to express a demand in its proper sense. In like\nmanner, \u201ctransaction,\u201d the French word for a compromise, is translated\ninto the English word transaction; while, curiously enough, the inverse\nchange is taking place in France, where the word \u201ccompromis\u201d has lately\nbegun to be used for expressing the same idea. If this continues, the two\ncountries will have exchanged phrases.\n\nIndependently, however, of the generalization of names through their\nignorant misuse, there is a tendency in the same direction consistently\nwith a perfect knowledge of their meaning; arising from the fact, that the\nnumber of things known to us, and of which we feel a desire to speak,\nmultiply faster than the names for them. Except on subjects for which\nthere has been constructed a scientific terminology, with which\nunscientific persons do not meddle, great difficulty is generally found in\nbringing a new name into use; and independently of that difficulty, it is\nnatural to prefer giving to a new object a name which at least expresses\nits resemblance to something already known, since by predicating of it a\nname entirely new we at first convey no information. In this manner the\nname of a species often becomes the name of a genus; as _salt_, for\nexample, or _oil_; the former of which words originally denoted only the\nmuriate of soda, the latter, as its etymology indicates, only olive-oil;\nbut which now denote large and diversified classes of substances\nresembling these in some of their qualities, and connote only those common\nqualities, instead of the whole of the distinctive properties of olive-oil\nand sea-salt. The words _glass_ and _soap_ are used by modern chemists in\na similar manner, to denote genera of which the substances vulgarly so\ncalled are single species. And it often happens, as in those instances,\nthat the term keeps its special signification in addition to its more\ngeneral one, and becomes ambiguous, that is, two names instead of one.\n\nThese changes, by which words in ordinary use become more and more\ngeneralized, and less and less expressive, take place in a still greater\ndegree with the words which express the complicated phenomena of mind and\nsociety. Historians, travelers, and in general those who speak or write\nconcerning moral and social phenomena with which they are not familiarly\nacquainted, are the great agents in this modification of language. The\nvocabulary of all except unusually instructed as well as thinking persons,\nis, on such subjects, eminently scanty. They have a certain small set of\nwords to which they are accustomed, and which they employ to express\nphenomena the most heterogeneous, because they have never sufficiently\nanalyzed the facts to which those words correspond in their own country,\nto have attached perfectly definite ideas to the words. The first English\nconquerors of Bengal, for example, carried with them the phrase _landed\nproprietor_ into a country where the rights of individuals over the soil\nwere extremely different in degree, and even in nature, from those\nrecognized in England. Applying the term with all its English associations\nin such a state of things; to one who had only a limited right they gave\nan absolute right, from another because he had not an absolute right they\ntook away all right, drove whole classes of people to ruin and despair,\nfilled the country with banditti, created a feeling that nothing was\nsecure, and produced, with the best intentions, a disorganization of\nsociety which had not been produced in that country by the most ruthless\nof its barbarian invaders. Yet the usage of persons capable of so gross a\nmisapprehension determines the meaning of language; and the words they\nthus misuse grow in generality, until the instructed are obliged to\nacquiesce; and to employ those words (first freeing them from vagueness by\ngiving them a definite connotation) as generic terms, subdividing the\ngenera into species.\n\n\u00a7 4. While the more rapid growth of ideas than of names thus creates a\nperpetual necessity for making the same names serve, even if imperfectly,\non a greater number of occasions; a counter-operation is going on, by\nwhich names become on the contrary restricted to fewer occasions, by\ntaking on, as it were, additional connotation, from circumstances not\noriginally included in the meaning, but which have become connected with\nit in the mind by some accidental cause. We have seen above, in the words\n_pagan_ and _villain_, remarkable examples of the specialization of the\nmeaning of words from casual associations, as well as of the\ngeneralization of it in a new direction, which often follows.\n\nSimilar specializations are of frequent occurrence in the history even of\nscientific nomenclature. \u201cIt is by no means uncommon,\u201d says Dr. Paris, in\nhis _Pharmacologia_,(221) \u201cto find a word which is used to express general\ncharacters subsequently become the name of a specific substance in which\nsuch characters are predominant; and we shall find that some important\nanomalies in nomenclature may be thus explained. The term \u0391\u03c1\u03c3\u03b5\u03bd\u03af\u03ba\u03bf\u03bd, from\nwhich the word Arsenic is derived, was an ancient epithet applied to those\nnatural substances which possessed strong and acrimonious properties; and\nas the poisonous quality of arsenic was found to be remarkably powerful,\nthe term was especially applied to Orpiment, the form in which this metal\nmost usually occurred. So the term _Verbena_ (quasi _Herbena_) originally\ndenoted all those herbs that were held sacred on account of their being\nemployed in the rites of sacrifice, as we learn from the poets; but as\n_one_ herb was usually adopted upon these occasions, the word Verbena came\nto denote that particular herb _only_, and it is transmitted to us to this\nday under the same title, viz., Verbena or Vervain, and indeed until\nlately it enjoyed the medical reputation which its sacred origin conferred\nupon it, for it was worn suspended around the neck as an amulet.\n_Vitriol_, in the original application of the word, denoted _any_\ncrystalline body with a certain degree of transparency (_vitrum_); it is\nhardly necessary to observe that the term is now appropriated to a\nparticular species: in the same manner, Bark, which is a general term, is\napplied to express _one_ genus, and by way of eminence it has the article\n_The_ prefixed, as _The_ bark; the same observation will apply to the word\nOpium, which, in its primitive sense, signifies _any_ juice (\u1f40\u03c0\u1f78\u03c2,\n_Succus_), while it now only denotes _one_ species, viz., that of the\npoppy. So, again, _Elaterium_ was used by Hippocrates to signify various\ninternal applications, especially purgatives, of a violent and drastic\nnature (from the word \u1f10\u03bb\u03b1\u03cd\u03bd\u03c9, _agito_, _moveo_, _stimulo_), but by\nsucceeding authors it was exclusively applied to denote the active matter\nwhich subsides from the juice of the wild cucumber. The word _Fecula_,\nagain, originally meant to imply _any_ substance which was derived by\nspontaneous subsidence from a liquid (from _f\u00e6x_, the grounds or\nsettlement of _any_ liquor); afterward it was applied to Starch, which is\ndeposited in this manner by agitating the flour of wheat in water; and,\nlastly, it has been applied to a peculiar vegetable principle, which, like\nstarch, is insoluble in cold, but completely soluble in boiling water,\nwith which it forms a gelatinous solution. This indefinite meaning of the\nword _fecula_ has created numerous mistakes in pharmaceutic chemistry;\nElaterium, for instance, is said to be _fecula_, and, in the original\nsense of the word, it is properly so called, inasmuch as it is procured\nfrom a vegetable juice by spontaneous subsidence, but in the limited and\nmodern acceptation of the term it conveys an erroneous idea; for instead\nof the active principle of the juice residing in _fecula_, it is a\npeculiar proximate principle, _sui generis_, to which I have ventured to\nbestow the name of _Elatin_. For the same reason, much doubt and obscurity\ninvolve the meaning of the word _Extract_, because it is applied\n_generally_ to any substance obtained by the evaporation of a vegetable\nsolution, and _specifically_ to a peculiar proximate principle, possessed\nof certain characters, by which it is distinguished from every other\nelementary body.\u201d\n\nA generic term is always liable to become thus limited to a single\nspecies, or even individual, if people have occasion to think and speak of\nthat individual or species much oftener than of any thing else which is\ncontained in the genus. Thus by cattle, a stage-coachman will understand\nhorses; beasts, in the language of agriculturists, stands for oxen; and\nbirds, with some sportsmen, for partridges only. The law of language which\noperates in these trivial instances is the very same in conformity to\nwhich the terms \u0398\u03b5\u03cc\u03c2, Deus, and God, were adopted from Polytheism by\nChristianity, to express the single object of its own adoration. Almost\nall the terminology of the Christian Church is made up of words originally\nused in a much more general acceptation: _Ecclesia_, Assembly; _Bishop_,\nEpiscopus, Overseer; _Priest_, Presbyter, Elder; _Deacon_, Diaconus,\nAdministrator; _Sacrament_, a vow of allegiance; _Evangelium_, good\ntidings; and some words, as _Minister_, are still used both in the general\nand in the limited sense. It would be interesting to trace the progress by\nwhich _author_ came, in its most familiar sense, to signify a writer, and\n\u03c0\u03bf\u03af\u03b7\u03c4\u03b7\u03c2, or maker, a poet.\n\nOf the incorporation into the meaning of a term, of circumstances\naccidentally connected with it at some particular period, as in the case\nof Pagan, instances might easily be multiplied. Physician (\u03c6\u03c5\u03c3\u03af\u03ba\u03bf\u03c2, or\nnaturalist) became, in England, synonymous with a healer of diseases,\nbecause until a comparatively late period medical practitioners were the\nonly naturalists. _Clerc_, or clericus, a scholar, came to signify an\necclesiastic, because the clergy were for many centuries the only\nscholars.\n\nOf all ideas, however, the most liable to cling by association to any\nthing with which they have ever been connected by proximity, are those of\nour pleasures and pains, or of the things which we habitually contemplate\nas sources of our pleasures or pains. The additional connotation,\ntherefore, which a word soonest and most readily takes on, is that of\nagreeableness or painfulness, in their various kinds and degrees; of being\na good or bad thing; desirable or to be avoided; an object of hatred, of\ndread, contempt, admiration, hope, or love. Accordingly there is hardly a\nsingle name, expressive of any moral or social fact calculated to call\nforth strong affections either of a favorable or of a hostile nature,\nwhich does not carry with it decidedly and irresistibly a connotation of\nthose strong affections, or, at the least, of approbation or censure;\ninsomuch that to employ those names in conjunction with others by which\nthe contrary sentiments were expressed, would produce the effect of a\nparadox, or even a contradiction in terms. The baneful influence of a\nconnotation thus acquired, on the prevailing habits of thought, especially\nin morals and politics, has been well pointed out on many occasions by\nBentham. It gives rise to the fallacy of \u201cquestion-begging names.\u201d The\nvery property which we are inquiring whether a thing possesses or not, has\nbecome so associated with the name of the thing as to be part of its\nmeaning, insomuch that by merely uttering the name we assume the point\nwhich was to be made out; one of the most frequent sources of apparently\nself-evident propositions.\n\nWithout any further multiplication of examples to illustrate the changes\nwhich usage is continually making in the signification of terms, I shall\nadd, as a practical rule, that the logician, not being able to prevent\nsuch transformations, should submit to them with a good grace when they\nare irrevocably effected, and if a definition is necessary, define the\nword according to its new meaning; retaining the former as a second\nsignification, if it is needed, and if there is any chance of being able\nto preserve it either in the language of philosophy or in common use.\nLogicians can not _make_ the meaning of any but scientific terms; that of\nall other words is made by the collective human race. But logicians can\nascertain clearly what it is which, working obscurely, has guided the\ngeneral mind to a particular employment of a name; and when they have\nfound this, they can clothe it in such distinct and permanent terms, that\nmankind shall see the meaning which before they only felt, and shall not\nsuffer it to be afterward forgotten or misapprehended.\n\n\n\n\n                               Chapter VI.\n\n\nThe Principles Of A Philosophical Language Further Considered.\n\n\n\u00a7 1. We have, thus far, considered only one of the requisites of a\nlanguage adapted for the investigation of truth; that its terms shall each\nof them convey a determinate and unmistakable meaning. There are, however,\nas we have already remarked, other requisites; some of them important only\nin the second degree, but one which is fundamental, and barely yields in\npoint of importance, if it yields at all, to the quality which we have\nalready discussed at so much length. That the language may be fitted for\nits purposes, not only should every word perfectly express its meaning,\nbut there should be no important meaning without its word. Whatever we\nhave occasion to think of often, and for scientific purposes, ought to\nhave a name appropriated to it.\n\nThis requisite of philosophical language may be considered under three\ndifferent heads; that number of separate conditions being involved in it.\n\n\u00a7 2. First, there ought to be all such names, as are needful for making\nsuch a record of individual observations that the words of the record\nshall exactly show what fact it is which has been observed. In other\nwords, there should be an accurate Descriptive Terminology.\n\nThe only things which we can observe directly being our own sensations, or\nother feelings, a complete descriptive language would be one in which\nthere should be a name for every variety of elementary sensation or\nfeeling. Combinations of sensations or feelings may always be described,\nif we have a name for each of the elementary feelings which compose them;\nbut brevity of description, and clearness (which often depends very much\non brevity), are greatly promoted by giving distinctive names not to the\nelements alone, but also to all combinations which are of frequent\nrecurrence. On this occasion I can not do better than quote from Dr.\nWhewell(222) some of the excellent remarks which he has made on this\nimportant branch of our subject.\n\n\u201cThe meaning of [descriptive] technical terms can be fixed in the first\ninstance only by convention, and can be made intelligible only by\npresenting to the senses that which the terms are to signify. The\nknowledge of a color by its name can only be taught through the eye. No\ndescription can convey to a hearer what we mean by _apple-green_ or\n_French gray_. It might, perhaps, be supposed that, in the first example,\nthe term _apple_, referring to so familiar an object, sufficiently\nsuggests the color intended. But it may easily be seen that this is not\ntrue; for apples are of many different hues of green, and it is only by a\nconventional selection that we can appropriate the term to one special\nshade. When this appropriation is once made, the term refers to the\nsensation, and not to the parts of the term; for these enter into the\ncompound merely as a help to the memory, whether the suggestion be a\nnatural connection as in \u2018apple-green,\u2019 or a casual one as in \u2018French\ngray.\u2019 In order to derive due advantage from technical terms of the kind,\nthey must be associated _immediately_ with the perception to which they\nbelong; and not connected with it through the vague usages of common\nlanguage. The memory must retain the sensation; and the technical word\nmust be understood as directly as the most familiar word, and more\ndistinctly. When we find such terms as _tin-white_ or _pinchbeck-brown_,\nthe metallic color so denoted ought to start up in our memory without\ndelay or search.\n\n\u201cThis, which it is most important to recollect with respect to the simpler\nproperties of bodies, as color and form, is no less true with respect to\nmore compound notions. In all cases the term is fixed to a peculiar\nmeaning by convention; and the student, in order to use the word, must be\ncompletely familiar with the convention, so that he has no need to frame\nconjectures from the word itself. Such conjectures would always be\ninsecure, and often erroneous. Thus the term _papilionaceous_ applied to a\nflower is employed to indicate, not only a resemblance to a butterfly, but\na resemblance arising from five petals of a certain-peculiar shape and\narrangement; and even if the resemblance were much stronger than it is in\nsuch cases, yet, if it were produced in a different way, as, for example,\nby one petal, or two only, instead of a \u2018standard,\u2019 two \u2018wings,\u2019 and a\n\u2018keel\u2019 consisting of two parts more or less united into one, we should be\nno longer justified in speaking of it as a \u2018papilionaceous\u2019 flower.\u201d\n\nWhen, however, the thing named is, as in this last case, a combination of\nsimple sensations, it is not necessary, in order to learn the meaning of\nthe word, that the student should refer back to the sensations themselves;\nit may be communicated to him through the medium of other words; the\nterms, in short, may be defined. But the names of elementary sensations,\nor elementary feelings of any sort, can not be defined; nor is there any\nmode of making their signification known but by making the learner\nexperience the sensation, or referring him, through some known mark, to\nhis remembrance of having experienced it before. Hence it is only the\nimpressions on the outward senses, or those inward feelings which are\nconnected in a very obvious and uniform manner with outward objects, that\nare really susceptible of an exact descriptive language. The countless\nvariety of sensations which arise, for instance, from disease, or from\npeculiar physiological states, it would be in vain to attempt to name; for\nas no one can judge whether the sensation I have is the same with his, the\nname can not have, to us two, real community of meaning. The same may be\nsaid, to a considerable extent, of purely mental feelings. But in some of\nthe sciences which are conversant with external objects, it is scarcely\npossible to surpass the perfection to which this quality of a\nphilosophical language has been carried.\n\n\u201cThe formation(223) of an exact and extensive descriptive language for\nbotany has been executed with a degree of skill and felicity, which,\nbefore it was attained, could hardly have been dreamed of as attainable.\nEvery part of a plant has been named; and the form of every part, even the\nmost minute, has had a large assemblage of descriptive terms appropriated\nto it, by means of which the botanist can convey and receive knowledge of\nform and structure, as exactly as if each minute part were presented to\nhim vastly magnified. This acquisition was part of the Linn\u00e6an reform....\n\u2018Tournefort,\u2019 says Decandolle, \u2018appears to have been the first who really\nperceived the utility of fixing the sense of terms in such a way as always\nto employ the same word in the same sense, and always to express the same\nidea by the same words; but it was Linn\u00e6us who really created and fixed\nthis botanical language, and this is his fairest claim to glory, for by\nthis fixation of language he has shed clearness and precision over all\nparts of the science.\u2019\n\n\u201cIt is not necessary here to give any detailed account of the terms of\nbotany. The fundamental ones have been gradually introduced, as the parts\nof plants were more carefully and minutely examined. Thus the flower was\nnecessarily distinguished into the _calyx_, the _corolla_, the _stamens_,\nand the _pistils_; the sections of the corolla were termed _petals_ by\nColumna; those of the calyx were called _sepals_ by Necker. Sometimes\nterms of greater generality were devised; as _perianth_, to include the\ncalyx and corolla, whether one or both of these were present; _pericarp_,\nfor the part inclosing the grain, of whatever kind it be, fruit, nut, pod,\netc. And it may easily be imagined, that descriptive terms may, by\ndefinition and combination, become very numerous and distinct. Thus leaves\nmay be called _pinnatifid_, _pinnatipartite_, _pinnatisect_,\n_pinnatilobate_, _palmatifid_, _palmatipartite_, etc., and each of these\nwords designates different combinations of the modes and extent of the\ndivisions of the leaf with the divisions of its outline. In some cases,\narbitrary numerical relations are introduced into the definition: thus, a\nleaf is called _bilobate_, when it is divided into two parts by a notch;\nbut if the notch go to the middle of its length, it is _bifid_; if it go\nnear the base of the leaf, it is _bipartite_; if to the base, it is\n_bisect_. Thus, too, a pod of a cruciferous plant is a _siliqua_, if it is\nfour times as long as it is broad, but if it be shorter than this it is a\n_silicula_. Such terms being established, the form of the very complex\nleaf or frond of a fern (Hymenophyllum Wilsoni) is exactly conveyed by the\nfollowing phrase: \u2018fronds rigid pinnate, pinn\u00e6 recurved subunilateral,\npinnatifid, the segments linear undivided or bifid, spinuloso-serrate.\u2019\n\n\u201cOther characters, as well as form, are conveyed with the like precision:\nColor by means of a classified scale of colors.... This was done with most\nprecision by Werner, and his scale of colors is still the most usual\nstandard of naturalists. Werner also introduced a more exact terminology\nwith regard to other characters which are important in mineralogy, as\nlustre, hardness. But Mohs improved upon this step by giving a numerical\nscale of hardness, in which talc is 1, gypsum 2, calc spar 3, and so\non.... Some properties, as specific gravity, by their definition give at\nonce a numerical measure; and others, as crystalline form, require a very\nconsiderable array of mathematical calculation and reasoning, to point out\ntheir relations and gradations.\u201d\n\n\u00a7 3. Thus far of Descriptive Terminology, or of the language requisite for\nplacing on record our observation of individual instances. But when we\nproceed from this to Induction, or rather to that comparison of observed\ninstances which is the preparatory step toward it, we stand in need of an\nadditional and a different sort of general names.\n\nWhenever, for purposes of Induction, we find it necessary to introduce (in\nDr. Whewell\u2019s phraseology) some new general conception; that is, whenever\nthe comparison of a set of phenomena leads to the recognition in them of\nsome common circumstance, which, our attention not having been directed to\nit on any former occasion, is to us a new phenomenon; it is of importance\nthat this new conception, or this new result of abstraction, should have a\nname appropriated to it; especially if the circumstance it involves be one\nwhich leads to many consequences, or which is likely to be found also in\nother classes of phenomena. No doubt, in most cases of the kind, the\nmeaning might be conveyed by joining together several words already in\nuse. But when a thing has to be often spoken of, there are more reasons\nthan the saving of time and space, for speaking of it in the most concise\nmanner possible. What darkness would be spread over geometrical\ndemonstrations, if wherever the word _circle_ is used, the definition of a\ncircle were inserted instead of it. In mathematics and its applications,\nwhere the nature of the processes demands that the attention should be\nstrongly concentrated, but does not require that it should be widely\ndiffused, the importance of concentration also in the expressions has\nalways been duly felt; and a mathematician no sooner finds that he shall\noften have occasion to speak of the same two things together, than he at\nonce creates a term to express them whenever combined: just as, in his\nalgebraical operations, he substitutes for (_a_m + _b_n) p/q, or for\n_a_/_b_ + _b_/_c_ + _c_/_d_ + etc., the single letter P, Q, or S; not\nsolely to shorten his symbolical expressions, but to simplify the purely\nintellectual part of his operations, by enabling the mind to give its\nexclusive attention to the relation between the quantity S and the other\nquantities which enter into the equation, without being distracted by\nthinking unnecessarily of the parts of which S is itself composed.\n\nBut there is another reason, in addition to that of promoting perspicuity,\nfor giving a brief and compact name to each of the more considerable\nresults of abstraction which are obtained in the course of our\nintellectual phenomena. By naming them, we fix our attention upon them; we\nkeep them more constantly before the mind. The names are remembered, and\nbeing remembered, suggest their definition; while if instead of specific\nand characteristic names, the meaning had been expressed by putting\ntogether a number of other names, that particular combination of words\nalready in common use for other purposes would have had nothing to make\nitself remembered by. If we want to render a particular combination of\nideas permanent in the mind, there is nothing which clinches it like a\nname specially devoted to express it. If mathematicians had been obliged\nto speak of \u201cthat to which a quantity, in increasing or diminishing, is\nalways approaching nearer, so that the difference becomes less than any\nassignable quantity, but to which it never becomes exactly equal,\u201d instead\nof expressing all this by the simple phrase, \u201cthe limit of a quantity,\u201d we\nshould probably have long remained without most of the important truths\nwhich have been discovered by means of the relation between quantities of\nvarious kinds and their limits. If instead of speaking of _momentum_, it\nhad been necessary to say, \u201cthe product of the number of units of velocity\nin the velocity by the number of units of mass in the mass,\u201d many of the\ndynamical truths now apprehended by means of this complex idea would\nprobably have escaped notice, for want of recalling the idea itself with\nsufficient readiness and familiarity. And on subjects less remote from the\ntopics of popular discussion, whoever wishes to draw attention to some new\nor unfamiliar distinction among things, will find no way so sure as to\ninvent or select suitable names for the express purpose of marking it.\n\nA volume devoted to explaining what the writer means by civilization, does\nnot raise so vivid a conception of it as the single expression, that\nCivilization is a different thing from Cultivation; the compactness of\nthat brief designation for the contrasted quality being an equivalent for\na long discussion. So, if we would impress forcibly upon the understanding\nand memory the distinction between the two different conceptions of a\nrepresentative government, we can not more effectually do so than by\nsaying that Delegation is not Representation. Hardly any original thoughts\non mental or social subjects ever make their way among mankind, or assume\ntheir proper importance in the minds even of their inventors, until\naptly-selected words or phrases have, as it were, nailed them down and\nheld them fast.\n\n\u00a7 4. Of the three essential parts of a philosophical language, we have now\nmentioned two: a terminology suited for describing with precision the\nindividual facts observed; and a name for every common property of any\nimportance or interest, which we detect by comparing those facts;\nincluding (as the concretes corresponding to those abstract terms) names\nfor the classes which we artificially construct in virtue of those\nproperties, or as many of them, at least, as we have frequent occasion to\npredicate any thing of.\n\nBut there is a sort of classes, for the recognition of which no such\nelaborate process is necessary; because each of them is marked out from\nall others not by some one property, the detection of which may depend on\na difficult act of abstraction, but by its properties generally. I mean,\nthe Kinds of things, in the sense which, in this treatise, has been\nspecially attached to that term. By a Kind, it will be remembered, we mean\none of those classes which are distinguished from all others not by one or\na few definite properties, but by an unknown multitude of them; the\ncombination of properties on which the class is grounded, being a mere\nindex to an indefinite number of other distinctive attributes. The class\nhorse is a Kind, because the things which agree in possessing the\ncharacters by which we recognize a horse, agree in a great number of other\nproperties, as we know, and, it can not be doubted, in many more than we\nknow. Animal, again, is a Kind, because no definition that could be given\nof the name animal could either exhaust the properties common to all\nanimals, or supply premises from which the remainder of those properties\ncould be inferred. But a combination of properties which does not give\nevidence of the existence of any other independent peculiarities, does not\nconstitute a Kind. White horse, therefore, is not a Kind; because horses\nwhich agree in whiteness, do not agree in any thing else, except the\nqualities common to all horses, and whatever may be the causes or effects\nof that particular color.\n\nOn the principle that there should be a name for every thing which we have\nfrequent occasion to make assertions about, there ought evidently to be a\nname for every Kind; for as it is the very meaning of a Kind that the\nindividuals composing it have an indefinite multitude of properties in\ncommon, it follows that, if not with our present knowledge, yet with that\nwhich we may hereafter acquire, the Kind is a subject to which there will\nhave to be applied many predicates. The third component element of a\nphilosophical language, therefore, is that there shall be a name for every\nKind. In other words, there must not only be a terminology, but also a\nnomenclature.\n\nThe words Nomenclature and Terminology are employed by most authors almost\nindiscriminately; Dr. Whewell being, as far as I am aware, the first\nwriter who has regularly assigned to the two words different meanings. The\ndistinction, however, which he has drawn between them being real and\nimportant, his example is likely to be followed; and (as is apt to be the\ncase when such innovations in language are felicitously made) a vague\nsense of the distinction is found to have influenced the employment of the\nterms in common practice, before the expediency had been pointed out of\ndiscriminating them philosophically. Every one would say that the reform\neffected by Lavoisier and Guyton-Morveau in the language of chemistry\nconsisted in the introduction of a new nomenclature, not of a new\nterminology. Linear, lanceolate, oval, or oblong, serrated, dentate, or\ncrenate leaves, are expressions forming part of the terminology of botany,\nwhile the names \u201cViola odorata,\u201d and \u201cUlex Europ\u00e6us,\u201d belong to its\nnomenclature.\n\nA nomenclature may be defined, the collection of the names of all the\nKinds with which any branch of knowledge is conversant; or more properly,\nof all the lowest Kinds, or _infirm\u00e6 species_\u2014those which may be\nsubdivided indeed, but not into Kinds, and which generally accord with\nwhat in natural history are termed simply species. Science possesses two\nsplendid examples of a systematic nomenclature; that of plants and\nanimals, constructed by Linn\u00e6us and his successors, and that of chemistry,\nwhich we owe to the illustrious group of chemists who flourished in France\ntoward the close of the eighteenth century. In these two departments, not\nonly has every known species, or lowest Kind, a name assigned to it, but\nwhen new lowest Kinds are discovered, names are at once given to them on a\nuniform principle. In other sciences the nomenclature is not at present\nconstructed on any system, either because the species to be named are not\nnumerous enough to require one (as in geometry, for example), or because\nno one has yet suggested a suitable principle for such a system, as in\nmineralogy; in which the want of a scientifically constructed nomenclature\nis now the principal cause which retards the progress of the science.\n\n\u00a7 5. A word which carries on its face that it belongs to a nomenclature,\nseems at first sight to differ from other concrete general names in\nthis\u2014that its meaning does not reside in its connotation, in the\nattributes implied in it, but in its denotation, that is, in the\nparticular group of things which it is appointed to designate; and can\nnot, therefore, be unfolded by means of a definition, but must be made\nknown in another way. This opinion, however, appears to me erroneous.\nWords belonging to a nomenclature differ, I conceive, from other words\nmainly in this, that besides the ordinary connotation, they have a\npeculiar one of their own: besides connoting certain attributes, they also\nconnote that those attributes are distinctive of a Kind. The term\n\u201cperoxide of iron,\u201d for example, belonging by its form to the systematic\nnomenclature of chemistry, bears on its face that it is the name of a\npeculiar Kind of substance. It moreover connotes, like the name of any\nother class, some portion of the properties common to the class; in this\ninstance the property of being a compound of iron and the largest dose of\noxygen with which iron will combine. These two things, the fact of being\nsuch a compound, and the fact of being a Kind, constitute the connotation\nof the name peroxide of iron. When we say of the substance before us, that\nit is the peroxide of iron, we thereby assert, first, that it is a\ncompound of iron and a maximum of oxygen, and next, that the substance so\ncomposed is a peculiar Kind of substance.\n\nNow, this second part of the connotation of any word belonging to a\nnomenclature is as essential a portion of its meaning as the first part,\nwhile the definition only declares the first; and hence the appearance\nthat the signification of such terms can not be conveyed by a definition:\nwhich appearance, however, is fallacious. The name Viola odorata denotes a\nKind, of which a certain number of characters, sufficient to distinguish\nit, are enunciated in botanical works. This enumeration of characters is\nsurely, as in other cases, a definition of the name. No, say some, it is\nnot a definition, for the name Viola odorata does not mean those\ncharacters; it means that particular group of plants, and the characters\nare selected from among a much greater number, merely as marks by which to\nrecognize the group. But to this I reply, that the name does not mean that\ngroup, for it would be applied to that group no longer than while the\ngroup is believed to be an _infima species_; if it were to be discovered\nthat several distinct Kinds have been confounded under this one name, no\none would any longer apply the name Viola odorata to the whole of the\ngroup, but would apply it, if retained at all, to one only of the Kinds\nretained therein. What is imperative, therefore, is not that the name\nshall denote one particular collection of objects, but that it shall\ndenote a Kind, and a lowest Kind. The form of the name declares that,\nhappen what will, it is to denote an _infima species_; and that,\ntherefore, the properties which it connotes, and which are expressed in\nthe definition, are to be connoted by it no longer than while we continue\nto believe that those properties, when found together, indicate a Kind,\nand that the whole of them are found in no more than one Kind.\n\nWith the addition of this peculiar connotation, implied in the form of\nevery word which belongs to a systematic nomenclature; the set of\ncharacters which is employed to discriminate each Kind from all other\nKinds (and which is a real definition) constitutes as completely as in any\nother case the whole meaning of the term. It is no objection to say that\n(as is often the case in natural history) the set of characters may be\nchanged, and another substituted as being better suited for the purpose of\ndistinction, while the word, still continuing to denote the same group or\nthings, is not considered to have changed its meaning. For this is no more\nthan may happen in the case of any other general name: we may, in\nreforming its connotation, leave its denotation untouched; and it is\ngenerally desirable to do so. The connotation, however, is not the less\nfor this the real meaning, for we at once apply the name wherever the\ncharacters set down in the definition are found; and that which\nexclusively guides us in applying the term, must constitute its\nsignification. If we find, contrary to our previous belief, that the\ncharacters are not peculiar to one species, we cease to use the term\nco-extensively with the characters; but then it is because the other\nportion of the connotation fails; the condition that the class must be a\nKind. The connotation, therefore, is still the meaning; the set of\ndescriptive characters is a true definition; and the meaning is unfolded,\nnot indeed (as in other cases) by the definition alone, but by the\ndefinition and the form of the word taken together.\n\n\u00a7 6. We have now analyzed what is implied in the two principal requisites\nof a philosophical language; first, precision, or definiteness; and,\nsecondly, completeness. Any further remarks on the mode of constructing a\nnomenclature must be deferred until we treat of Classification; the mode\nof naming the Kinds of things being necessarily subordinate to the mode of\narranging those Kinds into larger classes. With respect to the minor\nrequisites of terminology, some of them are well stated and illustrated in\nthe \u201cAphorisms concerning the Language of Science,\u201d included in Dr.\nWhewell\u2019s _Philosophy of the Inductive Sciences_. These, as being of\nsecondary importance in the peculiar point of view of Logic, I shall not\nfurther refer to, but shall confine my observations to one more quality,\nwhich, next to the two already treated of, appears to be the most valuable\nwhich the language of science can possess. Of this quality a general\nnotion may be conveyed by the following aphorism:\n\nWhenever the nature of the subject permits our reasoning processes to be,\nwithout danger, carried on mechanically, the language should be\nconstructed on as mechanical principles as possible; while, in the\ncontrary case, it should be so constructed that there shall be the\ngreatest possible obstacles to a merely mechanical use of it.\n\nI am aware that this maxim requires much explanation, which I shall at\nonce proceed to give. At first, as to what is meant by using a language\nmechanically. The complete or extreme case of the mechanical use of\nlanguage, is when it is used without any consciousness of a meaning, and\nwith only the consciousness of using certain visible or audible marks in\nconformity to technical rules previously laid down. This extreme case is\nnowhere realized except in the figures of arithmetic, and still more the\nsymbols of algebra, a language unique in its kind, and approaching as\nnearly to perfection, for the purposes to which it is destined, as can,\nperhaps, be said of any creation of the human mind. Its perfection\nconsists in the completeness of its adaptation to a purely mechanical use.\nThe symbols are mere counters, without even the semblance of a meaning\napart from the convention which is renewed each time they are employed,\nand which is altered at each renewal, the same symbol _a_ or _x_ being\nused on different occasions to represent things which (except that, like\nall things, they are susceptible of being numbered) have no property in\ncommon. There is nothing, therefore, to distract the mind from the set of\nmechanical operations which are to be performed upon the symbols, such as\nsquaring both sides of the equation, multiplying or dividing them by the\nsame or by equivalent symbols, and so forth. Each of these operations, it\nis true, corresponds to a syllogism; represents one step of a\nratiocination relating not to the symbols, but to the things signified by\nthem. But as it has been found practicable to frame a technical form, by\nconforming to which we can make sure of finding the conclusion of the\nratiocination, our end can be completely attained without our ever\nthinking of any thing but the symbols. Being thus intended to work merely\nas mechanism, they have the qualities which mechanism ought to have. They\nare of the least possible bulk, so that they take up scarcely any room,\nand waste no time in their manipulation; they are compact, and fit so\nclosely together that the eye can take in the whole at once of almost\nevery operation which they are employed to perform.\n\nThese admirable properties of the symbolical language of mathematics have\nmade so strong an impression on the minds of many thinkers, as to have led\nthem to consider the symbolical language in question as the ideal type of\nphilosophical language generally; to think that names in general, or (as\nthey are fond of calling them) signs, are fitted for the purposes of\nthought in proportion as they can be made to approximate to the\ncompactness, the entire unmeaningness, and the capability of being used as\ncounters without a thought of what they represent, which are\ncharacteristic of the _a_ and _b_, the _x_ and _y_, of algebra. This\nnotion has led to sanguine views of the acceleration of the progress of\nscience by means which, I conceive, can not possibly conduce to that end,\nand forms part of that exaggerated estimate of the influence of signs,\nwhich has contributed in no small degree to prevent the real laws of our\nintellectual operations from being rightly understood.\n\nIn the first place, a set of signs by which we reason without\nconsciousness of their meaning, can be serviceable, at most, only in our\ndeductive operations. In our direct inductions we can not for a moment\ndispense with a distinct mental image of the phenomena, since the whole\noperation turns on a perception of the particulars in which those\nphenomena agree and differ. But, further, this reasoning by counters is\nonly suitable to a very limited portion even of our deductive processes.\nIn our reasonings respecting numbers, the only general principles which we\never have occasion to introduce are these, Things which are equal to the\nsame thing are equal to one another, and The sums or differences of equal\nthings are equal; with their various corollaries. Not only can no\nhesitation ever arise respecting the applicability of these principles,\nsince they are true of all magnitudes whatever; but every possible\napplication of which they are susceptible, may be reduced to a technical\nrule; and such, in fact, the rules of the calculus are. But if the symbols\nrepresent any other things than mere numbers, let us say even straight or\ncurve lines, we have then to apply theorems of geometry not true of all\nlines without exception, and to select those which are true of the lines\nwe are reasoning about. And how can we do this unless we keep completely\nin mind what particular lines these are? Since additional geometrical\ntruths may be introduced into the ratiocination in any stage of its\nprogress, we can not suffer ourselves, during even the smallest part of\nit, to use the names mechanically (as we use algebraical symbols) without\nan image annexed to them. It is only after ascertaining that the solution\nof a question concerning lines can be made to depend on a previous\nquestion concerning numbers, or, in other words, after the question has\nbeen (to speak technically) reduced to an equation, that the unmeaning\nsigns become available, and that the nature of the facts themselves to\nwhich the investigation relates can be dismissed from the mind. Up to the\nestablishment of the equation, the language in which mathematicians carry\non their reasoning does not differ in character from that employed by\nclose reasoners on any other kind of subject.\n\nI do not deny that every correct ratiocination, when thrown into the\nsyllogistic shape, is conclusive from the mere form of the expression,\nprovided none of the terms used be ambiguous; and this is one of the\ncircumstances which have led some writers to think that if all names were\nso judiciously constructed and so carefully defined as not to admit of any\nambiguity, the improvement thus made in language would not only give to\nthe conclusions of every deductive science the same certainty with those\nof mathematics, but would reduce all reasonings to the application of a\ntechnical form, and enable their conclusiveness to be rationally assented\nto after a merely mechanical process, as is undoubtedly the case in\nalgebra. But, if we except geometry, the conclusions of which are already\nas certain and exact as they can be made, there is no science but that of\nnumber, in which the practical validity of a reasoning can be apparent to\nany person who has looked only at the reasoning itself. Whoever has\nassented to what was said in the last Book concerning the case of the\nComposition of Causes, and the still stronger case of the entire\nsupersession of one set of laws by another, is aware that geometry and\nalgebra are the only sciences of which the propositions are categorically\ntrue; the general propositions of all other sciences are true only\nhypothetically, supposing that no counteracting cause happens to\ninterfere. A conclusion, therefore, however correctly deduced, in point of\nform, from admitted laws of nature, will have no other than an\nhypothetical certainty. At every step we must assure ourselves that no\nother law of nature has superseded, or intermingled its operation with,\nthose which are the premises of the reasoning; and how can this be done by\nmerely looking at the words? We must not only be constantly thinking of\nthe phenomena themselves, but we must be constantly studying them; making\nourselves acquainted with the peculiarities of every case to which we\nattempt to apply our general principles.\n\nThe algebraic notation, considered as a philosophical language, is perfect\nin its adaptation to the subjects for which it is commonly employed,\nnamely those of which the investigations have already been reduced to the\nascertainment of a relation between numbers. But, admirable as it is for\nits own purpose, the properties by which it is rendered such are so far\nfrom constituting it the ideal model of philosophical language in general,\nthat the more nearly the language of any other branch of science\napproaches to it, the less fit that language is for its own proper\nfunctions. On all other subjects, instead of contrivances to prevent our\nattention from being distracted by thinking of the meaning of our signs,\nwe ought to wish for contrivances to make it impossible that we should\never lose sight of that meaning even for an instant.\n\nWith this view, as much meaning as possible should be thrown into the\nformation of the word itself; the aids of derivation and analogy being\nmade available to keep alive a consciousness of all that is signified by\nit. In this respect those languages have an immense advantage which form\ntheir compounds and derivatives from native roots, like the German, and\nnot from those of a foreign or dead language, as is so much the case with\nEnglish, French, and Italian; and the best are those which form them\naccording to fixed analogies, corresponding to the relations between the\nideas to be expressed. All languages do this more or less, but especially,\namong modern European languages, the German; while even that is inferior\nto the Greek, in which the relation between the meaning of a derivative\nword and that of its primitive is in general clearly marked by its mode of\nformation, except in the case of words compounded with prepositions, which\nare often, in both those languages, extremely anomalous.\n\nBut all that can be done, by the mode of constructing words, to prevent\nthem from degenerating into sounds passing through the mind without any\ndistinct apprehension of what they signify, is far too little for the\nnecessity of the case. Words, however well constructed originally, are\nalways tending, like coins, to have their inscription worn off by passing\nfrom hand to hand; and the only possible mode of reviving it is to be ever\nstamping it afresh, by living in the habitual contemplation of the\nphenomena themselves, and not resting in our familiarity with the words\nthat express them. If any one, having possessed himself of the laws of\nphenomena as recorded in words, whether delivered to him originally by\nothers, or even found out by himself, is content from thenceforth to live\namong these formul\u00e6, to think exclusively of them, and of applying them to\ncases as they arise, without keeping up his acquaintance with the\nrealities from which these laws were collected\u2014not only will he\ncontinually fail in his practical efforts, because he will apply his\nformul\u00e6 without duly considering whether, in this case and in that, other\nlaws of nature do not modify or supersede them; but the formul\u00e6 themselves\nwill progressively lose their meaning to him, and he will cease at last\neven to be capable of recognizing with certainty whether a case falls\nwithin the contemplation of his formula or not. It is, in short, as\nnecessary, on all subjects not mathematical, that the things on which we\nreason should be conceived by us in the concrete, and \u201cclothed in\ncircumstances,\u201d as it is in algebra that we should keep all\nindividualizing peculiarities sedulously out of view.\n\nWith this remark we close our observations on the Philosophy of Language.\n\n\n\n\n                               Chapter VII.\n\n\nOf Classification, As Subsidiary To Induction.\n\n\n\u00a7 1. There is, as has been frequently remarked in this work, a\nclassification of things, which is inseparable from the fact of giving\nthem general names. Every name which connotes an attribute, divides, by\nthat very fact, all things whatever into two classes, those which have the\nattribute and those which have it not; those of which the name can be\npredicated, and those of which it can not. And the division thus made is\nnot merely a division of such things as actually exist, or are known to\nexist, but of all such as may hereafter be discovered, and even of all\nwhich can be imagined.\n\nOn this kind of Classification we have nothing to add to what has\npreviously been said. The Classification which requires to be discussed as\na separate act of the mind, is altogether different. In the one, the\narrangement of objects in groups, and distribution of them into\ncompartments, is a mere incidental effect consequent on the use of names\ngiven for another purpose, namely that of simply expressing some of their\nqualities. In the other, the arrangement and distribution are the main\nobject, and the naming is secondary to, and purposely conforms itself to,\ninstead of governing, that more important operation.\n\nClassification, thus regarded, is a contrivance for the best possible\nordering of the ideas of objects in our minds; for causing the ideas to\naccompany or succeed one another in such a way as shall give us the\ngreatest command over our knowledge already acquired, and lead most\ndirectly to the acquisition of more. The general problem of\nClassification, in reference to these purposes, may be stated as follows:\nTo provide that things shall be thought of in such groups, and those\ngroups in such an order, as will best conduce to the remembrance and to\nthe ascertainment of their laws.\n\nClassification thus considered, differs from classification in the wider\nsense, in having reference to real objects exclusively, and not to all\nthat are imaginable: its object being the due co-ordination in our minds\nof those things only, with the properties of which we have actually\noccasion to make ourselves acquainted. But, on the other hand, it embraces\n_all_ really existing objects. We can not constitute any one class\nproperly, except in reference to a general division of the whole of\nnature; we can not determine the group in which any one object can most\nconveniently be placed, without taking into consideration all the\nvarieties of existing objects, all at least which have any degree of\naffinity with it. No one family of plants or animals could have been\nrationally constituted, except as part of a systematic arrangement of all\nplants or animals; nor could such a general arrangement have been properly\nmade, without first determining the exact place of plants and animals in a\ngeneral division of nature.\n\n\u00a7 2. There is no property of objects which may not be taken, if we please,\nas the foundation for a classification or mental grouping of those\nobjects; and in our first attempts we are likely to select for that\npurpose properties which are simple, easily conceived, and perceptible on\na first view, without any previous process of thought. Thus Tournefort\u2019s\narrangement of plants was founded on the shape and divisions of the\ncorolla; and that which is commonly called the Linn\u00e6an (though Linn\u00e6us\nalso suggested another and more scientific arrangement) was grounded\nchiefly on the number of the stamens and pistils.\n\nBut these classifications, which are at first recommended by the facility\nthey afford of ascertaining to what class any individual belongs, are\nseldom much adapted to the ends of that Classification which is the\nsubject of our present remarks. The Linn\u00e6an arrangement answers the\npurpose of making us think together of all those kinds of plants which\npossess the same number of stamens and pistils; but to think of them in\nthat manner is of little use, since we seldom have any thing to affirm in\ncommon of the plants which have a given number of stamens and pistils. If\nplants of the class Pentandria, order Monogynia, agreed in any other\nproperties, the habit of thinking and speaking of the plants under a\ncommon designation would conduce to our remembering those common\nproperties so far as they were ascertained, and would dispose us to be on\nthe lookout for such of them as were not yet known. But since this is not\nthe case, the only purpose of thought which the Linn\u00e6an classification\nserves is that of causing us to remember, better than we should otherwise\nhave done, the exact number of stamens and pistils of every species of\nplants. Now, as this property is of little importance or interest, the\nremembering it with any particular accuracy is of no moment. And, inasmuch\nas, by habitually thinking of plants in those groups, we are prevented\nfrom habitually thinking of them in groups which have a greater number of\nproperties in common, the effect of such a classification, when\nsystematically adhered to, upon our habits of thought, must be regarded as\nmischievous.\n\nThe ends of scientific classification are best answered, when the objects\nare formed into groups respecting which a greater number of general\npropositions can be made, and those propositions more important, than\ncould be made respecting any other groups into which the same things could\nbe distributed. The properties, therefore, according to which objects are\nclassified, should, if possible, be those which are causes of many other\nproperties; or, at any rate, which are sure marks of them. Causes are\npreferable, both as being the surest and most direct of marks, and as\nbeing themselves the properties on which it is of most use that our\nattention should be strongly fixed. But the property which is the cause of\nthe chief peculiarities of a class, is unfortunately seldom fitted to\nserve also as the diagnostic of the class. Instead of the cause, we must\ngenerally select some of its more prominent effects, which may serve as\nmarks of the other effects and of the cause.\n\nA classification thus formed is properly scientific or philosophical, and\nis commonly called a Natural, in contradistinction to a Technical or\nArtificial, classification or arrangement. The phrase Natural\nClassification seems most peculiarly appropriate to such arrangements as\ncorrespond, in the groups which they form, to the spontaneous tendencies\nof the mind, by placing together the objects most similar in their general\naspect; in opposition to those technical systems which, arranging things\naccording to their agreement in some circumstance arbitrarily selected,\noften throw into the same group objects which in the general aggregate of\ntheir properties present no resemblance, and into different and remote\ngroups, others which have the closest similarity. It is one of the most\nvalid recommendations of any classification to the character of a\nscientific one, that it shall be a natural classification in this sense\nalso; for the test of its scientific character is the number and\nimportance of the properties which can be asserted in common of all\nobjects included in a group; and properties on which the general aspect of\nthe things depends are, if only on that ground, important, as well as, in\nmost cases, numerous. But, though a strong recommendation, this\ncircumstance is not a _sine qua non_; since the most obvious properties of\nthings may be of trifling importance compared with others that are not\nobvious. I have seen it mentioned as a great absurdity in the Linn\u00e6an\nclassification, that it places (which by-the-way it does not) the violet\nby the side of the oak; it certainly dissevers natural affinities, and\nbrings together things quite as unlike as the oak and the violet are. But\nthe difference, apparently so wide, which renders the juxtaposition of\nthose two vegetables so suitable an illustration of a bad arrangement,\ndepends, to the common eye, mainly on mere size and texture; now if we\nmade it our study to adopt the classification which would involve the\nleast peril of similar _rapprochements_, we should return to the obsolete\ndivision into trees, shrubs, and herbs, which though of primary importance\nwith regard to mere general aspect, yet (compared even with so petty and\nunobvious a distinction as that into dicotyledons and monocotyledons)\nanswers to so few differences in the other properties of plants, that a\nclassification founded on it (independently of the indistinctness of the\nlines of demarcation) would be as completely artificial and technical as\nthe Linn\u00e6an.\n\nOur natural groups, therefore, must often be founded not on the obvious\nbut on the unobvious properties of things, when these are of greater\nimportance. But in such cases it is essential that there should be some\nother property or set of properties, more readily recognizable by the\nobserver, which co-exist with, and may be received as marks of, the\nproperties which are the real groundwork of the classification. A natural\narrangement, for example, of animals, must be founded in the main on their\ninternal structure, but (as M. Comte remarks) it would be absurd that we\nshould not be able to determine the genus and species of an animal without\nfirst killing it. On this ground, the preference, among zoological\nclassifications, is probably due to that of M. De Blainville, founded on\nthe differences in the external integuments; differences which correspond,\nmuch more accurately than might be supposed, to the really important\nvarieties, both in the other parts of the structure, and in the habits and\nhistory of the animals.\n\nThis shows, more strongly than ever, how extensive a knowledge of the\nproperties of objects is necessary for making a good classification of\nthem. And as it is one of the uses of such a classification that by\ndrawing attention to the properties on which it is founded, and which, if\nthe classification be good, are marks of many others, it facilitates the\ndiscovery of those others; we see in what manner our knowledge of things,\nand our classification of them, tend mutually and indefinitely to the\nimprovement of each other.\n\nWe said just now that the classification of objects should follow those of\ntheir properties which indicate not only the most numerous, but also the\nmost important peculiarities. What is here meant by importance? It has\nreference to the particular end in view; and the same objects, therefore,\nmay admit with propriety of several different classifications. Each\nscience or art forms its classification of things according to the\nproperties which fall within its special cognizance, or of which it must\ntake account in order to accomplish its peculiar practical end. A farmer\ndoes not divide plants, like a botanist, into dicotyledonous and\nmonocotyledonous, but into useful plants and weeds. A geologist divides\nfossils, not like a zoologist, into families corresponding to those of\nliving species, but into fossils of the paleozoic, mesozoic, and tertiary\nperiods, above the coal and below the coal, etc. Whales are or are not\nfish according to the purpose for which we are considering them. \u201cIf we\nare speaking of the internal structure and physiology of the animal, we\nmust not call them fish; for in these respects they deviate widely from\nfishes; they have warm blood, and produce and suckle their young as land\nquadrupeds do. But this would not prevent our speaking of the\n_whale-fishery_, and calling such animals _fish_ on all occasions\nconnected with this employment; for the relations thus arising depend upon\nthe animal\u2019s living in the water, and being caught in a manner similar to\nother fishes. A plea that human laws which mention fish do not apply to\nwhales, would be rejected at once by an intelligent judge.\u201d(224)\n\nThese different classifications are all good, for the purposes of their\nown particular departments of knowledge or practice. But when we are\nstudying objects not for any special practical end, but for the sake of\nextending our knowledge of the whole of their properties and relations, we\nmust consider as the most important attributes those which contribute\nmost, either by themselves or by their effects, to render the things like\none another, and unlike other things; which give to the class composed of\nthem the most marked individuality; which fill, as it were, the largest\nspace in their existence, and would most impress the attention of a\nspectator who knew all their properties but was not specially interested\nin any. Classes formed on this principle may be called, in a more emphatic\nmanner than any others, natural groups.\n\n\u00a7 3. On the subject of these groups Dr. Whewell lays down a theory,\ngrounded on an important truth, which he has, in some respects, expressed\nand illustrated very felicitously, but also, as it appears to me, with\nsome admixture of error. It will be advantageous, for both these reasons,\nto extract the statement of his doctrine in the very words he has used.\n\n\u201cNatural groups,\u201d according to this theory,(225) are \u201cgiven by Type, not\nby Definition.\u201d And this consideration accounts for that \u201cindefiniteness\nand indecision which we frequently find in the descriptions of such\ngroups, and which must appear so strange and inconsistent to any one who\ndoes not suppose these descriptions to assume any deeper ground of\nconnection than an arbitrary choice of the botanist. Thus in the family of\nthe rose-tree, we are told that the _ovules_ are _very rarely_ erect, the\n_stigmata usually_ simple. Of what use, it might be asked, can such loose\naccounts be? To which the answer is, that they are not inserted in order\nto distinguish the species, but in order to describe the family, and the\ntotal relations of the ovules and the stigmata of the family are better\nknown by this general statement. A similar observation may be made with\nregard to the Anomalies of each group, which occur so commonly, that Dr.\nLindley, in his _Introduction to the Natural System of Botany_, makes the\n\u2018Anomalies\u2019 an article in each family. Thus, part of the character of the\nRosace\u00e6 is, that they have alternate _stipulate_ leaves, and that the\n_albumen_ is _obliterated_; but yet in _Lowea_, one of the genera of this\nfamily, the stipul\u00e6 are _absent_; and the albumen is _present_ in another,\n_Neillia_. This implies, as we have already seen, that the artificial\ncharacter (or _diagnosis_, as Mr. Lindley calls it) is imperfect. It is,\nthough very nearly, yet not exactly, commensurate with the natural group;\nand hence in certain cases this character is made to yield to the general\nweight of natural affinities.\n\n\u201cThese views\u2014of classes determined by characters which can not be\nexpressed in words\u2014of propositions which state, not what happens in all\ncases, but only usually\u2014of particulars which are included in a class,\nthough they transgress the definition of it, may probably surprise the\nreader. They are so contrary to many of the received opinions respecting\nthe use of definitions, and the nature of scientific propositions, that\nthey will probably appear to many persons highly illogical and\nunphilosophical. But a disposition to such a judgment arises in a great\nmeasure from this, that the mathematical and mathematico-physical sciences\nhave, in a great degree, determined men\u2019s views of the general nature and\nform of scientific truth; while Natural History has not yet had time or\nopportunity to exert its due influence upon the current habits of\nphilosophizing. The apparent indefiniteness and inconsistency of the\nclassifications and definitions of Natural History belongs, in a far\nhigher degree, to all other except mathematical speculations; and the\nmodes in which approximations to exact distinctions and general truths\nhave been made in Natural History, may be worthy our attention, even for\nthe light they throw upon the best modes of pursuing truth of all kinds.\n\n\u201cThough in a Natural group of objects a definition can no longer be of any\nuse as a regulative principle, classes are not therefore left quite loose,\nwithout any certain standard or guide. The class is steadily fixed, though\nnot precisely limited; it is given, though not circumscribed; it is\ndetermined, not by a boundary-line without, but by a central point within;\nnot by what it strictly excludes, but by what it eminently includes; by an\nexample, not by a precept; in short, instead of a Definition we have a\nType for our director.\n\n\u201cA Type is an example of any class, for instance a species of a genus,\nwhich is considered as eminently possessing the character of the class.\nAll the species which have a greater affinity with this type-species than\nwith any others, form the genus, and are arranged about it, deviating from\nit in various directions and different degrees. Thus a genus may consist\nof several species which approach very near the type, and of which the\nclaim to a place with it is obvious; while there may be other species\nwhich straggle farther from this central knot, and which yet are clearly\nmore connected with it than with any other. And even if there should be\nsome species of which the place is dubious, and which appear to be equally\nbound to two generic types, it is easily seen that this would not destroy\nthe reality of the generic groups, any more than the scattered trees of\nthe intervening plain prevent our speaking intelligibly of the distinct\nforests of two separate hills.\n\n\u201cThe type-species of every genus, the type-genus of every family, is then,\none which possesses all the characters and properties of the genus in a\nmarked and prominent manner. The type of the Rose family has alternate\nstipulate leaves, wants the albumen, has the ovules not erect, has the\nstigmata simple, and besides these features, which distinguish it from the\nexceptions or varieties of its class, it has the features which make it\nprominent in its class. It is one of those which possess clearly several\nleading attributes; and thus, though we can not say of any one genus that\nit _must_ be the type of the family, or of any one species that it _must_\nbe the type of the genus, we are still not wholly to seek; the type must\nbe connected by many affinities with most of the others of its group; it\nmust be near the centre of the crowd, and not one of the stragglers.\u201d\n\nIn this passage (the latter part of which especially I can not help\nnoticing as an admirable example of philosophic style) Dr. Whewell has\nstated very clearly and forcibly, but (I think) without making all\nnecessary distinctions, one of the principles of a Natural Classification.\nWhat this principle is, what are its limits, and in what manner he seems\nto me to have overstepped them, will appear when we have laid down another\nrule of Natural Arrangement, which appears to me still more fundamental.\n\n\u00a7 4. The reader is by this time familiar with the general truth (which I\nrestate so often on account of the great confusion in which it is commonly\ninvolved), that there are in nature distinctions of Kind; distinctions not\nconsisting in a given number of definite properties _plus_ the effects\nwhich follow from those properties, but running through the whole nature,\nthrough the attributes generally, of the things so distinguished. Our\nknowledge of the properties of a Kind is never complete. We are always\ndiscovering, and expecting to discover, new ones. Where the distinction\nbetween two classes of things is not one of Kind, we expect to find their\nproperties alike, except where there is some reason for their being\ndifferent. On the contrary, when the distinction is in Kind, we expect to\nfind the properties different unless there be some cause for their being\nthe same. All knowledge of a Kind must be obtained by observation and\nexperiment upon the Kind itself; no inference respecting its properties\nfrom the properties of things not connected with it by Kind, goes for more\nthan the sort of presumption usually characterized as an analogy, and\ngenerally in one of its fainter degrees.\n\nSince the common properties of a true Kind, and consequently the general\nassertions which can be made respecting it, or which are certain to be\nmade hereafter as our knowledge extends, are indefinite and inexhaustible;\nand since the very first principle of natural classification is that of\nforming the classes so that the objects composing each may have the\ngreatest number of properties in common; this principle prescribes that\nevery such classification shall recognize and adopt into itself all\ndistinctions of Kind, which exist among the objects it professes to\nclassify. To pass over any distinctions of Kind, and substitute definite\ndistinctions, which, however considerable they may be, do not point to\nulterior unknown differences, would be to replace classes with more by\nclasses with fewer attributes in common; and would be subversive of the\nNatural Method of Classification.\n\nAccordingly all natural arrangements, whether the reality of the\ndistinction of Kinds was felt or not by their framers, have been led, by\nthe mere pursuit of their own proper end, to conform themselves to the\ndistinctions of Kind, so far as these have been ascertained at the time.\nThe species of Plants are not only real Kinds, but are probably, all of\nthem, real lowest Kinds, Infim\u00e6 Species; which, if we were to subdivide,\nas of course it is open to us to do, into sub-classes, the subdivision\nwould necessarily be founded on _definite_ distinctions, not pointing\n(apart from what may be known of their causes or effects) to any\ndifference beyond themselves.\n\nIn so far as a natural classification is grounded on real Kinds, its\ngroups are certainly not conventional: it is perfectly true that they do\nnot depend upon an arbitrary choice of the naturalist. But it does not\nfollow, nor, I conceive, is it true, that these classes are determined by\na type, and not by characters. To determine them by a type would be as\nsure a way of missing the Kind, as if we were to select a set of\ncharacters arbitrarily. They are determined by characters, but these are\nnot arbitrary. The problem is, to find a few definite characters which\npoint to the multitude of indefinite ones. Kinds are Classes between which\nthere is an impassable barrier; and what we have to seek is, marks whereby\nwe may determine on which side of the barrier an object takes its place.\nThe characters which will best do this should be chosen: if they are also\nimportant in themselves, so much the better. When we have selected the\ncharacters, we parcel out the objects according to those characters, and\nnot, I conceive, according to resemblance to a type. We do not compose the\nspecies Ranunculus acris, of all plants which bear a satisfactory degree\nof resemblance to a model buttercup, but of those which possess certain\ncharacters selected as marks by which we might recognize the possibility\nof a common parentage; and the enumeration of those characters is the\ndefinition of the species.\n\nThe question next arises, whether, as all Kinds must have a place among\nthe classes, so all the classes in a natural arrangement must be Kinds?\nAnd to this I answer, certainly not. The distinctions of Kinds are not\nnumerous enough to make up the whole of a classification. Very few of the\ngenera of plants, or even of the families, can be pronounced with\ncertainty to be Kinds. The great distinctions of Vascular and Cellular,\nDicotyledonous or Exogenous and Monocotyledonous or Endogenous plants, are\nperhaps differences of kind; the lines of demarcation which divide those\nclasses seem (though even on this I would not pronounce positively) to go\nthrough the whole nature of the plants. But the different species of a\ngenus, or genera of a family, usually have in common only a limited number\nof characters. A Rose does not seem to differ from a Rubus, or the\nUmbellifer\u00e6 from the Ranunculace\u00e6, in much else than the characters\nbotanically assigned to those genera or those families. Unenumerated\ndifferences certainly do exist in some cases; there are families of plants\nwhich have peculiarities of chemical composition, or yield products having\npeculiar effects on the animal economy. The Crucifer\u00e6 and Fungi contain an\nunusual proportion of nitrogen; the Labiat\u00e6 are the chief sources of\nessential oils, the Solane\u00e6 are very commonly narcotic, etc. In these and\nsimilar cases there are possibly distinctions of Kind; but it is by no\nmeans indispensable that there should be. Genera and Families may be\neminently natural, though marked out from one another by properties\nlimited in number; provided those properties are important, and the\nobjects contained in each genus or family resemble each other more than\nthey resemble any thing which is excluded from the genus or family.\n\nAfter the recognition and definition, then, of the _infim\u00e6 species_, the\nnext step is to arrange those _infim\u00e6 species_ into larger groups: making\nthese groups correspond to Kinds wherever it is possible, but in most\ncases without any such guidance. And in doing this it is true that we are\nnaturally and properly guided, in most cases at least, by resemblance to a\ntype. We form our groups round certain selected Kinds, each of which\nserves as a sort of exemplar of its group. But though the groups are\nsuggested by types, I can not think that a group when formed is\n_determined_ by the type; that in deciding whether a species belongs to\nthe group, a reference is made to the type, and not to the characters;\nthat the characters \u201ccan not be expressed in words.\u201d This assertion is\ninconsistent with Dr. Whewell\u2019s own statement of the fundamental principle\nof classification, namely, that \u201cgeneral assertions shall be possible.\u201d If\nthe class did not possess any characters in common, what general\nassertions would be possible respecting it? Except that they all resemble\neach other more than they resemble any thing else, nothing whatever could\nbe predicated of the class.\n\nThe truth is, on the contrary, that every genus or family is framed with\ndistinct reference to certain characters, and is composed, first and\nprincipally, of species which agree in possessing all those characters. To\nthese are added, as a sort of appendix, such other species, generally in\nsmall number, as possess _nearly_ all the properties selected; wanting\nsome of them one property, some another, and which, while they agree with\nthe rest _almost_ as much as these agree with one another, do not resemble\nin an equal degree any other group. Our conception of the class continues\nto be grounded on the characters; and the class might be defined, those\nthings which _either_ possess that set of characters, _or_ resemble the\nthings that do so, more than they resemble any thing else.\n\nAnd this resemblance itself is not, like resemblance between simple\nsensations, an ultimate fact, unsusceptible of analysis. Even the inferior\ndegree of resemblance is created by the possession of common characters.\nWhatever resembles the genus Rose more than it resembles any other genus,\ndoes so because it possesses a greater number of the characters of that\ngenus than of the characters of any other genus. Nor can there be any real\ndifficulty in representing, by an enumeration of characters, the nature\nand degree of the resemblance which is strictly sufficient to include any\nobject in the class. There are always some properties common to all things\nwhich are included. Others there often are, to which some things, which\nare nevertheless included, are exceptions. But the objects which are\nexceptions to one character are not exceptions to another; the resemblance\nwhich fails in some particulars must be made up for in others. The class,\ntherefore, is constituted by the possession of _all_ the characters which\nare universal, and _most_ of those which admit of exceptions. If a plant\nhad the ovules erect, the stigmata divided, possessed the albumen, and was\nwithout stipules, it possibly would not be classed among the Rosace\u00e6. But\nit may want any one, or more than one of these characters, and not be\nexcluded. The ends of a scientific classification are better answered by\nincluding it. Since it agrees so nearly, in its known properties, with the\nsum of the characters of the class, it is likely to resemble that class\nmore than any other in those of its properties which are still\nundiscovered.\n\nNot only, therefore, are natural groups, no less than any artificial\nclasses, determined by characters; they are constituted in contemplation\nof, and by reason of, characters. But it is in contemplation not of those\ncharacters only which are rigorously common to all the objects included in\nthe group, but of the entire body of characters, all of which are found in\nmost of those objects, and most of them in all. And hence our conception\nof the class, the image in our minds which is representative of it, is\nthat of a specimen complete in all the characters; most naturally a\nspecimen which, by possessing them all in the greatest degree in which\nthey are ever found, is the best fitted to exhibit clearly, and in a\nmarked manner, what they are. It is by a mental reference to this\nstandard, not instead of, but in illustration of, the definition of the\nclass, that we usually and advantageously determine whether any individual\nor species belongs to the class or not. And this, as it seems to me, is\nthe amount of truth contained in the doctrine of Types.\n\nWe shall see presently that where the classification is made for the\nexpress purpose of a special inductive inquiry, it is not optional, but\nnecessary for fulfilling the conditions of a correct Inductive Method,\nthat we should establish a type-species or genus, namely, the one which\nexhibits in the most eminent degree the particular phenomenon under\ninvestigation. But of this hereafter. It remains, for completing the\ntheory of natural groups, that a few words should be said on the\nprinciples of the nomenclature adapted to them.\n\n\u00a7 5. A Nomenclature in science is, as we have said, a system of the names\nof Kinds. These names, like other class-names, are defined by the\nenumeration of the characters distinctive of the class. The only merit\nwhich a set of names can have beyond this, is to convey, by the mode of\ntheir construction, as much information as possible: so that a person who\nknows the thing, may receive all the assistance which the name can give in\nremembering what he knows; while he who knows it not, may receive as much\nknowledge respecting it as the case admits of, by merely being told its\nname.\n\nThere are two modes of giving to the name of a Kind this sort of\nsignificance. The best, but which unfortunately is seldom practicable, is\nwhen the word can be made to indicate, by its formation, the very\nproperties which it is designed to connote. The name of a Kind does not,\nof course, connote all the properties of the Kind, since these are\ninexhaustible, but such of them as are sufficient to distinguish it; such\nas are sure marks of all the rest. Now, it is very rarely that one\nproperty, or even any two or three properties, can answer this purpose. To\ndistinguish the common daisy from all other species of plants would\nrequire the specification of many characters. And a name can not, without\nbeing too cumbrous for use, give indication, by its etymology or mode of\nconstruction, of more than a very small number of these. The possibility,\ntherefore, of an ideally perfect Nomenclature, is probably confined to the\none case in which we are happily in possession of something approaching to\nit\u2014the Nomenclature of elementary Chemistry. The substances, whether\nsimple or compound, with which chemistry is conversant, are Kinds, and, as\nsuch, the properties which distinguish each of them from the rest are\ninnumerable; but in the case of compound substances (the simple ones are\nnot numerous enough to require a systematic nomenclature), there is one\nproperty, the chemical composition, which is of itself sufficient to\ndistinguish the Kind; and is (with certain reservations not yet thoroughly\nunderstood) a sure mark of all the other properties of the compound. All\nthat was needful, therefore, was to make the name of every compound\nexpress, on the first hearing, its chemical composition; that is, to form\nthe name of the compound, in some uniform manner, from the names of the\nsimple substances which enter into it as elements. This was done, most\nskillfully and successfully, by the French chemists, though their\nnomenclature has become inadequate to the convenient expression of the\nvery complicated compounds now known to chemists. The only thing left\nunexpressed by them was the exact proportion in which the elements were\ncombined; and even this, since the establishment of the atomic theory, it\nhas been found possible to express by a simple adaptation of their\nphraseology.\n\nBut where the characters which must be taken into consideration, in order\nsufficiently to designate the Kind, are too numerous to be all signified\nin the derivation of the name, and where no one of them is of such\npreponderant importance as to justify its being singled out to be so\nindicated, we may avail ourselves of a subsidiary resource. Though we can\nnot indicate the distinctive properties of the Kind, we may indicate its\nnearest natural affinities, by incorporating into its name the name of the\nproximate natural group of which it is one of the species. On this\nprinciple is founded the admirable binary nomenclature of botany and\nzoology. In this nomenclature the name of every species consists of the\nname of the genus, or natural group next above it, with a word added to\ndistinguish the particular species. The last portion of the compound name\nis sometimes taken from some _one_ of the peculiarities in which that\nspecies differs from others of the genus; as Clematis _integrifolia_,\nPotentilla _alba_, Viola _palustris_, Artemisia _vulgaris_; sometimes from\na circumstance of an historical nature, as Narcissus _poeticus_,\nPotentilla _tormentilla_ (indicating that the plant is that which was\nformerly known by the latter name), Exacum _Candollii_ (from the fact that\nDe Candolle was its first discoverer); and sometimes the word is purely\nconventional, as Thlaspi _bursapastoris_, Ranunculus _thora_; it is of\nlittle consequence which; since the second, or, as it is usually called,\nthe specific name, could at most express, independently of convention, no\nmore than a very small portion of the connotation of the term. But by\nadding to this the name of the superior genus, we may make the best amends\nwe can for the impossibility of so contriving the name as to express all\nthe distinctive characters of the Kind. We make it, at all events, express\nas many of those characters as are common to the proximate natural group\nin which the Kind is included. If even those common characters are so\nnumerous or so little familiar as to require a further extension of the\nsame resource, we might, instead of a binary, adopt a ternary\nnomenclature, employing not only the name of the genus, but that of the\nnext natural group in order of generality above the genus, commonly called\nthe Family. This was done in the mineralogical nomenclature proposed by\nProfessor Mohs. \u201cThe names framed by him were not composed of two, but of\nthree elements, designating respectively the Species, the Genus, and the\nOrder; thus he has such species as _Rhombohedral Lime Haloide_,\n_Octohedral Fluor Haloide_, _Prismatic Hal Baryte_.\u201d(226) The binary\nconstruction, however, has been found sufficient in botany and zoology,\nthe only sciences in which this general principle has hitherto been\nsuccessfully adopted in the construction of a nomenclature.\n\nBesides the advantage which this principle of nomenclature possesses, in\ngiving to the names of species the greatest quantity of independent\nsignificance which the circumstances of the case admit of, it answers the\nfurther end of immensely economizing the use of names, and preventing an\notherwise intolerable burden on the memory. When the names of species\nbecome extremely numerous, some artifice (as Dr. Whewell(227) observes)\nbecomes absolutely necessary to make it possible to recollect or apply\nthem. \u201cThe known species of plants, for example, were ten thousand in the\ntime of Linn\u00e6us, and are now probably sixty thousand. It would be useless\nto endeavor to frame and employ separate names for each of these species.\nThe division of the objects into a subordinated system of classification\nenables us to introduce a Nomenclature which does not require this\nenormous number of names. Each of the genera has its name, and the species\nare marked by the addition of some epithet to the name of the genus. In\nthis manner about seventeen hundred generic names, with a moderate number\nof specific names, were found by Linn\u00e6us sufficient to designate with\nprecision all the species of vegetables known at his time.\u201d And though the\nnumber of generic names has since greatly increased, it has not increased\nin any thing like the proportion of the multiplication of known species.\n\n\n\n\n                              Chapter VIII.\n\n\nOf Classification By Series.\n\n\n\u00a7 1. Thus far, we have considered the principles of scientific\nclassification so far only as relates to the formation of natural groups;\nand at this point most of those who have attempted a theory of natural\narrangement, including, among the rest, Dr. Whewell, have stopped. There\nremains, however, another, and a not less important portion of the theory,\nwhich has not yet, as far as I am aware, been systematically treated of by\nany writer except M. Comte. This is, the arrangement of the natural groups\ninto a natural series.(228)\n\nThe end of Classification, as an instrument for the investigation of\nnature, is (as before stated) to make us think of those objects together\nwhich have the greatest number of important common properties; and which,\ntherefore, we have oftenest occasion, in the course of our inductions, for\ntaking into joint consideration. Our ideas of objects are thus brought\ninto the order most conducive to the successful prosecution of inductive\ninquiries generally. But when the purpose is to facilitate some particular\ninductive inquiry, more is required. To be instrumental to that purpose,\nthe classification must bring those objects together, the simultaneous\ncontemplation of which is likely to throw most light upon the particular\nsubject. That subject being the laws of some phenomenon or some set of\nconnected phenomena; the very phenomenon or set of phenomena in question\nmust be chosen as the groundwork of the classification.\n\nThe requisites of a classification intended to facilitate the study of a\nparticular phenomenon, are, first to bring into one class all Kinds of\nthings which exhibit that phenomenon, in whatever variety of forms or\ndegrees; and, secondly, to arrange those Kinds in a series according to\nthe degree in which they exhibit it, beginning with those which exhibit\nmost of it, and terminating with those which exhibit least. The principal\nexample, as yet, of such a classification, is afforded by comparative\nanatomy and physiology, from which, therefore, our illustrations shall be\ntaken.\n\n\u00a7 2. The object being supposed to be, the investigation of the laws of\nanimal life; the first step, after forming the most distinct conception of\nthe phenomenon itself, possible in the existing state of our knowledge, is\nto erect into one great class (that of animals) all the known Kinds of\nbeings where that phenomenon presents itself; in however various\ncombinations with other properties, and in however different degrees. As\nsome of these Kinds manifest the general phenomenon of animal life in a\nvery high degree, and others in an insignificant degree, barely sufficient\nfor recognition; we must, in the next place, arrange the various Kinds in\na series, following one another according to the degrees in which they\nseverally exhibit the phenomenon; beginning therefore with man, and ending\nwith the most imperfect kinds of zoophytes.\n\nThis is merely saying that we should put the instances, from which the law\nis to be inductively collected, into the order which is implied in one of\nthe four Methods of Experimental Inquiry discussed in the preceding Book;\nthe fourth Method, that of Concomitant Variations. As formerly remarked,\nthis is often the only method to which recourse can be had, with assurance\nof a true conclusion, in cases in which we have but limited means of\neffecting, by artificial experiments, a separation of circumstances\nusually conjoined. The principle of the method is, that facts which\nincrease or diminish together, and disappear together, are either cause\nand effect, or effects of a common cause. When it has been ascertained\nthat this relation really subsists between the variations, a connection\nbetween the facts themselves may be confidently laid down, either as a law\nof nature or only as an empirical law, according to circumstances.\n\nThat the application of this Method must be preceded by the formation of\nsuch a series as we have described, is too obvious to need being pointed\nout; and the mere arrangement of a set of objects in a series, according\nto the degrees in which they exhibit some fact of which we are seeking the\nlaw, is too naturally suggested by the necessities of our inductive\noperations, to require any lengthened illustration here. But there are\ncases in which the arrangement required for the special purpose becomes\nthe determining principle of the classification of the same objects for\ngeneral purposes. This will naturally and properly happen, when those laws\nof the objects which are sought in the special inquiry enact so principal\na part in the general character and history of those objects\u2014exercise so\nmuch influence in determining all the phenomena of which they are either\nthe agents or the theatre\u2014that all other differences existing among the\nobjects are fittingly regarded as mere modifications of the one phenomenon\nsought; effects determined by the co-operation of some incidental\ncircumstance with the laws of that phenomenon. Thus in the case of\nanimated beings, the differences between one class of animals and another\nmay reasonably be considered as mere modifications of the general\nphenomenon, animal life; modifications arising either from the different\ndegrees in which that phenomenon is manifested in different animals, or\nfrom the intermixture of the effects of incidental causes peculiar to the\nnature of each, with the effects produced by the general laws of life;\nthose laws still exercising a predominant influence over the result. Such\nbeing the case, no other inductive inquiry respecting animals can be\nsuccessfully carried on, except in subordination to the great inquiry into\nthe universal laws of animal life; and the classification of animals best\nsuited to that one purpose, is the most suitable to all the other purposes\nof zoological science.\n\n\u00a7 3. To establish a classification of this sort, or even to apprehend it\nwhen established, requires the power of recognizing the essential\nsimilarity of a phenomenon, in its minuter degrees and obscurer forms,\nwith what is called the _same_ phenomenon in the greatest perfection of\nits development; that is, of identifying with each other all phenomena\nwhich differ only in degree, and in properties which we suppose to be\ncaused by difference of degree. In order to recognize this identity, or,\nin other words, this exact similarity of quality, the assumption of a\ntype-species is indispensable. We must consider as the type of the class,\nthat among the Kinds included in it, which exhibits the properties\nconstitutive of the class, in the highest degree; conceiving the other\nvarieties as instances of degeneracy, as it were, from that type;\ndeviations from it by inferior intensity of the characteristic property or\nproperties. For every phenomenon is best studied (_c\u00e6teris paribus_) where\nit exists in the greatest intensity. It is there that the effects which\neither depend on it, or depend on the same causes with it, will also exist\nin the greatest degree. It is there, consequently, and only there, that\nthose effects of it, or joint effects with it, can become fully known to\nus, so that we may learn to recognize their smaller degrees, or even their\nmere rudiments, in cases in which the direct study would have been\ndifficult or even impossible. Not to mention that the phenomenon in its\nhigher degrees may be attended by effects or collateral circumstances\nwhich in its smaller degrees do not occur at all, requiring for their\nproduction in any sensible amount a greater degree of intensity of the\ncause than is there met with. In man, for example (the species in which\nboth the phenomenon of animal and that of organic life exist in the\nhighest degree), many subordinate phenomena develop themselves in the\ncourse of his animated existence, which the inferior varieties of animals\ndo not show. The knowledge of these properties may nevertheless be of\ngreat avail toward the discovery of the conditions and laws of the general\nphenomenon of life, which is common to man with those inferior animals.\nAnd they are, even, rightly considered as properties of animated nature\nitself; because they may evidently be affiliated to the general laws of\nanimated nature; because we may fairly presume that some rudiments or\nfeeble degrees of those properties would be recognized in all animals by\nmore perfect organs, or even by more perfect instruments, than ours; and\nbecause those may be correctly termed properties of a class, which a thing\nexhibits exactly in proportion as it belongs to the class, that is, in\nproportion as it possesses the main attributes constitutive of the class.\n\n\u00a7 4. It remains to consider how the internal distribution of the series\nmay most properly take place; in what manner it should be divided into\nOrders, Families, and Genera.\n\nThe main principle of division must of course be natural affinity; the\nclasses formed must be natural groups; and the formation of these has\nalready been sufficiently treated of. But the principles of natural\ngrouping must be applied in subordination to the principle of a natural\nseries. The groups must not be so constituted as to place in the same\ngroup things which ought to occupy different points of the general scale.\nThe precaution necessary to be observed for this purpose is, that the\n_primary_ divisions must be grounded not on all distinctions\nindiscriminately, but on those which correspond to variations in the\ndegree of the main phenomenon. The series of Animated Nature should be\nbroken into parts at the points where the variation in the degree of\nintensity of the main phenomenon (as marked by its principal characters,\nSensation, Thought, Voluntary Motion, etc.) begins to be attended by\nconspicuous changes in the miscellaneous properties of the animal. Such\nwell-marked changes take place, for example, where the class Mammalia\nends; at the points where Fishes are separated from Insects, Insects from\nMollusca, etc. When so formed, the primary natural groups will compose the\nseries by mere juxtaposition, without redistribution; each of them\ncorresponding to a definite portion of the scale. In like manner each\nfamily should, if possible, be so subdivided, that one portion of it shall\nstand higher and the other lower, though of course contiguous, in the\ngeneral scale; and only when this is impossible is it allowable to ground\nthe remaining subdivisions on characters having no determinable connection\nwith the main phenomenon.\n\nWhere the principal phenomenon so far transcends in importance all other\nproperties on which a classification could be grounded, as it does in the\ncase of animated existence, any considerable deviation from the rule last\nlaid down is in general sufficiently guarded against by the first\nprinciple of a natural arrangement, that of forming the groups according\nto the most important characters. All attempts at a scientific\nclassification of animals, since first their anatomy and physiology were\nsuccessfully studied, have been framed with a certain degree of\ninstinctive reference to a natural series, and have accorded in many more\npoints than they have differed, with the classification which would most\nnaturally have been grounded on such a series. But the accordance has not\nalways been complete; and it still is often a matter of discussion, which\nof several classifications best accords with the true scale of intensity\nof the main phenomenon. Cuvier, for example, has been justly criticised\nfor having formed his natural groups, with an undue degree of reference to\nthe mode of alimentation, a circumstance directly connected only with\norganic life, and not leading to the arrangement most appropriate for the\npurposes of an investigation of the laws of animal life, since both\ncarnivorous and herbivorous or frugivorous animals are found at almost\nevery degree in the scale of animal perfection. Blainville\u2019s\nclassification has been considered by high authorities to be free from\nthis defect; as representing correctly, by the mere order of the principal\ngroups, the successive degeneracy of animal nature from its highest to its\nmost imperfect exemplification.\n\n\u00a7 5. A classification of any large portion of the field of nature in\nconformity to the foregoing principles, has hitherto been found\npracticable only in one great instance, that of animals. In the case even\nof vegetables, the natural arrangement has not been carried beyond the\nformation of natural groups. Naturalists have found, and probably will\ncontinue to find it impossible to form those groups into any series, the\nterms of which correspond to real gradations in the phenomenon of\nvegetative or organic life. Such a difference of degree may be traced\nbetween the class of Vascular Plants and that of Cellular, which includes\nlichens, alg\u00e6, and other substances whose organization is simpler and more\nrudimentary than that of the higher order of vegetables, and which\ntherefore approach nearer to mere inorganic nature. But when we rise much\nabove this point, we do not find any sufficient difference in the degree\nin which different plants possess the properties of organization and life.\nThe dicotyledons are of more complex structure, and somewhat more perfect\norganization, than the monocotyledons; and some dicotyledonous families,\nsuch as the Composit\u00e6, are rather more complex in their organization than\nthe rest. But the differences are not of a marked character, and do not\npromise to throw any particular light upon the conditions and laws of\nvegetable life and development. If they did, the classification of\nvegetables would have to be made, like that of animals, with reference to\nthe scale or series indicated.\n\nAlthough the scientific arrangements of organic nature afford as yet the\nonly complete example of the true principles of rational classification,\nwhether as to the formation of groups or of series, those principles are\napplicable to all cases in which mankind are called upon to bring the\nvarious parts of any extensive subject into mental co-ordination. They are\nas much to the point when objects are to be classed for purposes of art or\nbusiness, as for those of science. The proper arrangement, for example, of\na code of laws, depends on the same scientific conditions as the\nclassifications in natural history; nor could there be a better\npreparatory discipline for that important function, than the study of the\nprinciples of a natural arrangement, not only in the abstract, but in\ntheir actual application to the class of phenomena for which they were\nfirst elaborated, and which are still the best school for learning their\nuse. Of this the great authority on codification, Bentham, was perfectly\naware; and his early _Fragment on Government_, the admirable introduction\nto a series of writings unequaled in their department, contains clear and\njust views (as far as they go) on the meaning of a natural arrangement,\nsuch as could scarcely have occurred to any one who lived anterior to the\nage of Linn\u00e6us and Bernard de Jussieu.\n\n\n\n\n                                 Book V.\n\n\nON FALLACIES.\n\n\n    \u201cErrare non modo affirmando et negando, sed etiam sentiendo, et in\n    tacit\u00e2 hominum cogitatione contingit.\u201d\u2014HOBBES, _Computatio sive\n    Logica_, chap. v.\n\n    \u201cIl leur semble qu\u2019il n\u2019y a qu\u2019\u00e0 douter par fantaisie, et qu\u2019il\n    n\u2019y a qu\u2019\u00e0 dire en g\u00e9n\u00e9ral que notre nature est infirme; que notre\n    esprit est plein d\u2019aveuglement: qu\u2019il faut avoir un grand soin de\n    se d\u00e9faire de ses pr\u00e9jug\u00e9s, et autres choses semblables. Ils\n    pensent que cela suffit pour ne plus se laisser s\u00e9duire \u00e0 ses\n    sens, et pour ne plus se tromper du tout. Il ne suffit pas de dire\n    que l\u2019esprit est foible, il faut lui faire sentir ses foiblesses.\n    Ce n\u2019est pas assez de dire qu\u2019il est sujet \u00e0 l\u2019erreur, il faut lui\n    d\u00e9couvrir en quoi consistent ses erreurs.\u201d\u2014MALEBRANCHE, _Recherche\n    de la V\u00e9rit\u00e9_.\n\n\n\n\n                                Chapter I.\n\n\nOf Fallacies In General.\n\n\n\u00a7 1. It is a maxim of the school-men, that \u201ccontrariorum eadem est\nscientia:\u201d we never really know what a thing is, unless we are also able\nto give a sufficient account of its opposite. Conformably to this maxim,\none considerable section, in most treatises on Logic, is devoted to the\nsubject of Fallacies; and the practice is too well worthy of observance,\nto allow of our departing from it. The philosophy of reasoning, to be\ncomplete, ought to comprise the theory of bad as well as of good\nreasoning.\n\nWe have endeavored to ascertain the principles by which the sufficiency of\nany proof can be tested, and by which the nature and amount of evidence\nneedful to prove any given conclusion can be determined beforehand. If\nthese principles were adhered to, then although the number and value of\nthe truths ascertained would be limited by the opportunities, or by the\nindustry, ingenuity, and patience, of the individual inquirer, at least\nerror would not be embraced instead of truth. But the general consent of\nmankind, founded on their experience, vouches for their being far indeed\nfrom even this negative kind of perfection in the employment of their\nreasoning powers.\n\nIn the conduct of life\u2014in the practical business of mankind\u2014wrong\ninferences, incorrect interpretations of experience, unless after much\nculture of the thinking faculty, are absolutely inevitable; and with most\npeople, after the highest degree of culture they ever attain, such\nerroneous inferences, producing corresponding errors in conduct, are\nlamentably frequent. Even in the speculations to which eminent intellects\nhave systematically devoted themselves, and in reference to which the\ncollective mind of the scientific world is always at hand to aid the\nefforts and correct the aberrations of individuals, it is only from the\nmore perfect sciences, from those of which the subject-matter is the least\ncomplicated, that opinions not resting on a correct induction have at\nlength, generally speaking, been expelled. In the departments of inquiry\nrelating to the more complex phenomena of nature, and especially those of\nwhich the subject is man, whether as a moral and intellectual, a social,\nor even as a physical being; the diversity of opinions still prevalent\namong instructed persons, and the equal confidence with which those of the\nmost contrary ways of thinking cling to their respective tenets, are proof\nnot only that right modes of philosophizing are not yet generally adopted\non those subjects, but that wrong ones are; that inquirers have not only\nin general missed the truth, but have often embraced error; that even the\nmost cultivated portion of our species have not yet learned to abstain\nfrom drawing conclusions which the evidence does not warrant.\n\nThe only complete safeguard against reasoning ill, is the habit of\nreasoning well; familiarity with the principles of correct reasoning, and\npractice in applying those principles. It is, however, not unimportant to\nconsider what are the most common modes of bad reasoning; by what\nappearances the mind is most likely to be seduced from the observance of\ntrue principles of induction; what, in short, are the most common and most\ndangerous varieties of Apparent Evidence, whereby persons are misled into\nopinions for which there does not exist evidence really conclusive.\n\nA catalogue of the varieties of apparent evidence which are not real\nevidence, is an enumeration of Fallacies. Without such an enumeration,\ntherefore, the present work would be wanting in an essential point. And\nwhile writers who included in their theory of reasoning nothing more than\nratiocination, have in consistency with this limitation, confined their\nremarks to the fallacies which have their seat in that portion of the\nprocess of investigation; we, who profess to treat of the whole process,\nmust add to our directions for performing it rightly, warnings against\nperforming it wrongly in any of its parts: whether the ratiocinative or\nthe experimental portion of it be in fault, or the fault lie in dispensing\nwith ratiocination and induction altogether.\n\n\u00a7 2. In considering the sources of unfounded inference, it is unnecessary\nto reckon the errors which arise, not from a wrong method, nor even from\nignorance of the right one, but from a casual lapse, through hurry or\ninattention, in the application of the true principles of induction. Such\nerrors, like the accidental mistakes in casting up a sum, do not call for\nphilosophical analysis or classification; theoretical considerations can\nthrow no light upon the means of avoiding them. In the present treatise\nour attention is required, not to mere inexpertness in performing the\noperation in the right way (the only remedies for which are increased\nattention and more sedulous practice), but to the modes of performing it\nin a way fundamentally wrong; the conditions under which the human mind\npersuades itself that it has sufficient grounds for a conclusion which it\nhas not arrived at by any of the legitimate methods of induction\u2014which it\nhas not, even carelessly or overhastily, endeavored to test by those\nlegitimate methods.\n\n\u00a7 3. There is another branch of what may be called the Philosophy of\nError, which must be mentioned here, though only to be excluded from our\nsubject. The sources of erroneous opinions are twofold, moral and\nintellectual. Of these, the moral do not fall within the compass of this\nwork. They may be classed under two general heads: Indifference to the\nattainment of truth, and Bias; of which last the most common case is that\nin which we are biased by our wishes; but the liability is almost as great\nto the undue adoption of a conclusion which is disagreeable to us, as of\none which is agreeable, if it be of a nature to bring into action any of\nthe stronger passions. Persons of timid character are the more predisposed\nto believe any statement, the more it is calculated to alarm them. Indeed\nit is a psychological law, deducible from the most general laws of the\nmental constitution of man, that any strong passion renders us credulous\nas to the existence of objects suitable to excite it.\n\nBut the moral causes of opinions, though with most persons the most\npowerful of all, are but remote causes; they do not act directly, but by\nmeans of the intellectual causes; to which they bear the same relation\nthat the circumstances called, in the theory of medicine, _predisposing_\ncauses, bear to _exciting_ causes. Indifference to truth can not, in and\nby itself, produce erroneous belief; it operates by preventing the mind\nfrom collecting the proper evidences, or from applying to them the test of\na legitimate and rigid induction; by which omission it is exposed\nunprotected to the influence of any species of apparent evidence which\noffers itself spontaneously, or which is elicited by that smaller quantity\nof trouble which the mind may be willing to take. As little is Bias a\ndirect source of wrong conclusions. We can not believe a proposition only\nby wishing, or only by dreading, to believe it. The most violent\ninclination to find a set of propositions true, will not enable the\nweakest of mankind to believe them without a vestige of intellectual\ngrounds\u2014without any, even apparent, evidence. It acts indirectly, by\nplacing the intellectual grounds of belief in an incomplete or distorted\nshape before his eyes. It makes him shrink from the irksome labor of a\nrigorous induction, when he has a misgiving that its result may be\ndisagreeable; and in such examination as he does institute, it makes him\nexert that which _is_ in a certain measure voluntary, his attention,\nunfairly, giving a larger share of it to the evidence which seems\nfavorable to the desired conclusion, a smaller to that which seems\nunfavorable. It operates, too, by making him look out eagerly for reasons,\nor apparent reasons, to support opinions which are conformable, or resist\nthose which are repugnant, to his interests or feelings; and when the\ninterests or feelings are common to great numbers of persons, reasons are\naccepted and pass current, which would not for a moment be listened to in\nthat character if the conclusion had nothing more powerful than its\nreasons to speak in its behalf. The natural or acquired partialities of\nmankind are continually throwing up philosophical theories, the sole\nrecommendation of which consists in the premises they afford for proving\ncherished doctrines, or justifying favorite feelings; and when any one of\nthese theories has been so thoroughly discredited as no longer to serve\nthe purpose, another is always ready to take its place. This propensity,\nwhen exercised in favor of any widely-spread persuasion or sentiment, is\noften decorated with complimentary epithets; and the contrary habit of\nkeeping the judgment in complete subordination to evidence, is stigmatized\nby various hard names, as skepticism, immorality, coldness,\nhard-heartedness, and similar expressions according to the nature of the\ncase. But though the opinions of the generality of mankind, when not\ndependent on mere habit and inculcation, have their root much more in the\ninclinations than in the intellect, it is a necessary condition to the\ntriumph of the moral bias that it should first pervert the understanding.\nEvery erroneous inference, though originating in moral causes, involves\nthe intellectual operation of admitting insufficient evidence as\nsufficient; and whoever was on his guard against all kinds of inconclusive\nevidence which can be mistaken for conclusive, would be in no danger of\nbeing led into error even by the strongest bias. There are minds so\nstrongly fortified on the intellectual side, that they could not blind\nthemselves to the light of truth, however really desirous of doing so;\nthey could not, with all the inclination in the world, pass off upon\nthemselves bad arguments for good ones. If the sophistry of the intellect\ncould be rendered impossible, that of the feelings, having no instrument\nto work with, would be powerless. A comprehensive classification of all\nthose things which, not being evidence, are liable to appear such to the\nunderstanding, will, therefore, of itself include all errors of judgment\narising from moral causes, to the exclusion only of errors of practice\ncommitted against better knowledge.\n\nTo examine, then, the various kinds of apparent evidence which are not\nevidence at all, and of apparently conclusive evidence which do not really\namount to conclusiveness, is the object of that part of our inquiry into\nwhich we are about to enter.\n\nThe subject is not beyond the compass of classification and comprehensive\nsurvey. The things, indeed, which are not evidence of any given\nconclusion, are manifestly endless, and this negative property, having no\ndependence on any positive ones, can not be made the groundwork of a real\nclassification. But the things which, not being evidence, are susceptible\nof being mistaken for it, are capable of a classification having reference\nto the positive property which they possess of appearing to be evidence.\nWe may arrange them, at our choice, on either of two principles; according\nto the cause which makes them appear to be evidence, not being so; or\naccording to the particular kind of evidence which they simulate. The\nClassification of Fallacies which will be attempted in the ensuing\nchapter, is founded on these considerations jointly.\n\n\n\n\n                               Chapter II.\n\n\nClassification Of Fallacies.\n\n\n\u00a7 1. In attempting to establish certain general distinctions which shall\nmark out from one another the various kinds of Fallacious Evidence, we\npropose to ourselves an altogether different aim from that of several\neminent thinkers, who have given, under the name of Political or other\nFallacies, a mere enumeration of a certain number of erroneous opinions;\nfalse general propositions which happen to be often met with; _loci\ncommunes_ of bad arguments on some particular subject. Logic is not\nconcerned with the false opinions which people happen to entertain, but\nwith the manner in which they come to entertain them. The question is not,\nwhat facts have at any time been erroneously supposed to be proof of\ncertain other facts, but what property in the facts it was which led any\none to this mistaken supposition.\n\nWhen a fact is supposed, though incorrectly, to be evidentiary of, or a\nmark of, some other fact, there must be a cause of the error; the supposed\nevidentiary fact must be connected in some particular manner with the fact\nof which it is deemed evidentiary\u2014must stand in some particular relation\nto it, without which relation it would not be regarded in that light. The\nrelation may either be one resulting from the simple contemplation of the\ntwo facts side by side with one another, or it may depend on some process\nof mind, by which a previous association has been established between\nthem. Some peculiarity of relation, however, there must be; the fact which\ncan, even by the wildest aberration, be supposed to prove another fact,\nmust stand in some special position with regard to it; and if we could\nascertain and define that special position, we should perceive the origin\nof the error.\n\nWe can not regard one fact as evidentiary of another, unless we believe\nthat the two are always, or in the majority of cases, conjoined. If we\nbelieve A to be evidentiary of B, if when we see A we are inclined to\ninfer B from it, the reason is because we believe that wherever A is, B\nalso either always or for the most part exists, either as an antecedent, a\nconsequent, or a concomitant. If when we see A we are inclined not to\nexpect B\u2014if we believe A to be evidentiary of the absence of B\u2014it is\nbecause we believe that where A is, B either is never, or at least seldom,\nfound. Erroneous conclusions, in short, no less than correct conclusions,\nhave an invariable relation to a general formula, either expressed or\ntacitly implied. When we infer some fact from some other fact which does\nnot really prove it, we either have admitted, or, if we maintained\nconsistency, ought to admit, some groundless general proposition\nrespecting the conjunction of the two phenomena.\n\nFor every property, therefore, in facts, or in our mode of considering\nfacts, which leads us to believe that they are habitually conjoined when\nthey are not, or that they are not when in reality they are, there is a\ncorresponding kind of Fallacy; and an enumeration of fallacies would\nconsist in a specification of those properties in facts, and those\npeculiarities in our mode of considering them, which give rise to this\nerroneous opinion.\n\n\u00a7 2. To begin, then; the supposed connection, or repugnance, between the\ntwo facts, may either be a conclusion from evidence (that is, from some\nother proposition or propositions), or may be admitted without any such\nground; admitted, as the phrase is, on its own evidence; embraced as\nself-evident, as an axiomatic truth. This gives rise to the first great\ndistinction, that between Fallacies of Inference and Fallacies of Simple\nInspection. In the latter division must be included not only all cases in\nwhich a proposition is believed and held for true, literally without any\nextrinsic evidence, either of specific experience or general reasoning;\nbut those more frequent cases in which simple inspection creates a\n_presumption_ in favor of a proposition; not sufficient for belief, but\nsufficient to cause the strict principles of a regular induction to be\ndispensed with, and creating a predisposition to believe it on evidence\nwhich would be seen to be insufficient if no such presumption existed.\nThis class, comprehending the whole of what may be termed Natural\nPrejudices, and which I shall call indiscriminately Fallacies of Simple\nInspection or Fallacies _a priori_, shall be placed at the head of our\nlist.\n\nFallacies of Inference, or erroneous conclusions from supposed evidence,\nmust be subdivided according to the nature of the apparent evidence from\nwhich the conclusions are drawn; or (what is the same thing) according to\nthe particular kind of sound argument which the fallacy in question\nsimulates. But there is a distinction to be first drawn, which does not\nanswer to any of the divisions of sound arguments, but arises out of the\nnature of bad ones. We may know exactly what our evidence is, and yet draw\na false conclusion from it; we may conceive precisely what our premises\nare, what alleged matters of fact, or general principles, are the\nfoundation of our inference; and yet, because the premises are false, or\nbecause we have inferred from them what they will not support, our\nconclusion may be erroneous. But a case, perhaps even more frequent, is\nthat in which the error arises from not conceiving our premises with due\nclearness, that is (as shown in the preceding Book(229)), with due fixity:\nforming one conception of our evidence when we collect or receive it, and\nanother when we make use of it; or unadvisedly, and in general\nunconsciously, substituting, as we proceed, different premises in the\nplace of those with which we set out, or a different conclusion for that\nwhich we undertook to prove. This gives existence to a class of fallacies\nwhich may be justly termed (in a phrase borrowed from Bentham) Fallacies\nof Confusion; comprehending, among others, all those which have their\nsource in language, whether arising from the vagueness or ambiguity of our\nterms, or from casual associations with them.\n\nWhen the fallacy is not one of Confusion, that is, when the proposition\nbelieved, and the evidence on which it is believed, are steadily\napprehended and unambiguously expressed, there remain to be made two cross\ndivisions. The Apparent Evidence may be either particular facts, or\nforegone generalizations; that is, the process may simulate either simple\nInduction or Deduction; and again, the evidence, whether consisting of\nsupposed facts or of general propositions, may be false in itself, or,\nbeing true, may fail to bear out the conclusion attempted to be founded on\nit. This gives us first, Fallacies of Induction and Fallacies of\nDeduction, and then a subdivision of each of these, according as the\nsupposed evidence is false, or true but inconclusive.\n\nFallacies of Induction, where the facts on which the induction proceeds\nare erroneous, may be termed Fallacies of Observation. The term is not\nstrictly accurate, or, rather, not accurately co-extensive with the class\nof fallacies which I propose to designate by it. Induction is not always\ngrounded on facts immediately observed, but sometimes on facts inferred;\nand when these last are erroneous, the error may not be, in the literal\nsense of the term, an instance of bad observation, but of bad inference.\nIt will be convenient, however, to make only one class of all the\ninductions of which the error lies in not sufficiently ascertaining the\nfacts on which the theory is grounded; whether the cause of failure be\nmalobservation, or simple non-observation, and whether the malobservation\nbe direct, or by means of intermediate marks which do not prove what they\nare supposed to prove. And in the absence of any comprehensive term to\ndenote the ascertainment, by whatever means, of the facts on which an\ninduction is grounded, I will venture to retain for this class of\nfallacies, under the explanation now given, the title of Fallacies of\nObservation.\n\nThe other class of inductive fallacies, in which the facts are correct,\nbut the conclusion not warranted by them, are properly denominated\nFallacies of Generalization; and these, again, fall into various\nsubordinate classes or natural groups, some of which will be enumerated in\ntheir proper place.\n\nWhen we now turn to Fallacies of Deduction, namely those modes of\nincorrect argumentation in which the premises, or some of them, are\ngeneral propositions, and the argument a ratiocination; we may of course\nsubdivide these also into two species similar to the two preceding,\nnamely, those which proceed on false premises, and those of which the\npremises, though true, do not support the conclusion. But of these\nspecies, the first must necessarily fall under some one of the heads\nalready enumerated. For the error must be either in those premises which\nare general propositions, or in those which assert individual facts. In\nthe former case it is an Inductive Fallacy, of one or the other class; in\nthe latter it is a Fallacy of Observation; unless, in either case, the\nerroneous premise has been assumed on simple inspection, in which case the\nfallacy is _a priori_. Or, finally, the premises, of whichever kind they\nare, may never have been conceived in so distinct a manner as to produce\nany clear consciousness by what means they were arrived at; as in the case\nof what is called reasoning in a circle; and then the fallacy is one of\nConfusion.\n\nThere remain, therefore, as the only class of fallacies having properly\ntheir seat in deduction, those in which the premises of the ratiocination\ndo not bear out its conclusion; the various cases, in short, of vicious\nargumentation, provided against by the rules of the syllogism. We shall\ncall these, Fallacies of Ratiocination.\n\n\u00a7 3. We must not, however, expect to find that men\u2019s actual errors always,\nor even commonly, fall so unmistakably under some one of these classes, as\nto be incapable of being referred to any other. Erroneous arguments do not\nadmit of such a sharply cut division as valid arguments do. An argument\nfully stated, with all its steps distinctly set out, in language not\nsusceptible of misunderstanding, must, if it be erroneous, be so in some\none of these five modes unequivocally; or indeed of the first four, since\nthe fifth, on such a supposition, would vanish. But it is not in the\nnature of bad reasoning to express itself thus unambiguously. When a\nsophist, whether he is imposing on himself or attempting to impose on\nothers, can be constrained to throw his sophistry into so distinct a form,\nit needs, in a large proportion of cases, no further exposure.\n\nIn all arguments, everywhere but in the schools, some of the links are\nsuppressed; _a fortiori_ when the arguer either intends to deceive, or is\na lame and inexpert thinker, little accustomed to bring his reasoning\nprocesses to any test; and it is in those steps of the reasoning which are\nmade in this tacit and half-conscious, or even wholly unconscious manner,\nthat the error oftenest lurks. In order to detect the fallacy, the\nproposition thus silently assumed must be supplied; but the reasoner, most\nlikely, has never really asked himself what he was assuming; his confuter,\nunless permitted to extort it from him by the Socratic mode of\ninterrogation, must himself judge what the suppressed premise ought to be\nin order to support the conclusion. And hence, in the words of Archbishop\nWhately, \u201cit must be often a matter of doubt, or, rather, of arbitrary\nchoice, not only to which genus each _kind_ of fallacy should be referred,\nbut even to which kind to refer any one _individual_ fallacy; for since,\nin any course of argument, _one_ premise is usually suppressed, it\nfrequently happens in the case of a fallacy, that the hearers are left to\nthe alternative of supplying _either_ a premise which is _not true_, or\n_else_, one which _does not prove_ the conclusion; _e.g._, if a man\nexpatiates on the distress of the country, and thence argues that the\ngovernment is tyrannical, we must suppose him to assume _either_ that\n\u2018every distressed country is under a tyranny,\u2019 which is a manifest\nfalsehood, _or_ merely that \u2018every country under a tyranny is distressed,\u2019\nwhich, however true, proves nothing, the middle term being undistributed.\u201d\nThe former would be ranked, in our distribution, among fallacies of\ngeneralization, the latter among those of ratiocination. \u201cWhich are we to\nsuppose the speaker meant us to understand? Surely\u201d (if he understood\nhimself) \u201cjust whichever each of his hearers might happen to prefer: some\nmight assent to the false premise; others allow the unsound syllogism.\u201d\n\nAlmost all fallacies, therefore, might in strictness be brought under our\nfifth class, Fallacies of Confusion. A fallacy can seldom be absolutely\nreferred to any of the other classes; we can only say, that if all the\nlinks were filled up which should be capable of being supplied in a valid\nargument, it would either stand thus (forming a fallacy of one class), or\nthus (a fallacy of another); or at furthest we may say, that the\nconclusion is most _likely_ to have originated in a fallacy of such and\nsuch a class. Thus, in the illustration just quoted, the error committed\nmay be traced with most probability to a fallacy of generalization; that\nof mistaking an uncertain mark, or piece of evidence, for a certain one;\nconcluding from an effect to some one of its possible causes, when there\nare others which would have been equally capable of producing it.\n\nYet, though the five classes run into each other, and a particular error\noften seems to be arbitrarily assigned to one of them rather than to any\nof the rest, there is considerable use in so distinguishing them. We shall\nfind it convenient to set apart, as Fallacies of Confusion, those of which\nconfusion is the most obvious characteristic; in which no other cause can\nbe assigned for the mistake committed, than neglect or inability to state\nthe question properly, and to apprehend the evidence with definiteness and\nprecision. In the remaining four classes I shall place not only the cases\nin which the evidence is clearly seen to be what it is, and yet a wrong\nconclusion drawn from it, but also those in which, although there be\nconfusion, the confusion is not the sole cause of the error, but there is\nsome shadow of a ground for it in the nature of the evidence itself. And\nin distributing these cases of partial confusion among the four classes, I\nshall, when there can be any hesitation as to the precise seat of the\nfallacy, suppose it to be in that part of the process in which, from the\nnature of the case, and the tendencies of the human mind, an error would\nin the particular circumstances be the most probable.\n\nAfter these observations we shall proceed, without further preamble, to\nconsider the five classes in their order.\n\n\n\n\n                               Chapter III.\n\n\nFallacies Of Simple Inspection; Or _A Priori_ Fallacies.\n\n\n\u00a7 1. The tribe of errors of which we are to treat in the first instance,\nare those in which no actual inference takes place at all; the proposition\n(it can not in such cases be called a conclusion) being embraced, not as\nproved, but as requiring no proof; as a self-evident truth; or else as\nhaving such intrinsic verisimilitude, that external evidence not in itself\namounting to proof, is sufficient in aid of the antecedent presumption.\n\nAn attempt to treat this subject comprehensively would be a transgression\nof the bounds prescribed to this work, since it would necessitate the\ninquiry which, more than any other, is the grand question of what is\ncalled metaphysics, viz., What are the propositions which may reasonably\nbe received without proof? That there must be some such propositions all\nare agreed, since there can not be an infinite series of proof, a chain\nsuspended from nothing. But to determine what these propositions are, is\nthe _opus magnum_ of the more recondite mental philosophy. Two principal\ndivisions of opinion on the subject have divided the schools of philosophy\nfrom its first dawn. The one recognizes no ultimate premises but the facts\nof our subjective consciousness; our sensations, emotions, intellectual\nstates of mind, and volitions. These, and whatever by strict rules of\ninduction can be derived from these, it is possible, according to this\ntheory, for us to know; of all else we must remain in ignorance. The\nopposite school hold that there are other existences, suggested indeed to\nour minds by these subjective phenomena, but not inferable from them, by\nany process either of deduction or of induction; which, however, we must,\nby the constitution of our mental nature, recognize as realities; and\nrealities, too, of a higher order than the phenomena of our consciousness,\nbeing the efficient causes and necessary substrata of all Phenomena. Among\nthese entities they reckon Substances, whether matter or spirit; from the\ndust under our feet to the soul, and from that to Deity. All these,\naccording to them, are preternatural or supernatural beings, having no\nlikeness in experience, though experience is entirely a manifestation of\ntheir agency. Their existence, together with more or less of the laws to\nwhich they conform in their operations, are, on this theory, apprehended\nand recognized as real by the mind itself intuitively; experience (whether\nin the form of sensation or of mental feeling) having no other part in the\nmatter than as affording facts which are consistent with these necessary\npostulates of reason, and which are explained and accounted for by them.\n\nAs it is foreign to the purpose of the present treatise to decide between\nthese conflicting theories, we are precluded from inquiring into the\nexistence, or defining the extent and limits, of knowledge _a priori_, and\nfrom characterizing the kind of correct assumption which the fallacy of\nincorrect assumption, now under consideration, simulates. Yet since it is\nallowed on both sides that such assumptions are often made improperly, we\nmay find it practicable, without entering into the ultimate metaphysical\ngrounds of the discussion, to state some speculative propositions, and\nsuggest some practical cautions, respecting the forms in which such\nunwarranted assumptions are most likely to be made.\n\n\u00a7 2. In the cases in which, according to the thinkers of the ontological\nschool, the mind apprehends, by intuition, things, and the laws of things,\nnot cognizable by our sensitive faculty; those intuitive, or supposed\nintuitive, perceptions are undistinguishable from what the opposite school\nare accustomed to call ideas of the mind. When they themselves say that\nthey perceive the things by an immediate act of a faculty given for that\npurpose by their Creator, it would be said of them by their opponents that\nthey find an idea or conception in their own minds, and from the idea or\nconception, infer the existence of a corresponding objective reality. Nor\nwould this be an unfair statement, but a mere version into other words of\nthe account given by many of themselves; and one to which the more\nclear-sighted of them might, and generally do, without hesitation,\nsubscribe. Since, therefore, in the cases which lay the strongest claims\nto be examples of knowledge _a priori_, the mind proceeds from the idea of\na thing to the reality of the thing itself, we can not be surprised by\nfinding that illicit assumptions _a priori_ consist in doing the same\nthing erroneously; in mistaking subjective facts for objective, laws of\nthe percipient mind for laws of the perceived object, properties of the\nideas or conceptions for properties of the things conceived.\n\nAccordingly, a large proportion of the erroneous thinking which exists in\nthe world proceeds on a tacit assumption, that the same order must obtain\namong the objects in nature which obtains among our ideas of them. That if\nwe always think of two things together, the two things must always exist\ntogether. That if one thing makes us think of another as preceding or\nfollowing it, that other must precede it or follow it in actual fact. And\nconversely, that when we can not conceive two things together they can not\nexist together, and that their combination may, without further evidence,\nbe rejected from the list of possible occurrences.\n\nFew persons, I am inclined to think, have reflected on the great extent to\nwhich this fallacy has prevailed, and prevails, in the actual beliefs and\nactions of mankind. For a first illustration of it we may refer to a large\nclass of popular superstitions. If any one will examine in what\ncircumstances most of those things agree, which in different ages and by\ndifferent portions of the human race have been considered as omens or\nprognostics of some interesting event, whether calamitous or fortunate;\nthey will be found very generally characterized by this peculiarity, that\nthey cause the mind to _think_ of that, of which they are therefore\nsupposed to forbode the actual occurrence. \u201cTalk of the devil and he will\nappear,\u201d has passed into a proverb. Talk of the devil, that is, raise the\nidea, and the reality will follow. In times when the appearance of that\npersonage in a visible form was thought to be no unfrequent occurrence, it\nhas doubtless often happened to persons of vivid imagination and\nsusceptible nerves, that talking of the devil has caused them to fancy\nthey saw him; as even in our more incredulous days, listening to ghost\nstories predisposes us to see ghosts; and thus, as a prop to the _a\npriori_ fallacy, there might come to be added an auxiliary fallacy of\nmalobservation, with one of false generalization grounded on it. Fallacies\nof different orders often herd or cluster together in this fashion, one\nsmoothing the way for another. But the origin of the superstition is\nevidently that which we have assigned. In like manner, it has been\nuniversally considered unlucky to speak of misfortune.\n\nThe day on which any calamity happened has been considered an unfortunate\nday, and there has been a feeling everywhere, and in some nations a\nreligious obligation, against transacting any important business on that\nday. For on such a day our thoughts are likely to be of misfortune. For a\nsimilar reason, any untoward occurrence in commencing an undertaking has\nbeen considered ominous of failure; and often, doubtless, has really\ncontributed to it by putting the persons engaged in the enterprise more or\nless out of spirits; but the belief has equally prevailed where the\ndisagreeable circumstance was, independently of superstition, too\ninsignificant to depress the spirits by any influence of its own. All know\nthe story of C\u00e6sar\u2019s accidentally stumbling in the act of landing on the\nAfrican coast; and the presence of mind with which he converted the\ndireful presage into a favorable one by exclaiming, \u201cAfrica, I embrace\nthee.\u201d Such omens, it is true, were often conceived as warnings of the\nfuture, given by a friendly or a hostile deity; but this very superstition\ngrew out of a pre-existing tendency; the god was supposed to send, as an\nindication of what was to come, something which people were already\ndisposed to consider in that light. So in the case of lucky or unlucky\nnames. Herodotus tells us how the Greeks, on the way to Mycale, were\nencouraged in their enterprise by the arrival of a deputation from Samos,\none of the members of which was named Hegesistratus, the leader of armies.\n\nCases may be pointed out in which something which could have no real\neffect but to make persons _think_ of misfortune, was regarded not merely\nas a prognostic, but as something approaching to an actual cause of it.\nThe \u03b5\u1f50\u03c6\u03ae\u03bc\u03b5\u03b9 of the Greeks, and _favete linguis_, or _bona verba qu\u00e6so_, of\nthe Romans, evince the care with which they endeavored to repress the\nutterance of any word expressive or suggestive of ill fortune; not from\nnotions of delicate politeness, to which their general mode of conduct and\nfeeling had very little reference, but from _bona fide_ alarm lest the\nevent so suggested to the imagination should in fact occur. Some vestige\nof a similar superstition has been known to exist among uneducated persons\neven in our own day: it is thought an unchristian thing to talk of, or\nsuppose, the death of any person while he is alive. It is known how\ncareful the Romans were to avoid, by an indirect mode of speech, the\nutterance of any word directly expressive of death or other calamity; how\ninstead of _mortuus est_ they said _vixit_; and \u201cbe the event fortunate or\n_otherwise_\u201d instead of _adverse_. The name Maleventum, of which Salmasius\nso sagaciously detected the Thessalian origin (\u039c\u03b1\u03bb\u03cc\u03b5\u03b9\u03c2, \u039c\u03b1\u03bb\u03bf\u03ad\u03bd\u03c4\u03bf\u03c2), they\nchanged into the highly propitious denomination, Beneventum; Egesta into\nSegesta; and Epidamnus, a name so interesting in its associations to the\nreader of Thucydides, they exchanged for Dyrrhachium, to escape the perils\nof a word suggestive of _damnum_ or detriment.\n\n\u201cIf a hare cross the highway,\u201d says Sir Thomas Browne,(230) \u201cthere are few\nabove threescore that are not perplexed thereat; which notwithstanding is\nbut an augurial terror, according to that received expression,\n_Inauspicatum dat iter oblatus lepus_. And the ground of the conceit was\nprobably no greater than this, that a fearful animal passing by us\nportended unto us something to be feared; as upon the like consideration\nthe meeting of a fox presaged some future imposture.\u201d Such superstitions\nas these last must be the result of study; they are too recondite for\nnatural or spontaneous growth. But when the attempt was once made to\nconstruct a science of predictions, any association, though ever so faint\nor remote, by which an object could be connected in however far-fetched a\nmanner with ideas either of prosperity or of danger and misfortune, was\nenough to determine its being classed among good or evil omens.\n\nAn example of rather a different kind from any of these, but falling under\nthe same principle, is the famous attempt on which so much labor and\ningenuity were expended by the alchemists, to make gold potable. The\nmotive to this was a conceit that potable gold could be no other than the\nuniversal medicine; and why gold? Because it was so precious. It must have\nall marvelous properties as a physical substance, because the mind was\nalready accustomed to marvel at it.\n\nFrom a similar feeling, \u201cevery substance,\u201d says Dr. Paris,(231) \u201cwhose\norigin is involved in mystery, has at different times been eagerly applied\nto the purposes of medicine. Not long since, one of those showers which\nare now known to consist of the excrements of insects, fell in the north\nof Italy; the inhabitants regarded it as manna, or some supernatural\npanacea, and they swallowed it with such avidity, that it was only by\nextreme address that a small quantity was obtained for a chemical\nexamination.\u201d The superstition, in this instance, though doubtless partly\nof a religious character, probably in part also arose from the prejudice\nthat a wonderful thing must of course have wonderful properties.\n\n\u00a7 3. The instances of _a priori_ fallacy which we have hitherto cited\nbelong to the class of vulgar errors, and do not now, nor in any but a\nrude age ever could, impose upon minds of any considerable attainments.\nBut those to which we are about to proceed, have been, and still are, all\nbut universally prevalent among thinkers. The same disposition to give\nobjectivity to a law of the mind\u2014to suppose that what is true of our ideas\nof things must be true of the things themselves\u2014exhibits itself in many of\nthe most accredited modes of philosophical investigation, both on physical\nand on metaphysical subjects. In one of its most undisguised\nmanifestations, it embodies itself in two maxims, which lay claim to\naxiomatic truth: Things which we can not think of together, can not\nco-exist; and Things which we can not help thinking of together, must\nco-exist. I am not sure that the maxims were ever expressed in these\nprecise words, but the history both of philosophy and of popular opinions\nabounds with exemplifications of both forms of the doctrine.\n\nTo begin with the latter of them: Things which we can not think of except\ntogether, must exist together. This is assumed in the generally received\nand accredited mode of reasoning which concludes that A must accompany B\nin point of fact, because \u201cit is involved in the idea.\u201d Such thinkers do\nnot reflect that the idea, being a result of abstraction, ought to conform\nto the facts, and can not make the facts conform to it. The argument is at\nmost admissible as an appeal to authority; a surmise, that what is now\npart of the idea, must, before it became so, have been found by previous\ninquirers in the facts. Nevertheless, the philosopher who more than all\nothers made professions of rejecting authority, Descartes, constructed his\nsystem on this very basis. His favorite device for arriving at truth, even\nin regard to outward things, was by looking into his own mind for it.\n\u201cCredidi me,\u201d says his celebrated maxim, \u201cpro regul\u00e2 generali sumere\nposse, omne id quod vald\u00e8 dilucid\u00e8 et distinct\u00e8 concipiebam, verum esse;\u201d\nwhatever can be very clearly conceived must certainly exist; that is, as\nhe afterward explains it, if the idea includes existence. And on this\nground he infers that geometrical figures really exist, because they can\nbe distinctly conceived. Whenever existence is \u201cinvolved in an idea,\u201d a\nthing conformable to the idea must really exist; which is as much as to\nsay, whatever the idea contains must have its equivalent in the thing; and\nwhat we are not able to leave out of the idea can not be absent from the\nreality.(232) This assumption pervades the philosophy not only of\nDescartes, but of all the thinkers who received their impulse mainly from\nhim, in particular the two most remarkable among them, Spinoza and\nLeibnitz, from whom the modern German metaphysical philosophy is\nessentially an emanation. I am indeed disposed to think that the fallacy\nnow under consideration has been the cause of two-thirds of the bad\nphilosophy, and especially of the bad metaphysics, which the human mind\nhas never ceased to produce. Our general ideas contain nothing but what\nhas been put into them, either by our passive experience, or by our active\nhabits of thought; and the metaphysicians in all ages, who have attempted\nto construct the laws of the universe by reasoning from our supposed\nnecessities of thought, have always proceeded, and only could proceed, by\nlaboriously finding in their own minds what they themselves had formerly\nput there, and evolving from their ideas of things what they had first\ninvolved in those ideas. In this way all deeply-rooted opinions and\nfeelings are enabled to create apparent demonstrations of their truth and\nreasonableness, as it were, out of their own substance.\n\nThe other form of the fallacy: Things which we can not think of together\ncan not exist together\u2014including as one of its branches, that what we can\nnot think of as existing can not exist at all\u2014may thus be briefly\nexpressed: Whatever is inconceivable must be false.\n\nAgainst this prevalent doctrine I have sufficiently argued in a former\nBook,(233) and nothing is required in this place but examples. It was long\nheld that Antipodes were impossible because of the difficulty which was\nfound in conceiving persons with their heads in the same direction as our\nfeet. And it was one of the received arguments against the Copernican\nsystem, that we can not conceive so great a void space as that system\nsupposes to exist in the celestial regions. When men\u2019s imaginations had\nalways been used to conceive the stars as firmly set in solid spheres,\nthey naturally found much difficulty in imagining them in so different,\nand, as it doubtless appeared to them, so precarious a situation. But they\nhad no right to mistake the limitation (whether natural, or, as it in fact\nproved, only artificial) of their own faculties, for an inherent\nlimitation of the possible modes of existence in the universe.\n\nIt may be said in objection, that the error in these cases was in the\nminor premise, not the major; an error of fact, not of principle; that it\ndid not consist in supposing that what is inconceivable can not be true,\nbut in supposing antipodes to be inconceivable, when present experience\nproves that they can be conceived. Even if this objection were allowed,\nand the proposition that what is inconceivable can not be true were\nsuffered to remain unquestioned as a speculative truth, it would be a\ntruth on which no practical consequence could ever be founded, since, on\nthis showing, it is impossible to affirm of any proposition, not being a\ncontradiction in terms, that it is inconceivable. Antipodes were really,\nnot fictitiously, inconceivable to our ancestors: they are indeed\nconceivable to us; and as the limits of our power of conception have been\nso largely extended, by the extension of our experience and the more\nvaried exercise of our imagination, so may posterity find many\ncombinations perfectly conceivable to them which are inconceivable to us.\nBut, as beings of limited experience, we must always and necessarily have\nlimited conceptive powers; while it does not by any means follow that the\nsame limitation obtains in the possibilities of Nature, nor even in her\nactual manifestations.\n\nRather more than a century and a half ago it was a scientific maxim,\ndisputed by no one, and which no one deemed to require any proof, that \u201ca\nthing can not act where it is not.\u201d(234) With this weapon the Cartesians\nwaged a formidable war against the theory of gravitation, which, according\nto them, involving so obvious an absurdity, must be rejected _in limine_:\nthe sun could not possibly act upon the earth, not being there. It was not\nsurprising that the adherents of the old systems of astronomy should urge\nthis objection against the new; but the false assumption imposed equally\non Newton himself, who, in order to turn the edge of the objection,\nimagined a subtle ether which filled up the space between the sun and the\nearth, and by its intermediate agency was the proximate cause of the\nphenomena of gravitation. \u201cIt is inconceivable,\u201d said Newton, in one of\nhis letters to Dr. Bentley,(235) \u201cthat inanimate brute matter should,\nwithout the mediation of something else, which is not material, operate\nupon and affect other matter _without mutual contact_.... That gravity\nshould be innate, inherent, and essential to matter, so that one body may\nact on another, at a distance, through a vacuum, without the mediation of\nany thing else, by and through which their action and force may be\nconveyed from one to another, is to me so great an absurdity, that I\nbelieve no man, who in philosophical matters has a competent faculty of\nthinking, can ever fall into it.\u201d This passage should be hung up in the\ncabinet of every cultivator of science who is ever tempted to pronounce a\nfact impossible because it appears to him inconceivable. In our own day\none would be more tempted, though with equal injustice, to reverse the\nconcluding observation, and consider the seeing any absurdity at all in a\nthing so simple and natural, to be what really marks the absence of \u201ca\ncompetent faculty of thinking.\u201d No one now feels any difficulty in\nconceiving gravity to be, as much as any other property is, \u201cinherent and\nessential to matter,\u201d nor finds the comprehension of it facilitated in the\nsmallest degree by the supposition of an ether (though some recent\ninquirers do give this as an explanation of it); nor thinks it at all\nincredible that the celestial bodies can and do act where they, in actual\nbodily presence, are not. To us it is not more wonderful that bodies\nshould act upon one another \u201cwithout mutual contact,\u201d than that they\nshould do so when in contact; we are familiar with both these facts, and\nwe find them equally inexplicable, but equally easy to believe. To Newton,\nthe one, because his imagination was familiar with it, appeared natural\nand a matter of course, while the other, for the contrary reason, seemed\ntoo absurd to be credited.\n\nIt is strange that any one, after such a warning, should rely implicitly\non the evidence _a priori_ of such propositions as these, that matter can\nnot think; that space, or extension, is infinite; that nothing can be made\nout of nothing (_ex nihilo nihil fit_). Whether these propositions are\ntrue or not this is not the place to determine, nor even whether the\nquestions are soluble by the human faculties. But such doctrines are no\nmore self-evident truths, than the ancient maxim that a thing can not act\nwhere it is not, which probably is not now believed by any educated person\nin Europe.(236) Matter can not think; why? because we _can not conceive_\nthought to be annexed to any arrangement of material particles. Space is\ninfinite, because having never known any part of it which had not other\nparts beyond it, we _can not conceive_ an absolute termination. _Ex nihilo\nnihil fit_, because having never known any physical product without a\npre-existing physical material, we _can not_, or think we can not,\n_imagine_ a creation out of nothing. But these things may in themselves be\nas conceivable as gravitation without an intervening medium, which Newton\nthought too great an absurdity for any person of a competent faculty of\nphilosophical thinking to admit: and even supposing them not conceivable,\nthis, for aught we know, may be merely one of the limitations of our very\nlimited minds, and not in nature at all.\n\nNo writer has more directly identified himself with the fallacy now under\nconsideration, or has embodied it in more distinct terms, than Leibnitz.\nIn his view, unless a thing was not merely conceivable, but even\nexplainable, it could not exist in nature. All _natural_ phenomena,\naccording to him, must be susceptible of being accounted for _a priori_.\nThe only facts of which no explanation could be given but the will of God,\nwere miracles properly so called. \u201cJe reconnais,\u201d says he,(237) \u201cqu\u2019il\nn\u2019est pas permis de nier ce qu\u2019on n\u2019entend pas; mais j\u2019ajoute qu\u2019on a\ndroit de nier (au moins dans l\u2019ordre naturel) ce que absolument n\u2019est\npoint intelligible ni explicable. Je soutiens aussi ... qu\u2019enfin la\nconception des cr\u00e9atures n\u2019est pas la mesure du pouvoir de Dieu, mais que\nleur conceptivit\u00e9, ou force de concevoir, est la mesure du pouvoir de la\nnature, tout ce qui est conforme \u00e0 l\u2019ordre naturel pouvant \u00eatre con\u00e7u ou\nentendu par quelque cr\u00e9ature.\u201d\n\nNot content with assuming that nothing can be true which we are unable to\nconceive, scientific inquirers have frequently given a still further\nextension to the doctrine, and held that, even of things not altogether\ninconceivable, that which we can conceive with the greatest ease is\nlikeliest to be true. It was long an admitted axiom, and is not yet\nentirely discredited, that \u201cnature always acts by the simplest means,\u201d\n_i.e._, by those which are most easily conceivable.(238) A large\nproportion of all the errors ever committed in the investigation of the\nlaws of nature, have arisen from the assumption that the most familiar\nexplanation or hypothesis must be the truest.\n\nOne of the most instructive facts in scientific history is the pertinacity\nwith which the human mind clung to the belief that the heavenly bodies\nmust move in circles, or be carried round by the revolution of spheres;\nmerely because those were in themselves the simplest suppositions: though,\nto make them accord with the facts which were ever contradicting them more\nand more, it became necessary to add sphere to sphere and circle to\ncircle, until the original simplicity was converted into almost\ninextricable complication.\n\n\u00a7 4. We pass to another _a priori_ fallacy or natural prejudice, allied to\nthe former, and originating, as that does, in the tendency to presume an\nexact correspondence between the laws of the mind and those of things\nexternal to it. The fallacy may be enunciated in this general\nform\u2014Whatever can be thought of apart exists apart: and its most\nremarkable manifestation consists in the personification of abstractions.\nMankind in all ages have had a strong propensity to conclude that wherever\nthere is a name, there must be a distinguishable separate entity\ncorresponding to the name; and every complex idea which the mind has\nformed for itself by operating upon its conceptions of individual things,\nwas considered to have an outward objective reality answering to it. Fate,\nChance, Nature, Time, Space, were real beings, nay, even gods. If the\nanalysis of qualities in the earlier part of this work be correct, names\nof qualities and names of substances stand for the very same sets of facts\nor phenomena; _whiteness_ and _a white thing_ are only different phrases,\nrequired by convenience for speaking of the same external fact under\ndifferent relations. Not such, however, was the notion which this verbal\ndistinction suggested of old, either to the vulgar or to the scientific.\nWhiteness was an entity, inhering or sticking in the white substance: and\nso of all other qualities. So far was this carried, that even concrete\ngeneral terms were supposed to be, not names of indefinite numbers of\nindividual substances, but names of a peculiar kind of entities termed\nUniversal Substances. Because we can think and speak of man in general,\nthat is, of all persons in so far as possessing the common attributes of\nthe species, without fastening our thoughts permanently on some one\nindividual person; therefore man in general was supposed to be, not an\naggregate of individual persons, but an abstract or universal man,\ndistinct from these.\n\nIt may be imagined what havoc metaphysicians trained in these habits made\nwith philosophy, when they came to the largest generalizations of all.\n_Substanti\u00e6 Secund\u00e6_ of any kind were bad enough, but such Substanti\u00e6\nSecund\u00e6 as \u03c4\u1f78 \u1f44\u03bd, for example, and \u03c4\u1f78 \u1f14\u03bd, standing for peculiar entities\nsupposed to be inherent in all things which _exist_, or in all which are\nsaid to be _one_, were enough to put an end to all intelligible\ndiscussion; especially since, with a just perception that the truths which\nphilosophy pursues are _general_ truths, it was soon laid down that these\ngeneral substances were the only subjects of science, being immutable,\nwhile individual substances cognizable by the senses, being in a perpetual\nflux, could not be the subject of real knowledge. This misapprehension of\nthe import of general language constitutes Mysticism, a word so much\noftener written and spoken than understood. Whether in the Vedas, in the\nPlatonists, or in the Hegelians, mysticism is neither more nor less than\nascribing objective existence to the subjective creations of our own\nfaculties, to ideas or feelings of the mind; and believing that by\nwatching and contemplating these ideas of its own making, it can read in\nthem what takes place in the world without.\n\n\u00a7 5. Proceeding with the enumeration of _a priori_ fallacies, and\nendeavoring to arrange them with as much reference as possible to their\nnatural affinities, we come to another, which is also nearly allied to the\nfallacy preceding the last, standing in the same relation to one variety\nof it as the fallacy last mentioned does to the other. This, too,\nrepresents nature as under incapacities corresponding to those of our\nintellect; but instead of only asserting that nature can not do a thing\nbecause we can not conceive it done, goes the still greater length of\naverring that nature does a particular thing, on the sole ground that we\ncan see no reason why she should not. Absurd as this seems when so plainly\nstated, it is a received principle among scientific authorities for\ndemonstrating _a priori_ the laws of physical phenomena. A phenomenon must\nfollow a certain law, because we see no reason why it should deviate from\nthat law in one way rather than in another. This is called the Principle\nof the Sufficient Reason;(239) and by means of it philosophers often\nflatter themselves that they are able to establish, without any appeal to\nexperience, the most general truths of experimental physics.\n\nTake, for example, two of the most elementary of all laws, the law of\ninertia and the first law of motion. A body at rest can not, it is\naffirmed, begin to move unless acted upon by some external force; because,\nif it did, it must either move up or down, forward or backward, and so\nforth; but if no outward force acts upon it, there can be _no reason_ for\nits moving up rather than down, or down rather than up, etc., _ergo_, it\nwill not move at all.\n\nThis reasoning I conceive to be entirely fallacious, as indeed Dr. Brown,\nin his treatise on Cause and Effect, has shown with great acuteness and\njustness of thought. We have before remarked, that almost every fallacy\nmay be referred to different genera by different modes of filling up the\nsuppressed steps; and this particular one may, at our option, be brought\nunder _petitio principii_. It supposes that nothing can be a \u201csufficient\nreason\u201d for a body\u2019s moving in one particular direction, except some\nexternal force. But this is the very thing to be proved. Why not some\n_internal_ force? Why not the law of the thing\u2019s own nature? Since these\nphilosophers think it necessary to prove the law of inertia, they of\ncourse do not suppose _it_ to be self-evident; they must, therefore, be of\nopinion that previously to all proof, the supposition of a body\u2019s moving\nby internal impulse is an admissible hypothesis; but if so, why is not the\nhypothesis also admissible, that the internal impulse acts naturally in\nsome one particular direction, not in another? If spontaneous motion might\nhave been the law of matter, why not spontaneous motion toward the sun,\ntoward the earth, or toward the zenith? Why not, as the ancients supposed,\ntoward a particular place in the universe, appropriated to each particular\nkind of substance? Surely it is not allowable to say that spontaneity of\nmotion is credible in itself, but not credible if supposed to take place\nin any determinate direction.\n\nIndeed, if any one chose to assert that all bodies when uncontrolled set\nout in a direct line toward the North Pole, he might equally prove his\npoint by the principle of the Sufficient Reason. By what right is it\nassumed that a state of rest is the particular state which can not be\ndeviated from without special cause? Why not a state of motion, and of\nsome particular sort of motion? Why may we not say that the natural state\nof a horse left to himself is to amble, because otherwise he must either\ntrot, gallop, or stand still, and because we know no reason why he should\ndo one of these rather than another? If this is to be called an unfair use\nof the \u201csufficient reason,\u201d and the other a fair one, there must be a\ntacit assumption that a state of rest is more natural to a horse than a\nstate of ambling. If this means that it is the state which the animal will\nassume when left to himself, that is the very point to be proved; and if\nit does not mean this, it can only mean that a state of rest is the\nsimplest state, and therefore the most likely to prevail in nature, which\nis one of the fallacies or natural prejudices we have already examined.\n\nSo again of the First Law of Motion; that a body once moving will, if left\nto itself, continue to move uniformly in a straight line. An attempt is\nmade to prove this law by saying, that if not, the body must deviate\neither to the right or to the left, and that there is no reason why it\nshould do one more than the other. But who could know, antecedently to\nexperience, whether there was a reason or not? Might it not be the nature\nof bodies, or of some particular bodies, to deviate toward the right? or\nif the supposition is preferred, toward the east, or south? It was long\nthought that bodies, terrestrial ones at least, had a natural tendency to\ndeflect downward; and there is no shadow of any thing objectionable in the\nsupposition, except that it is not true. The pretended proof of the law of\nmotion is even more manifestly untenable than that of the law of inertia,\nfor it is flagrantly inconsistent; it assumes that the continuance of\nmotion in the direction first taken is more natural than deviation either\nto the right or to the left, but denies that one of these can possibly be\nmore natural than the other. All these fancies of the possibility of\nknowing what is natural or not natural by any other means than experience,\nare, in truth, entirely futile. The real and only proof of the laws of\nmotion, or of any other law of the universe, is experience; it is simply\nthat no other suppositions explain or are consistent with the facts of\nuniversal nature.\n\nGeometers have, in all ages, been open to the imputation of endeavoring to\nprove the most general facts of the outward world by sophistical\nreasoning, in order to avoid appeals to the senses. Archimedes, says\nProfessor Playfair,(240) established some of the elementary propositions\nof statics by a process in which he \u201cborrows no principle from experiment,\nbut establishes his conclusion entirely by reasoning _a priori_. He\nassumes, indeed, that equal bodies, at the ends of the equal arms of a\nlever, will balance one another; and also that a cylinder or\nparallelopiped of homogeneous matter, will be balanced about its centre of\nmagnitude. These, however, are not inferences from experience; they are,\nproperly speaking, conclusions deduced from the principle of the\nSufficient Reason.\u201d And to this day there are few geometers who would not\nthink it far more scientific to establish these or any other premises in\nthis way, than to rest their evidence on that familiar experience which in\nthe case in question might have been so safely appealed to.\n\n\u00a7 6. Another natural prejudice, of most extensive prevalence, and which\nhad a great share in producing the errors fallen into by the ancients in\ntheir physical inquiries, was this: That the differences in nature must\ncorrespond to our received distinctions: that effects which we are\naccustomed, in popular language, to call by different names, and arrange\nin different classes, must be of different natures, and have different\ncauses. This prejudice, so evidently of the same origin with those already\ntreated of, marks more especially the earliest stage of science, when it\nhas not yet broken loose from the trammels of every-day phraseology. The\nextraordinary prevalence of the fallacy among the Greek philosophers may\nbe accounted for by their generally knowing no other language than their\nown; from which it was a consequence that their ideas followed the\naccidental or arbitrary combinations of that language, more completely\nthan can happen among the moderns to any but illiterate persons. They had\ngreat difficulty in distinguishing between things which their language\nconfounded, or in putting mentally together things which it distinguished;\nand could hardly combine the objects in nature, into any classes but those\nwhich were made for them by the popular phrases of their own country; or\nat least could not help fancying those classes to be natural and all\nothers arbitrary and artificial. Accordingly, scientific investigation\namong the Greek schools of speculation and their followers in the Middle\nAges, was little more than a mere sifting and analyzing of the notions\nattached to common language. They thought that by determining the meaning\nof words, they could become acquainted with facts. \u201cThey took for\ngranted,\u201d says Dr. Whewell,(241) \u201cthat philosophy must result from the\nrelations of those notions which are involved in the common use of\nlanguage, and they proceeded to seek it by studying such notions.\u201d In his\nnext chapter, Dr. Whewell has so well illustrated and exemplified this\nerror, that I shall take the liberty of quoting him at some length.\n\n\u201cThe propensity to seek for principles in the common usages of language\nmay be discerned at a very early period. Thus we have an example of it in\na saying which is reported of Thales, the founder of Greek philosophy.\nWhen he was asked, \u2018What is the _greatest_ thing?\u2019 he replied \u2018_Place_;\nfor all other things are _in_ the world, but the world is _in_ it.\u2019 In\nAristotle we have the consummation of this mode of speculation. The usual\npoint from which he starts in his inquiries is, that _we say_ thus or thus\nin common language. Thus, when he has to discuss the question whether\nthere be, in any part of the universe, a void, or space in which there is\nnothing, he inquires first in how many senses we say that one thing is\n_in_ another. He enumerates many of these; we say the part is in the\nwhole, as the finger is _in_ the hand; again we say, the species is in the\ngenus, as man is included _in_ animal; again, the government of Greece is\n_in_ the king; and various other senses are described and exemplified, but\nof all these _the most proper_ is when we say a thing is _in_ a vessel,\nand generally _in place_. He next examines what _place_ is, and comes to\nthis conclusion, that \u2018if about a body there be another body including it,\nit is in place, and if not, not.\u2019 A body moves when it changes its place;\nbut he adds, that if water be in a vessel, the vessel being at rest, the\nparts of the water may still move, for they are included by each other; so\nthat while the whole does not change its place, the parts may change their\nplace in a circular order. Proceeding then to the question of a _void_, he\nas usual examines the different senses in which the term is used, and\nadopts as the most proper, _place without matter_, with no useful result.\n\n\u201cAgain, in a question concerning mechanical action, he says, \u2018When a man\nmoves a stone by pushing it with a stick, _we_ say both that the man moves\nthe stone, and that the stick moves the stone, but the latter _more\nproperly_.\u2019\n\n\u201cAgain, we find the Greek philosophers applying themselves to extract\ntheir dogmas from the most general and abstract notions which they could\ndetect; for example, from the conception of the Universe as One or as Many\nthings. They tried to determine how far we may, or must, combine with\nthese conceptions that of a whole, of parts, of number, of limits, of\nplace, of beginning or end, of full or void, of rest or motion, of cause\nand effect, and the like. The analysis of such conceptions with such a\nview, occupies, for instance, almost the whole of Aristotle\u2019s Treatise on\nthe Heavens.\u201d\n\nThe following paragraph merits particular attention: \u201cAnother mode of\nreasoning, very widely applied in these attempts, was the _doctrine of\ncontrarieties_, in which it was assumed that adjectives or substances\nwhich are in common language, or in some abstract mode of conception,\nopposed to each other, must point at some fundamental antithesis in\nnature, which it is important to study. Thus Aristotle says that the\nPythagoreans, from the contrasts which number suggests, collected ten\nprinciples\u2014Limited and Unlimited, Odd and Even, One and Many, Right and\nLeft, Male and Female, Rest and Motion, Straight and Curved, Light and\nDarkness, Good and Evil, Square and Oblong.... Aristotle himself deduced\nthe doctrine of four elements and other dogmas by oppositions of the same\nkind.\u201d\n\nOf the manner in which, from premises obtained in this way, the ancients\nattempted to deduce laws of nature, an example is given in the same work a\nfew pages further on. \u201cAristotle decides that there is no void on such\narguments as this. In a void there could be no difference of up and down;\nfor as in nothing there are no differences, so there are none in a\nprivation or negation; but a void is merely a privation or negation of\nmatter; therefore, in a void, bodies could not move up and down, which it\nis in their nature to do. It is easily seen\u201d (Dr. Whewell very justly\nadds) \u201cthat such a mode of reasoning elevates the familiar forms of\nlanguage, and the intellectual connections of terms, to a supremacy over\nfacts; making truth depend upon whether terms are or are not privative,\nand whether we say that bodies fall _naturally_.\u201d\n\nThe propensity to assume that the same relations obtain between objects\nthemselves, which obtain between our ideas of them, is here seen in the\nextreme stage of its development. For the mode of philosophizing,\nexemplified in the foregoing instances, assumes no less than that the\nproper way of arriving at knowledge of nature, is to study nature itself\nsubjectively; to apply our observation and analysis not to the facts, but\nto the common notions entertained of the facts.\n\nMany other equally striking examples may be given of the tendency to\nassume that things which for the convenience of common life are placed in\ndifferent classes, must differ in every respect. Of this nature was the\nuniversal and deeply-rooted prejudice of antiquity and the Middle Ages,\nthat celestial and terrestrial phenomena must be essentially different,\nand could in no manner or degree depend on the same laws. Of the same\nkind, also, was the prejudice against which Bacon contended, that nothing\nproduced by nature could be successfully imitated by man: \u201cCalorem solis\net ignis toto genere differre; ne scilicet homines putent se per opera\nignis, aliquid simile iis qu\u00e6 in Natura fiunt, educere et formare posse;\u201d\nand again, \u201cCompositionem tantum opus Hominis, Mistionem vero opus solius\nNatur\u00e6 esse: ne scilicet homines sperent aliquam ex arte Corporum\nnaturalium generationem aut transformationem.\u201d(242) The grand distinction\nin the ancient scientific speculations, between natural and violent\nmotions, though not without a plausible foundation in the appearances\nthemselves, was doubtless greatly recommended to adoption by its\nconformity to this prejudice.\n\n\u00a7 7. From the fundamental error of the scientific inquirers of antiquity,\nwe pass, by a natural association, to a scarcely less fundamental one of\ntheir great rival and successor, Bacon. It has excited the surprise of\nphilosophers that the detailed system of inductive logic, which this\nextraordinary man labored to construct, has been turned to so little\ndirect use by subsequent inquirers, having neither continued, except in a\nfew of its generalities, to be recognized as a theory, nor having\nconducted in practice to any great scientific results. But this, though\nnot unfrequently remarked, has scarcely received any plausible\nexplanation; and some, indeed, have preferred to assert that all rules of\ninduction are useless, rather than suppose that Bacon\u2019s rules are grounded\non an insufficient analysis of the inductive process. Such, however, will\nbe seen to be the fact, as soon as it is considered, that Bacon entirely\noverlooked Plurality of Causes. All his rules tacitly imply the\nassumption, so contrary to all we now know of nature, that a phenomenon\ncan not have more than one cause.\n\nWhen he is inquiring into what he terms the forma _calidi aut frigidi,\ngravis aut levis, sicci aut humidi_, and the like, he never for an instant\ndoubts that there is some one thing, some invariable condition or set of\nconditions, which is present in all cases of heat, or cold, or whatever\nother phenomenon he is considering; the only difficulty being to find what\nit is; which accordingly he tries to do by a process of elimination,\nrejecting or excluding, by negative instances, whatever is not the _forma_\nor cause, in order to arrive at what is. But, that this _forma_ or cause\nis _one_ thing, and that it is the same in all hot objects, he has no more\ndoubt of, than another person has that there is always some cause _or\nother_. In the present state of knowledge it could not be necessary, even\nif we had not already treated so fully of the question, to point out how\nwidely this supposition is at variance with the truth. It is particularly\nunfortunate for Bacon that, falling into this error, he should have fixed\nalmost exclusively upon a class of inquiries in which it was especially\nfatal; namely, inquiries into the causes of the sensible qualities of\nobjects. For his assumption, groundless in every case, is false in a\npeculiar degree with respect to those sensible qualities. In regard to\nscarcely any of them has it been found possible to trace any unity of\ncause, any set of conditions invariably accompanying the quality. The\nconjunctions of such qualities with one another constitute the variety of\nKinds, in which, as already remarked, it has not been found possible to\ntrace any law. Bacon was seeking for what did not exist. The phenomenon of\nwhich he sought for the one cause has oftenest no cause at all, and when\nit has, depends (as far as hitherto ascertained) on an unassignable\nvariety of distinct causes.\n\nAnd on this rock every one must split, who represents to himself as the\nfirst and fundamental problem of science to ascertain what is the cause of\na given effect, rather than what are the effects of a given cause. It was\nshown, in an early stage of our inquiry into the nature of Induction,(243)\nhow much more ample are the resources which science commands for the\nlatter than for the former inquiry, since it is upon the latter only that\nwe can throw any direct light by means of experiment; the power of\nartificially producing an effect, implying a previous knowledge of at\nleast one of its causes. If we discover the causes of effects, it is\ngenerally by having previously discovered the effects of causes; the\ngreatest skill in devising crucial instances for the former purpose may\nonly end, as Bacon\u2019s physical inquiries did, in no result at all. Was it\nthat his eagerness to acquire the power of producing for man\u2019s benefit\neffects of practical importance to human life, rendering him impatient of\npursuing that end by a circuitous route, made even him, the champion of\nexperiment, prefer the direct mode, though one of mere observation, to the\nindirect, in which alone experiment was possible? Or had even Bacon not\nentirely cleared his mind from the notion of the ancients, that \u201crerum\ncognoscere _causas_\u201d was the sole object of philosophy, and that to\ninquire into the _effects_ of things belonged to servile and mechanical\narts?\n\nIt is worth remarking that, while the only efficient mode of cultivating\nspeculative science was missed from an undue contempt of manual\noperations, the false speculative views thus engendered gave in their turn\na false direction to such practical and mechanical aims as were suffered\nto exist. The assumption universal among the ancients and in the Middle\nAges, that there were _principles_ of heat and cold, dryness and moisture,\netc., led directly to a belief in alchemy; in a transmutation of\nsubstances, a change from one Kind into another. Why should it not be\npossible to make gold? Each of the characteristic properties of gold has\nits _forma_, its essence, its set of conditions, which if we could\ndiscover, and learn how to realize, we could superinduce that particular\nproperty upon any other substance, upon wood, or iron, or lime, or clay.\nIf, then, we could effect this with respect to every one of the essential\nproperties of the precious metal, we should have converted the other\nsubstance into gold. Nor did this, if once the premises were granted,\nappear to transcend the real powers of mankind. For daily experience\nshowed that almost every one of the distinctive sensible properties of any\nobject, its consistence, its color, its taste, its smell, its shape,\nadmitted of being totally changed by fire, or water, or some other\nchemical agent. The _form\u00e6_ of all those qualities seeming, therefore, to\nbe within human power either to produce or to annihilate, not only did the\ntransmutation of substances appear abstractedly possible, but the\nemployment of the power, at our choice, for practical ends, seemed by no\nmeans hopeless.(244)\n\nA prejudice, universal in the ancient world, and from which Bacon was so\nfar from being free, that it pervaded and vitiated the whole practical\npart of his system of logic, may with good reason be ranked high in the\norder of Fallacies of which we are now treating.\n\n\u00a7 8. There remains one _a priori_ fallacy or natural prejudice, the most\ndeeply-rooted, perhaps, of all which we have enumerated; one which not\nonly reigned supreme in the ancient world, but still possesses almost\nundisputed dominion over many of the most cultivated minds; and some of\nthe most remarkable of the numerous instances by which I shall think it\nnecessary to exemplify it, will be taken from recent thinkers. This is,\nthat the conditions of a phenomenon must, or at least probably will,\nresemble the phenomenon itself.\n\nConformably to what we have before remarked to be of frequent occurrence,\nthis fallacy might without much impropriety have been placed in a\ndifferent class, among Fallacies of Generalization; for experience does\nafford a certain degree of countenance to the assumption. The cause does,\nin very many cases, resemble its effect; like produces like. Many\nphenomena have a direct tendency to perpetuate their own existence, or to\ngive rise to other phenomena similar to themselves. Not to mention forms\nactually moulded on one another, as impressions on wax and the like, in\nwhich the closest resemblance between the effect and its cause is the very\nlaw of the phenomenon; all motion tends to continue itself, with its own\nvelocity, and in its own original direction; and the motion of one body\ntends to set others in motion, which is indeed the most common of the\nmodes in which the motions of bodies originate. We need scarcely refer to\ncontagion, fermentation, and the like; or to the production of effects by\nthe growth or expansion of a germ or rudiment resembling on a smaller\nscale the completed phenomenon, as in the growth of a plant or animal from\nan embryo, that embryo itself deriving its origin from another plant or\nanimal of the same kind. Again, the thoughts or reminiscences, which are\neffects of our past sensations, resemble those sensations; feelings\nproduce similar feelings by way of sympathy; acts produce similar acts by\ninvoluntary or voluntary imitation. With so many appearances in its favor,\nno wonder if a presumption naturally grew up, that causes must\n_necessarily_ resemble their effects, and that like could _only_ be\nproduced by like.\n\nThis principle of fallacy has usually presided over the fantastical\nattempts to influence the course of nature by conjectural means, the\nchoice of which was not directed by previous observation and experiment.\nThe guess almost always fixed upon some means which possessed features of\nreal or apparent resemblance to the end in view. If a charm was wanted, as\nby Ovid\u2019s Medea, to prolong life, all long-lived animals, or what were\nesteemed such, were collected and brewed into a broth:\n\n\n           nec defuit illic\n    Squamea Cinyphii tenuis membrana chelydri\n    Vivacisque jecur cervi: quibus insuper addit\n    Ora caputque novem cornicis s\u00e6cula pass\u00e6.\n\n\nA similar notion was embodied in the celebrated medical theory called the\n\u201cDoctrine of Signatures,\u201d \u201cwhich is no less,\u201d says Dr. Paris,(245) \u201cthan a\nbelief that every natural substance which possesses any medicinal virtue\nindicates by an obvious and well-marked external character the disease for\nwhich it is a remedy, or the object for which it should be employed.\u201d This\noutward character was generally some feature of resemblance, real or\nfantastical, either to the effect it was supposed to produce, or to the\nphenomenon over which its power was thought to be exercised. \u201cThus the\nlungs of a fox must be a specific for asthma, because that animal is\nremarkable for its strong powers of respiration. Turmeric has a brilliant\nyellow color, which indicates that it has the power of curing the\njaundice; for the same reason, poppies must relieve diseases of the head;\nAgaricus those of the bladder; _Cassia fistula_ the affections of the\nintestines, and Aristolochia the disorders of the uterus: the polished\nsurface and stony hardness which so eminently characterize the seeds of\nthe Lithospermum officinale (common gromwell) were deemed a certain\nindication of their efficacy in calculous and gravelly disorders; for a\nsimilar reason, the roots of the Saxifraga granulata (white saxifrage)\ngained reputation in the cure of the same disease; and the Euphrasia\n(eye-bright) acquired fame, as an application in complaints of the eye,\nbecause it exhibits a black spot in its corolla resembling the pupil. The\nblood-stone, the Heliotropium of the ancients, from the occasional small\nspecks or points of a blood-red color exhibited on its green surface, is\neven at this very day employed in many parts of England and Scotland to\nstop a bleeding from the nose; and nettle tea continues a popular remedy\nfor the cure of _Urticaria_. It is also asserted that some substances bear\nthe _signatures_ of the humors, as the petals of the red rose that of the\nblood, and the roots of rhubarb and the flowers of saffron that of the\nbile.\u201d\n\nThe early speculations respecting the chemical composition of bodies were\nrendered abortive by no circumstance more than by their invariably taking\nfor granted that the properties of the elements must resemble those of the\ncompounds which were formed from them.\n\nTo descend to more modern instances; it was long thought, and was stoutly\nmaintained by the Cartesians and even by Leibnitz against the Newtonian\nsystem (nor did Newton himself, as we have seen, contest the assumption,\nbut eluded it by an arbitrary hypothesis), that nothing (of a physical\nnature at least) could account for motion, except previous motion; the\nimpulse or impact of some other body. It was very long before the\nscientific world could prevail upon itself to admit attraction and\nrepulsion (_i.e._, spontaneous tendencies of particles to approach or\nrecede from one another) as ultimate laws, no more requiring to be\naccounted for than impulse itself, if indeed the latter were not, in\ntruth, resolvable into the former. From the same source arose the\ninnumerable hypotheses devised to explain those classes of motion which\nappeared more mysterious than others because there was no obvious mode of\nattributing them to impulse, as for example the voluntary motions of the\nhuman body. Such were the interminable systems of vibrations propagated\nalong the nerves, or animal spirits rushing up and down between the\nmuscles and the brain; which, if the facts could have been proved, would\nhave been an important addition to our knowledge of physiological laws;\nbut the mere invention, or arbitrary supposition of them, could not unless\nby the strongest delusion be supposed to render the phenomena of animal\nlife more comprehensible, or less mysterious. Nothing, however, seemed\nsatisfactory, but to make out that motion was caused by motion; by\nsomething like itself. If it was not one kind of motion, it must be\nanother. In like manner it was supposed that the physical qualities of\nobjects must arise from some similar quality, or perhaps only some quality\nbearing the same name, in the particles or atoms of which the objects were\ncomposed; that a sharp taste, for example, must arise from sharp\nparticles. And reversing the inference, the effects produced by a\nphenomenon must, it was supposed, resemble in their physical attributes\nthe phenomenon itself. The influences of the planets were supposed to be\nanalogous to their visible peculiarities: Mars, being of a red color,\nportended fire and slaughter; and the like.\n\nPassing from physics to metaphysics, we may notice among the most\nremarkable fruits of this _a priori_ fallacy two closely analogous\ntheories, employed in ancient and modern times to bridge over the chasm\nbetween the world of mind and that of matter; the _species sensibiles_ of\nthe Epicureans, and the modern doctrine of perception by means of ideas.\nThese theories are indeed, probably, indebted for their existence not\nsolely to the fallacy in question, but to that fallacy combined with\nanother natural prejudice already adverted to, that a thing can not act\nwhere it is not. In both doctrines it is assumed that the phenomenon which\ntakes place _in us_ when we see or touch an object, and which we regard as\nan effect of that object, or rather of its presence to our organs, must of\nnecessity resemble very closely the outward object itself. To fulfill this\ncondition, the Epicureans supposed that objects were constantly projecting\nin all directions impalpable images of themselves, which entered at the\neyes and penetrated to the mind; while modern metaphysicians, though they\nrejected this hypothesis, agreed in deeming it necessary to suppose that\nnot the thing itself, but a mental image or representation of it, was the\ndirect object of perception. Dr. Reid had to employ a world of argument\nand illustration to familiarize people with the truth, that the sensations\nor impressions on our minds need not necessarily be copies of, or bear any\nresemblance to, the causes which produce them; in opposition to the\nnatural prejudice which led people to assimilate the action of bodies upon\nour senses, and through them upon our minds, to the transfer of a given\nform from one object to another by actual moulding. The works of Dr. Reid\nare even now the most effectual course of study for detaching the mind\nfrom the prejudice of which this was an example. And the value of the\nservice which he thus rendered to popular philosophy is not much\ndiminished, although we may hold, with Brown, that he went too far in\nimputing the \u201cideal theory\u201d as an actual tenet, to the generality of the\nphilosophers who preceded him, and especially to Locke and Hume; for if\nthey did not themselves consciously fall into the error, unquestionably\nthey often led their readers into it.\n\nThe prejudice, that the conditions of a phenomenon must resemble the\nphenomenon, is occasionally exaggerated, at least verbally, into a still\nmore palpable absurdity; the conditions of the thing are spoken of as if\nthey _were_ the very thing itself. In Bacon\u2019s model inquiry, which\noccupies so great a space in the _Novum Organum_, the _inquisitio in\nformam calidi_, the conclusion which he favors is that heat is a kind of\nmotion; meaning of course not the feeling of heat, but the conditions of\nthe feeling; meaning, therefore, only that wherever there is heat, there\nmust first be a particular kind of motion; but he makes no distinction in\nhis language between these two ideas, expressing himself as if heat, and\nthe conditions of heat, were one and the same thing. So the elder Darwin,\nin the beginning of his _Zoonomia_, says, \u201cThe word _idea_ has various\nmeanings in the writers of metaphysics; it is here used simply for those\nnotions of external things which our organs of sense bring us acquainted\nwith originally\u201d (thus far the proposition, though vague, is\nunexceptionable in meaning), \u201cand is defined a contraction, a motion, or\nconfiguration, of the fibres which constitute the immediate organ of\nsense.\u201d Our _notions_, a configuration of the fibres! What kind of\nlogician must he be who thinks that a phenomenon is _defined_ to _be_ the\ncondition on which he supposes it to depend? Accordingly he says soon\nafter, not that our ideas are caused by, or consequent on, certain organic\nphenomena, but \u201cour ideas _are_ animal motions of the organs of sense.\u201d\nAnd this confusion runs through the four volumes of the _Zoonomia_; the\nreader never knows whether the writer is speaking of the effect, or of its\nsupposed cause; of the idea, a state of mental consciousness, or of the\nstate of the nerves and brain which he considers it to presuppose.\n\nI have given a variety of instances in which the natural prejudice, that\ncauses and their effects must resemble one another, has operated in\npractice so as to give rise to serious errors. I shall now go further, and\nproduce from writings even of the present or very recent times, instances\nin which this prejudice is laid down as an established principle. M.\nVictor Cousin, in the last of his celebrated lectures on Locke, enunciates\nthe maxim in the following unqualified terms: \u201cTout ce qui est vrai de\nl\u2019effet, est vrai de la cause.\u201d A doctrine to which, unless in some\npeculiar and technical meaning of the words cause and effect, it is not to\nbe imagined that any person would literally adhere; but he who could so\nwrite must be far enough from seeing that the very reverse might be the\neffect; that there is nothing impossible in the supposition that no one\nproperty which is true of the effect might be true of the cause. Without\ngoing quite so far in point of expression, Coleridge, in his _Biographia\nLiteraria_,(246) affirms as an \u201cevident truth,\u201d that \u201cthe law of causality\nholds only between homogeneous things, _i.e._, things having some common\nproperty,\u201d and therefore \u201ccan not extend from one world into another, its\nopposite;\u201d hence, as mind and matter have no common property, mind can not\nact upon matter, nor matter upon mind. What is this but the _a priori_\nfallacy of which we are speaking? The doctrine, like many others of\nColeridge, is taken from Spinoza, in the first book of whose _Ethica_ (_De\nDeo_) it stands as the Third Proposition, \u201cQu\u00e6 res nihil commune inter se\nhabent, earum una alterius causa esse non potest,\u201d and is there proved\nfrom two so-called axioms, equally gratuitous with itself; but Spinoza\never systematically consistent, pursued the doctrine to its inevitable\nconsequence, the materiality of God.\n\nThe same conception of impossibility led the ingenious and subtle mind of\nLeibnitz to his celebrated doctrine of a pre-established harmony. He, too,\nthought that mind could not act upon matter, nor matter upon mind, and\nthat the two, therefore, must have been arranged by their Maker like two\nclocks, which, though unconnected with one another, strike simultaneously,\nand always point to the same hour. Malebranche\u2019s equally famous theory of\nOccasional Causes was another form of the same conception; instead of\nsupposing the clocks originally arranged to strike together, he held that\nwhen the one strikes, God interposes, and makes the other strike in\ncorrespondence with it.\n\nDescartes, in like manner, whose works are a rich mine of almost every\ndescription of _a priori_ fallacy, says that the Efficient Cause must at\nleast have all the perfections of the effect, and for this singular\nreason: \u201cSi enim ponamus aliquid in ide\u00e2 reperiri quod non fuerit in ejus\ncaus\u00e2, hoc igitur habet a nihilo;\u201d of which it is scarcely a parody to\nsay, that if there be pepper in the soup there must be pepper in the cook\nwho made it, since otherwise the pepper would be without a cause. A\nsimilar fallacy is committed by Cicero, in his second book _De Finibus_,\nwhere, speaking in his own person against the Epicureans, he charges them\nwith inconsistency in saying that the pleasures of the mind had their\norigin from those of the body, and yet that the former were more valuable,\nas if the effect could surpass the cause. \u201cAnimi voluptas oritur propter\nvoluptatem corporis, et major est animi voluptas quam corporis? ita fit ut\ngratulator, l\u00e6tior sit quam is cui gratulatur.\u201d Even that, surely, is not\nan impossibility; a person\u2019s good fortune has often given more pleasure to\nothers than it gave to the person himself.\n\nDescartes, with no less readiness, applies the same principle the converse\nway, and infers the nature of the effects from the assumption that they\nmust, in this or that property or in all their properties, resemble their\ncause. To this class belong his speculations, and those of so many others\nafter him, tending to infer the order of the universe, not from\nobservation, but by _a priori_ reasoning from supposed qualities of the\nGodhead. This sort of inference was probably never carried to a greater\nlength than it was in one particular instance by Descartes, when, as a\nproof of one of his physical principles, that the quantity of motion in\nthe universe is invariable, he had recourse to the immutability of the\nDivine Nature. Reasoning of a very similar character is, however, nearly\nas common now as it was in his time, and does duty largely as a means of\nfencing off disagreeable conclusions. Writers have not yet ceased to\noppose the theory of divine benevolence to the evidence of physical facts,\nto the principle of population for example. And people seem in general to\nthink that they have used a very powerful argument, when they have said,\nthat to suppose some proposition true, would be a reflection on the\ngoodness or wisdom of the Deity. Put into the simplest possible terms,\ntheir argument is, \u201cIf it had depended on me, I would not have made the\nproposition true, therefore it is not true.\u201d Put into other words, it\nstands thus: \u201cGod is perfect, therefore (what I think) perfection must\nobtain in nature.\u201d But since in reality every one feels that nature is\nvery far from perfect, the doctrine is never applied consistently. It\nfurnishes an argument which (like many others of a similar character)\npeople like to appeal to when it makes for their own side. Nobody is\nconvinced by it, but each appears to think that it puts religion on his\nside of the question, and that it is a useful weapon of offense for\nwounding an adversary.\n\nAlthough several other varieties of _a priori_ fallacy might probably be\nadded to those here specified, these are all against which it seems\nnecessary to give any special caution. Our object is to open, without\nattempting or affecting to exhaust, the subject. Having illustrated,\ntherefore, this first class of Fallacies at sufficient length, I shall\nproceed to the second.\n\n\n\n\n                               Chapter IV.\n\n\nFallacies Of Observation.\n\n\n\u00a7 1. From the Fallacies which are properly Prejudices, or presumptions\nantecedent to, and superseding, proof, we pass to those which lie in the\nincorrect performance of the proving process. And as Proof, in its widest\nextent, embraces one or more, or all, of three processes, Observation,\nGeneralization, and Deduction, we shall consider in their order the errors\ncapable of being committed in these three operations. And first, of the\nfirst mentioned.\n\nA fallacy of misobservation may be either negative or positive; either\nNon-observation or Mal-observation. It is non-observation, when all the\nerror consists in overlooking, or neglecting, facts or particulars which\nought to have been observed. It is mal-observation, when something is not\nsimply unseen, but seen wrong; when the fact or phenomenon, instead of\nbeing recognized for what it is in reality, is mistaken for something\nelse.\n\n\u00a7 2. Non-observation may either take place by overlooking instances, or by\noverlooking some of the circumstances of a given instance. If we were to\nconclude that a fortune-teller was a true prophet, from not adverting to\nthe cases in which his predictions had been falsified by the event, this\nwould be non-observation of instances; but if we overlooked or remained\nignorant of the fact that in cases where the predictions had been\nfulfilled, he had been in collusion with some one who had given him the\ninformation on which they were grounded, this would be non-observation of\ncircumstances.\n\nThe former case, in so far as the act of induction from insufficient\nevidence is concerned, does not fall under this second class of Fallacies,\nbut under the third, Fallacies of Generalization. In every such case,\nhowever, there are two defects or errors instead of one; there is the\nerror of treating the insufficient evidence as if it were sufficient,\nwhich is a Fallacy of the third class; and there is the insufficiency\nitself; the not having better evidence; which, when such evidence, or, in\nother words, when other instances, were to be had, is Non-observation; and\nthe erroneous inference, so far as it is to be attributed to this cause,\nis a Fallacy of the second class.\n\nIt belongs not to our purpose to treat of non-observation as arising from\ncasual inattention, from general slovenliness of mental habits, want of\ndue practice in the use of the observing faculties, or insufficient\ninterest in the subject. The question pertinent to logic is\u2014Granting the\nwant of complete competency in the observer, on what point is that\ninsufficiency on his part likely to lead him wrong? or rather, what sorts\nof instances, or of circumstances in any given instance, are most likely\nto escape the notice of observers generally; of mankind at large.\n\n\u00a7 3. First, then, it is evident that when the instances on one side of a\nquestion are more likely to be remembered and recorded than those on the\nother; especially if there be any strong motive to preserve the memory of\nthe first, but not of the latter; these last are likely to be overlooked,\nand escape the observation of the mass of mankind. This is the recognized\nexplanation of the credit given, in spite of reason and evidence, to many\nclasses of impostors; to quack-doctors, and fortune-tellers in all ages;\nto the \u201ccunning man\u201d of modern times, and the oracles of old. Few have\nconsidered the extent to which this fallacy operates in practice, even in\nthe teeth of the most palpable negative evidence. A striking example of it\nis the faith which the uneducated portion of the agricultural classes, in\nthis and other countries, continue to repose in the prophecies as to\nweather supplied by almanac-makers; though every season affords to them\nnumerous cases of completely erroneous prediction; but as every season\nalso furnishes some cases in which the prediction is fulfilled, this is\nenough to keep up the credit of the prophet, with people who do not\nreflect on the number of instances requisite for what we have called, in\nour inductive terminology, the Elimination of Chance; since a certain\nnumber of casual coincidences not only may but will happen, between any\ntwo unconnected events.\n\nColeridge, in one of the essays in the _Friend_, has illustrated the\nmatter we are now considering, in discussing the origin of a proverb,\n\u201cwhich, differently worded, is to be found in all the languages of\nEurope,\u201d viz., \u201cFortune favors fools.\u201d He ascribes it partly to the\n\u201ctendency to exaggerate all effects that seem disproportionate to their\nvisible cause, and all circumstances that are in any way strongly\ncontrasted with our notions of the persons under them.\u201d Omitting some\nexplanations which would refer the error to mal-observation, or to the\nother species of non-observation (that of circumstances), I take up the\nquotation further on. \u201cUnforeseen coincidences may have greatly helped a\nman, yet if they have done for him only what possibly from his own\nabilities he might have effected for himself, his good luck will excite\nless attention, and the instances be less remembered. That clever men\nshould attain their objects seems natural, and we neglect the\ncircumstances that perhaps produced that success of themselves without the\nintervention of skill or foresight; but we dwell on the fact and remember\nit, as something strange, when the same happens to a weak or ignorant man.\nSo too, though the latter should fail in his undertakings from\nconcurrences that might have happened to the wisest man, yet his failure\nbeing no more than might have been expected and accounted for from his\nfolly, it lays no hold on our attention, but fleets away among the other\nundistinguished waves in which the stream of ordinary life murmurs by us,\nand is forgotten. Had it been as true as it was notoriously false, that\nthose all-embracing discoveries, which have shed a dawn of _science_ on\nthe _art_ of chemistry, and give no obscure promise of some one great\nconstitutive law, in the light of which dwell dominion and the power of\nprophecy; if these discoveries, instead of having been, as they really\nwere, preconcerted by meditation, and evolved out of his own intellect,\nhad occurred by a set of lucky _accidents_ to the illustrious father and\nfounder of philosophic alchemy; if they had presented themselves to\nProfessor Davy exclusively in consequence of his _luck_ in possessing a\nparticular galvanic battery; if this battery, as far as Davy was\nconcerned, had itself been an _accident_, and not (as in point of fact it\nwas) desired and obtained by him for the purpose of insuring the testimony\nof experience to his principles, and in order to bind down material nature\nunder the inquisition of reason, and force from her, as by torture,\nunequivocal answers to _prepared_ and _preconceived_ questions\u2014yet still\nthey would not have been talked of or described as instances of _luck_,\nbut as the natural results of his admitted genius and known skill. But\nshould an accident have disclosed similar discoveries to a mechanic at\nBirmingham or Sheffield, and if the man should grow rich in consequence,\nand partly by the envy of his neighbors and partly with good reason, be\nconsidered by them as a man _below par_ in the general powers of his\nunderstanding; then, \u2018Oh, what a lucky fellow! Well, Fortune _does_ favor\nfools\u2014that\u2019s for certain! It is always so!\u2019 And forthwith the exclaimer\nrelates half a dozen similar instances. Thus accumulating the one sort of\nfacts and never collecting the other, we do, as poets in their diction,\nand quacks of all denominations do in their reasoning, put a part for the\nwhole.\u201d\n\nThis passage very happily sets forth the manner in which, under the loose\nmode of induction which proceeds _per enumerationem simplicem_, not\nseeking for instances of such a kind as to be decisive of the question,\nbut generalizing from any which occur, or rather which are remembered,\nopinions grow up with the apparent sanction of experience, which have no\nfoundation in the laws of nature at all. \u201cItaque recte respondit ille\u201d (we\nmay say with Bacon(247)), \u201cqui cum suspensa tabula in templo ei\nmonstraretur eorum, qui vota solverant, quod naufragii periculo elapsi\nsint, atque interrogando premeretur, anne tum quidem Deorum numen\nagnosceret, qu\u00e6sivit denuo, _At ubi sunt illi depicti qui post vota\nnuncupata perierunt_? Eadem ratio est fere omnis superstitionis, ut in\nAstrologicis, in Somniis, Ominibus, Nemesibus, et hujusmodi; in quibus,\nhomines delectati hujusmodi vanitatibus, advertunt eventus, ubi implentur;\nast ubi fallunt, licet multo frequentius, tamen negligunt, et pr\u00e6tereunt.\u201d\nAnd he proceeds to say that, independently of the love of the marvelous,\nor any other bias in the inclinations, there is a natural tendency in the\nintellect itself to this kind of fallacy; since the mind is more moved by\naffirmative instances, though negative ones are of most use in philosophy:\n\u201cIs tamen humano intellectui error est proprius et perpetuus, ut magis\nmoveatur et excitetur Affirmativis quam Negativis; cum rite et ordine\n\u00e6quum se utrique pr\u00e6bere debeat; quin contra, in omni Axiomate vero\nconstituendo, major vis est instanti\u00e6 negativ\u00e6.\u201d\n\nBut the greatest of all causes of non-observation is a preconceived\nopinion. This it is which, in all ages, has made the whole race of\nmankind, and every separate section of it, for the most part unobservant\nof all facts, however abundant, even when passing under their own eyes,\nwhich are contradictory to any first appearance, or any received tenet. It\nis worth while to recall occasionally to the oblivious memory of mankind\nsome of the striking instances in which opinions that the simplest\nexperiment would have shown to be erroneous, continued to be entertained\nbecause nobody ever thought of trying that experiment. One of the most\nremarkable of these was exhibited in the Copernican controversy. The\nopponents of Copernicus argued that the earth did not move, because if it\ndid, a stone let fall from the top of a high tower would not reach the\nground at the foot of the tower, but at a little distance from it, in a\ncontrary direction to the earth\u2019s course; in the same manner (said they)\nas, if a ball is let drop from the mast-head while the ship is in full\nsail, it does not fall exactly at the foot of the mast, but nearer to the\nstern of the vessel. The Copernicans would have silenced these objectors\nat once if they had _tried_ dropping a ball from the mast-head, since they\nwould have found that it does fall exactly at the foot, as the theory\nrequires; but no; they admitted the spurious fact, and struggled vainly to\nmake out a difference between the two cases. \u201cThe ball was no _part_ of\nthe ship\u2014and the motion forward was not _natural_, either to the ship or\nto the ball. The stone, on the other hand, let fall from the top of the\ntower, was a _part_ of the earth; and therefore, the diurnal and annular\nrevolutions which were _natural_ to the earth, were also _natural_ to the\nstone; the stone would, therefore, retain the same motion with the tower,\nand strike the ground precisely at the bottom of it.\u201d(248)\n\nOther examples, scarcely less striking, are recorded by Dr. Whewell,(249)\nwhere imaginary laws of nature have continued to be received as real,\nmerely because no person had steadily looked at facts which almost every\none had the opportunity of observing. \u201cA vague and loose mode of looking\nat facts very easily observable, left men for a long time under the belief\nthat a body ten times as heavy as another falls ten times as fast; that\nobjects immersed in water are always magnified, without regard to the form\nof the surface; that the magnet exerts an irresistible force; that crystal\nis always found associated with ice; and the like. These and many others\nare examples how blind and careless man can be even in observation of the\nplainest and commonest appearances; and they show us that the mere\nfaculties of perception, although constantly exercised upon innumerable\nobjects, may long fail in leading to any exact knowledge.\u201d\n\nIf even on physical facts, and these of the most obvious character, the\nobserving faculties of mankind can be to this degree the passive slaves of\ntheir preconceived impressions, we need not be surprised that this should\nbe so lamentably true as all experience attests it to be, on things more\nnearly connected with their stronger feelings\u2014on moral, social, and\nreligious subjects. The information which an ordinary traveler brings back\nfrom a foreign country, as the result of the evidence of his senses, is\nalmost always such as exactly confirms the opinions with which he set out.\nHe has had eyes and ears for such things only as he expected to see. Men\nread the sacred books of their religion, and pass unobserved therein\nmultitudes of things utterly irreconcilable with even their own notions of\nmoral excellence. With the same authorities before them, different\nhistorians, alike innocent of intentional misrepresentation, see only what\nis favorable to Protestants or Catholics, royalists or republicans,\nCharles I. or Cromwell; while others, having set out with the\npreconception that extremes must be in the wrong, are incapable of seeing\ntruth and justice when these are wholly on one side.\n\nThe influence of a preconceived theory is well exemplified in the\nsuperstitions of barbarians respecting the virtues of medicaments and\ncharms. The negroes, among whom coral, as of old among ourselves, is worn\nas an amulet, affirm, according to Dr. Paris,(250) that its color \u201cis\nalways affected by the state of health of the wearer, it becoming paler in\ndisease.\u201d On a matter open to universal observation, a general proposition\nwhich has not the smallest vestige of truth is received as a result of\nexperience; the preconceived opinion preventing, it would seem, any\nobservation whatever on the subject.\n\n\u00a7 4. For illustration of the first species of non-observation, that of\nInstances, what has now been stated may suffice. But there may also be\nnon-observation of some material circumstances, in instances which have\nnot been altogether overlooked\u2014nay, which may be the very instances on\nwhich the whole superstructure of a theory has been founded. As, in the\ncases hitherto examined, a general proposition was too rashly adopted, on\nthe evidence of particulars, true indeed, but insufficient to support it;\nso in the cases to which we now turn, the particulars themselves have been\nimperfectly observed, and the singular propositions on which the\ngeneralization is grounded, or some at least of those singular\npropositions, are false.\n\nSuch, for instance, was one of the mistakes committed in the celebrated\nphlogistic theory; a doctrine which accounted for combustion by the\nextrication of a substance called phlogiston, supposed to be contained in\nall combustible matter. The hypothesis accorded tolerably well with\nsuperficial appearances; the ascent of flame naturally suggests the escape\nof a substance; and the visible residuum of ashes, in bulk and weight,\ngenerally falls extremely short of the combustible material. The error\nwas, non-observation of an important portion of the actual residue,\nnamely, the gaseous products of combustion. When these were at last\nnoticed and brought into account, it appeared to be a universal law, that\nall substances gain instead of losing weight by undergoing combustion; and\nafter the usual attempt to accommodate the old theory to the new fact by\nmeans of an arbitrary hypothesis (that phlogiston had the quality of\npositive levity instead of gravity), chemists were conducted to the true\nexplanation, namely, that instead of a substance separated, there was, on\nthe contrary, a substance absorbed.\n\nMany of the absurd practices which have been deemed to possess medicinal\nefficacy, have been indebted for their reputation to non-observance of\nsome accompanying circumstance which was the real agent in the cures\nascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby:\n\u201cWhenever any wound had been inflicted, this powder was applied to the\nweapon that had inflicted it, which was, moreover, covered with ointment,\nand dressed two or three times a day. The wound itself, in the mean time,\nwas directed to be brought together, and carefully bound up with clean\nlinen rags, but, _above all, to be let alone_ for seven days, at the end\nof which period the bandages were removed, when the wound was generally\nfound perfectly united. The triumph of the cure was decreed to the\nmysterious agency of the sympathetic powder which had been so assiduously\napplied to the weapon, whereas it is hardly necessary to observe that the\npromptness of the cure depended on the total exclusion of air from the\nwound, and upon the sanative operations of nature not having received any\ndisturbance from the officious interference of art. The result, beyond all\ndoubt, furnished the first hint which led surgeons to the improved\npractice of healing wounds by what is technically called the _first\nintention_.\u201d(251) \u201cIn all records,\u201d adds Dr. Paris, of \u201cextraordinary\ncures performed by mysterious agents, there is a great desire to conceal\nthe remedies and other curative means which were simultaneously\nadministered with them; thus Oribasius commends in high terms a necklace\nof P\u00e6ony root for the cure of epilepsy; but we learn that he always took\ncare to accompany its use with copious evacuations, although he assigns to\nthem no share of credit in the cure. In later times we have a good\nspecimen of this species of deception, presented to us in a work on\nscrofula by Mr. Morley, written, as we are informed, for the sole purpose\nof restoring the much-injured character and use of the Vervain; in which\nthe author directs the root of this plant to be tied with a yard of white\nsatin ribbon around the neck, where it is to remain until the patient is\ncured; but mark\u2014during this interval he calls to his aid the most active\nmedicines in the materia medica.\u201d(252)\n\nIn other cases, the cures really produced by rest, regimen, and amusement\nhave been ascribed to the medicinal, or occasionally to the supernatural,\nmeans which were put in requisition. \u201cThe celebrated John Wesley, while he\ncommemorates the triumph of sulphur and supplication over his bodily\ninfirmity, forgets to appreciate the resuscitating influence of four\nmonths\u2019 repose from his apostolic labors; and such is the disposition of\nthe human mind to place confidence in the operation of mysterious agents,\nthat we find him more disposed to attribute his cure to a brown paper\nplaster of egg and brimstone, than to Dr. Fothergill\u2019s salutary\nprescription of country air, rest, asses\u2019 milk, and horse exercise.\u201d(253)\n\nIn the following example, the circumstance overlooked was of a somewhat\ndifferent character. \u201cWhen the yellow fever raged in America, the\npractitioners trusted exclusively to the copious use of mercury; at first\nthis plan was deemed so universally efficacious, that, in the enthusiasm\nof the moment, it was triumphantly proclaimed that death never took place\nafter the mercury had evinced its effect upon the system: all this was\nvery true, but it furnished no proof of the efficacy of that metal, since\nthe disease in its aggravated form was so rapid in its career, that it\nswept away its victims long before the system could be brought under\nmercurial influence, while in its milder shape it passed off equally well\nwithout any assistance from art.\u201d(254)\n\nIn these examples the circumstance overlooked was cognizable by the\nsenses. In other cases, it is one the knowledge of which could only be\narrived at by reasoning; but the fallacy may still be classed under the\nhead to which, for want of a more appropriate name, we have given the\nappellation Fallacies of Non-observation. It is not the nature of the\nfaculties which ought to have been employed, but the non-employment of\nthem, which constitutes this Natural Order of Fallacies. Wherever the\nerror is negative, not positive; wherever it consists especially in\n_overlooking_, in being ignorant or unmindful of some fact which, if known\nand attended to, would have made a difference in the conclusion arrived\nat; the error is properly placed in the Class which we are considering. In\nthis Class, there is not, as in all other fallacies there is, a positive\nmisestimate of evidence actually had. The conclusion would be just, if the\nportion which is seen of the case were the whole of it; but there is\nanother portion overlooked, which vitiates the result.\n\nFor instance, there is a remarkable doctrine which has occasionally found\na vent in the public speeches of unwise legislators, but which only in one\ninstance that I am aware of has received the sanction of a philosophical\nwriter, namely, M. Cousin, who in his preface to the _Gorgias_ of Plato,\ncontending that punishment must have some other and higher justification\nthan the prevention of crime, makes use of this argument\u2014that if\npunishment were only for the sake of example, it would be indifferent\nwhether we punished the innocent or the guilty, since the punishment,\nconsidered as an example, is equally efficacious in either case. Now we\nmust, in order to go along with this reasoning, suppose, that the person\nwho feels himself under temptation, observing somebody punished, concludes\nhimself to be in danger of being punished likewise, and is terrified\naccordingly. But it is forgotten that if the person punished is supposed\nto be innocent, or even if there be any doubt of his guilt, the spectator\nwill reflect that his own danger, whatever it may be, is not contingent on\nhis guiltiness, but threatens him equally if he remains innocent, and how,\ntherefore, is he deterred from guilt by the apprehension of such\npunishment? M. Cousin supposes that people will be dissuaded from guilt by\nwhatever renders the condition of the guilty more perilous, forgetting\nthat the condition of the innocent (also one of the elements in the\ncalculation) is, in the case supposed, made perilous in precisely an equal\ndegree. This is a fallacy of overlooking; or of non-observation, within\nthe intent of our classification.\n\nFallacies of this description are the great stumbling-block to correct\nthinking in political economy. The economical workings of society afford\nnumerous cases in which the effects of a cause consist of two sets of\nphenomena: the one immediate, concentrated, obvious to all eyes, and\npassing, in common apprehension, for the whole effect; the other widely\ndiffused, or lying deeper under the surface, and which is exactly contrary\nto the former. Take, for instance, the common notion so plausible at the\nfirst glance, of the encouragement given to industry by lavish\nexpenditure. A, who spends his whole income, and even his capital, in\nexpensive living, is supposed to give great employment to labor. B, who\nlives on a small portion, and invests the remainder in the funds, is\nthought to give little or no employment. For every body sees the gains\nwhich are made by A\u2019s tradesmen, servants, and others, while his money is\nspending. B\u2019s savings, on the contrary, pass into the hands of the person\nwhose stock he purchased, who with it pays a debt he owed to some banker,\nwho lends it again to some merchant or manufacturer; and the capital being\nlaid out in hiring spinners and weavers, or carriers and the crews of\nmerchant vessels, not only gives immediate employment to at least as much\nindustry as A employs during the whole of his career, but coming back with\nincrease by the sale of the goods which have been manufactured or\nimported, forms a fund for the employment of the same and perhaps a\ngreater quantity of labor in perpetuity. But the observer does not see,\nand therefore does not consider, what becomes of B\u2019s money; he does see\nwhat is done with A\u2019s; he observes the amount of industry which A\u2019s\nprofusion feeds; he observes not the far greater quantity which it\nprevents from being fed; and thence the prejudice, universal to the time\nof Adam Smith, that prodigality encourages industry, and parsimony is a\ndiscouragement to it.\n\nThe common argument against free trade was a fallacy of the same nature.\nThe purchaser of British silk encourages British industry; the purchaser\nof Lyons silk encourages only French; the former conduct is patriotic, the\nlatter ought to be prevented by law. The circumstance is overlooked, that\nthe purchaser of any foreign commodity necessarily causes, directly or\nindirectly, the export of an equivalent value of some article of home\nproduction (beyond what would otherwise be exported), either to the same\nforeign country or to some other; which fact, though from the complication\nof the circumstances it can not always be verified by specific\nobservation, no observation can possibly be brought to contradict, while\nthe evidence of reasoning on which it rests is irrefragable. The fallacy\nis, therefore, the same as in the preceding case, that of seeing a part\nonly of the phenomena, and imagining that part to be the whole; and may be\nranked among Fallacies of Non-observation.\n\n\u00a7 5. To complete the examination of the second of our five classes, we\nhave now to speak of Mal-observation; in which the error does not lie in\nthe fact that something is unseen, but that something seen is seen wrong.\n\nPerception being infallible evidence of whatever is really perceived, the\nerror now under consideration can be committed no otherwise than by\nmistaking for conception what is, in fact, inference. We have formerly\nshown how intimately the two are blended in almost every thing which is\ncalled observation, and still more in every Description.(255) What is\nactually on any occasion perceived by our senses being so minute in\namount, and generally so unimportant a portion of the state of facts which\nwe wish to ascertain or to communicate; it would be absurd to say that\neither in our observations, or in conveying their result to others, we\nought not to mingle inference with fact; all that can be said is, that\nwhen we do so we ought to be aware of what we are doing, and to know what\npart of the assertion rests on consciousness, and is therefore\nindisputable, what part on inference, and is therefore questionable.\n\nOne of the most celebrated examples of a universal error produced by\nmistaking an inference for the direct evidence of the senses, was the\nresistance made, on the ground of common sense, to the Copernican system.\nPeople fancied they _saw_ the sun rise and set, the stars revolve in\ncircles round the pole. We now know that they saw no such thing; what they\nreally saw was a set of appearances, equally reconcilable with the theory\nthey held and with a totally different one. It seems strange that such an\ninstance as this of the testimony of the senses pleaded with the most\nentire conviction in favor of something which was a mere inference of the\njudgment, and, as it turned out, a false inference, should not have opened\nthe eyes of the bigots of common sense, and inspired them with a more\nmodest distrust of the competency of mere ignorance to judge the\nconclusions of cultivated thought.\n\nIn proportion to any person\u2019s deficiency of knowledge and mental\ncultivation is, generally, his inability to discriminate between his\ninferences and the perceptions on which they were grounded. Many a\nmarvelous tale, many a scandalous anecdote, owes its origin to this\nincapacity. The narrator relates, not what he saw or heard, but the\nimpression which he derived from what he saw or heard, and of which\nperhaps the greater part consisted of inference, though the whole is\nrelated, not as inference but as matter of fact. The difficulty of\ninducing witnesses to restrain within any moderate limits the intermixture\nof their inferences with the narrative of their perceptions, is well known\nto experienced cross-examiners; and still more is this the case when\nignorant persons attempt to describe any natural phenomenon. \u201cThe simplest\nnarrative,\u201d says Dugald Stewart,(256) \u201cof the most illiterate observer\ninvolves more or less of hypothesis; nay, in general, it will be found\nthat, in proportion to his ignorance, the greater is the number of\nconjectural principles involved in his statements. A village apothecary\n(and, if possible, in a still greater degree, an experienced nurse) is\nseldom able to describe the plainest case, without employing a phraseology\nof which every word is a theory: whereas a simple and genuine\nspecification of the phenomena which mark a particular disease; a\nspecification unsophisticated by fancy, or by preconceived opinions, may\nbe regarded as unequivocal evidence of a mind trained by long and\nsuccessful study to the most difficult of all arts, that of the faithful\n_interpretation_ of nature.\u201d\n\nThe universality of the confusion between perceptions and the inferences\ndrawn from them, and the rarity of the power to discriminate the one from\nthe other, ceases to surprise us when we consider that in the far greater\nnumber of instances the actual perceptions of our senses are of no\nimportance or interest to us except as marks from which we infer something\nbeyond them. It is not the color and superficial extension perceived by\nthe eye that are important to us, but the object, of which those visible\nappearances testify the presence; and where the sensation itself is\nindifferent, as it generally is, we have no motive to attend particularly\nto it, but acquire a habit of passing it over without distinct\nconsciousness, and going on at once to the inference. So that to know what\nthe sensation actually was, is a study in itself, to which painters, for\nexample, have to train themselves by special and long-continued discipline\nand application. In things farther removed from the dominion of the\noutward senses, no one who has not great experience in psychological\nanalysis is competent to break this intense association; and when such\nanalytic habits do not exist in the requisite degree, it is hardly\npossible to mention any of the habitual judgments of mankind on subjects\nof a high degree of abstraction, from the being of a God and the\nimmortality of the soul down to the multiplication table, which are not,\nor have not been, considered as matter of direct intuition. So strong is\nthe tendency to ascribe an intuitive character to judgments which are mere\ninferences, and often false ones. No one can doubt that many a deluded\nvisionary has actually believed that he was directly inspired from Heaven,\nand that the Almighty had conversed with him face to face; which yet was\nonly, on his part, a conclusion drawn from appearances to his senses, or\nfeelings in his internal consciousness, which afforded no warrant for any\nsuch belief. A caution, therefore, against this class of errors, is not\nonly needful but indispensable; though to determine whether, on any of the\ngreat questions of metaphysics, such errors are actually committed,\nbelongs not to this place, but, as I have so often said, to a different\nscience.\n\n\n\n\n                                Chapter V.\n\n\nFallacies Of Generalization.\n\n\n\u00a7 1. The class of Fallacies of which we are now to speak, is the most\nextensive of all; embracing a greater number and variety of unfounded\ninferences than any of the other classes, and which it is even more\ndifficult to reduce to sub-classes or species. If the attempt made in the\npreceding books to define the principles of well-grounded generalization\nhas been successful, all generalizations not conformable to those\nprinciples might, in a certain sense, be brought under the present class;\nwhen, however, the rules are known and kept in view, but a casual lapse\ncommitted in the application of them, this is a blunder, not a fallacy. To\nentitle an error of generalization to the latter epithet, it must be\ncommitted on principle; there must lie in it some erroneous general\nconception of the inductive process; the legitimate mode of drawing\nconclusions from observation and experiment must be fundamentally\nmisconceived.\n\nWithout attempting any thing so chimerical as an exhaustive classification\nof all the misconceptions which can exist on the subject, let us content\nourselves with noting, among the cautions which might be suggested, a few\nof the most useful and needful.\n\n\u00a7 2. In the first place, there are certain kinds of generalization which,\nif the principles already laid down be correct, _must_ be groundless;\nexperience can not afford the necessary conditions for establishing them\nby a correct induction. Such, for instance, are all inferences from the\norder of nature existing on the earth, or in the solar system, to that\nwhich may exist in remote parts of the universe; where the phenomena, for\naught we know, may be entirely different, or may succeed one another\naccording to different laws, or even according to no fixed law at all.\nSuch, again, in matters dependent on causation, are all universal\nnegatives, all propositions that assert impossibility. The non-existence\nof any given phenomenon, however uniformly experience may as yet have\ntestified to the fact, proves at most that no cause, adequate to its\nproduction, has yet manifested itself; but that no such causes exist in\nnature can only be inferred if we are so foolish as to suppose that we\nknow all the forces in nature. The supposition would at least be premature\nwhile our acquaintance with some even of those which we do know is so\nextremely recent. And however much our knowledge of nature may hereafter\nbe extended, it is not easy to see how that knowledge could ever be\ncomplete, or how, if it were, we could ever be assured of its being so.\n\nThe only laws of nature which afford sufficient warrant for attributing\nimpossibility (even with reference to the existing order of nature, and to\nour own region of the universe) are, first, those of number and extension,\nwhich are paramount to the laws of the succession of phenomena, and not\nexposed to the agency of counteracting causes; and, secondly, the\nuniversal law of causality itself. That no valuation in any effect or\nconsequent will take place while the whole of the antecedents remain the\nsame, may be affirmed with full assurance. But, that the addition of some\nnew antecedent might not entirely alter and subvert the accustomed\nconsequent, or that antecedents competent to do this do not exist in\nnature, we are in no case empowered positively to conclude.\n\n\u00a7 3. It is next to be remarked that all generalizations which profess,\nlike the theories of Thales, Democritus, and others of the early Greek\nspeculators, to resolve all things into some one element, or like many\nmodern theories, to resolve phenomena radically different into the same,\nare necessarily false. By radically different phenomena I mean impressions\non our senses which differ in quality, and not merely in degree. On this\nsubject what appeared necessary was said in the chapter on the Limits to\nthe Explanation of Laws of Nature; but as the fallacy is even in our own\ntimes a common one, I shall touch on it somewhat further in this place.\n\nWhen we say that the force which retains the planets in their orbits is\nresolved into gravity, or that the force which makes substances combine\nchemically is resolved into electricity, we assert in the one case what\nis, and in the other case what might, and probably will ultimately, be a\nlegitimate result of induction. In both these cases motion is resolved\ninto motion. The assertion is, that a case of motion, which was supposed\nto be special, and to follow a distinct law of its own, conforms to and is\nincluded in the general law which regulates another class of motions. But,\nfrom these and similar generalizations, countenance and currency have been\ngiven to attempts to resolve, not motion into motion, but heat into\nmotion, light into motion, sensation itself into motion; states of\nconsciousness into states of the nervous system, as in the ruder forms of\nthe materialist philosophy; vital phenomena into mechanical or chemical\nprocesses, as in some schools of physiology.\n\nNow I am far from pretending that it may not be capable of proof, or that\nit is not an important addition to our knowledge if proved, that certain\nmotions in the particles of bodies are the _conditions_ of the production\nof heat or light; that certain assignable physical modifications of the\nnerves may be the conditions not only of our sensations or emotions, but\neven of our thoughts; that certain mechanical and chemical conditions may,\nin the order of nature, be sufficient to determine to action the\nphysiological laws of life. All I insist upon, in common with every\nthinker who entertains any clear idea of the logic of science, is, that it\nshall not be supposed that by proving these things one step would be made\ntoward a real explanation of heat, light, or sensation; or that the\ngeneric peculiarity of those phenomena can be in the least degree evaded\nby any such discoveries, however well established. Let it be shown, for\ninstance, that the most complex series of physical causes and effects\nsucceed one another in the eye and in the brain to produce a sensation of\ncolor; rays falling on the eye, refracted, converging, crossing one\nanother, making an inverted image on the retina, and after this a\nmotion\u2014let it be a vibration, or a rush of nervous fluid, or whatever else\nyou are pleased to suppose, along the optic nerve\u2014a propagation of this\nmotion to the brain itself, and as many more different motions as you\nchoose; still, at the end of these motions, there is something which is\nnot motion, there is a feeling or sensation of color. Whatever number of\nmotions we may be able to interpolate, and whether they be real or\nimaginary, we shall still find, at the end of the series, a motion\nantecedent and a color consequent. The mode in which any one of the\nmotions produces the next, may possibly be susceptible of explanation by\nsome general law of motion: but the mode in which the last motion produces\nthe sensation of color, can not be explained by any law of motion; it is\nthe law of color: which is, and must always remain, a peculiar thing.\nWhere our consciousness recognizes between two phenomena an inherent\ndistinction; where we are sensible of a difference which is not merely of\ndegree, and feel that no adding one of the phenomena to itself would\nproduce the other; any theory which attempts to bring either under the\nlaws of the other must be false; though a theory which merely treats the\none as a cause or condition of the other, may possibly be true.\n\n\u00a7 4. Among the remaining forms of erroneous generalization, several of\nthose most worthy of and most requiring notice have fallen under our\nexamination in former places, where, in investigating the rules of correct\ninduction, we have had occasion to advert to the distinction between it\nand some common mode of the incorrect. In this number is what I have\nformerly called the natural Induction of uninquiring minds, the induction\nof the ancients, which proceeds _per enumerationem simplicem_: \u201cThis,\nthat, and the other A are B, I can not think of any A which is not B,\ntherefore every A is B.\u201d As a final condemnation of this rude and slovenly\nmode of generalization, I will quote Bacon\u2019s emphatic denunciation of it;\nthe most important part, as I have more than once ventured to assert, of\nthe permanent service rendered by him to philosophy. \u201cInductio qu\u00e6\nprocedit per enumerationem simplicem, res puerilis est, et precario\nconcludit\u201d (concludes only _by your leave_, or provisionally), \u201cet\npericulo exponitur ab instanti\u00e2 contradictori\u00e2, et plerumque secundum\npauciora quam par est, et _ex his tantummodo qu\u00e6 pr\u00e6sto sunt pronunciat_.\nAt Inductio qu\u00e6 ad inventionem et demonstrationem Scientiarum et Artium\nerit utilis, Naturam separare debet, per rejectiones et exclusiones\ndebitas; ac deinde post negativas tot quot sufficiunt, super affirmativas\nconcludere.\u201d\n\nI have already said that the mode of Simple Enumeration is still the\ncommon and received method of Induction in whatever relates to man and\nsociety. Of this a very few instances, more by way of memento than of\ninstruction, may suffice. What, for example, is to be thought of all the\n\u201ccommon-sense\u201d maxims for which the following may serve as the universal\nformula, \u201cWhatsoever has never been, will never be.\u201d As for example:\nnegroes have never been as civilized as whites sometimes are, therefore it\nis impossible they should be so. Women, as a class, are supposed not to\nhave hitherto been equal in intellect to men, therefore they are\nnecessarily inferior. Society can not prosper without this or the other\ninstitution; _e.g._, in Aristotle\u2019s time, without slavery; in later times,\nwithout an established priesthood, without artificial distinctions of\nrank, etc. One poor person in a thousand, educated, while the nine hundred\nand ninety-nine remain uneducated, has usually aimed at raising himself\nout of his class, therefore education makes people dissatisfied with the\ncondition of a laborer. Bookish men, taken from speculative pursuits and\nset to work on something they know nothing about, have generally been\nfound or thought to do it ill; therefore philosophers are unfit for\nbusiness, etc., etc. All these are inductions by simple enumeration.\nReasons having some reference to the canons of scientific investigation\nhave been attempted to be given, however unsuccessfully, for some of these\npropositions; but to the multitude of those who parrot them, the\n_enumeratio simplex, ex __ his tantummodo qu\u00e6 pr\u00e6sto sunt pronuncians_, is\nthe sole evidence. Their fallacy consists in this, that they are\ninductions without elimination: there has been no real comparison of\ninstances, nor even ascertainment of the material facts in any given\ninstance. There is also the further error, of forgetting that such\ngeneralizations, even if well established, could not be ultimate truths,\nbut must be results of laws much more elementary; and therefore, until\ndeduced from such, could at most be admitted as empirical laws, holding\ngood within the limits of space and time by which the particular\nobservations that suggested the generalization were bounded.\n\nThis error, of placing mere empirical laws, and laws in which there is no\ndirect evidence of causation, on the same footing of certainty as laws of\ncause and effect, an error which is at the root of perhaps the greater\nnumber of bad inductions, is exemplified only in its grossest form in the\nkind of generalizations to which we have now referred. These, indeed, do\nnot possess even the degree of evidence which pertains to a\nwell-ascertained empirical law; but admit of refutation on the empirical\nground itself, without ascending to casual laws. A little reflection,\nindeed, will show that mere negations can only form the ground of the\nlowest and least valuable kind of empirical law. A phenomenon has never\nbeen noticed; this only proves that the conditions of that phenomenon have\nnot yet occurred in experience, but does not prove that they may not occur\nhereafter. There is a better kind of empirical law than this, namely, when\na phenomenon which is observed presents within the limits of observation a\nseries of gradations, in which a regularity, or something like a\nmathematical law, is perceptible; from which, therefore, something may be\nrationally presumed as to those terms of the series which are beyond the\nlimits of observation. But in negation there are no gradations, and no\nseries; the generalizations, therefore, which deny the possibility of any\ngiven condition of man and society merely because it has never yet been\nwitnessed, can not possess this higher degree of validity even as\nempirical laws. What is more, the minuter examination which that higher\norder of empirical laws presupposes, being applied to the subject-matter\nof these, not only does not confirm but actually refutes them. For in\nreality the past history of Man and Society, instead of exhibiting them as\nimmovable, unchangeable, incapable of ever presenting new phenomena, shows\nthem, on the contrary, to be, in many most important particulars, not only\nchangeable, but actually undergoing a progressive change. The empirical\nlaw, therefore, best expressive, in most cases, of the genuine result of\nobservation, would be, not that such and such a phenomenon will continue\nunchanged, but that it will continue to change in some particular manner.\n\nAccordingly, while almost all generalizations relating to Man and Society,\nantecedent to the last fifty or sixty years, have erred in the gross way\nwhich we have attempted to characterize, namely, by implicitly assuming\nthat nature and society will forever revolve in the same orbit, and\nexhibit essentially the same phenomena; which is also the vulgar error of\nthe ostentatiously practical, the votaries of so-called common sense, in\nour day, especially in Great Britain; the more thinking minds of the\npresent age, having applied a more minute analysis to the past records of\nour race, have for the most part adopted a contrary opinion, that the\nhuman species is in a state of necessary progression, and that from the\nterms of the series which are past we may infer positively those which are\nyet to come. Of this doctrine, considered as a philosophical tenet, we\nshall have occasion to speak more fully in the concluding Book. If not, in\nall its forms, free from error, it is at least free from the gross and\nerror which we previously exemplified. But, in all except the most\neminently philosophical minds, it is infected with precisely the same\n_kind_ of fallacy as that is. For we must remember that even this other\nand better generalization, the progressive change in the condition of the\nhuman species, is, after all, but an empirical law; to which, too, it is\nnot difficult to point out exceedingly large exceptions; and even if these\ncould be got rid of, either by disputing the facts or by explaining and\nlimiting the theory, the general objection remains valid against the\nsupposed law, as applicable to any other than what, in our third book,\nwere termed Adjacent Cases. For not only is it no ultimate, but not even a\ncausal law. Changes do indeed take place in human affairs, but every one\nof those changes depends on determinate causes; the \u201cprogressiveness of\nthe species\u201d is not a cause, but a summary expression for the general\nresult of all the causes. So soon as, by a quite different sort of\ninduction, it shall be ascertained what causes have produced these\nsuccessive changes, from the beginning of history, in so far as they have\nreally taken place, and by what causes of a contrary tendency they have\nbeen occasionally checked or entirely counteracted, we may then be\nprepared to predict the future with reasonable foresight; we may be in\npossession of the real _law_ of the future; and may be able to declare on\nwhat circumstances the continuance of the same onward movement will\neventually depend. But this it is the error of many of the more advanced\nthinkers, in the present age, to overlook; and to imagine that the\nempirical law collected from a mere comparison of the condition of our\nspecies at different past times, is a real law, is _the_ law of its\nchanges, not only past but also to come. The truth is, that the causes on\nwhich the phenomena of the moral world depend, are in every age, and\nalmost in every country, combined in some different proportion; so that it\nis scarcely to be expected that the general result of them all should\nconform very closely, in its details at least, to any uniformly\nprogressive series. And all generalizations which affirm that mankind have\na tendency to grow better or worse, richer or poorer, more cultivated or\nmore barbarous, that population increases faster than subsistence, or\nsubsistence than population, that inequality of fortune has a tendency to\nincrease or to break down, and the like, propositions of considerable\nvalue as empirical laws within certain (but generally rather narrow)\nlimits, are in reality true or false according to times and circumstances.\n\nWhat we have said of empirical generalizations from times past to times\nstill to come, holds equally true of similar generalizations from present\ntimes to times past; when persons whose acquaintance with moral and social\nfacts is confined to their own age, take the men and the things of that\nage for the type of men and things in general, and apply without scruple\nto the interpretation of the events of history, the empirical laws which\nrepresent sufficiently for daily guidance the common phenomena of human\nnature at that time and in that particular state of society. If examples\nare wanted, almost every historical work, until a very recent period,\nabounded in them. The same may be said of those who generalize empirically\nfrom the people of their own country to the people of other countries, as\nif human beings felt, judged, and acted everywhere in the same manner.\n\n\u00a7 5. In the foregoing instances, the distinction is confounded between\nempirical laws, which express merely the customary order of the succession\nof effects, and the laws of causation on which the effects depend. There\nmay, however, be incorrect generalization when this mistake is not\ncommitted; when the investigation takes its proper direction, that of\ncauses, and the result erroneously obtained purports to be a really causal\nlaw.\n\nThe most vulgar form of this fallacy is that which is commonly called\n_post hoc, ergo propter hoc_, or, _cum hoc, ergo propter hoc_. As when it\nwas inferred that England owed her industrial pre-eminence to her\nrestrictions on commerce; as when the old school of financiers, and some\nspeculative writers, maintained that the national debt was one of the\ncauses of national prosperity; as when the excellence of the Church, of\nthe Houses of Lords and Commons, of the procedure of the law courts, etc.,\nwere inferred from the mere fact that the country had prospered under\nthem. In such cases as these, if it can be rendered probable by other\nevidence that the supposed causes have some tendency to produce the effect\nascribed to them, the fact of its having been produced, though only in one\ninstance, is of some value as a verification by specific experience; but\nin itself it goes scarcely any way at all toward establishing such a\ntendency, since, admitting the effect, a hundred other antecedents could\nshow an equally strong title of _that_ kind to be considered as the cause.\n\nIn these examples we see bad generalization _a posteriori_, or empiricism\nproperly so called; causation inferred from casual conjunction, without\neither due elimination, or any presumption arising from known properties\nof the supposed agent. But bad generalization _a priori_ is fully as\ncommon; which is properly called false theory; conclusions drawn, by way\nof deduction, from properties of some one agent which is known or supposed\nto be present, all other co-existing agents being overlooked. As the\nformer is the error of sheer ignorance, so the latter is especially that\nof semi-instructed minds; and is mainly committed in attempting to explain\ncomplicated phenomena by a simpler theory than their nature admits of. As\nwhen one school of physicians sought for the universal principle of all\ndisease in \u201clentor and morbid viscidity of the blood,\u201d and imputing most\nbodily derangements to mechanical obstructions, thought to cure them by\nmechanical remedies;(257) while another, the chemical school,\n\u201cacknowledged no source of disease but the presence of some hostile acid\nor alkali, or some deranged condition in the chemical composition of the\nfluid or solid parts,\u201d and conceived, therefore, that \u201call remedies must\nact by producing chemical changes in the body.\u201d We find Tournefort busily\nengaged in testing every vegetable juice, in order to discover in it some\ntraces of an acid or alkaline ingredient, which might confer upon it\nmedicinal activity. The fatal errors into which such an hypothesis was\nliable to betray the practitioner, received an awful illustration in the\nhistory of the memorable fever that raged at Leyden in the year 1699, and\nwhich consigned two-thirds of the population of that city to an untimely\ngrave; an event which in a great measure depended upon the Professor\nSylvius de la Boe, who having just embraced the chemical doctrines of Van\nHelmont, assigned the origin of the distemper to a prevailing acid, and\ndeclared that its cure could alone [only] be effected by the copious\nadministration of absorbent and testaceous medicines.(258)\n\nThese aberrations in medical theory have their exact parallels in\npolitics. All the doctrines which ascribe absolute goodness to particular\nforms of government, particular social arrangements, and even to\nparticular modes of education, without reference to the state of\ncivilization and the various distinguishing characters of the society for\nwhich they are intended, are open to the same objection\u2014that of assuming\none class of influencing circumstances to be the paramount rulers of\nphenomena which depend in an equal or greater degree on many others. But\non these considerations it is the less necessary that we should now dwell,\nas they will occupy our attention more largely in the concluding Book.\n\n\u00a7 6. The last of the modes of erroneous generalization to which I shall\nadvert, is that to which we may give the name of False Analogies. This\nFallacy stands distinguished from those already treated of by the\npeculiarity that it does not even simulate a complete and conclusive\ninduction, but consists in the misapplication of an argument which is at\nbest only admissible as an inconclusive presumption, where real proof is\nunattainable.\n\nAn argument from analogy, is an inference that what is true in a certain\ncase is true in a case known to be somewhat similar, but not known to be\nexactly parallel, that is, to be similar in all the material\ncircumstances. An object has the property B: another object is not known\nto have that property, but resembles the first in a property A, not known\nto be connected with B; and the conclusion to which the analogy points, is\nthat this object has the property B also. As, for example, that the\nplanets are inhabited, because the earth is so. The planets resemble the\nearth in describing elliptical orbits round the sun, in being attracted by\nit and by one another, in being nearly spherical, revolving on their axes,\netc.; and, as we have now reason to believe from the revelations of the\nspectroscope, are composed, in great part at least, of similar materials;\nbut it is not known that any of these properties, or all of them together,\nare the conditions on which the possession of inhabitants is dependent, or\nare marks of those conditions. Nevertheless, so long as we do not know\nwhat the conditions are, they _may_ be connected by some law of nature\nwith those common properties; and to the extent of that possibility the\nplanets are more likely to be inhabited than if they did not resemble the\nearth at all. This non-assignable and generally small increase of\nprobability, beyond what would otherwise exist, is all the evidence which\na conclusion can derive from analogy. For if we have the slightest reason\nto suppose any real connection between the two properties A and B, the\nargument is no longer one of analogy. If it had been ascertained (I\npurposely put an absurd supposition) that there was a connection by\ncausation between the fact of revolving on an axis and the existence of\nanimated beings, or if there were any reasonable ground for even\nsuspecting such a connection, a probability would arise of the existence\nof inhabitants in the planets, which might be of any degree of strength,\nup to a complete induction; but we should then infer the fact from the\nascertained or presumed law of causation, and not from the analogy of the\nearth.\n\nThe name analogy, however, is sometimes employed by extension to denote\nthose arguments of an inductive character but not amounting to a real\ninduction, which are employed to strengthen the argument drawn from a\nsimple resemblance. Though A, the property common to the two cases, can\nnot be shown to be the cause or effect of B, the analogical reasoner will\nendeavor to show that there is some less close degree of connection\nbetween them; that A is one of a set of conditions from which, when all\nunited, B would result; or is an occasional effect of some cause which has\nbeen known also to produce B; and the like. Any of which things, if shown,\nwould render the existence of B by so much more probable, than if there\nhad not been even that amount of known connection between B and A.\n\nNow an error or fallacy of analogy may occur in two ways. Sometimes it\nconsists in employing an argument of either of the above kinds with\ncorrectness indeed, but overrating its probative force. This very common\naberration is sometimes supposed to be particularly incident to persons\ndistinguished for their imagination; but in reality it is the\ncharacteristic intellectual vice of those whose imaginations are barren,\neither from want of exercise, natural defect, or the narrowness of their\nrange of ideas. To such minds objects present themselves clothed in but\nfew properties; and as, therefore, few analogies between one object and\nanother occur to them, they almost invariably overrate the degree of\nimportance of those few: while one whose fancy takes a wider range,\nperceives and remembers so many analogies tending to conflicting\nconclusions, that he is much less likely to lay undue stress on any of\nthem. We always find that those are the greatest slaves to metaphorical\nlanguage who have but one set of metaphors.\n\nBut this is only one of the modes of error in the employment of arguments\nof analogy. There is another, more properly deserving the name of fallacy;\nnamely, when resemblance in one point is inferred from resemblance in\nanother point, though there is not only no evidence to connect the two\ncircumstances by way of causation, but the evidence tends positively to\ndisconnect them. This is properly the Fallacy of False Analogies.\n\nAs a first instance, we may cite that favorite argument in defense of\nabsolute power, drawn from the analogy of paternal government in a family,\nwhich government, however much in need of control, is not and can not be\ncontrolled by the children themselves, while they remain children.\nPaternal government, says the argument, works well; therefore, despotic\ngovernment in a state will work well. I waive, as not pertinent in this\nplace, all that could be said in qualification of the alleged excellence\nof paternal government. However this might be, the argument from the\nfamily to the state would not the less proceed on a false analogy;\nimplying that the beneficial working of parental government depends, in\nthe family, on the only point which it has in common with political\ndespotism, namely, irresponsibility. Whereas it depends, when real, not on\nthat but on two other circumstances of the case, the affection of the\nparent for the children, and the superiority of the parent in wisdom and\nexperience; neither of which properties can be reckoned on, or are at all\nlikely to exist, between a political despot and his subjects; and when\neither of these circumstances fails even in the family, and the influence\nof the irresponsibility is allowed to work uncorrected, the result is any\nthing but good government. This, therefore, is a false analogy.\n\nAnother example is the not uncommon _dictum_ that bodies politic have\nyouth, maturity, old age, and death, like bodies natural; that after a\ncertain duration of prosperity, they tend spontaneously to decay. This\nalso is a false analogy, because the decay of the vital powers in an\nanimated body can be distinctly traced to the natural progress of those\nvery changes of structure which, in their earlier stages, constitutes its\ngrowth to maturity; while in the body politic the progress of those\nchanges can not, generally speaking, have any effect but the still further\ncontinuance of growth: it is the stoppage of that progress, and the\ncommencement of retrogression, that alone would constitute decay. Bodies\npolitic die, but it is of disease, or violent death; they have no old age.\n\nThe following sentence from Hooker\u2019s _Ecclesiastical Polity_ is an\ninstance of a false analogy from physical bodies to what are called bodies\npolitic. \u201cAs there could be in natural bodies no motion of any thing\nunless there were some which moveth all things, and continueth immovable;\neven so in politic societies there must be some unpunishable, or else no\nman shall suffer punishment.\u201d There is a double fallacy here, for not only\nthe analogy, but the premise from which it is drawn, is untenable. The\nnotion that there must be something immovable which moves all other\nthings, is the old scholastic error of a _primum mobile_.\n\nThe following instance I quote from Archbishop Whately\u2019s _Rhetoric_: \u201cIt\nwould be admitted that a great and permanent diminution in the quantity of\nsome useful commodity, such as corn, or coal, or iron, throughout the\nworld, would be a serious and lasting loss; and again, that if the fields\nand coal-mines yielded regularly double quantities, with the same labor,\nwe should be so much the richer; hence it might be inferred, that if the\nquantity of gold and silver in the world were diminished one-half, or were\ndoubled, like results would follow; the utility of these metals, for the\npurposes of coin, being very great. Now there are many points of\nresemblance and many of difference, between the precious metals on the one\nhand, and corn, coal, etc., on the other; but the important circumstance\nto the supposed argument is, that the _utility_ of gold and silver (as\ncoin, which is far the chief) _depends on their value_, which is regulated\nby their scarcity; or rather, to speak strictly, by the difficulty of\nobtaining them; whereas, if corn and coal were ten times as abundant\n(_i.e._, more easily obtained), a bushel of either would still be as\nuseful as now. But if it were twice as easy to procure gold as it is, a\nsovereign would be twice as large; if only half as easy, it would be of\nthe size of a half-sovereign, and this (besides the trifling circumstance\nof the cheapness or dearness of gold ornaments) would be all the\ndifference. The analogy, therefore, fails in the point essential to the\nargument.\u201d\n\nThe same author notices, after Bishop Copleston, the case of False Analogy\nwhich consists in inferring from the similarity in many respects between\nthe metropolis of a country and the heart of the animal body, that the\nincreased size of the metropolis is a disease.\n\nSome of the false analogies on which systems of physics were confidently\ngrounded in the time of the Greek philosophers, are such as we now call\nfanciful, not that the resemblances are not often real, but that it is\nlong since any one has been inclined to draw from them the inferences\nwhich were then drawn. Such, for instance, are the curious speculations of\nthe Pythagoreans on the subject of numbers. Finding that the distances of\nthe planets bore, or seemed to bear, to one another a proportion not\nvarying much from that of the divisions of the monochord, they inferred\nfrom it the existence of an inaudible music, that of the spheres; as if\nthe music of a harp had depended solely on the numerical proportions, and\nnot on the material, nor even on the existence of any material, any\nstrings at all. It has been similarly imagined that certain combinations\nof numbers, which were found to prevail in some natural phenomena, must\nrun through the whole of nature: as that there must be four elements,\nbecause there are four possible combinations of hot and cold, wet and dry;\nthat there must be seven planets, because there were seven metals, and\neven because there were seven days of the week. Kepler himself thought\nthat there could be only six planets, because there were only five regular\nsolids. With these we may class the reasonings, so common in the\nspeculations of the ancients, founded on a supposed _perfection_ in\nnature; meaning by nature the customary order of events as they take place\nof themselves without human interference. This also is a rude guess at an\nanalogy supposed to pervade all phenomena, however dissimilar. Since what\nwas thought to be perfection appeared to obtain in some phenomena, it was\ninferred (in opposition to the plainest evidence) to obtain in all. \u201cWe\nalways suppose that which is better to take place in nature, if it be\npossible,\u201d says Aristotle; and the vaguest and most heterogeneous\nqualities being confounded together under the notion of being _better_,\nthere was no limit to the wildness of the inferences. Thus, because the\nheavenly bodies were \u201cperfect,\u201d they must move in circles and uniformly.\nFor \u201cthey\u201d (the Pythagoreans) \u201cwould not allow,\u201d says Geminus,(259) \u201cof\nany such disorder among divine and eternal things, as that they should\nsometimes move quicker and sometimes slower, and sometimes stand still;\nfor no one would tolerate such anomaly in the movements even of a man, who\nwas decent and orderly. The occasions of life, however, are often reasons\nfor men going quicker or slower; but in the incorruptible nature of the\nstars, it is not possible that any cause can be alleged of quickness or\nslowness.\u201d It is seeking an argument of analogy very far, to suppose that\nthe stars must observe the rules of decorum in gait and carriage\nprescribed for themselves by the long-bearded philosophers satirized by\nLucian.\n\nAs late as the Copernican controversy it was urged as an argument in favor\nof the true theory of the solar system, that it placed the fire, the\nnoblest element, in the centre of the universe. This was a remnant of the\nnotion that the order of nature must be perfect, and that perfection\nconsisted in conformity to rules of precedency in dignity, either real or\nconventional. Again, reverting to numbers: certain numbers were _perfect_,\ntherefore those numbers must obtain in the great phenomena of nature. Six\nwas a perfect number, that is, equal to the sum of all its factors; an\nadditional reason why there must be exactly six planets. The Pythagoreans,\non the other hand, attributed perfection to the number ten; but agreed in\nthinking that the perfect number must be somehow realized in the heavens;\nand knowing only of nine heavenly bodies, to make up the enumeration, they\nasserted \u201cthat there was an _antichthon_, or counter-earth, on the other\nside of the sun, invisible to us.\u201d(260) Even Huygens was persuaded that\nwhen the number of the heavenly bodies had reached twelve, it could not\nadmit of any further increase. Creative power could not go beyond that\nsacred number.\n\nSome curious instances of false analogy are to be found in the arguments\nof the Stoics to prove the equality of all crimes, and the equal\nwretchedness of all who had not realized their idea of perfect virtue.\nCicero, toward the end of his Fourth Book, _De Finibus_, states some of\nthese as follows: \u201cUt, inquit, in fidibus plurimis, si nulla earum ita\ncontenta numeris sit, ut concentum servare possit, omnes \u00e6que incontent\u00e6\nsunt; sic peccata, quia discrepant, \u00e6que discrepant; paria sunt igitur.\u201d\nTo which Cicero himself aptly answers, \u201c\u00e6que contingit omnibus fidibus, ut\nincontent\u00e6 sint; illud non continuo, ut \u00e6que incontent\u00e6.\u201d The Stoic\nresumes: \u201cUt enim, inquit, gubernator \u00e6que peccat, si palearum navem\nevertit, et si auri; item \u00e6que peccat qui parentem, et qui servum, injuri\u00e2\nverberat;\u201d assuming, that because the magnitude of the interest at stake\nmakes no difference in the mere defect of skill, it can make none in the\nmoral defect: a false analogy. Again, \u201cQuis ignorat, si plures ex alto\nemergere velint, propius fore eos quidem ad respirandum, qui ad summam jam\naquam appropinquant, sed nihilo magis respirare posse, quam eos, qui sunt\nin profundo? Nihil ergo adjuvat procedere, et progredi in virtute,\nquominus miserrimus sit, antequam ad eam pervenerit, quoniam in aqu\u00e2 nihil\nadjuvat: et quoniam catuli, qui jam despecturi sunt, c\u00e6ci \u00e6que, et ii qui\nmodo nati; Platonem quoque necesse est, quoniam nondum videbat sapientiam,\n\u00e6que c\u00e6cum animo, ac Phalarim fuisse.\u201d Cicero, in his own person, combats\nthese false analogies by other analogies tending to an opposite\nconclusion. \u201cIsta similia non sunt, Cato.... Illa sunt similia; hebes\nacies est cuipiam oculorum: corpore alius languescit: hi curatione\nadhibit\u00e2 levantur in dies: alter valet plus quotidie: alter videt. Hi\nsimiles sunt omnibus, qui virtuti student; levantur vitiis, levantur\nerroribus.\u201d\n\n\u00a7 7. In these and all other arguments drawn from remote analogies, and\nfrom metaphors, which are cases of analogy, it is apparent (especially\nwhen we consider the extreme facility of raising up contrary analogies and\nconflicting metaphors) that, so far from the metaphor or analogy proving\nany thing, the applicability of the metaphor is the very thing to be made\nout. It has to be shown that in the two cases asserted to be analogous,\nthe same law is really operating; that between the known resemblance and\nthe inferred one there is some connection by means of causation. Cicero\nand Cato might have bandied opposite analogies forever; it rested with\neach of them to prove by just induction, or at least to render probable,\nthat the case resembled the one set of analogous cases and not the other,\nin the circumstances on which the disputed question really hinged.\nMetaphors, for the most part, therefore, assume the proposition which they\nare brought to prove: their use is, to aid the apprehension of it; to make\nclearly and vividly comprehended what it is that the person who employs\nthe metaphor is proposing to make out; and sometimes also, by what media\nhe proposes to do so. For an apt metaphor, though it can not prove, often\nsuggests the proof.\n\nFor instance, when D\u2019Alembert (I believe) remarked that in certain\ngovernments only two creatures find their way to the highest places, the\neagle and the serpent, the metaphor not only conveys with great vividness\nthe assertion intended, but contributes toward substantiating it, by\nsuggesting, in a lively manner, the means by which the two opposite\ncharacters thus typified effect their rise. When it is said that a certain\nperson misunderstands another because the lesser of two objects can not\ncomprehend the greater, the application of what is true in the literal\nsense of the word _comprehend_, to its metaphorical sense, points to the\nfact which is the ground and justification of the assertion, viz., that\none mind can not thoroughly understand another unless it can contain it in\nitself, that is, unless it possesses all that is contained in the other.\nWhen it is urged as an argument for education, that if the soil is left\nuncultivated, weeds will spring up, the metaphor, though no proof, but a\nstatement of the thing to be proved, states it in terms which, by\nsuggesting a parallel case, put the mind upon the track of the real proof.\nFor, the reason why weeds grow in an uncultivated soil, is that the seeds\nof worthless products exist everywhere, and can germinate and grow in\nalmost all circumstances, while the reverse is the case with those which\nare valuable; and this being equally true of mental products, this mode of\nconveying an argument, independently of its rhetorical advantages, has a\nlogical value; since it not only suggests the grounds of the conclusion,\nbut points to another case in which those grounds have been found, or at\nleast deemed to be, sufficient.\n\nOn the other hand, when Bacon, who is equally conspicuous in the use and\nabuse of figurative illustration, says that the stream of time has brought\ndown to us only the least valuable part of the writings of the ancients,\nas a river carries froth and straws floating on its surface, while more\nweighty objects sink to the bottom; this, even if the assertion\nillustrated by it were true, would be no good illustration, there being no\nparity of cause. The levity by which substances float on a stream, and the\nlevity which is synonymous with worthlessness, have nothing in common\nexcept the name; and (to show how little value there is in the metaphor)\nwe need only change the word into _buoyancy_, to turn the semblance of\nargument involved in Bacon\u2019s illustration against himself.\n\nA metaphor, then, is not to be considered as an argument, but as an\nassertion that an argument exists; that a parity subsists between the case\nfrom which the metaphor is drawn and that to which it is applied. This\nparity may exist though the two cases be apparently very remote from one\nanother; the only resemblance existing between them may be a resemblance\nof relations, an analogy in Ferguson\u2019s and Archbishop Whately\u2019s sense: as\nin the preceding instance, in which an illustration from agriculture was\napplied to mental cultivation.\n\n\u00a7 8. To terminate the subject of Fallacies of Generalization, it remains\nto be said, that the most fertile source of them is bad classification:\nbringing together in one group, and under one name, things which have no\ncommon properties, or none but such as are too unimportant to allow\ngeneral propositions of any considerable value to be made respecting the\nclass. The misleading effect is greatest, when a word which in common use\nexpresses some definite fact, is extended by slight links of connection to\ncases in which that fact does not exist, but some other or others, only\nslightly resembling it. Thus Bacon,(261) in speaking of the _Idola_ or\nFallacies arising from notions _temere et in\u00e6qualiter \u00e0 rebus abstract\u00e6_,\nexemplifies them by the notion of Humidum or Wet, so familiar in the\nphysics of antiquity and of the Middle Ages. \u201cInvenietur verbum istud,\nHumidum, nihil aliud quam nota confusa diversarum actionum, qu\u00e6 nullam\nconstantiam aut reductionem patiuntur. Significat enim, et quod circa\naliud corpus facile se circumfundit; et quod in se est indeterminabile,\nnec consistere potest; et quod facile cedit undique; et quod facile se\ndividit et dispergit; et quod facile se unit et colligit; et quod facile\nfluit, et in motu ponitur; et quod alteri corpori facile adh\u00e6ret, idque\nmadefacit; et quod facile reducitur in liquidum, sive colliquatur, cum\nantea consisteret. Itaque quum ad hujus nominis pr\u00e6dicationem et\nimpositionem ventum sit; si alia accipias, flamma humida est; si alia\naccipias, aer humidus non est; si alia, pulvis minutus humidus est; si\nalia, vitrum humidum est: ut facile appareat, istam notionem ex aqu\u00e2\ntantum, et communibus et vulgaribus liquoribus, absque ull\u00e2 debit\u00e2\nverificatione, temere abstractam esse.\u201d\n\nBacon himself is not exempt from a similar accusation when inquiring into\nthe nature of heat: where he occasionally proceeds like one who, seeking\nfor the cause of hardness, after examining that quality in iron, flint,\nand diamond, should expect to find that it is something which can be\ntraced also in hard water, a hard knot, and a hard heart.\n\nThe word \u03ba\u03af\u03bd\u03b7\u03c3\u03b9\u03c2 in the Greek philosophy, and the words Generation and\nCorruption, both then and long afterward, denoted such a multitude of\nheterogeneous phenomena, that any attempt at philosophizing in which those\nwords were used was almost as necessarily abortive as if the word _hard_\nhad been taken to denote a class including all the things mentioned above.\n\u039a\u03af\u03bd\u03b7\u03c3\u03b9\u03c2, for instance, which properly signified motion, was taken to\ndenote not only all motion but even all change: \u1f00\u03bb\u03bb\u03bf\u03af\u03c9\u03c3\u03b9\u03c2 being recognized\nas one of the modes of \u03ba\u03af\u03bd\u03b7\u03c3\u03b9\u03c2. The effect was, to connect with every form\nof \u1f00\u03bb\u03bb\u03bf\u03af\u03c9\u03c3\u03b9\u03c2 or change, ideas drawn from motion in the proper and literal\nsense, and which had no real connection with any other kind of \u03ba\u03af\u03bd\u03b7\u03c3\u03b9\u03c2\nthan that. Aristotle and Plato labored under a continual embarrassment\nfrom this misuse of terms. But if we proceed further in this direction we\nshall encroach upon the Fallacy of Ambiguity, which belongs to a different\nclass, the last in order of our classification, Fallacies of Confusion.\n\n\n\n\n                               Chapter VI.\n\n\nFallacies Of Ratiocination.\n\n\n\u00a7 1. We have now, in our progress through the classes of Fallacies,\narrived at those to which, in the common books of logic, the appellation\nis in general exclusively appropriated; those which have their seat in the\nratiocinative or deductive part of the investigation of truth. Of these\nfallacies it is the less necessary for us to insist at any length, as they\nhave been most satisfactorily treated in a work familiar to almost all, in\nthis country at least, who feel any interest in these speculations,\nArchbishop Whately\u2019s _Logic_. Against the more obvious forms of this class\nof fallacies, the rules of the syllogism are a complete protection. Not\n(as we have so often said) that ratiocination can not be good unless it be\nin the form of a syllogism; but that, by showing it in that form, we are\nsure to discover if it be bad, or at least if it contain any fallacy of\nthis class.\n\n\u00a7 2. Among Fallacies of Ratiocination, we ought perhaps to include the\nerrors committed in processes which have the appearance only, not the\nreality, of an inference from premises; the fallacies connected with the\nconversion and \u00e6quipollency of propositions. I believe errors of this\ndescription to be far more frequently committed than is generally\nsupposed, or than their extreme obviousness might seem to admit of. For\nexample, the simple conversion of a universal affirmative proposition, All\nA are B, therefore all B are A, I take to be a very common form of error:\nthough committed, like many other fallacies, oftener in the silence of\nthought than in express words, for it can scarcely be clearly enunciated\nwithout being detected. And so with another form of fallacy, not\nsubstantially different from the preceding: the erroneous conversion of an\nhypothetical proposition. The proper converse of an hypothetical\nproposition is this: If the consequent be false, the antecedent is false;\nbut this, If the consequent be true, the antecedent is true, by no means\nholds good, but is an error corresponding to the simple conversion of a\nuniversal affirmative. Yet hardly any thing is more common than for\npeople, in their private thoughts, to draw this inference. As when the\nconclusion is accepted, which it so often is, for proof of the premises.\nThat the premises can not be true if the conclusion is false, is the\nunexceptionable foundation of the legitimate mode of reasoning called\n_reductio ad absurdum_. But people continually think and express\nthemselves, as if they also believed that the premises can not be false if\nthe conclusion is true. The truth, or supposed truth, of the inferences\nwhich follow from a doctrine, often enables it to find acceptance in spite\nof gross absurdities in it. How many philosophical systems which had\nscarcely any intrinsic recommendation, have been received by thoughtful\nmen because they were supposed to lend additional support to religion,\nmorality, some favorite view of politics, or some other cherished\npersuasion: not merely because their wishes were thereby enlisted on its\nside, but because its leading to what they deemed sound conclusions\nappeared to them a strong presumption in favor of its truth: though the\npresumption, when viewed in its true light, amounted only to the absence\nof that particular evidence of falsehood, which would have resulted from\nits leading by correct inference to something already known to be false.\n\nAgain, the very frequent error in conduct, of mistaking reverse of wrong\nfor right, is the practical form of a logical error with respect to the\nOpposition of Propositions. It is committed for want of the habit of\ndistinguishing the _contrary_ of a proposition from the _contradictory_ of\nit, and of attending to the logical canon, that contrary propositions,\nthough they can not both be true, may both be false. If the error were to\nexpress itself in words, it would run distinctly counter to this canon. It\ngenerally, however, does not so express itself, and to compel it to do so\nis the most effectual method of detecting and exposing it.\n\n\u00a7 3. Among Fallacies of Ratiocination are to be ranked, in the first\nplace, all the cases of vicious syllogism laid down in the books. These\ngenerally resolve themselves into having more than three terms to the\nsyllogism, either avowedly, or in the covert mode of an undistributed\nmiddle term, or an _illicit process_ of one of the two extremes. It is\nnot, indeed, very easy fully to convict an argument of falling under any\none of these vicious cases in particular; for the reason already more than\nonce referred to, that the premises are seldom formally set out: if they\nwere, the fallacy would impose upon nobody; and while they are not, it is\nalmost always to a certain degree optional in what manner the suppressed\nlink shall be filled up. The rules of the syllogism are rules for\ncompelling a person to be aware of the whole of what he must undertake to\ndefend if he persists in maintaining his conclusion. He has it almost\nalways in his power to make his syllogism good by introducing a false\npremise; and hence it is scarcely ever possible decidedly to affirm that\nany argument involves a bad syllogism: but this detracts nothing from the\nvalue of the syllogistic rules, since it is by them that a reasoner is\ncompelled distinctly to make his election what premises he is prepared to\nmaintain. The election made, there is generally so little difficulty in\nseeing whether the conclusion follows from the premises set out, that we\nmight without much logical impropriety have merged this fourth class of\nfallacies in the fifth, or Fallacies of Confusion.\n\n\u00a7 4. Perhaps, however, the commonest, and certainly the most dangerous\nfallacies of this class, are those which do not lie in a single syllogism,\nbut slip in between one syllogism and another in a chain of argument, and\nare committed by _changing the premises_. A proposition is proved, or an\nacknowledged truth laid down, in the first part of an argumentation, and\nin the second a further argument is founded not on the same proposition,\nbut on some other, resembling it sufficiently to be mistaken for it.\nInstances of this fallacy will be found in almost all the argumentative\ndiscourses of unprecise thinkers; and we need only here advert to one of\nthe obscurer forms of it, recognized by the school-men as the fallacy _\u00e0\ndicto secundum quid ad dictum simpliciter_. This is committed when, in the\npremises, a proposition is asserted with a qualification, and the\nqualification lost sight of in the conclusion; or oftener, when a\nlimitation or condition, though not asserted, is necessary to the truth of\nthe proposition, but is forgotten when that proposition comes to be\nemployed as a premise. Many of the bad arguments in vogue belong to this\nclass of error. The premise is some admitted truth, some common maxim, the\nreasons or evidence for which have been forgotten, or are not thought of\nat the time, but if they had been thought of would have shown the\nnecessity of so limiting the premise that it would no longer have\nsupported the conclusion drawn from it.\n\nOf this nature is the fallacy in what is called, by Adam Smith and others,\nthe Mercantile Theory in Political Economy. That theory sets out from the\ncommon maxim, that whatever brings in money enriches; or that every one is\nrich in proportion to the quantity of money he obtains. From this it is\nconcluded that the value of any branch of trade, or of the trade of the\ncountry altogether, consists in the balance of money it brings in; that\nany trade which carries more money out of the country than it draws into\nit is a losing trade; that therefore money should be attracted into the\ncountry and kept there, by prohibitions and bounties; and a train of\nsimilar corollaries. All for want of reflecting that if the riches of an\nindividual are in proportion to the quantity of money he can command, it\nis because that is the measure of his power of purchasing money\u2019s worth;\nand is therefore subject to the proviso that he is not debarred from\nemploying his money in such purchases. The premise, therefore, is only\ntrue _secundum quid_; but the theory assumes it to be true absolutely, and\ninfers that increase of money is increase of riches, even when produced by\nmeans subversive of the condition under which alone money can be riches.\n\nA second instance is, the argument by which it used to be contended,\nbefore the commutation of tithe, that tithes fell on the landlord, and\nwere a deduction from rent; because the rent of tithe-free land was always\nhigher than that of land of the same quality, and the same advantages of\nsituation, subject to tithe. Whether it be true or not that a tithe falls\non rent, a treatise on Logic is not the place to examine; but it is\ncertain that this is no proof of it. Whether the proposition be true or\nfalse, tithe-free land must, by the necessity of the case, pay a higher\nrent. For if tithes do not fall on rent, it must be because they fall on\nthe consumer; because they raise the price of agricultural produce. But if\nthe produce be raised in price, the farmer of tithe-free as well as the\nfarmer of tithed land gets the benefit. To the latter the rise is but a\ncompensation for the tithe he pays; to the first, who pays none, it is\nclear gain, and therefore enables him, and if there be freedom of\ncompetition, forces him, to pay so much more rent to his landlord. The\nquestion remains, to what class of fallacies this belongs. The premise is,\nthat the owner of tithed land receives less rent than the owner of\ntithe-free land; the conclusion is, that therefore he receives less than\nhe himself would receive if tithe were abolished. But the premise is only\ntrue conditionally; the owner of tithed land receives less than what the\nowner of tithe-free land is enabled to receive _when other lands are\ntithed_; while the conclusion is applied to a state of circumstances in\nwhich that condition fails, and in which, by consequence, the premise will\nnot be true. The fallacy, therefore, is _\u00e0 dicto secundum quid ad dictum\nsimpliciter_.\n\nA third example is the opposition sometimes made to legitimate\ninterferences of government in the economical affairs of society, grounded\non a misapplication of the maxim, that an individual is a better judge\nthan the government of what is for his own pecuniary interest. This\nobjection was urged to Mr. Wakefield\u2019s principle of colonization; the\nconcentration of the settlers, by fixing such a price on unoccupied land\nas may preserve the most desirable proportion between the quantity of land\nin culture and the laboring population. Against this it was argued, that\nif individuals found it for their advantage to occupy extensive tracts of\nland, they, being better judges of their own interest than the legislature\n(which can only proceed on general rules), ought not to be restrained from\ndoing so. But in this argument it was forgotten that the fact of a\nperson\u2019s taking a large tract of land is evidence only that it is his\ninterest to take as much as other people, but not that it might not be for\nhis interest to content himself with less, if he could be assured that\nother people would do so too; an assurance which nothing but a government\nregulation can give. If all other people took much, and he only a little,\nhe would reap none of the advantages derived from the concentration of the\npopulation and the consequent possibility of procuring labor for hire, but\nwould have placed himself, without equivalent, in a situation of voluntary\ninferiority. The proposition, therefore, that the quantity of land which\npeople will take when left to themselves is that which is most for their\ninterest to take, is true only _secundum quid_: it is only their interest\nwhile they have no guarantee for the conduct of one another. But the\narrangement disregards the limitation, and takes the proposition for true\n_simpliciter_.\n\nOne of the conditions oftenest dropped, when what would otherwise be a\ntrue proposition is employed as a premise for proving others, is the\ncondition of _time_. It is a principle of political economy that prices,\nprofits, wages, etc., \u201calways find their level;\u201d but this is often\ninterpreted as if it meant that they are always, or generally, _at_ their\nlevel, while the truth is, as Coleridge epigrammatically expresses it,\nthat they are always _finding_ their level, \u201cwhich might be taken as a\nparaphrase or ironical definition of a storm.\u201d\n\nUnder the same head of fallacy (_\u00e0 dicto secundum quid ad dictum\nsimpliciter_) might be placed all the errors which are vulgarly called\nmisapplications of abstract truths; that is, where a principle, true (as\nthe common expression is) _in the abstract_, that is, all modifying causes\nbeing supposed absent, is reasoned on as if it were true absolutely, and\nno modifying circumstance could ever by possibility exist. This very\ncommon form of error it is not requisite that we should exemplify here, as\nit will be particularly treated of hereafter in its application to the\nsubjects on which it is most frequent and most fatal, those of politics\nand society.(262)\n\n\n\n\n                               Chapter VII.\n\n\nFallacies Of Confusion.\n\n\n\u00a7 1. Under this fifth and last class it is convenient to arrange all those\nfallacies in which the source of error is not so much a false estimate of\nthe probative force of known evidence, as an indistinct, indefinite, and\nfluctuating conception of what the evidence is.\n\nAt the head of these stands that multitudinous body of fallacious\nreasonings in which the source of error is the ambiguity of terms: when\nsomething which is true if a word be used in a particular sense, is\nreasoned on as if it were true in another sense. In such a case there is\nnot a mal-estimation of evidence, because there is not properly any\nevidence to the point at all; there is evidence, but to a different point,\nwhich from a confused apprehension of the meaning of the terms used, is\nsupposed to be the same. This error will naturally be oftener committed in\nour ratiocinations than in our direct inductions, because in the former we\nare deciphering our own or other people\u2019s notes, while in the latter we\nhave the things themselves present, either to the senses or to the memory.\nExcept, indeed, when the induction is not from individual cases to a\ngenerality, but from generalities to a still higher generalization; in\nthat case the fallacy of ambiguity may affect the inductive process as\nwell as the ratiocinative. It occurs in ratiocination in two ways: when\nthe middle term is ambiguous, or when one of the terms of the syllogism is\ntaken in one sense in the premises, and in another sense in the\nconclusion.\n\nSome good exemplifications of this fallacy are given by Archbishop\nWhately. \u201cOne case,\u201d says he, \u201cwhich may be regarded as coming under the\nhead of Ambiguous Middle, is (what I believe logical writers mean by\n\u2018_Fallacia Figur\u00e6 Dictionis_\u2019) the fallacy built on the grammatical\nstructure of language, from men\u2019s usually taking for granted that\n_paronymous_ (or _conjugate_) words, _i.e._, those belonging to each\nother, as the substantive, adjective, verb, etc., of the same root, have a\nprecisely corresponding meaning; which is by no means universally the\ncase. Such a fallacy could not indeed be even exhibited in strict logical\nform, which would preclude even the attempt at it, since it has two middle\nterms in sound as well as sense. But nothing is more common in practice\nthan to vary continually the terms employed, with a view to grammatical\nconvenience; nor is there any thing unfair in such a practice, as long as\nthe _meaning_ is preserved unaltered; _e.g._, \u2018murder should be punished\nwith death; this man is a murderer, therefore he deserves to die,\u2019 etc.\nHere we proceed on the assumption (in this case just) that to commit\nmurder, and to be a murderer\u2014to deserve death, and to be one who ought to\ndie, are, respectively, equivalent expressions; and it would frequently\nprove a heavy inconvenience to be debarred this kind of liberty; but the\nabuse of it gives rise to the Fallacy in question; _e.g._, _projectors_\nare unfit to be trusted; this man has formed a _project_, therefore he is\nunfit to be trusted: here the sophist proceeds on the hypothesis that he\nwho forms a _project_ must be a _projector_: whereas the bad sense that\ncommonly attaches to the latter word, is not at all implied in the former.\nThis fallacy may often be considered as lying not in the Middle, but in\none of the terms of the Conclusion; so that the conclusion drawn shall not\nbe, in reality, at all warranted by the premises, though it will appear to\nbe so, by means of the grammatical affinity of the words; _e.g._, to be\nacquainted with the guilty is a _presumption_ of guilt; this man is so\nacquainted, therefore we may _presume_ that he is guilty: this argument\nproceeds on the supposition of an exact correspondence between _presume_\nand _presumption_, which, however, does not really exist; for\n\u2018presumption\u2019 is commonly used to express a kind of _slight suspicion_;\nwhereas, \u2018to presume\u2019 amounts to actual belief. There are innumerable\ninstances of a non-correspondence in paronymous words, similar to that\nabove instanced; as between _art_ and _artful_, _design_ and _designing_,\n_faith_ and _faithful_, etc.; and the more slight the variation of the\nmeaning, the more likely is the fallacy to be successful; for when the\nwords have become so widely removed in sense as \u2018pity\u2019 and \u2018pitiful,\u2019\nevery one would perceive such a fallacy, nor would it be employed but in\njest.(263)\n\n\u201cThe present Fallacy is nearly allied to, or rather, perhaps, may be\nregarded as a branch of, that founded on _etymology_\u2014viz., when a term is\nused, at one time in its customary, and at another in its etymological\nsense. Perhaps no example of this can be found that is more extensively\nand mischievously employed than in the case of the word _representative_:\nassuming that its right meaning must correspond exactly with the strict\nand original sense of the verb \u2018represent,\u2019 the sophist persuades the\nmultitude that a member of the House of Commons is bound to be guided in\nall points by the opinion of his constituents; and, in short, to be merely\ntheir _spokesman_; whereas law and custom, which in this case may be\nconsidered as fixing the meaning of the term, require no such thing, but\nenjoin the representative to act according to the best of his _own_\njudgment, and on his own responsibility.\u201d\n\nThe following are instances of great practical importance, in which\narguments are habitually founded on a verbal ambiguity.\n\nThe mercantile public are frequently led into this fallacy by the phrase\n\u201cscarcity of money.\u201d In the language of commerce, \u201cmoney\u201d has two\nmeanings: _currency_, or the circulating medium; and _capital seeking\ninvestment_, especially investment on loan. In this last sense the word is\nused when the \u201cmoney market\u201d is spoken of, and when the \u201cvalue of money\u201d\nis said to be high or low, the rate of interest being meant. The\nconsequence of this ambiguity is, that as soon as scarcity of money in the\nlatter of these senses begins to be felt\u2014as soon as there is difficulty of\nobtaining loans, and the rate of interest is high\u2014it is concluded that\nthis must arise from causes acting upon the quantity of money in the other\nand more popular sense; that the circulating medium must have diminished\nin quantity, or ought to be increased. I am aware that, independently of\nthe double meaning of the term, there are in the facts themselves some\npeculiarities, giving an apparent support to this error; but the ambiguity\nof the language stands on the very threshold of the subject, and\nintercepts all attempts to throw light upon it.\n\nAnother ambiguous expression which continually meets us in the political\ncontroversies of the present time, especially in those which relate to\norganic changes, is the phrase \u201cinfluence of property\u201d\u2014which is sometimes\nused for the influence of respect for superior intelligence or gratitude\nfor the kind offices which persons of large property have it so much in\ntheir power to bestow; at other times for the influence of fear; fear of\nthe worst sort of power, which large property also gives to its possessor,\nthe power of doing mischief to dependents. To confound these two, is the\nstanding fallacy of ambiguity brought against those who seek to purify the\nelectoral system from corruption and intimidation. Persuasive influence,\nacting through the conscience of the voter, and carrying his heart and\nmind with it, is beneficial\u2014therefore (it is pretended) coercive\ninfluence, which compels him to forget that he is a moral agent, or to act\nin opposition to his moral convictions, ought not to be placed under\nrestraint.\n\nAnother word which is often turned into an instrument of the fallacy of\nambiguity, is Theory. In its most proper acceptation, theory means the\ncompleted result of philosophical induction from experience. In that\nsense, there are erroneous as well as true theories, for induction may be\nincorrectly performed, but theory of some sort is the necessary result of\nknowing any thing of a subject, and having put one\u2019s knowledge into the\nform of general propositions for the guidance of practice. In this, the\nproper sense of the word, Theory is the explanation of practice. In\nanother and a more vulgar sense, theory means any mere fiction of the\nimagination, endeavoring to conceive how a thing may possibly have been\nproduced, instead of examining how it was produced. In this sense only are\ntheory and theorists unsafe guides; but because of this, ridicule or\ndiscredit is attempted to be attached to theory in its proper sense, that\nis, to legitimate generalization, the end and aim of all philosophy; and a\nconclusion is represented as worthless, just because that has been done\nwhich, if done correctly, constitutes the highest worth that a principle\nfor the guidance of practice can possess, namely, to comprehend in a few\nwords the real law on which a phenomenon depends, or some property or\nrelation which is universally true of it.\n\n\u201cThe Church\u201d is sometimes understood to mean the clergy alone, sometimes\nthe whole body of believers, or at least of communicants. The declamations\nrespecting the inviolability of church property are indebted for the\ngreater part of their apparent force to this ambiguity. The clergy, being\ncalled the church, are supposed to be the real owners of what is called\nchurch property; whereas they are in truth only the managing members of a\nmuch larger body of proprietors, and enjoy on their own part a mere\nusufruct, not extending beyond a life interest.\n\nThe following is a Stoical argument taken from Cicero, _De Finibus_, book\nthe third: \u201cQuod est bonum, omne laudabile est. Quod autem laudabile est,\nomne honestum est. Bonum igitur quod est, honestum est.\u201d Here the\nambiguous word is _laudabile_, which in the minor premise means any thing\nwhich mankind are accustomed, on good grounds, to admire or value; as\nbeauty, for instance, or good fortune: but in the major, it denotes\nexclusively moral qualities. In much the same manner the Stoics endeavored\nlogically to justify as philosophical truths, their figurative and\nrhetorical expressions of ethical sentiment: as that the virtuous man is\nalone free, alone beautiful, alone a king, etc. Whoever has virtue has\nGood (because it has been previously determined not to call any thing else\ngood); but, again, Good necessarily includes freedom, beauty, and even\nkingship, all these being good things; therefore whoever has virtue has\nall these.\n\nThe following is an argument of Descartes to prove, in his _a priori_\nmanner, the being of a God. The conception, says he, of an infinite Being\nproves the real existence of such a being. For if there is not really any\nsuch being, _I_ must have made the conception; but if I could make it, I\ncan also unmake it; which evidently is not true; therefore there must be,\nexternally to myself, an archetype, from which the conception was derived.\nIn this argument (which, it may be observed, would equally prove the real\nexistence of ghosts and of witches) the ambiguity is in the pronoun _I_,\nby which, in one place, is to be understood my _will_, in another the\n_laws of my nature_. If the conception, existing as it does in my mind,\nhad no original without, the conclusion would unquestionably follow that\n_I_ made it; that is, the laws of my nature must have somehow evolved it:\nbut that my _will_ made it, would not follow. Now when Descartes afterward\nadds that I can not unmake the conception, he means that I can not get rid\nof it by an act of my will: which is true, but is not the proposition\nrequired. I can as much unmake this conception as I can any other: no\nconception which I have once had, can I ever dismiss by mere volition; but\nwhat some of the laws of my nature have produced, other laws, or those\nsame laws in other circumstances, may, and often do, subsequently efface.\n\nAnalogous to this are some of the ambiguities in the free-will\ncontroversy; which, as they will come under special consideration in the\nconcluding Book, I only mention _memori\u00e6 caus\u00e2_. In that discussion, too,\nthe word _I_ is often shifted from one meaning to another, at one time\nstanding for my volitions, at another time for the actions which are the\nconsequences of them, or the mental dispositions from which they proceed.\nThe latter ambiguity is exemplified in an argument of Coleridge (in his\n_Aids to Reflection_), in support of the freedom of the will. It is not\ntrue, he says, that a man is governed by motives; \u201cthe man makes the\nmotive, not the motive the man;\u201d the proof being that \u201cwhat is a strong\nmotive to one man is no motive at all to another.\u201d The premise is true,\nbut only amounts to this, that different persons have different degrees of\nsusceptibility to the same motive; as they have also to the same\nintoxicating liquid, which, however, does not prove that they are free to\nbe drunk or not drunk, whatever quantity of the fluid they may drink. What\nis proved is, that certain mental conditions in the person himself must\nco-operate, in the production of the act, with the external inducement;\nbut those mental conditions also are the effect of causes; and there is\nnothing in the argument to prove that they can arise without a cause\u2014that\na spontaneous determination of the will, without any cause at all, ever\ntakes place, as the free-will doctrine supposes.\n\nThe double use, in the free-will controversy, of the word Necessity, which\nsometimes stands only for Certainty, at other times for Compulsion;\nsometimes for what _can not_ be prevented, at other times only for what we\nhave reason to be assured _will_ not; we shall have occasion hereafter to\npursue to some of its ulterior consequences.\n\nA most important ambiguity, both in common and in metaphysical language,\nis thus pointed out by Archbishop Whately in the Appendix to his Logic:\n\u201c_Same_ (as well as _One_, _Identical_, and other words derived from them)\nis used frequently in a sense very different from its primary one, as\napplicable to a _single_ object; being employed to denote great\n_similarity_. When several objects are undistinguishably alike, _one\nsingle description_ will apply equally to any of them; and thence they are\nsaid to be all of _one and the same_ nature, appearance, etc. As, _e.g._,\nwhen we say \u2018this house is built of the _same_ stone with such another,\u2019\nwe only mean that the stones are undistinguishable in their qualities; not\nthat the one building was pulled down, and the other constructed with the\nmaterials. Whereas _sameness_, in the primary sense, does not even\nnecessarily imply similarity; for if we say of any man that he is greatly\naltered since such a time, we understand, and indeed imply by the very\nexpression, that he is _one person_, though different in several\nqualities. It is worth observing also, that Same, in the secondary sense,\nadmits, according to popular usage, of degrees: we speak of two things\nbeing _nearly_ the same, but not entirely: personal identity does not\nadmit of degrees. Nothing, perhaps, has contributed more to the error of\nRealism than inattention to this ambiguity. When several persons are said\nto have _one and the same_ opinion, thought, or idea, many men,\noverlooking the true simple statement of the case, which is, that they are\n_all thinking alike_, look for something more abstruse and mystical, and\nimagine there must be some _One Thing_, in the primary sense, though not\nan individual which is present at once in the mind of each of these\npersons; and thence readily sprung Plato\u2019s theory of Ideas, each of which\nwas, according to him, one real, eternal object, existing entire and\ncomplete in each of the individual objects that are known by one name.\u201d\n\nIt is, indeed, not a matter of inference, but of authentic history, that\nPlato\u2019s doctrine of Ideas, and the Aristotelian doctrine (in this respect\nsimilar to the Platonic) of substantial forms and second substances, grew\nup in the precise way here pointed out; from the supposed necessity of\nfinding, in things which were said to have the _same_ nature, or the\n_same_ qualities, something which was the _same_ in the very sense in\nwhich a man is the same as himself. All the idle speculations respecting\n\u03c4\u1f78 \u1f44\u03bd, \u03c4\u1f78 \u1f15\u03bd, \u03c4\u1f78 \u1f45\u03bc\u03bf\u03b9\u03bf\u03bd, and similar abstractions, so common in the\nancient and in some modern schools of thought, sprang from the same\nsource. The Aristotelian logicians saw, however, one case of the\nambiguity, and provided against it with their peculiar felicity in the\ninvention of technical language, when they distinguished things which\ndiffered both _specie_ and _numero_, from those which differed _numero\ntantum_, that is, which were exactly alike (in some particular respect at\nleast) but were distinct individuals. An extension of this distinction to\nthe two meanings of the word Same, namely, things which are the same\n_specie tantum_, and a thing which is the same _numero_ as well as\n_specie_, would have prevented the confusion which has been a source of so\nmuch darkness and such an abundance of positive error in metaphysical\nphilosophy.\n\nOne of the most singular examples of the length to which a thinker of\neminence may be led away by an ambiguity of language, is afforded by this\nvery case. I refer to the famous argument by which Bishop Berkeley\nflattered himself that he had forever put an end to \u201cskepticism, atheism,\nand irreligion.\u201d It is briefly as follows: I thought of a thing yesterday;\nI ceased to think of it; I think of it again to-day. I had, therefore, in\nmy mind yesterday an _idea_ of the object; I have also an idea of it\nto-day; this idea is evidently not another, but the very same idea. Yet an\nintervening time elapsed in which I had it not. Where was the idea during\nthis interval? It must have been somewhere; it did not cease to exist;\notherwise the idea I had yesterday could not be the _same_ idea; no more\nthan the man I see alive to-day can be the same whom I saw yesterday if\nthe man has died in the mean while. Now an idea can not be conceived to\nexist anywhere except in a mind; and hence there must exist a Universal\nMind, in which all ideas have their permanent residence during the\nintervals of their conscious presence in our own minds.\n\nIt is evident that Berkeley here confounded sameness _numero_ with\nsameness _specie_, that is, with exact resemblance, and assumed the former\nwhere there was only the latter; not perceiving that when we say we have\nthe same thought to-day which we had yesterday, we do not mean the same\nindividual thought, but a thought exactly similar: as we say that we have\nthe same illness which we had last year, meaning only the same sort of\nillness.\n\nIn one remarkable instance the scientific world was divided into two\nfuriously hostile parties by an ambiguity of language affecting a branch\nof science which, more completely than most others, enjoys the advantage\nof a precise and well-defined terminology. I refer to the famous dispute\nrespecting the vis viva, the history of which is given at large in\nProfessor Playfair\u2019s Dissertation. The question was, whether the _force_\nof a moving body was proportional (its mass being given) to its velocity\nsimply, or to the square of its velocity: and the ambiguity was in the\nword Force. \u201cOne of the effects,\u201d says Playfair, \u201cproduced by a moving\nbody is proportional to the square of the velocity, while another is\nproportional to the velocity simply:\u201d from whence clearer thinkers were\nsubsequently led to establish a double measure of the efficiency of a\nmoving power, one being called _vis viva_, and the other _momentum_. About\nthe facts, both parties were from the first agreed: the only question was,\nwith which of the two effects the term _force_ should be, or could most\nconveniently be, associated. But the disputants were by no means aware\nthat this was all; they thought that force was one thing, the production\nof effects another; and the question, by which set of effects the force\nwhich produced both the one and the other should be measured, was supposed\nto be a question not of terminology, but of fact.\n\nThe ambiguity of the word Infinite is the real fallacy in the amusing\nlogical puzzle of Achilles and the Tortoise, a puzzle which has been too\nhard for the ingenuity or patience of many philosophers, and which no less\na thinker than Sir William Hamilton considered as insoluble; as a sound\nargument, though leading to a palpable falsehood. The fallacy, as Hobbes\nhinted, lies in the tacit assumption that whatever is infinitely divisible\nis infinite; but the following solution (to the invention of which I have\nno claim) is more precise and satisfactory.\n\nThe argument is, let Achilles run ten times as fast as the tortoise, yet\nif the tortoise has the start, Achilles will never overtake him. For\nsuppose them to be at first separated by an interval of a thousand feet:\nwhen Achilles has run these thousand feet, the tortoise will have got on a\nhundred; when Achilles has run those hundred, the tortoise will have run\nten, and so on forever: therefore Achilles may run forever without\novertaking the tortoise.\n\nNow the \u201cforever,\u201d in the conclusion, means, for any length of time that\ncan be supposed; but in the premises, \u201cever\u201d does not mean any _length_ of\ntime; it means any _number of subdivisions_ of time. It means that we may\ndivide a thousand feet by ten, and that quotient again by ten, and so on\nas often as we please; that there never needs be an end to the\nsubdivisions of the distance, nor consequently to those of the time in\nwhich it is performed. But an unlimited number of subdivisions may be made\nof that which is itself limited. The argument proves no other infinity of\nduration than may be embraced within five minutes. As long as the five\nminutes are not expired, what remains of them may be divided by ten, and\nagain by ten, as often as we like, which is perfectly compatible with\ntheir being only five minutes altogether. It proves, in short, that to\npass through this finite space requires a time which is infinitely\ndivisible, but not an infinite time; the confounding of which distinction\nHobbes had already seen to be the gist of the fallacy.\n\nThe following ambiguities of the word _right_ (in addition to the obvious\nand familiar one of _a_ right and the _adjective_ right) are extracted\nfrom a forgotten paper of my own, in a periodical:\n\n\u201cSpeaking morally, you are said to have a right to do a thing, if all\npersons are morally bound not to hinder you from doing it. But, in another\nsense, to have a right to do a thing is the opposite of having _no_ right\nto do it, _i.e._, of being under a moral obligation to forbear doing it.\nIn this sense, to say that you have a right to do a thing, means that you\nmay do it without any breach of duty on your part; that other persons not\nonly ought not to hinder you, but have no cause to think worse of you for\ndoing it. This is a perfectly distinct proposition from the preceding. The\nright which you have by virtue of a duty incumbent upon other persons, is\nobviously quite a different thing from a right consisting in the absence\nof any duty incumbent upon yourself. Yet the two things are perpetually\nconfounded. Thus, a man will say he has a right to publish his opinions;\nwhich may be true in this sense, that it would be a breach of duty in any\nother person to interfere and prevent the publication: but he assumes\nthereupon that, in publishing his opinions, he himself violates no duty;\nwhich may either be true or false, depending, as it does, on his having\ntaken due pains to satisfy himself, first, that the opinions are true, and\nnext, that their publication in this manner, and at this particular\njuncture, will probably be beneficial to the interests of truth on the\nwhole.\n\n\u201cThe second ambiguity is that of confounding a right of any kind, with a\nright to enforce that right by resisting or punishing a violation of it.\nPeople will say, for example, that they have a right to good government,\nwhich is undeniably true, it being the moral duty of their governors to\ngovern them well. But in granting this, you are supposed to have admitted\ntheir right or liberty to turn out their governors, and perhaps to punish\nthem, for having failed in the performance of this duty; which, far from\nbeing the same thing, is by no means universally true, but depends on an\nimmense number of varying circumstances,\u201d requiring to be conscientiously\nweighed before adopting or acting on such a resolution. This last example\nis (like others which have been cited) a case of fallacy within fallacy;\nit involves not only the second of the two ambiguities pointed out, but\nthe first likewise.\n\nOne not unusual form of the Fallacy of Ambiguous Terms is known\ntechnically as the Fallacy of Composition and Division; when the same term\nis collective in the premises, distributive in the conclusion, or _vic\u00e8 __\nversa_; or when the middle term is collective in one premise, distributive\nin the other. As if one were to say (I quote from Archbishop Whately),\n\u201cAll the angles of a triangle are equal to two right angles: A B C is an\nangle of a triangle; therefore A B C is equal to two right angles....\nThere is no fallacy more common, or more likely to deceive, than the one\nnow before us. The form in which it is most usually employed is to\nestablish some truth, separately, concerning _each single_ member of a\ncertain class, and thence to infer the same of the _whole collectively_.\u201d\nAs in the argument one sometimes hears, to prove that the world could do\nwithout great men. If Columbus (it is said) had never lived, America would\nstill have been discovered, at most only a few years later; if Newton had\nnever lived, some other person would have discovered the law of\ngravitation; and so forth. Most true: these things would have been done,\nbut in all probability not till some one had again been found with the\nqualities of Columbus or Newton. Because any one great man might have had\nhis place supplied by other great men, the argument concludes that all\ngreat men could have been dispensed with. The term \u201cgreat men\u201d is\ndistributive in the premises and collective in the conclusion.\n\n\u201cSuch also is the fallacy which probably operates on most adventurers in\nlotteries; _e.g._, \u2018the gaining of a high prize is no uncommon occurrence;\nand what is no uncommon occurrence may reasonably be expected; therefore\nthe gaining of a high prize may reasonably be expected;\u2019 the conclusion,\nwhen applied to the individual (as in practice it is), must be understood\nin the sense of \u2018reasonably expected _by a certain individual_;\u2019 therefore\nfor the major premise to be true, the middle term must be understood to\nmean, \u2018no uncommon occurrence to some one _particular_ person;\u2019 whereas\nfor the minor (which has been placed first) to be true, you must\nunderstand it of \u2018no uncommon occurrence to _some one or other_;\u2019 and thus\nyou will have the Fallacy of Composition.\n\n\u201cThis is a Fallacy with which men are extremely apt to deceive\n_themselves_; for when a multitude of particulars are presented to the\nmind, many are too weak or too indolent to take a comprehensive view of\nthem, but confine their attention to each single point, by turns; and then\ndecide, infer, and act accordingly; _e.g._, the imprudent spendthrift,\nfinding that he is able to afford this, _or_ that, _or_ the other expense,\nforgets that _all of them together_ will ruin him.\u201d The debauchee destroys\nhis health by successive acts of intemperance, because no _one_ of those\nacts would be of itself sufficient to do him any serious harm. A sick\nperson reasons with himself, \u201cone, and another, and another, of my\nsymptoms do not prove that I have a fatal disease;\u201d and practically\nconcludes that all taken together do not prove it.\n\n\u00a7 2. We have now sufficiently exemplified one of the principal Genera in\nthis Order of Fallacies; where, the source of error being the ambiguity of\nterms, the premises are verbally what is required to support the\nconclusion, but not really so. In the second great Fallacy of Confusion\nthey are neither verbally nor really sufficient, though, from their\nmultiplicity and confused arrangement, and still oftener from defect of\nmemory, they are not seen to be what they are. The fallacy I mean is that\nof Petitio Principii, or begging the question; including the more complex\nand not uncommon variety of it, which is termed Reasoning in a Circle.\n\nPetitio Principii, as defined by Archbishop Whately, is the fallacy \u201cin\nwhich the premise either appears manifestly to be the same as the\nconclusion, or is actually proved from the conclusion, or is such as would\nnaturally and properly so be proved.\u201d By the last clause I presume is\nmeant, that it is not susceptible of any other proof; for otherwise, there\nwould be no fallacy. To deduce from a proposition propositions from which\nit would itself more naturally be deduced, is often an allowable deviation\nfrom the usual didactic order; or at most, what, by an adaptation of a\nphrase familiar to mathematicians, may be called a logical\n_inelegance_.(264)\n\nThe employment of a proposition to prove that on which it is itself\ndependent for proof, by no means implies the degree of mental imbecility\nwhich might at first be supposed. The difficulty of comprehending how this\nfallacy could possibly be committed, disappears when we reflect that all\npersons, even the instructed, hold a great number of opinions without\nexactly recollecting how they came by them. Believing that they have at\nsome former time verified them by sufficient evidence, but having\nforgotten what the evidence was, they may easily be betrayed into deducing\nfrom them the very propositions which are alone capable of serving as\npremises for their establishment. \u201cAs if,\u201d says Archbishop Whately, \u201cone\nshould attempt to prove the being of a God from the authority of Holy\nWrit;\u201d which might easily happen to one with whom both doctrines, as\nfundamental tenets of his religious creed, stand on the same ground of\nfamiliar and traditional belief.\n\nArguing in a circle, however, is a stronger case of the fallacy, and\nimplies more than the mere passive reception of a premise by one who does\nnot remember how it is to be proved. It implies an actual attempt to prove\ntwo propositions reciprocally from one another; and is seldom resorted to,\nat least in express terms, by any person in his own speculations, but is\ncommitted by those who, being hard pressed by an adversary, are forced\ninto giving reasons for an opinion of which, when they began to argue,\nthey had not sufficiently considered the grounds. As in the following\nexample from Archbishop Whately: \u201cSome mechanicians attempt to prove (what\nthey ought to lay down as a probable but doubtful hypothesis)(265) that\nevery particle of matter gravitates equally: \u2018why?\u2019 \u2018because those bodies\nwhich contain more particles ever gravitate more strongly, _i.e._, are\nheavier:\u2019 \u2018but (it may be urged) those which are heaviest are not always\nmore bulky;\u2019 \u2018no, but they contain more particles, though more closely\ncondensed:\u2019 \u2018how do you know that?\u2019 \u2018because they are heavier:\u2019 \u2018how does\nthat prove it?\u2019 \u2018because all particles of matter gravitating equally, that\nmass which is specifically the heavier must needs have the more of them in\nthe same space.\u2019\u201d It appears to me that the fallacious reasoner, in his\nprivate thoughts, would not be likely to proceed beyond the first step. He\nwould acquiesce in the sufficiency of the reason first given, \u201cbodies\nwhich contain more particles are heavier.\u201d It is when he finds this\nquestioned, and is called upon to prove it, without knowing how, that he\ntries to establish his premise by supposing proved what he is attempting\nto prove by it. The most effectual way, in fact, of exposing a petitio\nprincipii, when circumstances allow of it, is by challenging the reasoner\nto prove his premises; which if he attempts to do, he is necessarily\ndriven into arguing in a circle.\n\nIt is not uncommon, however, for thinkers, and those not of the lowest\ndescription, to be led even in their own thoughts, not indeed into\nformally proving each of two propositions from the other, but into\nadmitting propositions which can only be so proved. In the preceding\nexample the two together form a complete and consistent, though\nhypothetical, explanation of the facts concerned. And the tendency to\nmistake mutual coherency for truth\u2014to trust one\u2019s safety to a strong chain\nthough it has no point of support\u2014is at the bottom of much which, when\nreduced to the strict forms of argumentation, can exhibit itself no\notherwise than as reasoning in a circle. All experience bears testimony to\nthe enthralling effect of neat concatenation in a system of doctrines, and\nthe difficulty with which people admit the persuasion that any thing which\nholds so well together can possibly fall.\n\nSince every case where a conclusion which can only be proved from certain\npremises is used for the proof of those premises, is a case of _petitio\nprincipii_, that fallacy includes a very great proportion of all incorrect\nreasoning. It is necessary, for completing our view of the fallacy, to\nexemplify some of the disguises under which it is accustomed to mask\nitself, and to escape exposure.\n\nA proposition would not be admitted by any person in his senses as a\ncorollary from itself, unless it were expressed in language which made it\nseem different. One of the commonest modes of so expressing it, is to\npresent the proposition itself in abstract terms, as a proof of the same\nproposition expressed in concrete language. This is a very frequent mode,\nnot only of pretended proof, but of pretended explanation; and is parodied\nwhen Moli\u00e8re (_Le Malade Imaginaire_) makes one of his absurd physicians\nsay,\n\n\n      Mihi a docto doctore,\n      Demandatur causam et rationem quare\n    Opium facit dormire.\n      A quoi respondeo,\n      Quia est in eo\n      Virtus dormitiva,\n    Cujus est natura\n      Sensus assoupire.\n\n\nThe words Nature and Essence are grand instruments of this mode of begging\nthe question, as in the well-known argument of the scholastic theologians,\nthat the mind thinks always, because the _essence_ of the mind is to\nthink. Locke had to point out, that if by essence is here meant some\nproperty which must manifest itself by actual exercise at all times, the\npremise is a direct assumption of the conclusion; while if it only means\nthat to think is the distinctive property of a mind, there is no\nconnection between the premise and the conclusion, since it is not\nnecessary that a distinctive property should be perpetually in action.\n\nThe following is one of the modes in which these abstract terms, Nature\nand Essence, are used as instruments of this fallacy. Some particular\nproperties of a thing are selected, more or less arbitrarily, to be termed\nits nature or essence; and when this has been done, these properties are\nsupposed to be invested with a kind of indefeasibleness; to have become\nparamount to all the other properties of the thing, and incapable of being\nprevailed over or counteracted by them. As when Aristotle, in a passage\nalready cited, \u201cdecides that there is no void on such arguments as this:\nin a void there could be no difference of up and down; for as in nothing\nthere are no differences, so there are none in a privation or negation;\nbut a void is merely a privation or negation of matter; therefore, in a\nvoid, bodies could not move up and down, which it is in their _nature_ to\ndo.\u201d(266) In other words, it is in the _nature_ of bodies to move up and\ndown, _ergo_ any physical fact which supposes them not so to move, can not\nbe authentic. This mode of reasoning, by which a bad generalization is\nmade to overrule all facts which contradict it, is Petitio Principii in\none of its most palpable forms.\n\nNone of the modes of assuming what should be proved are in more frequent\nuse than what are termed by Bentham \u201cquestion-begging appellatives;\u201d names\nwhich beg the question under the disguise of stating it. The most potent\nof these are such as have a laudatory or vituperative character. For\ninstance, in politics, the word Innovation. The dictionary meaning of this\nterm being merely \u201ca change to something new,\u201d it is difficult for the\ndefenders even of the most salutary improvement to deny that it is an\ninnovation; yet the word having acquired in common usage a vituperative\nconnotation in addition to its dictionary meaning, the admission is always\nconstrued as a large concession to the disadvantage of the thing proposed.\n\nThe following passage from the argument in refutation of the Epicureans,\nin the second book of Cicero, \u201cDe Finibus,\u201d affords a fine example of this\nsort of fallacy: \u201cEt quidem illud ipsum non nimium probo (et tantum\npatior) philosophum loqui de cupiditatibus finiendis. An potest cupiditas\nfiniri? tollenda est, atque extrahenda radicitus. Quis est enim, in quo\nsit cupiditas, quin recte cupidus dici possit? Ergo et avarus erit, sed\nfinite: adulter, verum habebit modum: et luxuriosus eodem modo. Qualis\nista philosophia est, qu\u00e6 non interitum afferat pravitatis, sed sit\ncontenta mediocritate vitiorum?\u201d The question was, whether certain\ndesires, when kept within bounds, are vices or not; and the argument\ndecides the point by applying to them a word (_cupiditas_) which _implies_\nvice. It is shown, however, in the remarks which follow, that Cicero did\nnot intend this as a serious argument, but as a criticism on what he\ndeemed an inappropriate expression. \u201cRem ipsam prorsus probo: elegantiam\ndesidero. Appellet h\u00e6c _desideria natur\u00e6_; cupiditatis nomen servet alio,\u201d\netc. But many persons, both ancient and modern, have employed this, or\nsomething equivalent to it, as a real and conclusive argument. We may\nremark that the passage respecting _cupiditas_ and _cupidus_ is also an\nexample of another fallacy already noticed, that of Paronymous Terms.\n\nMany more of the arguments of the ancient moralists, and especially of the\nStoics, fall within the definition of Petitio Principii. In the \u201cDe\nFinibus,\u201d for example, which I continue to quote as being probably the\nbest extant exemplification at once of the doctrines and the methods of\nthe schools of philosophy existing at that time; of what value as\narguments are such pleas as those of Cato in the third book: That if\nvirtue were not happiness, it could not be a thing to _boast_ of: That if\ndeath or pain were evils, it would be impossible not to fear them, and it\ncould not, therefore, be laudable to despise them, etc. In one way of\nviewing these arguments, they may be regarded as appeals to the authority\nof the general sentiment of mankind which had stamped its approval upon\ncertain actions and characters by the phrases referred to; but that such\ncould have been the meaning intended is very unlikely, considering the\ncontempt of the ancient philosophers for vulgar opinion. In any other\nsense they are clear cases of Petitio Principii, since the word laudable,\nand the idea of boasting, imply principles of conduct; and practical\nmaxims can only be proved from speculative truths, namely, from the\nproperties of the subject-matter, and can not, therefore, be employed to\nprove those properties. As well might it be argued that a government is\ngood because we ought to support it, or that there is a God because it is\nour duty to pray to him.\n\nIt is assumed by all the disputants in the \u201cDe Finibus\u201d as the foundation\nof the inquiry into the _summum bonum_, that \u201csapiens semper beatus est.\u201d\nNot simply that wisdom gives the best chance of happiness, or that wisdom\nconsists in knowing what happiness is, and by what things it is promoted;\nthese propositions would not have been enough for them; but that the sage\nalways is, and must of necessity be, happy. The idea that wisdom could be\nconsistent with unhappiness, was always rejected as inadmissible: the\nreason assigned by one of the interlocutors, near the beginning of the\nthird book, being, that if the wise could be unhappy, there was little use\nin pursuing wisdom. But by unhappiness they did not mean pain or\nsuffering; to that it was granted that the wisest person was liable in\ncommon with others: he was happy, because in possessing wisdom he had the\nmost valuable of all possessions, the most to be sought and prized of all\nthings, and to possess the most valuable thing was to be the most happy.\nBy laying it down, therefore, at the commencement of the inquiry, that the\nsage must be happy, the disputed question respecting the _summum bonum_\nwas in fact begged; with the further assumption, that pain and suffering,\nso far as they can co-exist with wisdom, are not unhappiness, and are no\nevil.\n\nThe following are additional instances of Petitio Principii, under more or\nless of disguise.\n\nPlato, in the _Sophistes_, attempts to prove that things may exist which\nare incorporeal, by the argument that justice and wisdom are incorporeal,\nand justice and wisdom must be something. Here, if by _something_ be\nmeant, as Plato did in fact mean, a thing capable of existing in and by\nitself, and not as a quality of some other thing, he begs the question in\nasserting that justice and wisdom must be something; if he means any thing\nelse, his conclusion is not proved. This fallacy might also be classed\nunder ambiguous middle-term; _something_, in the one premise, meaning some\nsubstance, in the other merely some object of thought, whether substance\nor attribute.\n\nIt was formerly an argument employed in proof of what is now no longer a\npopular doctrine, the infinite divisibility of matter, that every portion\nof matter however small, must at least have an upper and an under surface.\nThose who used this argument did not see that it assumed the very point in\ndispute, the impossibility of arriving at a minimum of thickness; for if\nthere be a minimum, its upper and under surface will of course be one; it\nwill be itself a surface, and no more. The argument owes its very\nconsiderable plausibility to this, that the premise does actually seem\nmore obvious than the conclusion, though really identical with it. As\nexpressed in the premise, the proposition appeals directly and in concrete\nlanguage to the incapacity of the human imagination for conceiving a\nminimum. Viewed in this light, it becomes a case of the _a priori_ fallacy\nor natural prejudice, that whatever can not be conceived can not exist.\nEvery fallacy of Confusion (it is almost unnecessary to repeat) will, if\ncleared up, become a fallacy of some other sort; and it will be found of\ndeductive or ratiocinative fallacies generally, that when they mislead,\nthere is mostly, as in this case, a fallacy of some other description\nlurking under them, by virtue of which chiefly it is that the verbal\njuggle, which is the outside or body of this kind of fallacy, passes\nundetected.\n\nEuler\u2019s Algebra, a book otherwise of great merit, but full, to\noverflowing, of logical errors in respect to the foundation of the\nscience, contains the following argument to prove that _minus_ multiplied\nby _minus_ gives _plus_, a doctrine the opprobrium of all mere\nmathematicians, and which Euler had not a glimpse of the true method of\nproving. He says _minus_ multiplied by _minus_ can not give _minus_; for\n_minus_ multiplied by _plus_ gives _minus_, and _minus_ multiplied by\n_minus_ can not give the same product as _minus_ multiplied by _plus_. Now\none is obliged to ask, why minus multiplied by minus must give any product\nat all? and if it does, why its product can not be the same as that of\nminus multiplied by plus? for this would seem, at the first glance, not\nmore absurd than that minus by minus should give the same as plus by plus,\nthe proposition which Euler prefers to it. The premise requires proof, as\nmuch as the conclusion; nor can it be proved, except by that more\ncomprehensive view of the nature of multiplication, and of algebraic\nprocesses in general, which would also supply a far better proof of the\nmysterious doctrine which Euler is here endeavoring to demonstrate.\n\nA striking instance of reasoning in a circle is that of some ethical\nwriters, who first take for their standard of moral truth what, being the\ngeneral, they deem to be the natural or instinctive sentiments and\nperceptions of mankind, and then explain away the numerous instances of\ndivergence from their assumed standard, by representing them as cases in\nwhich the perceptions are unhealthy. Some particular mode of conduct or\nfeeling is affirmed to be _unnatural_; why? because it is abhorrent to the\nuniversal and natural sentiments of mankind. Finding no such sentiment in\nyourself, you question the fact; and the answer is (if your antagonist is\npolite), that you are an exception, a peculiar case. But neither (say you)\ndo I find in the people of some other country, or of some former age, any\nsuch feeling of abhorrence; \u201cay, but their feelings were sophisticated and\nunhealthy.\u201d\n\nOne of the most notable specimens of reasoning in a circle is the doctrine\nof Hobbes, Rousseau, and others, which rests the obligations by which\nhuman beings are bound as members of society, on a supposed social\ncompact. I waive the consideration of the fictitious nature of the compact\nitself; but when Hobbes, through the whole Leviathan, elaborately deduces\nthe obligation of obeying the sovereign, not from the necessity or utility\nof doing so, but from a promise supposed to have been made by our\nancestors, on renouncing savage life and agreeing to establish political\nsociety, it is impossible not to retort by the question, Why are we bound\nto keep a promise made for us by others? or why bound to keep a promise at\nall? No satisfactory ground can be assigned for the obligation, except the\nmischievous consequences of the absence of faith and mutual confidence\namong mankind. We are, therefore, brought round to the interests of\nsociety, as the ultimate ground of the obligation of a promise; and yet\nthose interests are not admitted to be a sufficient justification for the\nexistence of government and law. Without a promise it is thought that we\nshould not be bound to that which is implied in all modes of living in\nsociety, namely, to yield a general obedience to the laws therein\nestablished; and so necessary is the promise deemed, that if none has\nactually been made, some additional safety is supposed to be given to the\nfoundations of society by feigning one.\n\n\u00a7 3. Two principal subdivisions of the class of Fallacies of Confusion\nhaving been disposed of; there remains a third, in which the confusion is\nnot, as in the Fallacy of Ambiguity, in misconceiving the import of the\npremises, nor, as in Petitio Principii, in forgetting what the premises\nare, but in mistaking the conclusion which is to be proved. This is the\nfallacy of Ignoratio Elenchi, in the widest sense of the phrase; also\ncalled by Archbishop Whately the Fallacy of Irrelevant Conclusion. His\nexamples and remarks are highly worthy of citation.\n\n\u201cVarious kinds of propositions are, according to the occasion, substituted\nfor the one of which proof is required; sometimes the particular for the\nuniversal; sometimes a proposition with different terms; and various are\nthe contrivances employed to effect and to conceal this substitution, and\nto make the conclusion which the sophist has drawn, answer practically the\nsame purpose as the one he ought to have established. We say, \u2018practically\nthe same purpose,\u2019 because it will very often happen that some _emotion_\nwill be excited, some sentiment impressed on the mind (by a dexterous\nemployment of this fallacy), such as shall bring men into the\n_disposition_ requisite for your purpose; though they may not have\nassented to, or even stated distinctly in their own minds, the\n_proposition_ which it was your business to establish. Thus if a sophist\nhas to defend one who has been guilty of some _serious_ offense, which he\nwishes to extenuate, though he is unable distinctly to prove that it is\nnot such, yet if he can succeed in _making the audience laugh_ at some\ncasual matter, he has gained practically the same point. So also if any\none has pointed out the extenuating circumstances in some particular case\nof offense, so as to show that it differs widely from the generality of\nthe same class, the sophist, if he finds himself unable to disprove these\ncircumstances, may do away the force of them, by simply _referring the\naction to that very class_, which no one can deny that it belongs to, and\nthe very name of which will excite a feeling of disgust sufficient to\ncounteract the extenuation; _e.g._, let it be a case of peculation, and\nthat many _mitigating_ circumstances have been brought forward which can\nnot be denied; the sophistical opponent will reply, \u2018Well, but after all,\nthe man is a _rogue_, and there is an end of it;\u2019 now in reality this was\n(by hypothesis) never the question; and the mere assertion of what was\nnever denied _ought_ not, in fairness, to be regarded as decisive; but,\npractically, the odiousness of the word, arising in great measure from the\nassociation of those very circumstances which belong to most of the class,\nbut which we have supposed to be _absent_ in _this particular_ instance,\nexcites precisely that feeling of disgust which, in effect, destroys the\nforce of the defense. In like manner we may refer to this head all cases\nof improper appeal to the passions, and every thing else which is\nmentioned by Aristotle as extraneous to the matter in hand (\u1f14\u03be\u03c9 \u03c4\u03bf\u1fe6\n\u03c0\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03bf\u03c2).\u201d\n\nAgain, \u201cinstead of proving that \u2018this prisoner has committed an atrocious\nfraud,\u2019 you prove that the fraud he is accused of is atrocious; instead of\nproving (as in the well-known tale of Cyrus and the two coats) that the\ntaller boy had a right to force the other boy to exchange coats with him,\nyou prove that the exchange would have been advantageous to both; instead\nof proving that the poor ought to be relieved in this way rather than in\nthat, you prove that the poor ought to be relieved; instead of proving\nthat the irrational agent\u2014whether a brute or a madman\u2014can never be\ndeterred from any act by apprehension of punishment (as, for instance, a\ndog from sheep-biting, by fear of being beaten), you prove that the\nbeating of one dog does not operate as an _example_ to _other_ dogs, etc.\n\n\u201cIt is evident that Ignoratio Elenchi may be employed as well for the\napparent refutation of your opponent\u2019s proposition, as for the apparent\nestablishment of your own; for it is substantially the same thing, to\nprove what was not denied or to disprove what was not asserted. The latter\npractice is not less common, and it is more offensive, because it\nfrequently amounts to a personal affront, in attributing to a person\nopinions, etc., which he perhaps holds in abhorrence. Thus, when in a\ndiscussion one party vindicates, on the ground of general expediency, a\nparticular instance of resistance to government in a case of intolerable\noppression, the opponent may gravely maintain, \u2018that we ought not to do\nevil that good may come;\u2019 a proposition which of course had never been\ndenied, the point in dispute being, \u2018whether resistance in this particular\ncase _were_ doing evil or not.\u2019 Or again, by way of disproving the\nassertion of the right of private judgment in religion, one may hear a\ngrave argument to prove that \u2018it is impossible every one can be _right in\nhis judgment_.\u2019\u201d\n\nThe works of controversial writers are seldom free from this fallacy. The\nattempts, for instance, to disprove the population doctrines of Malthus,\nhave been mostly cases of _ignoratio elenchi_. Malthus has been supposed\nto be refuted if it could be shown that in some countries or ages\npopulation has been nearly stationary; as if he had asserted that\npopulation always increases in a given ratio, or had not expressly\ndeclared that it increases only in so far as it is not restrained by\nprudence, or kept down by poverty and disease. Or, perhaps, a collection\nof facts is produced to prove that in some one country the people are\nbetter off with a dense population than they are in another country with a\nthin one; or that the people have become more numerous and better off at\nthe same time. As if the assertion were that a dense population could not\npossibly be well off; as if it were not part of the very doctrine, and\nessential to it, that where there is a more abundant production there may\nbe a greater population without any increase of poverty, or even with a\ndiminution of it.\n\nThe favorite argument against Berkeley\u2019s theory of the non-existence of\nmatter, and the most popularly effective, next to a \u201cgrin\u201d(267)\u2014an\nargument, moreover, which is not confined to \u201ccoxcombs,\u201d nor to men like\nSamuel Johnson, whose greatly overrated ability certainly did not lie in\nthe direction of metaphysical speculation, but is the stock argument of\nthe Scotch school of metaphysicians\u2014is a palpable Ignoratio Elenchi. The\nargument is perhaps as frequently expressed by gesture as by words, and\none of its commonest forms consists in knocking a stick against the\nground. This short and easy confutation overlooks the fact, that in\ndenying matter, Berkeley did not deny any thing to which our senses bear\nwitness, and therefore can not be answered by any appeal to them. His\nskepticism related to the supposed substratum, or hidden cause of the\nappearances perceived by our senses; the evidence of which, whatever may\nbe thought of its conclusiveness, is certainly not the evidence of sense.\nAnd it will always remain a signal proof of the want of metaphysical\nprofundity of Reid, Stewart, and, I am sorry to add, of Brown, that they\nshould have persisted in asserting that Berkeley, if he believed his own\ndoctrine, was bound to walk into the kennel, or run his head against a\npost. As if persons who do not recognize an occult cause of their\nsensations could not possibly believe that a fixed order subsists among\nthe sensations themselves. Such a want of comprehension of the distinction\nbetween a thing and its sensible manifestation, or, in metaphysical\nlanguage, between the noumenon and the phenomenon, would be impossible to\neven the dullest disciple of Kant or Coleridge.\n\nIt would be easy to add a greater number of examples of this fallacy, as\nwell as of the others which I have attempted to characterize. But a more\ncopious exemplification does not seem to be necessary; and the intelligent\nreader will have little difficulty in adding to the catalogue from his own\nreading and experience. We shall, therefore, here close our exposition of\nthe general principles of logic, and proceed to the supplementary inquiry\nwhich is necessary to complete our design.\n\n\n\n\n                                 Book VI.\n\n\nON THE LOGIC OF THE MORAL SCIENCES.\n\n\n    \u201cSi l\u2019homme peut pr\u00e9dire, avec une assurance presque enti\u00e8re, les\n    ph\u00e9nom\u00e8nes dont il conna\u00eet les lois; si lors m\u00eame qu\u2019elles lui\n    sont inconnues, il peut, d\u2019apr\u00e8s l\u2019exp\u00e9rience, pr\u00e9voir avec une\n    grande probabilit\u00e9 les \u00e9v\u00e9nements de l\u2019avenir; pourquoi\n    regarderait-on comme une entreprise chim\u00e9rique, celle de tracer\n    avec quelque vraisemblance le tableau des destin\u00e9es futures de\n    l\u2019esp\u00e8ce humaine, d\u2019apr\u00e8s les r\u00e9sultats de son histoire? Le seul\n    fondement de croyance dans les sciences naturelles, est cette\n    id\u00e9e, que les lois g\u00e9n\u00e9rales, connues ou ignor\u00e9es, qui r\u00e8glent les\n    ph\u00e9nom\u00e8nes de l\u2019univers, sont n\u00e9cessaires et constantes; et par\n    quelle raison ce principe serait-il moins vrai pour le\n    d\u00e9veloppement des facult\u00e9s intellectuelles et morales de l\u2019homme,\n    que pour les autres op\u00e9rations de la nature? Enfin, puisque des\n    opinions form\u00e9es d\u2019apr\u00e8s l\u2019exp\u00e9rience ... sont la seule r\u00e8gle de\n    la conduite des hommes les plus sages, pourquoi interdirait-on au\n    philosophe d\u2019appuyer ses conjectures sur cette m\u00eame base, pourvu\n    qu\u2019il ne leur attribue pas une certitude sup\u00e9rieure \u00e0 celle qui\n    peut na\u00eetre du nombre, de la constance, de l\u2019exactitude des\n    observations?\u201d\u2014CONDORCET, _Esquisse d\u2019un Tableau Historique des\n    Progr\u00e8s de l\u2019Esprit Humain_.\n\n\n\n\n                                Chapter I.\n\n\nIntroductory Remarks.\n\n\n\u00a7 1. Principles of Evidence and Theories of Method are not to be\nconstructed _a priori_. The laws of our rational faculty, like those of\nevery other natural agency, are only learned by seeing the agent at work.\nThe earlier achievements of science were made without the conscious\nobservance of any Scientific Method; and we should never have known by\nwhat process truth is to be ascertained, if we had not previously\nascertained many truths. But it was only the easier problems which could\nbe thus resolved: natural sagacity, when it tried its strength against the\nmore difficult ones, either failed altogether, or, if it succeeded here\nand there in obtaining a solution, had no sure means of convincing others\nthat its solution was correct. In scientific investigation, as in all\nother works of human skill, the way of obtaining the end is seen as it\nwere instinctively by superior minds in some comparatively simple case,\nand is then, by judicious generalization, adapted to the variety of\ncomplex cases. We learn to do a thing in difficult circumstances, by\nattending to the manner in which we have spontaneously done the same thing\nin easier ones.\n\nThis truth is exemplified by the history of the various branches of\nknowledge which have successively, in the ascending order of their\ncomplication, assumed the character of sciences; and will doubtless\nreceive fresh confirmation from those of which the final scientific\nconstitution is yet to come, and which are still abandoned to the\nuncertainties of vague and popular discussion. Although several other\nsciences have emerged from this state at a comparatively recent date, none\nnow remain in it except those which relate to man himself, the most\ncomplex and most difficult subject of study on which the human mind can be\nengaged.\n\nConcerning the physical nature of man, as an organized being\u2014though there\nis still much uncertainty and much controversy, which can only be\nterminated by the general acknowledgment and employment of stricter rules\nof induction than are commonly recognized\u2014there is, however, a\nconsiderable body of truths which all who have attended to the subject\nconsider to be fully established; nor is there now any radical\nimperfection in the method observed in the department of science by its\nmost distinguished modern teachers. But the laws of Mind, and, in even a\ngreater degree, those of Society, are so far from having attained a\nsimilar state of even partial recognition, that it is still a controversy\nwhether they are capable of becoming subjects of science in the strict\nsense of the term: and among those who are agreed on this point, there\nreigns the most irreconcilable diversity on almost every other. Here,\ntherefore, if anywhere, the principles laid down in the preceding Books\nmay be expected to be useful.\n\nIf on matters so much the most important with which human intellect can\noccupy itself a more general agreement is ever to exist among thinkers; if\nwhat has been pronounced \u201cthe proper study of mankind\u201d is not destined to\nremain the only subject which Philosophy can not succeed in rescuing from\nEmpiricism; the same process through which the laws of many simpler\nphenomena have by general acknowledgment been placed beyond dispute, must\nbe consciously and deliberately applied to those more difficult inquiries.\nIf there are some subjects on which the results obtained have finally\nreceived the unanimous assent of all who have attended to the proof, and\nothers on which mankind have not yet been equally successful; on which the\nmost sagacious minds have occupied themselves from the earliest date, and\nhave never succeeded in establishing any considerable body of truths, so\nas to be beyond denial or doubt; it is by generalizing the methods\nsuccessfully followed in the former inquiries, and adapting them to the\nlatter, that we may hope to remove this blot on the face of science. The\nremaining chapters are an endeavor to facilitate this most desirable\nobject.\n\n\u00a7 2. In attempting this, I am not unmindful how little can be done toward\nit in a mere treatise on Logic, or how vague and unsatisfactory all\nprecepts of Method must necessarily appear when not practically\nexemplified in the establishment of a body of doctrine. Doubtless, the\nmost effectual mode of showing how the sciences of Ethics and Politics may\nbe constructed would be to construct them: a task which, it needs scarcely\nbe said, I am not about to undertake. But even if there were no other\nexamples, the memorable one of Bacon would be sufficient to demonstrate,\nthat it is sometimes both possible and useful to point out the way, though\nwithout being one\u2019s self prepared to adventure far into it. And if more\nwere to be attempted, this at least is not a proper place for the attempt.\n\nIn substance, whatever can be done in a work like this for the Logic of\nthe Moral Sciences, has been or ought to have been accomplished in the\nfive preceding Books; to which the present can be only a kind of\nsupplement or appendix, since the methods of investigation applicable to\nmoral and social science must have been already described, if I have\nsucceeded in enumerating and characterizing those of science in general.\nIt remains, however, to examine which of those methods are more especially\nsuited to the various branches of moral inquiry; under what peculiar\nfacilities or difficulties they are there employed; how far the\nunsatisfactory state of those inquiries is owing to a wrong choice of\nmethods, how far to want of skill in the application of right ones; and\nwhat degree of ultimate success may be attained or hoped for by a better\nchoice or more careful employment of logical processes appropriate to the\ncase. In other words, whether moral sciences exist, or can exist; to what\ndegree of perfection they are susceptible of being carried; and by what\nselection or adaptation of the methods brought to view in the previous\npart of this work that degree of perfection is attainable.\n\nAt the threshold of this inquiry we are met by an objection, which, if not\nremoved, would be fatal to the attempt to treat human conduct as a subject\nof science. Are the actions of human beings, like all other natural\nevents, subject to invariable laws? Does that constancy of causation,\nwhich is the foundation of every scientific theory of successive\nphenomena, really obtain among them? This is often denied; and for the\nsake of systematic completeness, if not from any very urgent practical\nnecessity, the question should receive a deliberate answer in this place.\nWe shall devote to the subject a chapter apart.\n\n\n\n\n                               Chapter II.\n\n\nOf Liberty And Necessity.\n\n\n\u00a7 1. The question, whether the law of causality applies in the same strict\nsense to human actions as to other phenomena, is the celebrated\ncontroversy concerning the freedom of the will; which, from at least as\nfar back as the time of Pelagius, has divided both the philosophical and\nthe religious world. The affirmative opinion is commonly called the\ndoctrine of Necessity, as asserting human volitions and actions to be\nnecessary and inevitable. The negative maintains that the will is not\ndetermined, like other phenomena, by antecedents, but determines itself;\nthat our volitions are not, properly speaking, the effects of causes, or\nat least have no causes which they uniformly and implicitly obey.\n\nI have already made it sufficiently apparent that the former of these\nopinions is that which I consider the true one; but the misleading terms\nin which it is often expressed, and the indistinct manner in which it is\nusually apprehended, have both obstructed its reception, and perverted its\ninfluence when received. The metaphysical theory of free-will, as held by\nphilosophers (for the practical feeling of it, common in a greater or less\ndegree to all mankind, is in no way inconsistent with the contrary\ntheory), was invented because the supposed alternative of admitting human\nactions to be _necessary_ was deemed inconsistent with every one\u2019s\ninstinctive consciousness, as well as humiliating to the pride and even\ndegrading to the moral nature of man. Nor do I deny that the doctrine, as\nsometimes held, is open to these imputations; for the misapprehension in\nwhich I shall be able to show that they originate, unfortunately is not\nconfined to the opponents of the doctrine, but is participated in by many,\nperhaps we might say by most, of its supporters.\n\n\u00a7 2. Correctly conceived, the doctrine called Philosophical Necessity is\nsimply this: that, given the motives which are present to an individual\u2019s\nmind, and given likewise the character and disposition of the individual,\nthe manner in which he will act might be unerringly inferred; that if we\nknew the person thoroughly, and knew all the inducements which are acting\nupon him, we could foretell his conduct with as much certainty as we can\npredict any physical event. This proposition I take to be a mere\ninterpretation of universal experience, a statement in words of what every\none is internally convinced of. No one who believed that he knew\nthoroughly the circumstances of any case, and the characters of the\ndifferent persons concerned, would hesitate to foretell how all of them\nwould act. Whatever degree of doubt he may in fact feel, arises from the\nuncertainty whether he really knows the circumstances, or the character of\nsome one or other of the persons, with the degree of accuracy required;\nbut by no means from thinking that if he did know these things, there\ncould be any uncertainty what the conduct would be. Nor does this full\nassurance conflict in the smallest degree with what is called our feeling\nof freedom. We do not feel ourselves the less free, because those to whom\nwe are intimately known are well assured how we shall will to act in a\nparticular case. We often, on the contrary, regard the doubt what our\nconduct will be, as a mark of ignorance of our character, and sometimes\neven resent it as an imputation. The religious metaphysicians who have\nasserted the freedom of the will, have always maintained it to be\nconsistent with divine foreknowledge of our actions: and if with divine,\nthen with any other foreknowledge. We may be free, and yet another may\nhave reason to be perfectly certain what use we shall make of our freedom.\nIt is not, therefore, the doctrine that our volitions and actions are\ninvariable consequents of our antecedent states of mind, that is either\ncontradicted by our consciousness, or felt to be degrading.\n\nBut the doctrine of causation, when considered as obtaining between our\nvolitions and their antecedents, is almost universally conceived as\ninvolving more than this. Many do not believe, and very few practically\nfeel, that there is nothing in causation but invariable, certain, and\nunconditional sequence. There are few to whom mere constancy of succession\nappears a sufficiently stringent bond of union for so peculiar a relation\nas that of cause and effect. Even if the reason repudiates, the\nimagination retains, the feeling of some more intimate connection, of some\npeculiar tie, or mysterious constraint exercised by the antecedent over\nthe consequent. Now this it is which, considered as applying to the human\nwill, conflicts with our consciousness, and revolts our feelings. We are\ncertain that, in the case of our volitions, there is not this mysterious\nconstraint. We know that we are not compelled, as by a magical spell, to\nobey any particular motive. We feel, that if we wished to prove that we\nhave the power of resisting the motive, we could do so (that wish being,\nit needs scarcely be observed, a _new antecedent_); and it would be\nhumiliating to our pride, and (what is of more importance) paralyzing to\nour desire of excellence, if we thought otherwise. But neither is any such\nmysterious compulsion now supposed, by the best philosophical authorities,\nto be exercised by any other cause over its effect. Those who think that\ncauses draw their effects after them by a mystical tie, are right in\nbelieving that the relation between volitions and their antecedents is of\nanother nature. But they should go farther, and admit that this is also\ntrue of all other effects and their antecedents. If such a tie is\nconsidered to be involved in the word Necessity, the doctrine is not true\nof human actions; but neither is it then true of inanimate objects. It\nwould be more correct to say that matter is not bound by necessity, than\nthat mind is so.\n\nThat the free-will metaphysicians, being mostly of the school which\nrejects Hume\u2019s and Brown\u2019s analysis of Cause and Effect, should miss their\nway for want of the light which that analysis affords, can not surprise\nus. The wonder is, that the necessitarians, who usually admit that\nphilosophical theory, should in practice equally lose sight of it. The\nvery same misconception of the doctrine called Philosophical Necessity,\nwhich prevents the opposite party from recognizing its truth, I believe to\nexist more or less obscurely in the minds of most necessitarians, however\nthey may in words disavow it. I am much mistaken if they habitually feel\nthat the necessity which they recognize in actions is but uniformity of\norder, and capability of being predicted. They have a feeling as if there\nwere at bottom a stronger tie between the volitions and their causes; as\nif, when they asserted that the will is governed by the balance of\nmotives, they meant something more cogent than if they had only said, that\nwhoever knew the motives, and our habitual susceptibilities to them, could\npredict how we should will to act. They commit, in opposition to their own\nscientific system, the very same mistake which their adversaries commit in\nobedience to theirs; and in consequence do really in some instances suffer\nthose depressing consequences which their opponents erroneously impute to\nthe doctrine itself.\n\n\u00a7 3. I am inclined to think that this error is almost wholly an effect of\nthe associations with a word, and that it would be prevented, by\nforbearing to employ, for the expression of the simple fact of causation,\nso extremely inappropriate a term as Necessity. That word, in its other\nacceptations, involves much more than mere uniformity of sequence: it\nimplies irresistibleness. Applied to the will, it only means that, the\ngiven cause will be followed by the effect, subject to all possibilities\nof counteraction by other causes; but in common use it stands for the\noperation of those causes exclusively which are supposed too powerful to\nbe counteracted at all. When we say that all human actions take place of\nnecessity, we only mean that they will certainly happen if nothing\nprevents; when we say that dying of want, to those who can not get food,\nis a necessity, we mean that it will certainly happen whatever may be done\nto prevent it. The application of the same term to the agencies on which\nhuman actions depend, as is used to express those agencies of nature which\nare really uncontrollable, can not fail, when habitual, to create a\nfeeling of uncontrollableness in the former also. This, however, is a mere\nillusion. There are physical sequences which we call necessary, as death\nfor want of food or air; there are others which, though as much cases of\ncausation as the former, are not said to be necessary, as death from\npoison, which an antidote, or the use of the stomach-pump, will sometimes\navert. It is apt to be forgotten by people\u2019s feelings, even if remembered\nby their understandings, that human actions are in this last predicament:\nthey are never (except in some cases of mania) ruled by any one motive\nwith such absolute sway that there is no room for the influence of any\nother. The causes, therefore, on which action depends, are never\nuncontrollable; and any given effect is only necessary provided that the\ncauses tending to produce it are not controlled. That whatever happens,\ncould not have happened otherwise, unless something had taken place which\nwas capable of preventing it, no one surely needs hesitate to admit. But\nto call this by the name Necessity is to use the term in a sense so\ndifferent from its primitive and familiar meaning, from that which it\nbears in the common occasions of life, as to amount almost to a play upon\nwords. The associations derived from the ordinary sense of the term will\nadhere to it in spite of all we can do; and though the doctrine of\nNecessity, as stated by most who hold it, is very remote from fatalism, it\nis probable that most necessitarians are fatalists, more or less, in their\nfeelings.\n\nA fatalist believes, or half believes (for nobody is a consistent\nfatalist), not only that whatever is about to happen will be the\ninfallible result of the causes which produce it (which is the true\nnecessitarian doctrine), but moreover that there is no use in struggling\nagainst it; that it will happen, however we may strive to prevent it. Now,\na necessitarian, believing that our actions follow from our characters,\nand that our characters follow from our organization, our education, and\nour circumstances, is apt to be, with more or less of consciousness on his\npart, a fatalist as to his own actions, and to believe that his nature is\nsuch, or that his education and circumstances have so moulded his\ncharacter, that nothing can now prevent him from feeling and acting in a\nparticular way, or at least that no effort of his own can hinder it. In\nthe words of the sect which in our own day has most perseveringly\ninculcated and most perversely misunderstood this great doctrine, his\ncharacter is formed _for_ him, and not _by_ him; therefore his wishing\nthat it had been formed differently is of no use; he has no power to alter\nit. But this is a grand error. He has, to a certain extent, a power to\nalter his character. Its being, in the ultimate resort, formed for him, is\nnot inconsistent with its being, in part, formed _by_ him as one of the\nintermediate agents. His character is formed by his circumstances\n(including among these his particular organization); but his own desire to\nmould it in a particular way, is one of those circumstances, and by no\nmeans one of the least influential. We can not, indeed, directly will to\nbe different from what we are. But neither did those who are supposed to\nhave formed our characters directly will that we should be what we are.\nTheir will had no direct power except over their own actions. They made us\nwhat they did make us, by willing, not the end, but the requisite means;\nand we, when our habits are not too inveterate, can, by similarly willing\nthe requisite means, make ourselves different. If they could place us\nunder the influence of certain circumstances, we, in like manner, can\nplace ourselves under the influence of other circumstances. We are exactly\nas capable of making our own character, _if we will_, as others are of\nmaking it for us.\n\nYes (answers the Owenite), but these words, \u201cif we will,\u201d surrender the\nwhole point: since the will to alter our own character is given us, not by\nany efforts of ours, but by circumstances which we can not help, it comes\nto us either from external causes, or not at all. Most true: if the\nOwenite stops here, he is in a position from which nothing can expel him.\nOur character is formed by us as well as for us; but the wish which\ninduces us to attempt to form it is formed for us; and how? Not, in\ngeneral, by our organization, nor wholly by our education, but by our\nexperience; experience of the painful consequences of the character we\npreviously had; or by some strong feeling of admiration or aspiration,\naccidentally aroused. But to think that we have no power of altering our\ncharacter, and to think that we shall not use our power unless we desire\nto use it, are very different things, and have a very different effect on\nthe mind. A person who does not wish to alter his character, can not be\nthe person who is supposed to feel discouraged or paralyzed by thinking\nhimself unable to do it. The depressing effect of the fatalist doctrine\ncan only be felt where there _is_ a wish to do what that doctrine\nrepresents as impossible. It is of no consequence what we think forms our\ncharacter, when we have no desire of our own about forming it; but it is\nof great consequence that we should not be prevented from forming such a\ndesire by thinking the attainment impracticable, and that if we have the\ndesire, we should know that the work is not so irrevocably done as to be\nincapable of being altered.\n\nAnd indeed, if we examine closely, we shall find that this feeling, of our\nbeing able to modify our own character _if we wish_, is itself the feeling\nof moral freedom which we are conscious of. A person feels morally free\nwho feels that his habits or his temptations are not his masters, but he\ntheirs; who, even in yielding to them, knows that he could resist; that\nwere he desirous of altogether throwing them off, there would not be\nrequired for that purpose a stronger desire than he knows himself to be\ncapable of feeling. It is of course necessary, to render our consciousness\nof freedom complete, that we should have succeeded in making our character\nall we have hitherto attempted to make it; for if we have wished and not\nattained, we have, to that extent, not power over our own character; we\nare not free. Or at least, we must feel that our wish, if not strong\nenough to alter our character, is strong enough to conquer our character\nwhen the two are brought into conflict in any particular case of conduct.\nAnd hence it is said with truth, that none but a person of confirmed\nvirtue is completely free.\n\nThe application of so improper a term as Necessity to the doctrine of\ncause and effect in the matter of human character, seems to me one of the\nmost signal instances in philosophy of the abuse of terms, and its\npractical consequences one of the most striking examples of the power of\nlanguage over our associations. The subject will never be generally\nunderstood until that objectionable term is dropped. The free-will\ndoctrine, by keeping in view precisely that portion of the truth which the\nword Necessity puts out of sight, namely the power of the mind to\nco-operate in the formation of its own character, has given to its\nadherents a practical feeling much nearer to the truth than has generally\n(I believe) existed in the minds of necessitarians. The latter may have\nhad a stronger sense of the importance of what human beings can do to\nshape the characters of one another; but the free-will doctrine has, I\nbelieve, fostered in its supporters a much stronger spirit of\nself-culture.\n\n\u00a7 4. There is still one fact which requires to be noticed (in addition to\nthe existence of a power of self-formation) before the doctrine of the\ncausation of human actions can be freed from the confusion and\nmisapprehensions which surround it in many minds. When the will is said to\nbe determined by motives, a motive does not mean always, or solely, the\nanticipation of a pleasure or of a pain. I shall not here inquire whether\nit be true that, in the commencement, all our voluntary actions are mere\nmeans consciously employed to obtain some pleasure or avoid some pain. It\nis at least certain that we gradually, through the influence of\nassociation, come to desire the means without thinking of the end; the\naction itself becomes an object of desire, and is performed without\nreference to any motive beyond itself. Thus far, it may still be objected\nthat, the action having through association become pleasurable, we are, as\nmuch as before, moved to act by the anticipation of a pleasure, namely,\nthe pleasure of the action itself. But granting this, the matter does not\nend here. As we proceed in the formation of habits, and become accustomed\nto will a particular act or a particular course of conduct because it is\npleasurable, we at last continue to will it without any reference to its\nbeing pleasurable. Although, from some change in us or in our\ncircumstances, we have ceased to find any pleasure in the action, or\nperhaps to anticipate any pleasure as the consequence of it, we still\ncontinue to desire the action, and consequently to do it. In this manner\nit is that habits of hurtful excess continue to be practiced although they\nhave ceased to be pleasurable; and in this manner also it is that the\nhabit of willing to persevere in the course which he has chosen, does not\ndesert the moral hero, even when the reward, however real, which he\ndoubtless receives from the consciousness of well-doing, is any thing but\nan equivalent for the sufferings he undergoes, or the wishes which he may\nhave to renounce.\n\nA habit of willing is commonly called a purpose; and among the causes of\nour volitions, and of the actions which flow from them, must be reckoned\nnot only likings and aversions, but also purposes. It is only when our\npurposes have become independent of the feelings of pain or pleasure from\nwhich they originally took their rise, that we are said to have a\nconfirmed character. \u201cA character,\u201d says Novalis, \u201cis a completely\nfashioned will:\u201d and the will, once so fashioned, may be steady and\nconstant, when the passive susceptibilities of pleasure and pain are\ngreatly weakened or materially changed.\n\nWith the corrections and explanations now given, the doctrine of the\ncausation of our volitions by motives, and of motives by the desirable\nobjects offered to us, combined with our particular susceptibilities of\ndesire, may be considered, I hope, as sufficiently established for the\npurposes of this treatise.(268)\n\n\n\n\n                               Chapter III.\n\n\nThat There Is, Or May Be, A Science Of Human Nature.\n\n\n\u00a7 1. It is a common notion, or at least it is implied in many common modes\nof speech, that the thoughts, feelings, and actions of sentient beings are\nnot a subject of science, in the same strict sense in which this is true\nof the objects of outward nature. This notion seems to involve some\nconfusion of ideas, which it is necessary to begin by clearing up.\n\nAny facts are fitted, in themselves, to be a subject of science which\nfollow one another according to constant laws, although those laws may not\nhave been discovered, nor even be discoverable by our existing resources.\nTake, for instance, the most familiar class of meteorological phenomena,\nthose of rain and sunshine. Scientific inquiry has not yet succeeded in\nascertaining the order of antecedence and consequence among these\nphenomena, so as to be able, at least in our regions of the earth, to\npredict them with certainty, or even with any high degree of probability.\nYet no one doubts that the phenomena depend on laws, and that these must\nbe derivative laws resulting from known ultimate laws, those of heat,\nelectricity, vaporization, and elastic fluids. Nor can it be doubted that\nif we were acquainted with all the antecedent circumstances, we could,\neven from those more general laws, predict (saving difficulties of\ncalculation) the state of the weather at any future time. Meteorology,\ntherefore, not only has in itself every natural requisite for being, but\nactually is, a science; though, from the difficulty of observing the facts\non which the phenomena depend (a difficulty inherent in the peculiar\nnature of those phenomena), the science is extremely imperfect; and were\nit perfect, might probably be of little avail in practice, since the data\nrequisite for applying its principles to particular instances would rarely\nbe procurable.\n\nA case may be conceived, of an intermediate character, between the\nperfection of science and this its extreme imperfection. It may happen\nthat the greater causes, those on which the principal part of the\nphenomena depends, are within the reach of observation and measurement; so\nthat if no other causes intervened, a complete explanation could be given\nnot only of the phenomena in general, but of all the variations and\nmodifications which it admits of. But inasmuch as other, perhaps many\nother causes, separately insignificant in their effects, co-operate or\nconflict in many or in all cases with those greater causes, the effect,\naccordingly, presents more or less of aberration from what would be\nproduced by the greater causes alone. Now if these minor causes are not so\nconstantly accessible, or not accessible at all, to accurate observation,\nthe principal mass of the effect may still, as before, be accounted for,\nand even predicted; but there will be variations and modifications which\nwe shall not be competent to explain thoroughly, and our predictions will\nnot be fulfilled accurately, but only approximately.\n\nIt is thus, for example, with the theory of the tides. No one doubts that\nTidology (as Dr. Whewell proposes to call it) is really a science. As much\nof the phenomena as depends on the attraction of the sun and moon is\ncompletely understood, and may, in any, even unknown, part of the earth\u2019s\nsurface, be foretold with certainty; and the far greater part of the\nphenomena depends on those causes. But circumstances of a local or casual\nnature, such as the configuration of the bottom of the ocean, the degree\nof confinement from shores, the direction of the wind, etc., influence, in\nmany or in all places, the height and time of the tide; and a portion of\nthese circumstances being either not accurately knowable, not precisely\nmeasurable, or not capable of being certainly foreseen, the tide in known\nplaces commonly varies from the calculated result of general principles by\nsome difference that we can not explain, and in unknown ones may vary from\nit by a difference that we are not able to foresee or conjecture.\nNevertheless, not only is it certain that these variations depend on\ncauses, and follow their causes by laws of unerring uniformity; not only,\ntherefore, is tidology a science, like meteorology, but it is, what\nhitherto at least meteorology is not, a science largely available in\npractice. General laws may be laid down respecting the tides, predictions\nmay be founded on those laws, and the result will in the main, though\noften not with complete accuracy, correspond to the predictions.\n\nAnd this is what is or ought to be meant by those who speak of sciences\nwhich are not _exact_ sciences. Astronomy was once a science, without\nbeing an exact science. It could not become exact until not only the\ngeneral course of the planetary motions, but the perturbations also, were\naccounted for, and referred to their causes. It has become an exact\nscience, because its phenomena have been brought under laws comprehending\nthe whole of the causes by which the phenomena are influenced, whether in\na great or only in a trifling degree, whether in all or only in some\ncases, and assigning to each of those causes the share of effect which\nreally belongs to it. But in the theory of the tides the only laws as yet\naccurately ascertained are those of the causes which affect the phenomenon\nin all cases, and in a considerable degree; while others which affect it\nin some cases only, or, if in all, only in a slight degree, have not been\nsufficiently ascertained and studied to enable us to lay down their laws;\nstill less to deduce the completed law of the phenomenon, by compounding\nthe effects of the greater with those of the minor causes. Tidology,\ntherefore, is not yet an exact science; not from any inherent incapacity\nof being so, but from the difficulty of ascertaining with complete\nprecision the real derivative uniformities. By combining, however, the\nexact laws of the greater causes, and of such of the minor ones as are\nsufficiently known, with such empirical laws or such approximate\ngeneralizations respecting the miscellaneous variations as can be obtained\nby specific observation, we can lay down general propositions which will\nbe true in the main, and on which, with allowance for the degree of their\nprobable inaccuracy, we may safely ground our expectations and our\nconduct.\n\n\u00a7 2. The science of human nature is of this description. It falls far\nshort of the standard of exactness now realized in Astronomy; but there is\nno reason that it should not be as much a science as Tidology is, or as\nAstronomy was when its calculations had only mastered the main phenomena,\nbut not the perturbations.\n\nThe phenomena with which this science is conversant being the thoughts,\nfeelings, and actions of human beings, it would have attained the ideal\nperfection of a science if it enabled us to foretell how an individual\nwould think, feel, or act throughout life, with the same certainty with\nwhich astronomy enables us to predict the places and the occultations of\nthe heavenly bodies. It needs scarcely be stated that nothing approaching\nto this can be done. The actions of individuals could not be predicted\nwith scientific accuracy, were it only because we can not foresee the\nwhole of the circumstances in which those individuals will be placed. But\nfurther, even in any given combination of (present) circumstances, no\nassertion, which is both precise and universally true, can be made\nrespecting the manner in which human beings will think, feel, or act. This\nis not, however, because every person\u2019s modes of thinking, feeling, and\nacting do not depend on causes; nor can we doubt that if, in the case of\nany individual, our data could be complete, we even now know enough of the\nultimate laws by which mental phenomena are determined, to enable us in\nmany cases to predict, with tolerable certainty, what, in the greater\nnumber of supposable combinations of circumstances, his conduct or\nsentiments would be. But the impressions and actions of human beings are\nnot solely the result of their present circumstances, but the joint result\nof those circumstances and of the characters of the individuals; and the\nagencies which determine human character are so numerous and diversified\n(nothing which has happened to the person throughout life being without\nits portion of influence), that in the aggregate they are never in any two\ncases exactly similar. Hence, even if our science of human nature were\ntheoretically perfect, that is, if we could calculate any character as we\ncan calculate the orbit of any planet, _from given data_; still, as the\ndata are never all given, nor ever precisely alike in different cases, we\ncould neither make positive predictions, nor lay down universal\npropositions.\n\nInasmuch, however, as many of those effects which it is of most importance\nto render amenable to human foresight and control are determined, like the\ntides, in an incomparably greater degree by general causes, than by all\npartial causes taken together; depending in the main on those\ncircumstances and qualities which are common to all mankind, or at least\nto large bodies of them, and only in a small degree on the idiosyncrasies\nof organization or the peculiar history of individuals; it is evidently\npossible with regard to all such effects, to make predictions which will\n_almost_ always be verified, and general propositions which are almost\nalways true. And whenever it is sufficient to know how the great majority\nof the human race, or of some nation or class of persons, will think,\nfeel, and act, these propositions are equivalent to universal ones. For\nthe purposes of political and social science this _is_ sufficient. As we\nformerly remarked,(269) an approximate generalization is, in social\ninquiries, for most practical purposes equivalent to an exact one; that\nwhich is only probable when asserted of individual human beings\nindiscriminately selected, being certain when affirmed of the character\nand collective conduct of masses.\n\nIt is no disparagement, therefore, to the science of Human Nature, that\nthose of its general propositions which descend sufficiently into detail\nto serve as a foundation for predicting phenomena in the concrete, are for\nthe most part only approximately true. But in order to give a genuinely\nscientific character to the study, it is indispensable that these\napproximate generalizations, which in themselves would amount only to the\nlowest kind of empirical laws, should be connected deductively with the\nlaws of nature from which they result; should be resolved into the\nproperties of the causes on which the phenomena depend. In other words,\nthe science of Human Nature may be said to exist in proportion as the\napproximate truths, which compose a practical knowledge of mankind, can be\nexhibited as corollaries from the universal laws of human nature on which\nthey rest; whereby the proper limits of those approximate truths would be\nshown, and we should be enabled to deduce others for any new state of\ncircumstances, in anticipation of specific experience.\n\nThe proposition now stated is the text on which the two succeeding\nchapters will furnish the comment.\n\n\n\n\n                               Chapter IV.\n\n\nOf The Laws Of Mind.\n\n\n\u00a7 1. What the Mind is, as well as what Matter is, or any other question\nrespecting Things in themselves, as distinguished from their sensible\nmanifestations, it would be foreign to the purposes of this treatise to\nconsider. Here, as throughout our inquiry, we shall keep clear of all\nspeculations respecting the mind\u2019s own nature, and shall understand by the\nlaws of mind those of mental Phenomena; of the various feelings or states\nof consciousness of sentient beings. These, according to the\nclassification we have uniformly followed, consist of Thoughts, Emotions,\nVolitions, and Sensations; the last being as truly states of Mind as the\nthree former. It is usual, indeed, to speak of sensations as states of\nbody, not of mind. But this is the common confusion, of giving one and the\nsame name to a phenomenon and to the approximate cause or conditions of\nthe phenomenon. The immediate antecedent of a sensation is a state of\nbody, but the sensation itself is a state of mind. If the word Mind means\nany thing, it means that which feels. Whatever opinion we hold respecting\nthe fundamental identity or diversity of matter and mind, in any case the\ndistinction between mental and physical facts, between the internal and\nthe external world, will always remain, as a matter of classification; and\nin that classification, sensations, like all other feelings, must be\nranked as mental phenomena. The mechanism of their production, both in the\nbody itself and in what is called outward nature, is all that can with any\npropriety be classed as physical.\n\nThe phenomena of mind, then, are the various feelings of our nature, both\nthose improperly called physical and those peculiarly designated as\nmental; and by the laws of mind, I mean the laws according to which those\nfeelings generate one another.\n\n\u00a7 2. All states of mind are immediately caused either by other states of\nmind, or by states of body. When a state of mind is produced by a state of\nmind, I call the law concerned in the case a law of Mind. When a state of\nmind is produced directly by a state of body, the law is a law of Body,\nand belongs to physical science.\n\nWith regard to those states of mind which are called sensations, all are\nagreed that these have for their immediate antecedents, states of body.\nEvery sensation has for its proximate cause some affection of the portion\nof our frame called the nervous system, whether this affection originates\nin the action of some external object, or in some pathological condition\nof the nervous organization itself. The laws of this portion of our\nnature\u2014the varieties of our sensations, and the physical conditions on\nwhich they proximately depend\u2014manifestly belong to the province of\nPhysiology.\n\nWhether the remainder of our mental states are similarly dependent on\nphysical conditions, is one of the _vexat\u00e6 questiones_ in the science of\nhuman nature. It is still disputed whether our thoughts, emotions, and\nvolitions are generated through the intervention of material mechanism;\nwhether we have organs of thought and of emotion, in the same sense in\nwhich we have organs of sensation. Many eminent physiologists hold the\naffirmative. These contend that a thought (for example) is as much the\nresult of nervous agency, as a sensation; that some particular state of\nour nervous system, in particular of that central portion of it called the\nbrain, invariably precedes, and is presupposed by, every state of our\nconsciousness. According to this theory, one state of mind is never really\nproduced by another: all are produced by states of body. When one thought\nseems to call up another by association, it is not really a thought which\nrecalls a thought; the association did not exist between the two thoughts,\nbut between the two states of the brain or nerves which preceded the\nthoughts: one of those states recalls the other, each being attended in\nits passage by the particular state of consciousness which is consequent\non it. On this theory the uniformities of succession among states of mind\nwould be mere derivative uniformities, resulting from the laws of\nsuccession of the bodily states which cause them. There would be no\noriginal mental laws, no Laws of Mind in the sense in which I use the\nterm, at all; and mental science would be a mere branch, though the\nhighest and most recondite branch, of the science of physiology. M. Comte,\naccordingly, claims the scientific cognizance of moral and intellectual\nphenomena exclusively for physiologists; and not only denies to\nPsychology, or Mental Philosophy properly so called, the character of a\nscience, but places it, in the chimerical nature of its objects and\npretensions, almost on a par with astrology.\n\nBut, after all has been said which can be said, it remains incontestable\nthat there exist uniformities of succession among states of mind, and that\nthese can be ascertained by observation and experiment. Further, that\nevery mental state has a nervous state for its immediate antecedent and\nproximate cause, though extremely probable, can not hitherto be said to be\nproved, in the conclusive manner in which this can be proved of\nsensations; and even were it certain, yet every one must admit that we are\nwholly ignorant of the characteristics of these nervous states; we know\nnot, and at present have no means of knowing, in what respect one of them\ndiffers from another; and our only mode of studying their successions or\nco-existences must be by observing the successions and co-existences of\nthe mental states, of which they are supposed to be the generators or\ncauses. The successions, therefore, which obtain among mental phenomena,\ndo not admit of being deduced from the physiological laws of our nervous\norganization; and all real knowledge of them must continue, for a long\ntime at least, if not always, to be sought in the direct study, by\nobservation and experiment, of the mental successions themselves. Since,\ntherefore, the order of our mental phenomena must be studied in those\nphenomena, and not inferred from the laws of any phenomena more general,\nthere is a distinct and separate Science of Mind.\n\nThe relations, indeed, of that science to the science of physiology must\nnever be overlooked or undervalued. It must by no means be forgotten that\nthe laws of mind may be derivative laws resulting from laws of animal\nlife, and that their truth, therefore, may ultimately depend on physical\nconditions; and the influence of physiological states or physiological\nchanges in altering or counteracting the mental successions, is one of the\nmost important departments of psychological study. But, on the other hand,\nto reject the resource of psychological analysis, and construct the theory\nof the mind solely on such data as physiology at present affords, seems to\nme as great an error in principle, and an even more serious one in\npractice. Imperfect as is the science of mind, I do not scruple to affirm\nthat it is in a considerably more advanced state than the portion of\nphysiology which corresponds to it; and to discard the former for the\nlatter appears, to me an infringement of the true canons of inductive\nphilosophy, which must produce, and which does produce, erroneous\nconclusions in some very important departments of the science of human\nnature.\n\n\u00a7 3. The subject, then, of Psychology is the uniformities of succession,\nthe laws, whether ultimate or derivative, according to which one mental\nstate succeeds another; is caused by, or at least, is caused to follow,\nanother. Of these laws some are general, others more special. The\nfollowing are examples of the most general laws:\n\nFirst. Whenever any state of consciousness has once been excited in us, no\nmatter by what cause, an inferior degree of the same state of\nconsciousness, a state of consciousness resembling the former, but\ninferior in intensity, is capable of being reproduced in us, without the\npresence of any such cause as excited it at first. Thus, if we have once\nseen or touched an object, we can afterward think of the object though it\nbe absent from our sight or from our touch. If we have been joyful or\ngrieved at some event, we can think of or remember our past joy or grief,\nthough no new event of a happy or painful nature has taken place. When a\npoet has put together a mental picture of an imaginary object, a Castle of\nIndolence, a Una, or a Hamlet, he can afterward think of the ideal object\nhe has created, without any fresh act of intellectual combination. This\nlaw is expressed by saying, in the language of Hume, that every mental\n_impression_ has its _idea_.\n\nSecondly. These ideas, or secondary mental states, are excited by our\nimpressions, or by other ideas, according to certain laws which are called\nLaws of Association. Of these laws the first is, that similar ideas tend\nto excite one another. The second is, that when two impressions have been\nfrequently experienced (or even thought of) either simultaneously or in\nimmediate succession, then whenever one of these impressions, or the idea\nof it, recurs, it tends to excite the idea of the other. The third law is,\nthat greater intensity in either or both of the impressions is equivalent,\nin rendering them excitable by one another, to a greater frequency of\nconjunction. These are the laws of ideas, on which I shall not enlarge in\nthis place, but refer the reader to works professedly psychological, in\nparticular to Mr. James Mill\u2019s _Analysis of the Phenomena of the Human\nMind_, where the principal laws of association, along with many of their\napplications, are copiously exemplified, and with a masterly hand.(270)\n\nThese simple or elementary Laws of Mind have been ascertained by the\nordinary methods of experimental inquiry; nor could they have been\nascertained in any other manner. But a certain number of elementary laws\nhaving thus been obtained, it is a fair subject of scientific inquiry how\nfar those laws can be made to go in explaining the actual phenomena. It is\nobvious that complex laws of thought and feeling not only may, but must,\nbe generated from these simple laws. And it is to be remarked, that the\ncase is not always one of Composition of Causes: the effect of concurring\ncauses is not always precisely the sum of the effects of those causes when\nseparate, nor even always an effect of the same kind with them. Reverting\nto the distinction which occupies so prominent a place in the theory of\ninduction, the laws of the phenomena of mind are sometimes analogous to\nmechanical, but sometimes also to chemical laws. When many impressions or\nideas are operating in the mind together, there sometimes takes place a\nprocess of a similar kind to chemical combination. When impressions have\nbeen so often experienced in conjunction, that each of them calls up\nreadily and instantaneously the ideas of the whole group, those ideas\nsometimes melt and coalesce into one another, and appear not several\nideas, but one; in the same manner as, when the seven prismatic colors are\npresented to the eye in rapid succession, the sensation produced is that\nof white. But as in this last case it is correct to say that the seven\ncolors when they rapidly follow one another _generate_ white, but not that\nthey actually _are_ white; so it appears to me that the Complex Idea,\nformed by the blending together of several simpler ones, should, when it\nreally appears simple (that is, when the separate elements are not\nconsciously distinguishable in it), be said to _result from_, or _be\ngenerated by_, the simple ideas, not to _consist_ of them. Our idea of an\norange really _consists_ of the simple ideas of a certain color, a certain\nform, a certain taste and smell, etc., because we can, by interrogating\nour consciousness, perceive all these elements in the idea. But we can not\nperceive, in so apparently simple a feeling as our perception of the shape\nof an object by the eye, all that multitude of ideas derived from other\nsenses, without which it is well ascertained that no such visual\nperception would ever have had existence; nor, in our idea of Extension,\ncan we discover those elementary ideas of resistance, derived from our\nmuscular frame, in which it has been conclusively shown that the idea\noriginates. These, therefore, are cases of mental chemistry; in which it\nis proper to say that the simple ideas generate, rather than that they\ncompose, the complex ones.\n\nWith respect to all the other constituents of the mind, its beliefs, its\nabstruser conceptions, its sentiments, emotions, and volitions, there are\nsome (among whom are Hartley and the author of the _Analysis_) who think\nthat the whole of these are generated from simple ideas of sensation, by a\nchemistry similar to that which we have just exemplified. These\nphilosophers have made out a great part of their case, but I am not\nsatisfied that they have established the whole of it. They have shown that\nthere is such a thing as mental chemistry; that the heterogeneous nature\nof a feeling A, considered in relation to B and C, is no conclusive\nargument against its being generated from B and C. Having proved this,\nthey proceed to show, that where A is found, B and C were, or may have\nbeen present, and why, therefore, they ask, should not A have been\ngenerated from B and C? But even if this evidence were carried to the\nhighest degree of completeness which it admits of; if it were shown (which\nhitherto it has not, in all cases, been) that certain groups of associated\nideas not only might have been, but actually were, present whenever the\nmore recondite mental feeling was experienced; this would amount only to\nthe Method of Agreement, and could not prove causation until confirmed by\nthe more conclusive evidence of the Method of Difference. If the question\nbe whether Belief is a mere case of close association of ideas, it would\nbe necessary to examine experimentally if it be true that any ideas\nwhatever, provided they are associated with the required degree of\ncloseness, give rise to belief. If the inquiry be into the origin of moral\nfeelings, the feeling for example of moral reprobation, it is necessary to\ncompare all the varieties of actions or states of mind which are ever\nmorally disapproved, and see whether in all these cases it can be shown,\nor reasonably surmised, that the action or state of mind had become\nconnected by association, in the disapproving mind, with some particular\nclass of hateful or disgusting ideas; and the method employed is, thus\nfar, that of Agreement. But this is not enough. Supposing this proved, we\nmust try further by the Method of Difference, whether this particular kind\nof hateful or disgusting ideas, when it becomes associated with an action\npreviously indifferent, will render that action a subject of moral\ndisapproval. If this question can be answered in the affirmative, it is\nshown to be a law of the human mind, that an association of that\nparticular description is the generating cause of moral reprobation. That\nall this is the case has been rendered extremely probable, but the\nexperiments have not been tried with the degree of precision necessary for\na complete and absolutely conclusive induction.(271)\n\nIt is further to be remembered, that even if all which this theory of\nmental phenomena contends for could be proved, we should not be the more\nenabled to resolve the laws of the more complex feelings into those of the\nsimpler ones. The generation of one class of mental phenomena from\nanother, whenever it can be made out, is a highly interesting fact in\npsychological chemistry; but it no more supersedes the necessity of an\nexperimental study of the generated phenomenon, than a knowledge of the\nproperties of oxygen and sulphur enables us to deduce those of sulphuric\nacid without specific observation and experiment. Whatever, therefore, may\nbe the final issue of the attempt to account for the origin of our\njudgments, our desires, or our volitions, from simpler mental phenomena,\nit is not the less imperative to ascertain the sequences of the complex\nphenomena themselves, by special study in conformity to the canons of\nInduction. Thus, in respect to Belief, psychologists will always have to\ninquire what beliefs we have by direct consciousness, and according to\nwhat laws one belief produces another; what are the laws in virtue of\nwhich one thing is recognized by the mind, either rightly or erroneously,\nas evidence of another thing. In regard to Desire, they will have to\nexamine what objects we desire naturally, and by what causes we are made\nto desire things originally indifferent, or even disagreeable to us; and\nso forth. It may be remarked that the general laws of association prevail\namong these more intricate states of mind, in the same manner as among the\nsimpler ones. A desire, an emotion, an idea of the higher order of\nabstraction, even our judgments and volitions, when they have become\nhabitual, are called up by association, according to precisely the same\nlaws as our simple ideas.\n\n\u00a7 4. In the course of these inquiries, it will be natural and necessary to\nexamine how far the production of one state of mind by another is\ninfluenced by any assignable state of body. The commonest observation\nshows that different minds are susceptible in very different degrees to\nthe action of the same psychological causes. The idea, for example, of a\ngiven desirable object will excite in different minds very different\ndegrees of intensity of desire. The same subject of meditation, presented\nto different minds, will excite in them very unequal degrees of\nintellectual action. These differences of mental susceptibility in\ndifferent individuals may be, first, original and ultimate facts; or,\nsecondly, they may be consequences of the previous mental history of those\nindividuals; or, thirdly and lastly, they may depend on varieties of\nphysical organization. That the previous mental history of the individuals\nmust have some share in producing or in modifying the whole of their\nmental character, is an inevitable consequence of the laws of mind; but\nthat differences of bodily structure also co-operate, is the opinion of\nall physiologists, confirmed by common experience. It is to be regretted\nthat hitherto this experience, being accepted in the gross, without due\nanalysis, has been made the groundwork of empirical generalizations most\ndetrimental to the progress of real knowledge.\n\nIt is certain that the natural differences which really exist in the\nmental predispositions or susceptibilities of different persons are often\nnot unconnected with diversities in their organic constitution. But it\ndoes not therefore follow that these organic differences must in all cases\ninfluence the mental phenomena directly and immediately. They often affect\nthem through the medium of their psychological causes. For example, the\nidea of some particular pleasure may excite in different persons, even\nindependently of habit or education, very different strengths of desire,\nand this may be the effect of their different degrees or kinds of nervous\nsusceptibility; but these organic differences, we must remember, will\nrender the pleasurable sensation itself more intense in one of these\npersons than in the other; so that the idea of the pleasure will also be\nan intenser feeling, and will, by the operation of mere mental laws,\nexcite an intenser desire, without its being necessary to suppose that the\ndesire itself is directly influenced by the physical peculiarity. As in\nthis, so in many cases, such differences in the kind or in the intensity\nof the physical sensations as must necessarily result from differences of\nbodily organization, will of themselves account for many differences not\nonly in the degree, but even in the kind, of the other mental phenomena.\nSo true is this, that even different _qualities_ of mind, different types\nof mental character, will naturally be produced by mere differences of\nintensity in the sensations generally; as is well pointed out in the able\nessay on Dr. Priestley, by Mr. Martineau, mentioned in a former chapter:\n\n\u201cThe sensations which form the elements of all knowledge are received\neither simultaneously or successively: when several are received\nsimultaneously, as the smell, the taste, the color, the form, etc., of a\nfruit, their association together constitutes our idea of an _object_;\nwhen received successively, their association makes up the idea of an\n_event_. Any thing, then, which favors the associations of synchronous\nideas will tend to produce a knowledge of objects, a perception of\nqualities; while any thing which favors association in the successive\norder, will tend to produce a knowledge of events, of the order of\noccurrences, and of the connection of cause and effect: in other words, in\nthe one case a perceptive mind, with a discriminate feeling of the\npleasurable and painful properties of things, a sense of the grand and the\nbeautiful will be the result: in the other, a mind attentive to the\nmovements and phenomena, a ratiocinative and philosophic intellect. Now it\nis an acknowledged principle, that all sensations experienced during the\npresence of any vivid impression become strongly associated with it, and\nwith each other; and does it not follow that the synchronous feelings of a\nsensitive constitution (_i.e._, the one which has vivid impressions) will\nbe more intimately blended than in a differently formed mind? If this\nsuggestion has any foundation in truth, it leads to an inference not\nunimportant; that where nature has endowed an individual with great\noriginal susceptibility, he will probably be distinguished by fondness for\nnatural history, a relish for the beautiful and great, and moral\nenthusiasm; where there is but a mediocrity of sensibility, a love of\nscience, of abstract truth, with a deficiency of taste and of fervor, is\nlikely to be the result.\u201d\n\nWe see from this example, that when the general laws of mind are more\naccurately known, and, above all, more skillfully applied to the detailed\nexplanation of mental peculiarities, they will account for many more of\nthose peculiarities than is ordinarily supposed. Unfortunately the\nreaction of the last and present generation against the philosophy of the\neighteenth century has produced a very general neglect of this great\ndepartment of analytical inquiry; of which, consequently, the recent\nprogress has been by no means proportional to its early promise. The\nmajority of those who speculate on human nature prefer dogmatically to\nassume that the mental differences which they perceive, or think they\nperceive, among human beings, are ultimate facts, incapable of being\neither explained or altered, rather than take the trouble of fitting\nthemselves, by the requisite processes of thought, for referring those\nmental differences to the outward causes by which they are for the most\npart produced, and on the removal of which they would cease to exist. The\nGerman school of metaphysical speculation, which has not yet lost its\ntemporary predominance in European thought, has had this among many other\ninjurious influences; and at the opposite extreme of the psychological\nscale, no writer, either of early or of recent date, is chargeable in a\nhigher degree with this aberration from the true scientific spirit, than\nM. Comte.\n\nIt is certain that, in human beings at least, differences in education and\nin outward circumstances are capable of affording an adequate explanation\nof by far the greatest portion of character; and that the remainder may be\nin great part accounted for by physical differences in the sensations\nproduced in different individuals by the same external or internal cause.\nThere are, however, some mental facts which do not seem to admit of these\nmodes of explanation. Such, to take the strongest case, are the various\ninstincts of animals, and the portion of human nature which corresponds to\nthose instincts. No mode has been suggested, even by way of hypothesis, in\nwhich these can receive any satisfactory, or even plausible, explanation\nfrom psychological causes alone; and there is great reason to think that\nthey have as positive, and even as direct and immediate, a connection with\nphysical conditions of the brain and nerves as any of our mere sensations\nhave. A supposition which (it is perhaps not superfluous to add) in no way\nconflicts with the indisputable fact that these instincts may be modified\nto any extent, or entirely conquered, in human beings, and to no\ninconsiderable extent even in some of the domesticated animals, by other\nmental influences, and by education.\n\nWhether organic causes exercise a direct influence over any other classes\nof mental phenomena, is hitherto as far from being ascertained as is the\nprecise nature of the organic conditions even in the case of instincts.\nThe physiology, however, of the brain and nervous system is in a state of\nsuch rapid advance, and is continually bringing forth such new and\ninteresting results, that if there be really a connection between mental\npeculiarities and any varieties cognizable by our senses in the structure\nof the cerebral and nervous apparatus, the nature of that connection is\nnow in a fair way of being found out. The latest discoveries in cerebral\nphysiology appear to have proved that any such connection which may exist\nis of a radically different character from that contended for by Gall and\nhis followers, and that, whatever may hereafter be found to be the true\ntheory of the subject, phrenology at least is untenable.\n\n\n\n\n                                Chapter V.\n\n\nOf Ethology, Or The Science Of The Formation Of Character.\n\n\n\u00a7 1. The laws of mind as characterized in the preceding chapter, compose\nthe universal or abstract portion of the philosophy of human nature; and\nall the truths of common experience, constituting a practical knowledge of\nmankind, must, to the extent to which they are truths, be results or\nconsequences of these. Such familiar maxims, when collected _a posteriori_\nfrom observation of life, occupy among the truths of the science the place\nof what, in our analysis of Induction, have so often been spoken of under\nthe title of Empirical Laws.\n\nAn Empirical Law (it will be remembered) is a uniformity, whether of\nsuccession or of co-existence, which holds true in all instances within\nour limits of observation, but is not of a nature to afford any assurance\nthat it would hold beyond those limits; either because the consequent is\nnot really the effect of the antecedent, but forms part along with it of a\nchain of effects flowing from prior causes not yet ascertained, or because\nthere is ground to believe that the sequence (though a case of causation)\nis resolvable into simpler sequences, and, depending therefore on a\nconcurrence of several natural agencies, is exposed to an unknown\nmultitude of possibilities of counteraction. In other words, an empirical\nlaw is a generalization, of which, not content with finding it true, we\nare obliged to ask, why is it true? knowing that its truth is not\nabsolute, but dependent on some more general conditions, and that it can\nonly be relied on in so far as there is ground of assurance that those\nconditions are realized.\n\nNow, the observations concerning human affairs collected from common\nexperience are precisely of this nature. Even if they were universally and\nexactly true within the bounds of experience, which they never are, still\nthey are not the ultimate laws of human action; they are not the\nprinciples of human nature, but results of those principles under the\ncircumstances in which mankind have happened to be placed. When the\nPsalmist \u201csaid in his haste that all men are liars,\u201d he enunciated what in\nsome ages and countries is borne out by ample experience; but it is not a\nlaw of man\u2019s nature to lie; though it is one of the consequences of the\nlaws of human nature, that lying is nearly universal when certain external\ncircumstances exist universally, especially circumstances productive of\nhabitual distrust and fear. When the character of the old is asserted to\nbe cautious, and of the young impetuous, this, again, is but an empirical\nlaw; for it is not because of their youth that the young are impetuous,\nnor because of their age that the old are cautious. It is chiefly, if not\nwholly, because the old, during their many years of life, have generally\nhad much experience of its various evils, and having suffered or seen\nothers suffer much from incautious exposure to them, have acquired\nassociations favorable to circumspection; while the young, as well from\nthe absence of similar experience as from the greater strength of the\ninclinations which urge them to enterprise, engage themselves in it more\nreadily. Here, then, is the _explanation_ of the empirical law; here are\nthe conditions which ultimately determine whether the law holds good or\nnot. If an old man has not been oftener than most young men in contact\nwith danger and difficulty, he will be equally incautious; if a youth has\nnot stronger inclinations than an old man, he probably will be as little\nenterprising. The empirical law derives whatever truth it has from the\ncausal laws of which it is a consequence. If we know those laws, we know\nwhat are the limits to the derivative law; while, if we have not yet\naccounted for the empirical law\u2014if it rests only on observation\u2014there is\nno safety in applying it far beyond the limits of time, place, and\ncircumstance in which the observations were made.\n\nThe really scientific truths, then, are not these empirical laws, but the\ncausal laws which explain them. The empirical laws of those phenomena\nwhich depend on known causes, and of which a general theory can therefore\nbe constructed, have, whatever may be their value in practice, no other\nfunction in science than that of verifying the conclusions of theory.\nStill more must this be the case when most of the empirical laws amount,\neven within the limits of observation, only to approximate\ngeneralizations.\n\n\u00a7 2. This, however, is not, so much as is sometimes supposed, a\npeculiarity of the sciences called moral. It is only in the simplest\nbranches of science that empirical laws are ever exactly true; and not\nalways in those. Astronomy, for example, is the simplest of all the\nsciences which explain, in the concrete, the actual course of natural\nevents. The causes or forces on which astronomical phenomena depend, are\nfewer in number than those which determine any other of the great\nphenomena of nature. Accordingly, as each effect results from the conflict\nof but few causes, a great degree of regularity and uniformity might be\nexpected to exist among the effects; and such is really the case: they\nhave a fixed order, and return in cycles. But propositions which should\nexpress, with absolute correctness, all the successive positions of a\nplanet until the cycle is completed, would be of almost unmanageable\ncomplexity, and could be obtained from theory alone. The generalizations\nwhich can be collected on the subject from direct observation, even such\nas Kepler\u2019s law, are mere approximations; the planets, owing to their\nperturbations by one another, do not move in exact ellipses. Thus even in\nastronomy, perfect exactness in the mere empirical laws is not to be\nlooked for; much less, then, in more complex subjects of inquiry.\n\nThe same example shows how little can be inferred against the universality\nor even the simplicity of the ultimate laws, from the impossibility of\nestablishing any but approximate empirical laws of the effects. The laws\nof causation according to which a class of phenomena are produced may be\nvery few and simple, and yet the effects themselves may be so various and\ncomplicated that it shall be impossible to trace any regularity whatever\ncompletely through them. For the phenomena in question may be of an\neminently modifiable character; insomuch that innumerable circumstances\nare capable of influencing the effect, although they may all do it\naccording to a very small number of laws. Suppose that all which passes in\nthe mind of man is determined by a few simple laws; still, if those laws\nbe such that there is not one of the facts surrounding a human being, or\nof the events which happen to him, that does not influence in some mode or\ndegree his subsequent mental history, and if the circumstances of\ndifferent human beings are extremely different, it will be no wonder if\nvery few propositions can be made respecting the details of their conduct\nor feelings, which will be true of all mankind.\n\nNow, without deciding whether the ultimate laws of our mental nature are\nfew or many, it is at least certain that they are of the above\ndescription. It is certain that our mental states, and our mental\ncapacities and susceptibilities, are modified, either for a time or\npermanently, by every thing which happens to us in life. Considering,\ntherefore, how much these modifying causes differ in the case of any two\nindividuals, it would be unreasonable to expect that the empirical laws of\nthe human mind, the generalizations which can be made respecting the\nfeelings or actions of mankind without reference to the causes that\ndetermine them, should be any thing but approximate generalizations. They\nare the common wisdom of common life, and as such are invaluable;\nespecially as they are mostly to be applied to cases not very dissimilar\nto those from which they were collected. But when maxims of this sort,\ncollected from Englishmen, come to be applied to Frenchmen, or when those\ncollected from the present day are applied to past or future generations,\nthey are apt to be very much at fault. Unless we have resolved the\nempirical law into the laws of the causes on which it depends, and\nascertained that those causes extend to the case which we have in view,\nthere can be no reliance placed in our inferences. For every individual is\nsurrounded by circumstances different from those of every other\nindividual; every nation or generation of mankind from every other nation\nor generation: and none of these differences are without their influence\nin forming a different type of character. There is, indeed, also a certain\ngeneral resemblance; but peculiarities of circumstances are continually\nconstituting exceptions even to the propositions which are true in the\ngreat majority of cases.\n\nAlthough, however, there is scarcely any mode of feeling or conduct which\nis, in the absolute sense, common to all mankind; and though the\ngeneralizations which assert that any given variety of conduct or feeling\nwill be found universally (however nearly they may approximate to truth\nwithin given limits of observation), will be considered as scientific\npropositions by no one who is at all familiar with scientific\ninvestigation; yet all modes of feeling and conduct met with among mankind\nhave causes which produce them; and in the propositions which assign those\ncauses will be found the explanation of the empirical laws, and the\nlimiting principle of our reliance on them. Human beings do not all feel\nand act alike in the same circumstances; but it is possible to determine\nwhat makes one person, in a given position, feel or act in one way,\nanother in another; how any given mode of feeling and conduct, compatible\nwith the general laws (physical and mental) of human nature, has been, or\nmay be, formed. In other words, mankind have not one universal character,\nbut there exist universal laws of the Formation of Character. And since it\nis by these laws, combined with the facts of each particular case, that\nthe whole of the phenomena of human action and feeling are produced, it is\non these that every rational attempt to construct the science of human\nnature in the concrete, and for practical purposes, must proceed.\n\n\u00a7 3. The laws, then, of the formation of character being the principal\nobject of scientific inquiry into human nature, it remains to determine\nthe method of investigation best fitted for ascertaining them. And the\nlogical principles according to which this question is to be decided, must\nbe those which preside over every other attempt to investigate the laws of\nvery complex phenomena. For it is evident that both the character of any\nhuman being, and the aggregate of the circumstances by which that\ncharacter has been formed, are facts of a high order of complexity. Now to\nsuch cases we have seen that the Deductive Method, setting out from\ngeneral laws, and verifying their consequences by specific experience, is\nalone applicable. The grounds of this great logical doctrine have formerly\nbeen stated; and its truth will derive additional support from a brief\nexamination of the specialties of the present case.\n\nThere are only two modes in which laws of nature can be\nascertained\u2014deductively and experimentally; including under the\ndenomination of experimental inquiry, observation as well as artificial\nexperiment. Are the laws of the formation of character susceptible of a\nsatisfactory investigation by the method of experimentation? Evidently\nnot; because, even if we suppose unlimited power of varying the experiment\n(which is abstractedly possible, though no one but an Oriental despot has\nthat power, or, if he had, would probably be disposed to exercise it), a\nstill more essential condition is wanting\u2014the power of performing any of\nthe experiments with scientific accuracy.\n\nThe instances requisite for the prosecution of a directly experimental\ninquiry into the formation of character, would be a number of human beings\nto bring up and educate, from infancy to mature age. And to perform any\none of these experiments with scientific propriety, it would be necessary\nto know and record every sensation or impression received by the young\npupil from a period long before it could speak; including its own notions\nrespecting the sources of all those sensations and impressions. It is not\nonly impossible to do this completely, but even to do so much of it as\nshould constitute a tolerable approximation. One apparently trivial\ncircumstance which eluded our vigilance might let in a train of\nimpressions and associations sufficient to vitiate the experiment as an\nauthentic exhibition of the effects flowing from given causes. No one who\nhas sufficiently reflected on education is ignorant of this truth; and\nwhoever has not, will find it most instructively illustrated in the\nwritings of Rousseau and Helvetius on that great subject.\n\nUnder this impossibility of studying the laws of the formation of\ncharacter by experiments purposely contrived to elucidate them, there\nremains the resource of simple observation. But if it be impossible to\nascertain the influencing circumstances with any approach to completeness\neven when we have the shaping of them ourselves, much more impossible is\nit when the cases are further removed from our observation, and altogether\nout of our control. Consider the difficulty of the very first step\u2014of\nascertaining what actually is the character of the individual, in each\nparticular case that we examine. There is hardly any person living\nconcerning some essential part of whose character there are not\ndifferences of opinion even among his intimate acquaintances; and a single\naction, or conduct continued only for a short time, goes a very little way\ntoward ascertaining it. We can only make our observations in a rough way\nand _en masse_; not attempting to ascertain completely in any given\ninstance, what character has been formed, and still less by what causes;\nbut only observing in what state of previous circumstances it is found\nthat certain marked mental qualities or deficiencies _oftenest_ exist.\nThese conclusions, besides that they are mere approximate generalizations,\ndeserve no reliance, even as such, unless the instances are sufficiently\nnumerous to eliminate not only chance, but every assignable circumstance\nin which a number of the cases examined may happen to have resembled one\nanother. So numerous and various, too, are the circumstances which form\nindividual character, that the consequence of any particular combination\nis hardly ever some definite and strongly marked character, always found\nwhere that combination exists, and not otherwise. What is obtained, even\nafter the most extensive and accurate observation, is merely a comparative\nresult; as, for example, that in a given number of Frenchmen, taken\nindiscriminately, there will be found more persons of a particular mental\ntendency, and fewer of the contrary tendency, than among an equal number\nof Italians or English, similarly taken; or thus: of a hundred Frenchmen\nand an equal number of Englishmen, fairly selected, and arranged according\nto the degree in which they possess a particular mental characteristic,\neach number, 1, 2, 3, etc., of the one series, will be found to possess\nmore of that characteristic than the corresponding number of the other.\nSince, therefore, the comparison is not one of kinds, but of ratios and\ndegrees; and since, in proportion as the differences are slight, it\nrequires a greater number of instances to eliminate chance, it can not\noften happen to any one to know a sufficient number of cases with the\naccuracy requisite for making the sort of comparison last mentioned; less\nthan which, however, would not constitute a real induction. Accordingly,\nthere is hardly one current opinion respecting the characters of nations,\nclasses, or descriptions of persons, which is universally acknowledged as\nindisputable.(272)\n\nAnd finally, if we could even obtain by way of experiment a much more\nsatisfactory assurance of these generalizations than is really possible,\nthey would still be only empirical laws. They would show, indeed, that\nthere was some connection between the type of character formed and the\ncircumstances existing in the case; but not what the precise connection\nwas, nor to which of the peculiarities of those circumstances the effect\nwas really owing. They could only, therefore, be received as results of\ncausation, requiring to be resolved into the general laws of the causes:\nuntil the determination of which, we could not judge within what limits\nthe derivative laws might serve as presumptions in cases yet unknown, or\neven be depended on as permanent in the very cases from which they were\ncollected. The French people had, or were supposed to have, a certain\nnational character; but they drive out their royal family and aristocracy,\nalter their institutions, pass through a series of extraordinary events\nfor the greater part of a century, and at the end of that time their\ncharacter is found to have undergone important changes. A long list of\nmental and moral differences are observed, or supposed to exist between\nmen and women; but at some future and, it may be hoped, not distant\nperiod, equal freedom and an equally independent social position come to\nbe possessed by both, and their differences of character are either\nremoved or totally altered.\n\nBut if the differences which we think we observe between French and\nEnglish, or between men and women, can be connected with more general\nlaws; if they be such as might be expected to be produced by the\ndifferences of government, former customs, and physical peculiarities in\nthe two nations, and by the diversities of education, occupations,\npersonal independence, and social privileges, and whatever original\ndifferences there may be in bodily strength and nervous sensibility\nbetween the two sexes; then, indeed, the coincidence of the two kinds of\nevidence justifies us in believing that we have both reasoned rightly and\nobserved rightly. Our observation, though not sufficient as proof, is\nample as verification. And having ascertained not only the empirical laws,\nbut the causes, of the peculiarities, we need be under no difficulty in\njudging how far they may be expected to be permanent, or by what\ncircumstances they would be modified or destroyed.\n\n\u00a7 4. Since then it is impossible to obtain really accurate propositions\nrespecting the formation of character from observation and experiment\nalone, we are driven perforce to that which, even if it had not been the\nindispensable, would have been the most perfect, mode of investigation,\nand which it is one of the principal aims of philosophy to extend; namely,\nthat which tries its experiments not on the complex facts, but on the\nsimple ones of which they are compounded; and after ascertaining the laws\nof the causes, the composition of which gives rise to the complex\nphenomena, then considers whether these will not explain and account for\nthe approximate generalizations which have been framed empirically\nrespecting the sequences of those complex phenomena. The laws of the\nformation of character are, in short, derivative laws, resulting from the\ngeneral laws of mind, and are to be obtained by deducing them from those\ngeneral laws by supposing any given set of circumstances, and then\nconsidering what, according to the laws of mind, will be the influence of\nthose circumstances on the formation of character.\n\nA science is thus formed, to which I would propose to give the name of\nEthology, or the Science of Character, from \u1f26\u03b8\u03bf\u03c2, a word more nearly\ncorresponding to the term \u201ccharacter\u201d as I here use it, than any other\nword in the same language. The name is perhaps etymologically applicable\nto the entire science of our mental and moral nature; but if, as is usual\nand convenient, we employ the name Psychology for the science of the\nelementary laws of mind, Ethology will serve for the ulterior science\nwhich determines the kind of character produced in conformity to those\ngeneral laws by any set of circumstances, physical and moral. According to\nthis definition, Ethology is the science which corresponds to the art of\neducation in the widest sense of the term, including the formation of\nnational or collective character as well as individual. It would indeed be\nvain to expect (however completely the laws of the formation of character\nmight be ascertained) that we could know so accurately the circumstances\nof any given case as to be able positively to predict the character that\nwould be produced in that case. But we must remember that a degree of\nknowledge far short of the power of actual prediction is often of much\npractical value. There may be great power of influencing phenomena, with a\nvery imperfect knowledge of the causes by which they are in any given\ninstance determined. It is enough that we know that certain means have a\n_tendency_ to produce a given effect, and that others have a tendency to\nfrustrate it. When the circumstances of an individual or of a nation are\nin any considerable degree under our control, we may, by our knowledge of\ntendencies, be enabled to shape those circumstances in a manner much more\nfavorable to the ends we desire, than the shape which they would of\nthemselves assume. This is the limit of our power; but within this limit\nthe power is a most important one.\n\nThis science of Ethology may be called the Exact Science of Human Nature;\nfor its truths are not, like the empirical laws which depend on them,\napproximate generalizations, but real laws. It is, however (as in all\ncases of complex phenomena), necessary to the exactness of the\npropositions, that they should be hypothetical only, and affirm\ntendencies, not facts. They must not assert that something will always, or\ncertainly, happen; but only that such and such will be the effect of a\ngiven cause, so far as it operates uncounteracted. It is a scientific\nproposition, that bodily strength tends to make men courageous; not that\nit always makes them so: that an interest on one side of a question tends\nto bias the judgment; not that it invariably does so: that experience\ntends to give wisdom; not that such is always its effect. These\npropositions, being assertive only of tendencies, are not the less\nuniversally true because the tendencies may be frustrated.\n\n\u00a7 5. While, on the one hand, Psychology is altogether, or principally, a\nscience of observation and experiment, Ethology, as I have conceived it,\nis, as I have already remarked, altogether deductive. The one ascertains\nthe simple laws of Mind in general, the other traces their operation in\ncomplex combinations of circumstances. Ethology stands to Psychology in a\nrelation very similar to that in which the various branches of natural\nphilosophy stand to mechanics. The principles of Ethology are properly the\nmiddle principles, the _axiomata media_ (as Bacon would have said) of the\nscience of mind: as distinguished, on the one hand, from the empirical\nlaws resulting from simple observation, and, on the other, from the\nhighest generalizations.\n\nAnd this seems a suitable place for a logical remark, which, though of\ngeneral application, is of peculiar importance in reference to the present\nsubject. Bacon has judiciously observed that the _axiomata media_ of every\nscience principally constitute its value. The lowest generalizations,\nuntil explained by and resolved into the middle principles of which they\nare the consequences, have only the imperfect accuracy of empirical laws;\nwhile the most general laws are _too_ general, and include too few\ncircumstances, to give sufficient indication of what happens in individual\ncases, where the circumstances are almost always immensely numerous. In\nthe importance, therefore, which Bacon assigns, in every science, to the\nmiddle principles, it is impossible not to agree with him. But I conceive\nhim to have been radically wrong in his doctrine respecting the mode in\nwhich these _axiomata media_ should be arrived at; though there is no one\nproposition laid down in his works for which he has been more\nextravagantly eulogized. He enunciates as a universal rule that induction\nshould proceed from the lowest to the middle principles, and from those to\nthe highest, never reversing that order, and, consequently, leaving no\nroom for the discovery of new principles by way of deduction at all. It is\nnot to be conceived that a man of his sagacity could have fallen into this\nmistake if there had existed in his time, among the sciences which treat\nof successive phenomena, one single instance of a deductive science, such\nas mechanics, astronomy, optics, acoustics, etc., now are. In those\nsciences it is evident that the higher and middle principles are by no\nmeans derived from the lowest, but the reverse. In some of them the very\nhighest generalizations were those earliest ascertained with any\nscientific exactness; as, for example (in mechanics), the laws of motion.\nThose general laws had not, indeed, at first the acknowledged universality\nwhich they acquired after having been successfully employed to explain\nmany classes of phenomena to which they were not originally seen to be\napplicable; as when the laws of motion were employed, in conjunction with\nother laws, to explain deductively the celestial phenomena. Still, the\nfact remains, that the propositions which were afterward recognized as the\nmost general truths of the science were, of all its accurate\ngeneralizations, those earliest arrived at. Bacon\u2019s greatest merit can not\ntherefore consist, as we are so often told that it did, in exploding the\nvicious method pursued by the ancients of flying to the highest\ngeneralizations first, and deducing the middle principles from them; since\nthis is neither a vicious nor an exploded, but the universally accredited\nmethod of modern science, and that to which it owes its greatest triumphs.\nThe error of ancient speculation did not consist in making the largest\ngeneralizations first, but in making them without the aid or warrant of\nrigorous inductive methods, and applying them deductively without the\nneedful use of that important part of the Deductive Method termed\nVerification.\n\nThe order in which truths of the various degrees of generality should be\nascertained can not, I apprehend, be prescribed by any unbending rule. I\nknow of no maxim which can be laid down on the subject, but to obtain\nthose first in respect to which the conditions of a real induction can be\nfirst and most completely realized. Now, wherever our means of\ninvestigation can reach causes, without stopping at the empirical laws of\nthe effects, the simplest cases, being those in which fewest causes are\nsimultaneously concerned, will be most amenable to the inductive process;\nand these are the cases which elicit laws of the greatest\ncomprehensiveness. In every science, therefore, which has reached the\nstage at which it becomes a science of causes, it will be usual as well as\ndesirable first to obtain the highest generalizations, and then deduce the\nmore special ones from them. Nor can I discover any foundation for the\nBaconian maxim, so much extolled by subsequent writers, except this: That\nbefore we attempt to explain deductively from more general laws any new\nclass of phenomena, it is desirable to have gone as far as is practicable\nin ascertaining the empirical laws of those phenomena; so as to compare\nthe results of deduction, not with one individual instance after another,\nbut with general propositions expressive of the points of agreement which\nhave been found among many instances. For if Newton had been obliged to\nverify the theory of gravitation, not by deducing from it Kepler\u2019s laws,\nbut by deducing all the observed planetary positions which had served\nKepler to establish those laws, the Newtonian theory would probably never\nhave emerged from the state of an hypothesis.(273)\n\nThe applicability of these remarks to the special case under consideration\ncan not admit of question. The science of the formation of character is a\nscience of causes. The subject is one to which those among the canons of\ninduction, by which laws of causation are ascertained, can be rigorously\napplied. It is, therefore, both natural and advisable to ascertain the\nsimplest, which are necessarily the most general, laws of causation first,\nand to deduce the middle principles from them. In other words, Ethology,\nthe deductive science, is a system of corollaries from Psychology, the\nexperimental science.\n\n\u00a7 6. Of these, the earlier alone has been, as yet, really conceived or\nstudied as a science; the other, Ethology, is still to be created. But its\ncreation has at length become practicable. The empirical laws, destined to\nverify its deductions, have been formed in abundance by every successive\nage of humanity; and the premises for the deductions are now sufficiently\ncomplete. Excepting the degree of uncertainty which still exists as to the\nextent of the natural differences of individual minds, and the physical\ncircumstances on which these may be dependent (considerations which are of\nsecondary importance when we are considering mankind in the average, or\n_en masse_), I believe most competent judges will agree that the general\nlaws of the different constituent elements of human nature are even now\nsufficiently understood to render it possible for a competent thinker to\ndeduce from those laws, with a considerable approach to certainty, the\nparticular type of character which would be formed in mankind generally by\nany assumed set of circumstances. A science of Ethology, founded on the\nlaws of Psychology, is therefore possible; though little has yet been\ndone, and that little not at all systematically, toward forming it. The\nprogress of this important but most imperfect science will depend on a\ndouble process: first, that of deducing theoretically the ethological\nconsequences of particular circumstances of position, and comparing them\nwith the recognized results of common experience; and, secondly, the\nreverse operation; increased study of the various types of human nature\nthat are to be found in the world; conducted by persons not only capable\nof analyzing and recording the circumstances in which these types\nseverally prevail, but also sufficiently acquainted with psychological\nlaws to be able to explain and account for the characteristics of the\ntype, by the peculiarities of the circumstances: the residuum alone, when\nthere proves to be any, being set down to the account of congenital\npredispositions.\n\nFor the experimental or _a posteriori_ part of this process, the materials\nare continually accumulating by the observation of mankind. So far as\nthought is concerned, the great problem of Ethology is to deduce the\nrequisite middle principles from the general laws of Psychology. The\nsubject to be studied is, the origin and sources of all those qualities in\nhuman beings which are interesting to us, either as facts to be produced,\nto be avoided, or merely to be understood; and the object is, to\ndetermine, from the general laws of mind, combined with the general\nposition of our species in the universe, what actual or possible\ncombinations of circumstances are capable of promoting or of preventing\nthe production of those qualities. A science which possesses middle\nprinciples of this kind, arranged in the order, not of causes, but of the\neffects which it is desirable to produce or to prevent, is duly prepared\nto be the foundation of the corresponding Art. And when Ethology shall be\nthus prepared, practical education will be the mere transformation of\nthose principles into a parallel system of precepts, and the adaptation of\nthese to the sum total of the individual circumstances which exist in each\nparticular case.\n\nIt is hardly necessary again to repeat that, as in every other deductive\nscience, verification _a posteriori_ must proceed _pari passu_ with\ndeduction _a priori_. The inference given by theory as to the type of\ncharacter which would be formed by any given circumstances must be tested\nby specific experience of those circumstances whenever obtainable; and the\nconclusions of the science as a whole must undergo a perpetual\nverification and correction from the general remarks afforded by common\nexperience respecting human nature in our own age, and by history\nrespecting times gone by. The conclusions of theory can not be trusted,\nunless confirmed by observation; nor those of observation, unless they can\nbe affiliated to theory, by deducing them from the laws of human nature,\nand from a close analysis of the circumstances of the particular\nsituation. It is the accordance of these two kinds of evidence separately\ntaken\u2014the consilience of _a priori_ reasoning and specific\nexperience\u2014which forms the only sufficient ground for the principles of\nany science so \u201cimmersed in matter,\u201d dealing with such complex and\nconcrete phenomena, as Ethology.\n\n\n\n\n                               Chapter VI.\n\n\nGeneral Considerations On The Social Science.\n\n\n\u00a7 1. Next after the science of individual man comes the science of man in\nsociety\u2014of the actions of collective masses of mankind, and the various\nphenomena which constitute social life.\n\nIf the formation of individual character is already a complex subject of\nstudy, this subject must be, in appearance at least, still more complex;\nbecause the number of concurrent causes, all exercising more or less\ninfluence on the total effect, is greater, in the proportion in which a\nnation, or the species at large, exposes a larger surface to the operation\nof agents, psychological and physical, than any single individual. If it\nwas necessary to prove, in opposition to an existing prejudice, that the\nsimpler of the two is capable of being a subject of science, the prejudice\nis likely to be yet stronger against the possibility of giving a\nscientific character to the study of Politics, and of the phenomena of\nSociety. It is, accordingly, but of yesterday that the conception of a\npolitical or social science has existed anywhere but in the mind of here\nand there an insulated thinker, generally very ill prepared for its\nrealization: though the subject itself has of all others engaged the most\ngeneral attention, and been a theme of interested and earnest discussions,\nalmost from the beginning of recorded time.\n\nThe condition, indeed, of politics as a branch of knowledge was, until\nvery lately, and has scarcely even yet ceased to be, that which Bacon\nanimadverted on, as the natural state of the sciences while their\ncultivation is abandoned to practitioners; not being carried on as a\nbranch of speculative inquiry, but only with a view to the exigencies of\ndaily practice, and the _fructifera experimenta_, therefore, being aimed\nat, almost to the exclusion of the _lucifera_. Such was medical\ninvestigation, before physiology and natural history began to be\ncultivated as branches of general knowledge. The only questions examined\nwere, what diet is wholesome, or what medicine will cure some given\ndisease; without any previous systematic inquiry into the laws of\nnutrition, and of the healthy and morbid action of the different organs,\non which laws the effect of any diet or medicine must evidently depend.\nAnd in politics the questions which engaged general attention were\nsimilar: Is such an enactment, or such a form of government, beneficial or\nthe reverse\u2014either universally, or to some particular community? without\nany previous inquiry into the general conditions by which the operation of\nlegislative measures, or the effects produced by forms of government, are\ndetermined. Students in politics thus attempted to study the pathology and\ntherapeutics of the social body, before they had laid the necessary\nfoundation in its physiology; to cure disease without understanding the\nlaws of health. And the result was such as it must always be when persons,\neven of ability, attempt to deal with the complex questions of a science\nbefore its simpler and more elementary truths have been established.\n\nNo wonder that, when the phenomena of society have so rarely been\ncontemplated in the point of view characteristic of science, the\nphilosophy of society should have made little progress; should contain few\ngeneral propositions sufficiently precise and certain for common inquirers\nto recognize in them a scientific character. The vulgar notion accordingly\nis, that all pretension to lay down general truths on politics and society\nis quackery; that no universality and no certainty are attainable in such\nmatters. What partly excuses this common notion is, that it is really not\nwithout foundation in one particular sense. A large proportion of those\nwho have laid claim to the character of philosophic politicians have\nattempted not to ascertain universal sequences, but to frame universal\nprecepts. They have imagined some one form of government, or system of\nlaws, to fit all cases\u2014a pretension well meriting the ridicule with which\nit is treated by practitioners, and wholly unsupported by the analogy of\nthe art to which, from the nature of its subject, that of politics must be\nthe most nearly allied. No one now supposes it possible that one remedy\ncan cure all diseases, or even the same disease in all constitutions and\nhabits of body.\n\nIt is not necessary even to the perfection of a science, that the\ncorresponding art should possess universal, or even general, rules. The\nphenomena of society might not only be completely dependent on known\ncauses, but the mode of action of all those causes might be reducible to\nlaws of considerable simplicity, and yet no two cases might admit of being\ntreated in precisely the same manner. So great might be the variety of\ncircumstances on which the results in different cases depend, that the art\nmight not have a single general precept to give, except that of watching\nthe circumstances of the particular case, and adapting our measures to the\neffects which, according to the principles of the science, result from\nthose circumstances. But although, in so complicated a class of subjects,\nit is impossible to lay down practical maxims of universal application, it\ndoes not follow that the phenomena do not conform to universal laws.\n\n\u00a7 2. All phenomena of society are phenomena of human nature, generated by\nthe action of outward circumstances upon masses of human beings; and if,\ntherefore, the phenomena of human thought, feeling, and action are subject\nto fixed laws, the phenomena of society can not but conform to fixed laws,\nthe consequence of the preceding. There is, indeed, no hope that these\nlaws, though our knowledge of them were as certain and as complete as it\nis in astronomy, would enable us to predict the history of society, like\nthat of the celestial appearances, for thousands of years to come. But the\ndifference of certainty is not in the laws themselves, it is in the data\nto which these laws are to be applied. In astronomy the causes influencing\nthe result are few, and change little, and that little according to known\nlaws; we can ascertain what they are now, and thence determine what they\nwill be at any epoch of a distant future. The data, therefore, in\nastronomy are as certain as the laws themselves. The circumstances, on the\ncontrary, which influence the condition and progress of society are\ninnumerable, and perpetually changing; and though they all change in\nobedience to causes, and therefore to laws, the multitude of the causes is\nso great as to defy our limited powers of calculation. Not to say that the\nimpossibility of applying precise numbers to facts of such a description\nwould set an impassable limit to the possibility of calculating them\nbeforehand, even if the powers of the human intellect were otherwise\nadequate to the task.\n\nBut, as before remarked, an amount of knowledge quite insufficient for\nprediction, may be most valuable for guidance. The science of society\nwould have attained a very high point of perfection if it enabled us, in\nany given condition of social affairs, in the condition, for instance, of\nEurope or any European country at the present time, to understand by what\ncauses it had, in any and every particular, been made what it was; whether\nit was tending to any, and to what, changes; what effects each feature of\nits existing state was likely to produce in the future; and by what means\nany of those effects might be prevented, modified, or accelerated, or a\ndifferent class of effects superinduced. There is nothing chimerical in\nthe hope that general laws, sufficient to enable us to answer these\nvarious questions for any country or time with the individual\ncircumstances of which we are well acquainted, do really admit of being\nascertained; and that the other branches of human knowledge, which this\nundertaking presupposes, are so far advanced that the time is ripe for its\ncommencement. Such is the object of the Social Science.\n\nThat the nature of what I consider the true method of the science may be\nmade more palpable, by first showing what that method is not, it will be\nexpedient to characterize briefly two radical misconceptions of the proper\nmode of philosophizing on society and government, one or other of which\nis, either explicitly or more often unconsciously, entertained by almost\nall who have meditated or argued respecting the logic of politics, since\nthe notion of treating it by strict rules, and on Baconian principles, has\nbeen current among the more advanced thinkers. These erroneous methods, if\nthe word method can be applied to erroneous tendencies arising from the\nabsence of any sufficiently distinct conception of method, may be termed\nthe Experimental, or Chemical, mode of investigation, and the Abstract, or\nGeometrical, mode. We shall begin with the former.\n\n\n\n\n                               Chapter VII.\n\n\nOf The Chemical, Or Experimental, Method In The Social Science.\n\n\n\u00a7 1. The laws of the phenomena of society are, and can be, nothing but the\nlaws of the actions and passions of human beings united together in the\nsocial state. Men, however, in a state of society are still men; their\nactions and passions are obedient to the laws of individual human nature.\nMen are not, when brought together, converted into another kind of\nsubstance, with different properties; as hydrogen and oxygen are different\nfrom water, or as hydrogen, oxygen, carbon, and azote, are different from\nnerves, muscles, and tendons. Human beings in society have no properties\nbut those which are derived from, and may be resolved into, the laws of\nthe nature of individual man. In social phenomena the Composition of\nCauses is the universal law.\n\nNow, the method of philosophizing which may be termed chemical overlooks\nthis fact, and proceeds as if the nature of man as an individual were not\nconcerned at all, or were concerned in a very inferior degree, in the\noperations of human beings in society. All reasoning in political or\nsocial affairs, grounded on principles of human nature, is objected to by\nreasoners of this sort, under such names as \u201cabstract theory.\u201d For the\ndirection of their opinions and conduct, they profess to demand, in all\ncases without exception, specific experience.\n\nThis mode of thinking is not only general with practitioners in politics,\nand with that very numerous class who (on a subject which no one, however\nignorant, thinks himself incompetent to discuss) profess to guide\nthemselves by common sense rather than by science; but is often\ncountenanced by persons with greater pretensions to instruction\u2014persons\nwho, having sufficient acquaintance with books and with the current ideas\nto have heard that Bacon taught mankind to follow experience, and to\nground their conclusions on facts instead of metaphysical dogmas, think\nthat, by treating political facts in as directly experimental a method as\nchemical facts, they are showing themselves true Baconians, and proving\ntheir adversaries to be mere syllogizers and school-men. As, however, the\nnotion of the applicability of experimental methods to political\nphilosophy can not co-exist with any just conception of these methods\nthemselves, the kind of arguments from experience which the chemical\ntheory brings forth as its fruits (and which form the staple, in this\ncountry especially, of parliamentary and hustings oratory), are such as,\nat no time since Bacon, would have been admitted to be valid in chemistry\nitself, or in any other branch of experimental science. They are such as\nthese: that the prohibition of foreign commodities must conduce to\nnational wealth, because England has flourished under it, or because\ncountries in general which have adopted it have flourished; that our laws,\nor our internal administration, or our constitution, are excellent for a\nsimilar reason; and the eternal arguments from historical examples, from\nAthens or Rome, from the fires in Smithfield or the French Revolution.\n\nI will not waste time in contending against modes of argumentation which\nno person with the smallest practice in estimating evidence could possibly\nbe betrayed into; which draw conclusions of general application from a\nsingle unanalyzed instance, or arbitrarily refer an effect to some one\namong its antecedents, without any process of elimination or comparison of\ninstances. It is a rule both of justice and of good sense to grapple not\nwith the absurdest, but with the most reasonable form of a wrong opinion.\nWe shall suppose our inquirer acquainted with the true conditions of\nexperimental investigation, and competent in point of acquirements for\nrealizing them, so far as they can be realized. He shall know as much of\nthe facts of history as mere erudition can teach\u2014as much as can be proved\nby testimony, without the assistance of any theory; and if those mere\nfacts, properly collated, can fulfill the conditions of a real induction,\nhe shall be qualified for the task.\n\nBut that no such attempt can have the smallest chance of success, has been\nabundantly shown in the tenth chapter of the Third Book.(274) We there\nexamined whether effects which depend on a complication of causes can be\nmade the subject of a true induction by observation and experiment; and\nconcluded, on the most convincing grounds, that they can not. Since, of\nall effects, none depend on so great a complication of causes as social\nphenomena, we might leave our case to rest in safety on that previous\nshowing. But a logical principle as yet so little familiar to the ordinary\nrun of thinkers, requires to be insisted on more than once, in order to\nmake the due impression; and the present being the case which of all\nothers exemplifies it the most strongly, there will be advantage in\nre-stating the grounds of the general maxim, as applied to the specialties\nof the class of inquiries now under consideration.\n\n\u00a7 2. The first difficulty which meets us in the attempt to apply\nexperimental methods for ascertaining the laws of social phenomena, is\nthat we are without the means of making artificial experiments. Even if we\ncould contrive experiments at leisure, and try them without limit, we\nshould do so under immense disadvantage; both from the impossibility of\nascertaining and taking note of all the facts of each case, and because\n(those facts being in a perpetual state of change), before sufficient time\nhad elapsed to ascertain the result of the experiment, some material\ncircumstances would always have ceased to be the same. But it is\nunnecessary to consider the logical objections which would exist to the\nconclusiveness of our experiments, since we palpably never have the power\nof trying any. We can only watch those which nature produces, or which are\nproduced for other reasons. We can not adapt our logical means to our\nwants, by varying the circumstances as the exigencies of elimination may\nrequire. If the spontaneous instances, formed by contemporary events and\nby the successions of phenomena recorded in history, afford a sufficient\nvariation of circumstances, an induction from specific experience is\nattainable; otherwise not. The question to be resolved is, therefore,\nwhether the requisites for induction respecting the causes of political\neffects or the properties of political agents, are to be met with in\nhistory? including under the term, contemporary history. And in order to\ngive fixity to our conceptions, it will be advisable to suppose this\nquestion asked in reference to some special subject of political inquiry\nor controversy; such as that frequent topic of debate in the present\ncentury, the operation of restrictive and prohibitory commercial\nlegislation upon national wealth. Let this, then, be the scientific\nquestion to be investigated by specific experience.\n\n\u00a7 3. In order to apply to the case the most perfect of the methods of\nexperimental inquiry, the Method of Difference, we require to find two\ninstances which tally in every particular except the one which is the\nsubject of inquiry. If two nations can be found which are alike in all\nnatural advantages and disadvantages; whose people resemble each other in\nevery quality, physical and moral, spontaneous and acquired; whose habits,\nusages, opinions, laws, and institutions are the same in all respects,\nexcept that one of them has a more protective tariff, or in other respects\ninterferes more with the freedom of industry; if one of these nations is\nfound to be rich and the other poor, or one richer than the other, this\nwill be an _experimentum crucis_: a real proof by experience, which of the\ntwo systems is most favorable to national riches. But the supposition that\ntwo such instances can be met with is manifestly absurd. Nor is such a\nconcurrence even abstractedly possible. Two nations which agreed in every\nthing except their commercial policy would agree also in that. Differences\nof legislation are not inherent and ultimate diversities; are not\nproperties of Kinds. They are effects of pre-existing causes. If the two\nnations differ in this portion of their institutions, it is from some\ndifference in their position, and thence in their apparent interests, or\nin some portion or other of their opinions, habits, and tendencies; which\nopens a view of further differences without any assignable limit, capable\nof operating on their industrial prosperity, as well as on every other\nfeature of their condition, in more ways than can be enumerated or\nimagined. There is thus a demonstrated impossibility of obtaining, in the\ninvestigations of the social science, the conditions required for the most\nconclusive form of inquiry by specific experience.\n\nIn the absence of the direct, we may next try, as in other cases, the\nsupplementary resource, called in a former place the Indirect Method of\nDifference; which, instead of two instances differing in nothing but the\npresence or absence of a given circumstance, compares two _classes_ of\ninstances respectively agreeing in nothing but the presence of a\ncircumstance on the one side and its absence on the other. To choose the\nmost advantageous case conceivable (a case far too advantageous to be ever\nobtained), suppose that we compare one nation which has a restrictive\npolicy with two or more nations agreeing in nothing but in permitting free\ntrade. We need not now suppose that either of these nations agrees with\nthe first in all its circumstances; one may agree with it in some of its\ncircumstances, and another in the remainder. And it may be argued, that if\nthese nations remain poorer than the restrictive nation, it can not be for\nwant either of the first or of the second set of circumstances, but it\nmust be for want of the protective system. If (we might say) the\nrestrictive nation had prospered from the one set of causes, the first of\nthe free-trade nations would have prospered equally; if by reason of the\nother, the second would; but neither has; therefore the prosperity was\nowing to the restrictions. This will be allowed to be a very favorable\nspecimen of an argument from specific experience in politics, and if this\nbe inconclusive, it would not be easy to find another preferable to it.\n\nYet, that it is inconclusive, scarcely requires to be pointed out. Why\nmust the prosperous nation have prospered from one cause exclusively?\nNational prosperity is always the collective result of a multitude of\nfavorable circumstances; and of these, the restrictive nation may unite a\ngreater number than either of the others, though it may have all of those\ncircumstances in common with either one or the other of them. Its\nprosperity may be partly owing to circumstances common to it with one of\nthose nations, and partly with the other, while they, having each of them\nonly half the number of favorable circumstances, have remained inferior.\nSo that the closest imitation which can be made, in the social science, of\na legitimate induction from direct experience, gives but a specious\nsemblance of conclusiveness, without any real value.\n\n\u00a7 4. The Method of Difference in either of its forms being thus completely\nout of the question, there remains the Method of Agreement. But we are\nalready aware of how little value this method is, in cases admitting\nPlurality of Causes; and social phenomena are those in which the plurality\nprevails in the utmost possible extent.\n\nSuppose that the observer makes the luckiest hit which could be given by\nany conceivable combination of chances; that he finds two nations which\nagree in no circumstance whatever, except in having a restrictive system,\nand in being prosperous; or a number of nations, all prosperous, which\nhave no antecedent circumstances common to them all but that of having a\nrestrictive policy. It is unnecessary to go into the consideration of the\nimpossibility of ascertaining from history, or even from contemporary\nobservation, that such is really the fact; that the nations agree in no\nother circumstance capable of influencing the case. Let us suppose this\nimpossibility vanquished, and the fact ascertained that they agree only in\na restrictive system as an antecedent, and industrial prosperity as a\nconsequent. What degree of presumption does this raise that the\nrestrictive system caused the prosperity? One so trifling as to be\nequivalent to none at all. That some one antecedent is the cause of a\ngiven effect, because all other antecedents have been found capable of\nbeing eliminated, is a just inference, only if the effect can have but one\ncause. If it admits of several, nothing is more natural than that each of\nthese should separately admit of being eliminated. Now, in the case of\npolitical phenomena, the supposition of unity of cause is not only wide of\nthe truth, but at an immeasurable distance from it. The causes of every\nsocial phenomenon which we are particularly interested about, security,\nwealth, freedom, good government, public virtue, general intelligence, or\ntheir opposites, are infinitely numerous, especially the external or\nremote causes, which alone are, for the most part, accessible to direct\nobservation. No one cause suffices of itself to produce any of these\nphenomena; while there are countless causes which have some influence over\nthem, and may co-operate either in their production or in their\nprevention. From the mere fact, therefore, of our having been able to\neliminate some circumstance, we can by no means infer that this\ncircumstance was not instrumental to the effect in some of the very\ninstances from which we have eliminated it. We can conclude that the\neffect is sometimes produced without it; but not that, when present, it\ndoes not contribute its share.\n\nSimilar objections will be found to apply to the Method of Concomitant\nVariations. If the causes which act upon the state of any society produced\neffects differing from one another in kind; if wealth depended on one\ncause, peace on another, a third made people virtuous, a fourth\nintelligent; we might, though unable to sever the causes from one another,\nrefer to each of them that property of the effect which waxed as it waxed,\nand which waned as it waned. But every attribute of the social body is\ninfluenced by innumerable causes; and such is the mutual action of the\nco-existing elements of society, that whatever affects any one of the more\nimportant of them, will by that alone, if it does not affect the others\ndirectly, affect them indirectly. The effects, therefore, of different\nagents not being different in quality, while the quantity of each is the\nmixed result of all the agents, the variations of the aggregate can not\nbear a uniform proportion to those of any one of its component parts.\n\n\u00a7 5. There remains the Method of Residues; which appears, on the first\nview, less foreign to this kind of inquiry than the three other methods,\nbecause it only requires that we should accurately note the circumstances\nof some one country, or state of society. Making allowance, thereupon, for\nthe effect of all causes whose tendencies are known, the residue which\nthose causes are inadequate to explain may plausibly be imputed to the\nremainder of the circumstances which are known to have existed in the\ncase. Something similar to this is the method which Coleridge(275)\ndescribes himself as having followed in his political essays in the\n_Morning Post_. \u201cOn every great occurrence I endeavored to discover in\npast history the event that most nearly resembled it. I procured, whenever\nit was possible, the contemporary historians, memorialists, and\npamphleteers. Then fairly subtracting the points of difference from those\nof likeness, as the balance favored the former or the latter, I\nconjectured that the result would be the same or different. As, for\ninstance, in the series of essays entitled \u2018A Comparison of France under\nNapoleon with Rome under the first C\u00e6sars,\u2019 and in those which followed,\n\u2018on the probable final restoration of the Bourbons.\u2019 The same plan I\npursued at the commencement of the Spanish Revolution, and with the same\nsuccess, taking the war of the United Provinces with Philip II. as the\ngroundwork of the comparison.\u201d In this inquiry he no doubt employed the\nMethod of Residues; for, in \u201csubtracting the points of difference from\nthose of likeness,\u201d he doubtless weighed, and did not content himself with\nnumbering, them: he doubtless took those points of agreement only which he\npresumed from their own nature to be capable of influencing the effect,\nand, allowing for that influence, concluded that the remainder of the\nresult would be referable to the points of difference.\n\nWhatever may be the efficacy of this method, it is, as we long ago\nremarked, not a method of pure observation and experiment; it concludes,\nnot from a comparison of instances, but from the comparison of an instance\nwith the result of a previous deduction. Applied to social phenomena, it\npresupposes that the causes from which part of the effect proceeded are\nalready known; and as we have shown that these can not have been known by\nspecific experience, they must have been learned by deduction from\nprinciples of human nature; experience being called in only as a\nsupplementary resource, to determine the causes which produced an\nunexplained residue. But if the principles of human nature may be had\nrecourse to for the establishment of some political truths, they may for\nall. If it be admissible to say, England must have prospered by reason of\nthe prohibitory system, because after allowing for all the other\ntendencies which have been operating, there is a portion of prosperity\nstill to be accounted for; it must be admissible to go to the same source\nfor the effect of the prohibitory system, and examine what account the\nlaws of human motives and actions will enable us to give of _its_\ntendencies. Nor, in fact, will the experimental argument amount to any\nthing, except in verification of a conclusion drawn from those general\nlaws. For we may subtract the effect of one, two, three, or four causes,\nbut we shall never succeed in subtracting the effect of all causes except\none; while it would be a curious instance of the dangers of too much\ncaution if, to avoid depending on _a priori_ reasoning concerning the\neffect of a single cause, we should oblige ourselves to depend on as many\nseparate _a priori_ reasonings as there are causes operating concurrently\nwith that particular cause in some given instance.\n\nWe have now sufficiently characterized the gross misconception of the mode\nof investigation proper to political phenomena, which I have termed the\nChemical Method. So lengthened a discussion would not have been necessary,\nif the claim to decide authoritatively on political doctrines were\nconfined to persons who had competently studied any one of the higher\ndepartments of physical science. But since the generality of those who\nreason on political subjects, satisfactorily to themselves and to a more\nor less numerous body of admirers, know nothing whatever of the methods of\nphysical investigation beyond a few precepts which they continue to parrot\nafter Bacon, being entirely unaware that Bacon\u2019s conception of scientific\ninquiry has done its work, and that science has now advanced into a higher\nstage, there are probably many to whom such remarks as the foregoing may\nstill be useful. In an age in which chemistry itself, when attempting to\ndeal with the more complex chemical sequences\u2014those of the animal or even\nthe vegetable organism\u2014has found it necessary to become, and has succeeded\nin becoming, a Deductive Science, it is not to be apprehended that any\nperson of scientific habits, who has kept pace with the general progress\nof the knowledge of nature, can be in danger of applying the methods of\nelementary chemistry to explore the sequences of the most complex order of\nphenomena in existence.\n\n\n\n\n                              Chapter VIII.\n\n\nOf The Geometrical, Or Abstract, Method.\n\n\n\u00a7 1. The misconception discussed in the preceding chapter is, as we said,\nchiefly committed by persons not much accustomed to scientific\ninvestigation: practitioners in politics, who rather employ the\ncommonplaces of philosophy to justify their practice than seek to guide\ntheir practice by philosophic principles; or imperfectly educated persons,\nwho, in ignorance of the careful selection and elaborate comparison of\ninstances required for the formation of a sound theory, attempt to found\none upon a few coincidences which they have casually noticed.\n\nThe erroneous method of which we are now to treat is, on the contrary,\npeculiar to thinking and studious minds. It never could have suggested\nitself but to persons of some familiarity with the nature of scientific\nresearch; who, being aware of the impossibility of establishing, by casual\nobservation or direct experimentation, a true theory of sequences so\ncomplex as are those of the social phenomena, have recourse to the simpler\nlaws which are immediately operative in those phenomena, and which are no\nother than the laws of the nature of the human beings therein concerned,\nThese thinkers perceive (what the partisans of the chemical or\nexperimental theory do not) that the science of society must necessarily\nbe deductive. But, from an insufficient consideration of the specific\nnature of the subject-matter\u2014and often because (their own scientific\neducation having stopped short in too early a stage) geometry stands in\ntheir minds as the type of all deductive science\u2014it is to geometry, rather\nthan to astronomy and natural philosophy, that they unconsciously\nassimilate the deductive science of society.\n\nAmong the differences between geometry (a science of co-existent facts,\naltogether independent of the laws of the succession of phenomena), and\nthose physical Sciences of Causation which have been rendered deductive,\nthe following is one of the most conspicuous: That geometry affords no\nroom for what so constantly occurs in mechanics and its applications, the\ncase of conflicting forces; of causes which counteract or modify one\nanother. In mechanics we continually find two or more moving forces\nproducing, not motion, but rest; or motion in a different direction from\nthat which would have been produced by either of the generating forces. It\nis true that the effect of the joint forces is the same when they act\nsimultaneously, as if they had acted one after another, or by turns; and\nit is in this that the difference between mechanical and chemical laws\nconsists. But still the effects, whether produced by successive or by\nsimultaneous action, do, wholly or in part, cancel one another: what the\none force does, the other, partly, or altogether undoes. There is no\nsimilar state of things in geometry. The result which follows from one\ngeometrical principle has nothing that conflicts with the result which\nfollows from another. What is proved true from one geometrical theorem,\nwhat would be true if no other geometrical principles existed, can not be\naltered and made no longer true by reason of some other geometrical\nprinciple. What is once proved true is true in all cases, whatever\nsupposition may be made in regard to any other matter.\n\nNow a conception similar to this last would appear to have been formed of\nthe social science, in the minds of the earlier of those who have\nattempted to cultivate it by a deductive method. Mechanics would be a\nscience very similar to geometry, if every motion resulted from one force\nalone, and not from a conflict of forces. In the geometrical theory of\nsociety, it seems to be supposed that this is really the case with the\nsocial phenomena; that each of them results always from only one force,\none single property of human nature.\n\nAt the point which we have now reached, it can not be necessary to say any\nthing either in proof or in illustration of the assertion that such is not\nthe true character of the social phenomena. There is not, among these most\ncomplex and (for that reason) most modifiable of all phenomena, any one\nover which innumerable forces do not exercise influence; which does not\ndepend on a conjunction of very many causes. We have not, therefore, to\nprove the notion in question to be an error, but to prove that the error\nhas been committed; that so mistaken a conception of the mode in which the\nphenomena of society are produced has actually been ascertained.\n\n\u00a7 2. One numerous division of the reasoners who have treated social facts\naccording to geometrical methods, not admitting any modification of one\nlaw by another, must for the present be left out of consideration, because\nin them this error is complicated with, and is the effect of, another\nfundamental misconception, of which we have already taken some notice, and\nwhich will be further treated of before we conclude. I speak of those who\ndeduce political conclusions not from laws of nature, not from sequences\nof phenomena, real or imaginary, but from unbending practical maxims.\nSuch, for example, are all who found their theory of politics on what is\ncalled abstract right, that is to say, on universal precepts; a pretension\nof which we have already noticed the chimerical nature. Such, in like\nmanner, are those who make the assumption of a social contract, or any\nother kind of original obligation, and apply it to particular cases by\nmere interpretation. But in this the fundamental error is the attempt to\ntreat an art like a science, and to have a deductive art; the\nirrationality of which will be shown in a future chapter. It will be\nproper to take our exemplification of the geometrical theory from those\nthinkers who have avoided this additional error, and who entertain, so\nfar, a juster idea of the nature of political inquiry.\n\nWe may cite, in the first instance, those who assume as the principle of\ntheir political philosophy that government is founded on fear; that the\ndread of each other is the one motive by which human beings were\noriginally brought into a state of society, and are still held in it. Some\nof the earlier scientific inquirers into politics, in particular Hobbes,\nassumed this proposition, not by implication, but avowedly, as the\nfoundation of their doctrine, and attempted to build a complete philosophy\nof politics thereupon. It is true that Hobbes did not find this one maxim\nsufficient to carry him through the whole of his subject, but was obliged\nto eke it out by the double sophism of an original contract. I call this a\ndouble sophism; first, as passing off a fiction for a fact, and, secondly,\nassuming a practical principle, or precept, as the basis of a theory;\nwhich is a _petitio principii_, since (as we noticed in treating of that\nFallacy) every rule of conduct, even though it be so binding a one as the\nobservance of a promise, must rest its own foundations on the theory of\nthe subject; and the theory, therefore, can not rest upon it.\n\n\u00a7 3. Passing over less important instances, I shall come at once to the\nmost remarkable example afforded by our own times of the geometrical\nmethod in politics; emanating from persons who are well aware of the\ndistinction between science and art; who knew that rules of conduct must\nfollow, not precede, the ascertainment of laws of nature, and that the\nlatter, not the former, is the legitimate field for the application of the\ndeductive method. I allude to the interest-philosophy of the Bentham\nschool.\n\nThe profound and original thinkers who are commonly known under this\ndescription, founded their general theory of government on one\ncomprehensive premise, namely, that men\u2019s actions are always determined by\ntheir interests. There is an ambiguity in this last expression; for, as\nthe same philosophers, especially Bentham, gave the name of an interest to\nany thing which a person likes, the proposition may be understood to mean\nonly this, that men\u2019s actions are always determined by their wishes. In\nthis sense, however, it would not bear out any of the consequences which\nthese writers drew from it; and the word, therefore, in their political\nreasonings, must be understood to mean (which is also the explanation they\nthemselves, on such occasions gave of it) what is commonly termed private,\nor worldly, interest.\n\nTaking the doctrine, then, in this sense, an objection presents itself _in\nlimine_ which might be deemed a fatal one, namely, that so sweeping a\nproposition is far from being universally true. Human beings are not\ngoverned in all their actions by their worldly interests. This, however,\nis by no means so conclusive an objection as it at first appears; because\nin politics we are for the most part concerned with the conduct, not of\nindividual persons, but either of a series of persons (as a succession of\nkings), or a body or mass of persons, as a nation, an aristocracy, or a\nrepresentative assembly. And whatever is true of a large majority of\nmankind, may without much error be taken for true of any succession of\npersons, considered as a whole, or of any collection of persons in which\nthe act of the majority becomes the act of the whole body. Although,\ntherefore, the maxim is sometimes expressed in a manner unnecessarily\nparadoxical, the consequences drawn from it will hold equally good if the\nassertion be limited as follows: Any succession of persons, or the\nmajority of any body of persons, will be governed in the bulk of their\nconduct by their personal interests. We are bound to allow to this school\nof thinkers the benefit of this more rational statement of their\nfundamental maxim, which is also in strict conformity to the explanations\nwhich, when considered to be called for, have been given by themselves.\n\nThe theory goes on to infer, quite correctly, that if the actions of\nmankind are determined in the main by their selfish interests, the only\nrulers who will govern according to the interest of the governed, are\nthose whose selfish interests are in accordance with it. And to this is\nadded a third proposition, namely, that no rulers have their selfish\ninterest identical with that of the governed, unless it be rendered so by\naccountability, that is, by dependence on the will of the governed. In\nother words (and as the result of the whole), that the desire of retaining\nor the fear of losing their power, and whatever is thereon consequent, is\nthe sole motive which can be relied on for producing on the part of rulers\na course of conduct in accordance with the general interest.\n\nWe have thus a fundamental theorem of political science, consisting of\nthree syllogisms, and depending chiefly on two general premises, in each\nof which a certain effect is considered as determined only by one cause,\nnot by a concurrence of causes. In the one, it is assumed that the actions\nof average rulers are determined solely by self-interest; in the other,\nthat the sense of identity of interest with the governed, is produced and\nproducible by no other cause than responsibility.\n\nNeither of these propositions is by any means true; the last is extremely\nwide of the truth.\n\nIt is not true that the actions even of average rulers are wholly, or any\nthing approaching to wholly, determined by their personal interest, or\neven by their own opinion of their personal interest. I do not speak of\nthe influence of a sense of duty, or feelings of philanthropy, motives\nnever to be mainly relied on, though (except in countries or during\nperiods of great moral debasement) they influence almost all rulers in\nsome degree, and some rulers in a very great degree. But I insist only on\nwhat is true of all rulers, viz., that the character and course of their\nactions is largely influenced (independently of personal calculation) by\nthe habitual sentiments and feelings, the general modes of thinking and\nacting, which prevail throughout the community of which they are members;\nas well as by the feelings, habits, and modes of thought which\ncharacterize the particular class in that community to which they\nthemselves belong. And no one will understand or be able to decipher their\nsystem of conduct, who does not take all these things into account. They\nare also much influenced by the maxims and traditions which have descended\nto them from other rulers, their predecessors; which maxims and traditions\nhave been known to retain an ascendancy during long periods, even in\nopposition to the private interests of the rulers for the time being. I\nput aside the influence of other less general causes. Although, therefore,\nthe private interest of the rulers or of the ruling class is a very\npowerful force, constantly in action, and exercising the most important\ninfluence upon their conduct, there is also, in what they do, a large\nportion which that private interest by no means affords a sufficient\nexplanation of; and even the particulars which constitute the goodness or\nbadness of their government, are in some, and no small degree, influenced\nby those among the circumstances acting upon them, which can not, with any\npropriety, be included in the term self-interest.\n\nTurning now to the other proposition, that responsibility to the governed\nis the only cause capable of producing in the rulers a sense of identity\nof interest with the community, this is still less admissible as a\nuniversal truth, than even the former. I am not speaking of perfect\nidentity of interest, which is an impracticable chimera; which, most\nassuredly, responsibility to the people does not give. I speak of identity\nin essentials; and the essentials are different at different places and\ntimes. There are a large number of cases in which those things which it is\nmost for the general interest that the rulers should do, are also those\nwhich they are prompted to do by their strongest personal interest, the\nconsolidation of their power. The suppression, for instance, of anarchy\nand resistance to law\u2014the complete establishment of the authority of the\ncentral government, in a state of society like that of Europe in the\nMiddle Ages\u2014is one of the strongest interests of the people, and also of\nthe rulers simply because they are the rulers; and responsibility on their\npart could not strengthen, though in many conceivable ways it might\nweaken, the motives prompting them to pursue this object. During the\ngreater part, of the reign of Queen Elizabeth, and of many other monarchs\nwho might be named, the sense of identity of interest between the\nsovereign and the majority of the people was probably stronger than it\nusually is in responsible governments; every thing that the people had\nmost at heart, the monarch had at heart too. Had Peter the Great, or the\nrugged savages whom he began to civilize, the truest inclination toward\nthe things which were for the real interest of those savages?\n\nI am not here attempting to establish a theory of government, and am not\ncalled upon to determine the proportional weight which ought to be given\nto the circumstances which this school of geometrical politicians left out\nof their system, and those which they took into it. I am only concerned to\nshow that their method was unscientific; not to measure the amount of\nerror which may have affected their practical conclusions.\n\nIt is but justice to them, however, to remark, that their mistake was not\nso much one of substance as of form, and consisted in presenting in a\nsystematic shape, and as the scientific treatment of a great philosophical\nquestion, what should have passed for that which it really was, the mere\npolemics of the day. Although the actions of rulers are by no means wholly\ndetermined by their selfish interests, it is chiefly as a security against\nthose selfish interests that constitutional checks are required; and for\nthat purpose such checks, in England, and the other nations of modern\nEurope, can in no manner be dispensed with. It is likewise true, that in\nthese same nations, and in the present age, responsibility to the governed\nis the only means practically available to create a feeling of identity of\ninterest, in the cases, and on the points, where that feeling does not\nsufficiently exist. To all this, and to the arguments which may be founded\non it in favor of measures for the correction of our representative\nsystem, I have nothing to object; but I confess my regret, that the small\nthough highly important portion of the philosophy of government, which was\nwanted for the immediate purpose of serving the cause of parliamentary\nreform, should have been held forth by thinkers of such eminence as a\ncomplete theory.\n\nIt is not to be imagined possible, nor is it true in point of fact, that\nthese philosophers regarded the few premises of their theory as including\nall that is required for explaining social phenomena, or for determining\nthe choice of forms of government and measures of legislation and\nadministration. They were too highly instructed, of too comprehensive\nintellect, and some of them of too sober and practical a character, for\nsuch an error. They would have applied, and did apply, their principles\nwith innumerable allowances. But it is not allowances that are wanted.\nThere is little chance of making due amends in the superstructure of a\ntheory for the want of sufficient breadth in its foundations. It is\nunphilosophical to construct a science out of a few of the agencies by\nwhich the phenomena are determined, and leave the rest to the routine of\npractice or the sagacity of conjecture. We either ought not to pretend to\nscientific forms, or we ought to study all the determining agencies\nequally, and endeavor, so far as it can be done, to include all of them\nwithin the pale of the science; else we shall infallibly bestow a\ndisproportionate attention upon those which our theory takes into account,\nwhile we misestimate the rest, and probably underrate their importance.\nThat the deductions should be from the whole and not from a part only of\nthe laws of nature that are concerned, would be desirable even if those\nomitted were so insignificant in comparison with the others, that they\nmight, for most purposes and on most occasions, be left out of the\naccount. But this is far indeed from being true in the social science. The\nphenomena of society do not depend, in essentials, on some one agency or\nlaw of human nature, with only inconsiderable modifications from others.\nThe whole of the qualities of human nature influence those phenomena, and\nthere is not one which influences them in a small degree. There is not\none, the removal or any great alteration of which would not materially\naffect the whole aspect of society, and change more or less the sequences\nof social phenomena generally.\n\nThe theory which has been the subject of these remarks is, in this country\nat least, the principal contemporary example of what I have styled the\ngeometrical method of philosophizing in the social science; and our\nexamination of it has, for this reason, been more detailed than would\notherwise have been suitable to a work like the present. Having now\nsufficiently illustrated the two erroneous methods, we shall pass without\nfurther preliminary to the true method; that which proceeds (conformably\nto the practice of the more complex physical sciences) deductively indeed,\nbut by deduction from many, not from one or a very few, original premises;\nconsidering each effect as (what it really is) an aggregate result of many\ncauses, operating sometimes through the same, sometimes through different\nmental agencies, or laws of human nature.\n\n\n\n\n                               Chapter IX.\n\n\nOf The Physical, Or Concrete Deductive, Method.\n\n\n\u00a7 1. After what has been said to illustrate the nature of the inquiry into\nsocial phenomena, the general character of the method proper to that\ninquiry is sufficiently evident, and needs only to be recapitulated, not\nproved. However complex the phenomena, all their sequences and\nco-existences result from the laws of the separate elements. The effect\nproduced, in social phenomena, by any complex set of circumstances,\namounts precisely to the sum of the effects of the circumstances taken\nsingly; and the complexity does not arise from the number of the laws\nthemselves, which is not remarkably great, but from the extraordinary\nnumber and variety of the data or elements\u2014of the agents which, in\nobedience to that small number of laws, co-operate toward the effect. The\nSocial Science, therefore (which, by a convenient barbarism, has been\ntermed Sociology), is a deductive science; not, indeed, after the model of\ngeometry, but after that of the more complex physical sciences. It infers\nthe law of each effect from the laws of causation on which that effect\ndepends; not, however, from the law merely of one cause, as in the\ngeometrical method, but by considering all the causes which conjunctly\ninfluence the effect, and compounding their laws with one another. Its\nmethod, in short, is the Concrete Deductive Method: that of which\nastronomy furnishes the most perfect, natural philosophy a somewhat less\nperfect, example, and the employment of which, with the adaptations and\nprecautions required by the subject, is beginning to regenerate\nphysiology.\n\nNor does it admit of doubt, that similar adaptations and precautions are\nindispensable in sociology. In applying to that most complex of all\nstudies what is demonstrably the sole method capable of throwing the light\nof science even upon phenomena of a far inferior degree of complication,\nwe ought to be aware that the same superior complexity which renders the\ninstrument of Deduction more necessary, renders it also more precarious;\nand we must be prepared to meet, by appropriate contrivances, this\nincrease of difficulty.\n\nThe actions and feelings of human beings in the social state, are, no\ndoubt, entirely governed by psychological and ethological laws: whatever\ninfluence any cause exercises upon the social phenomena, it exercises\nthrough those laws. Supposing therefore the laws of human actions and\nfeelings to be sufficiently known, there is no extraordinary difficulty in\ndetermining from those laws, the nature of the social effects which any\ngiven cause tends to produce. But when the question is that of compounding\nseveral tendencies together, and computing the aggregate result of many\nco-existent causes; and especially when, by attempting to predict what\nwill actually occur in a given case, we incur the obligation of estimating\nand compounding the influences of all the causes which happen to exist in\nthat case, we attempt a task to proceed far in which, surpasses the\ncompass of the human faculties.\n\nIf all the resources of science are not sufficient to enable us to\ncalculate, _a priori_, with complete precision, the mutual action of three\nbodies gravitating toward one another, it may be judged with what prospect\nof success we should endeavor to calculate the result of the conflicting\ntendencies which are acting in a thousand different directions and\npromoting a thousand different changes at a given instant in a given\nsociety; although we might and ought to be able, from the laws of human\nnature, to distinguish correctly enough the tendencies themselves, so far\nas they depend on causes accessible to our observation; and to determine\nthe direction which each of them, if acting alone, would impress upon\nsociety, as well as, in a general way at least, to pronounce that some of\nthese tendencies are more powerful than others.\n\nBut, without dissembling the necessary imperfections of the _a priori_\nmethod when applied to such a subject, neither ought we, on the other\nhand; to exaggerate them. The same objections which apply to the Method of\nDeduction in this its most difficult employment, apply to it, as we\nformerly showed,(276) in its easiest; and would even there have been\ninsuperable, if there had not existed, as was then fully explained, an\nappropriate remedy. This remedy consists in the process which, under the\nname of Verification, we have characterized as the third essential\nconstituent part of the Deductive Method; that of collating the\nconclusions of the ratiocination either with the concrete phenomena\nthemselves, or, when such are obtainable, with their empirical laws. The\nground of confidence in any concrete deductive science is not the _a\npriori_ reasoning itself, but the accordance between its results and those\nof observation _a posteriori_. Either of these processes, apart from the\nother, diminishes in value as the subject increases in complication, and\nthis is in so rapid a ratio as soon to become entirely worthless; but the\nreliance to be placed in the concurrence of the two sorts of evidence, not\nonly does not diminish in any thing like the same proportion, but is not\nnecessarily much diminished at all. Nothing more results than a\ndisturbance in the order of precedency of the two processes, sometimes\namounting to its actual inversion: insomuch that instead of deducing our\nconclusions by reasoning, and verifying them by observation, we in some\ncases begin by obtaining them provisionally from specific experience, and\nafterward connect them with the principles of human nature by _a priori_\nreasonings, which reasonings are thus a real Verification.\n\nThe only thinker who, with a competent knowledge of scientific methods in\ngeneral, has attempted to characterize the Method of Sociology, M. Comte,\nconsiders this inverse order as inseparably inherent in the nature of\nsociological speculation. He looks upon the social science as essentially\nconsisting of generalizations from history, verified, not originally\nsuggested, by deduction from the laws of human nature. Though there is a\ntruth contained in this opinion, of which I shall presently endeavor to\nshow the importance, I can not but think that this truth is enunciated in\ntoo unlimited a manner, and that there is considerable scope in\nsociological inquiry for the direct, as well as for the inverse, Deductive\nMethod.\n\nIt will, in fact, be shown in the next chapter, that there is a kind of\nsociological inquiries to which, from their prodigious complication, the\nmethod of direct deduction is altogether inapplicable, while by a happy\ncompensation it is precisely in these cases that we are able to obtain the\nbest empirical laws: to these inquiries, therefore, the Inverse Method is\nexclusively adapted. But there are also, as will presently appear, other\ncases in which it is impossible to obtain from direct observation any\nthing worthy the name of an empirical law; and it fortunately happens that\nthese are the very cases in which the Direct Method is least affected by\nthe objection which undoubtedly must always affect it in a certain degree.\n\nWe shall begin, then, by looking at the Social Science as a science of\ndirect Deduction, and considering what can be accomplished in it, and\nunder what limitations, by that mode of investigation. We shall, then, in\na separate chapter, examine and endeavor to characterize the inverse\nprocess.\n\n\u00a7 2. It is evident, in the first place, that Sociology, considered as a\nsystem of deductions _a priori_, can not be a science of positive\npredictions, but only of tendencies. We may be able to conclude, from the\nlaws of human nature applied to the circumstances of a given state of\nsociety, that a particular cause will operate in a certain manner unless\ncounteracted; but we can never be assured to what extent or amount it will\nso operate, or affirm with certainty that it will not be counteracted;\nbecause we can seldom know, even approximately, all the agencies which may\nco-exist with it, and still less calculate the \u201ccollective result\u201d of so\nmany combined elements. The remark, however, must here be once more\nrepeated, that knowledge insufficient for prediction may be most valuable\nfor guidance. It is not necessary for the wise conduct of the affairs of\nsociety, no more than of any one\u2019s private concerns, that we should be\nable to foresee infallibly the results of what we do. We must seek our\nobjects by means which may perhaps be defeated, and take precautions\nagainst dangers which possibly may never be realized. The aim of practical\npolitics is to surround any given society with the greatest possible\nnumber of circumstances of which the tendencies are beneficial, and to\nremove or counteract, as far as practicable, those of which the tendencies\nare injurious. A knowledge of the tendencies only, though without the\npower of accurately predicting their conjunct result, gives us to a\nconsiderable extent this power.\n\nIt would, however, be an error to suppose that even with respect to\ntendencies we could arrive in this manner at any great number of\npropositions which will be true in all societies without exception. Such a\nsupposition would be inconsistent with the eminently modifiable nature of\nthe social phenomena, and the multitude and variety of the circumstances\nby which they are modified\u2014circumstances never the same, or even nearly\nthe same, in two different societies, or in two different periods of the\nsame society. This would not be so serious an obstacle if, though the\ncauses acting upon society in general are numerous, those which influence\nany one feature of society were limited in number; for we might then\ninsulate any particular social phenomenon, and investigate its laws\nwithout disturbance from the rest. But the truth is the very opposite of\nthis. Whatever affects, in an appreciable degree, any one element of the\nsocial state, affects through it all the other elements. The mode of\nproduction of all social phenomena is one great case of Intermixture of\nLaws. We can never either understand in theory or command in practice the\ncondition of a society in any one respect, without taking into\nconsideration its condition in all other respects. There is no social\nphenomenon which is not more or less influenced by every other part of the\ncondition of the same society, and therefore by every cause which is\ninfluencing any other of the contemporaneous social phenomena. There is,\nin short, what physiologists term a _consensus_, similar to that existing\namong the various organs and functions of the physical frame of man and\nthe more perfect animals; and constituting one of the many analogies which\nhave rendered universal such expressions as the \u201cbody politic\u201d and \u201cbody\nnatural.\u201d It follows from this _consensus_, that unless two societies\ncould be alike in all the circumstances which surround and influence them\n(which would imply their being alike in their previous history), no\nportion whatever of the phenomena will, unless by accident, precisely\ncorrespond; no one cause will produce exactly the same effects in both.\nEvery cause, as its effect spreads through society, comes somewhere in\ncontact with different sets of agencies, and thus has its effects on some\nof the social phenomena differently modified; and these differences, by\ntheir reaction, produce a difference even in those of the effects which\nwould otherwise have been the same. We can never, therefore, affirm with\ncertainty that a cause which has a particular tendency in one people or in\none age will have exactly the same tendency in another, without referring\nback to our premises, and performing over again for the second age or\nnation, that analysis of the whole of its influencing circumstances which\nwe had already performed for the first. The deductive science of society\nwill not lay down a theorem, asserting in a universal manner the effect of\nany cause; but will rather teach us how to frame the proper theorem for\nthe circumstances of any given case. It will not give the laws of society\nin general, but the means of determining the phenomena of any given\nsociety from the particular elements or data of that society.\n\nAll the general propositions which can be framed by the deductive science,\nare therefore, in the strictest sense of the word, hypothetical. They are\ngrounded on some suppositious set of circumstances, and declare how some\ngiven cause would operate in those circumstances, supposing that no others\nwere combined with them. If the set of circumstances supposed have been\ncopied from those of any existing society, the conclusions will be true of\nthat society, provided, and in as far as, the effect of those\ncircumstances shall not be modified by others which have not been taken\ninto the account. If we desire a nearer approach to concrete truth, we can\nonly aim at it by taking, or endeavoring to take, a greater number of\nindividualizing circumstances into the computation.\n\nConsidering, however, in how accelerating a ratio the uncertainty of our\nconclusions increases as we attempt to take the effect of a greater number\nof concurrent causes into our calculations, the hypothetical combinations\nof circumstances on which we construct the general theorems of the\nscience, can not be made very complex, without so rapidly accumulating a\nliability to error as must soon deprive our conclusions of all value. This\nmode of inquiry, considered as a means of obtaining general propositions,\nmust, therefore, on pain of frivolity, be limited to those classes of\nsocial facts which, though influenced like the rest by all sociological\nagents, are under the _immediate_ influence, principally at least, of a\nfew only.\n\n\u00a7 3. Notwithstanding the universal _consensus_ of the social phenomena,\nwhereby nothing which takes place in any part of the operations of society\nis without its share of influence on every other part; and notwithstanding\nthe paramount ascendancy which the general state of civilization and\nsocial progress in any given society must hence exercise over all the\npartial and subordinate phenomena; it is not the less true that different\nspecies of social facts are in the main dependent, immediately and in the\nfirst resort, on different kinds of causes; and therefore not only may\nwith advantage, but must, be studied apart: just as in the natural body we\nstudy separately the physiology and pathology of each of the principal\norgans and tissues, though every one is acted upon by the state of all the\nothers; and though the peculiar constitution and general state of health\nof the organism co-operates with, and often preponderates over, the local\ncauses, in determining the state of any particular organ.\n\nOn these considerations is grounded the existence of distinct and\nseparate, though not independent, branches or departments of sociological\nspeculation.\n\nThere is, for example, one large class of social phenomena in which the\nimmediately determining causes are principally those which act through the\ndesire of wealth, and in which the psychological law mainly concerned is\nthe familiar one, that a greater gain is preferred to a smaller. I mean,\nof course, that portion of the phenomena of society which emanate from the\nindustrial, or productive, operations of mankind; and from those of their\nacts through which the distribution of the products of those industrial\noperations takes place, in so far as not effected by force, or modified by\nvoluntary gift. By reasoning from that one law of human nature, and from\nthe principal outward circumstances (whether universal or confined to\nparticular states of society) which operate upon the human mind through\nthat law, we may be enabled to explain and predict this portion of the\nphenomena of society, so far as they depend on that class of circumstances\nonly; overlooking the influence of any other of the circumstances of\nsociety; and therefore neither tracing back the circumstances which we do\ntake into account, to their possible origin in some other facts in the\nsocial state, nor making allowance for the manner in which any of those\nother circumstances may interfere with, and counteract or modify, the\neffect of the former. A department of science may thus be constructed,\nwhich has received the name of Political Economy.\n\nThe motive which suggests the separation of this portion of the social\nphenomena from the rest, and the creation of a distinct branch of science\nrelating to them is\u2014that they do _mainly_ depend, at least in the first\nresort, on one class of circumstances only; and that even when other\ncircumstances interfere, the ascertainment of the effect due to the one\nclass of circumstances alone, is a sufficiently intricate and difficult\nbusiness to make it expedient to perform it once for all, and then allow\nfor the effect of the modifying circumstances; especially as certain fixed\ncombinations of the former are apt to recur often, in conjunction with\never-varying circumstances of the latter class.\n\nPolitical Economy, as I have said on another occasion, concerns itself\nonly with \u201csuch of the phenomena of the social state as take place in\nconsequence of the pursuit of wealth. It makes entire abstraction of every\nother human passion or motive; except those which may be regarded as\nperpetually antagonizing principles to the desire of wealth, namely,\naversion to labor, and desire of the present enjoyment of costly\nindulgences. These it takes, to a certain extent, into its calculations,\nbecause these do not merely, like our other desires, occasionally conflict\nwith the pursuit of wealth, but accompany it always as a drag or\nimpediment, and are therefore inseparably mixed up in the consideration of\nit. Political Economy considers mankind as occupied solely in acquiring\nand consuming wealth; and aims at showing what is the course of action\ninto which mankind, living in a state of society, would be impelled, if\nthat motive, except in the degree in which it is checked by the two\nperpetual counter-motives above adverted to, were absolute ruler of all\ntheir actions. Under the influence of this desire, it shows mankind\naccumulating wealth, and employing that wealth in the production of other\nwealth; sanctioning by mutual agreement the institution of property;\nestablishing laws to prevent individuals from encroaching upon the\nproperty of others by force or fraud; adopting various contrivances for\nincreasing the productiveness of their labor; settling the division of the\nproduce by agreement, under the influence of competition (competition\nitself being governed by certain laws, which laws are therefore the\nultimate regulators of the division of the produce); and employing certain\nexpedients (as money, credit, etc.) to facilitate the distribution. All\nthese operations, though many of them are really the result of a plurality\nof motives, are considered by political economy as flowing solely from the\ndesire of wealth. The science then proceeds to investigate the laws which\ngovern these several operations, under the supposition that man is a being\nwho is determined, by the necessity of his nature, to prefer a greater\nportion of wealth to a smaller, in all cases, without any other exception\nthan that constituted by the two counter-motives already specified. Not\nthat any political economist was ever so absurd as to suppose that mankind\nare really thus constituted, but because this is the mode in which science\nmust necessarily proceed. When an effect depends on a concurrence of\ncauses, these causes must be studied one at a time, and their laws\nseparately investigated, if we wish, through the causes, to obtain the\npower of either predicting or controlling the effect; since the law of the\neffect is compounded of the laws of all the causes which determine it. The\nlaw of the centripetal and that of the projectile force must have been\nknown, before the motions of the earth and planets could be explained, or\nmany of them predicted. The same is the case with the conduct of man in\nsociety. In order to judge how he will act under the variety of desires\nand aversions which are concurrently operating upon him, we must know how\nhe would act under the exclusive influence of each one in particular.\nThere is, perhaps, no action of a man\u2019s life in which he is neither under\nthe immediate nor under the remote influence of any impulse but the mere\ndesire of wealth. With respect to those parts of human conduct of which\nwealth is not even the principal object, to these political economy does\nnot pretend that its conclusions are applicable. But there are also\ncertain departments of human affairs, in which the acquisition of wealth\nis the main and acknowledged end. It is only of these that political\neconomy takes notice. The manner in which it necessarily proceeds is that\nof treating the main and acknowledged end as if it were the sole end;\nwhich, of all hypotheses equally simple, is the nearest to the truth. The\npolitical economist inquires, what are the actions which would be produced\nby this desire, if within the departments in question it were unimpeded by\nany other. In this way a nearer approximation is obtained than would\notherwise be practicable to the real order of human affairs in those\ndepartments. This approximation has then to be corrected by making proper\nallowance for the effects of any impulses of a different description,\nwhich can be shown to interfere with the result in any particular case.\nOnly in a few of the most striking cases (such as the important one of the\nprinciple of population) are these corrections interpolated into the\nexpositions of political economy itself; the strictness of purely\nscientific arrangement being thereby somewhat departed from, for the sake\nof practical utility. So far as it is known, or may be presumed, that the\nconduct of mankind in the pursuit of wealth is under the collateral\ninfluence of any other of the properties of our nature than the desire of\nobtaining the greatest quantity of wealth with the least labor and\nself-denial, the conclusions of political economy will so far fail of\nbeing applicable to the explanation or prediction of real events, until\nthey are modified by a correct allowance for the degree of influence\nexercised by the other cause.\u201d(277)\n\nExtensive and important practical guidance may be derived, in any given\nstate of society, from general propositions such as those above indicated;\neven though the modifying influence of the miscellaneous causes which the\ntheory does not take into account, as well as the effect of the general\nsocial changes in progress, be provisionally overlooked. And though it has\nbeen a very common error of political economists to draw conclusions from\nthe elements of one state of society, and apply them to other states in\nwhich many of the elements are not the same, it is even then not\ndifficult, by tracing back the demonstrations, and introducing the new\npremises in their proper places, to make the same general course of\nargument which served for the one case, serve for the others too.\n\nFor example, it has been greatly the custom of English political\neconomists to discuss the laws of the distribution of the produce of\nindustry, on a supposition which is scarcely realized anywhere out of\nEngland and Scotland, namely, that the produce is \u201cshared among three\nclasses, altogether distinct from one another, laborers, capitalists, and\nlandlords; and that all these are free agents, permitted in law and in\nfact to set upon their labor, their capital, and their land, whatever\nprice they are able to get for it. The conclusions of the science, being\nall adapted to a society thus constituted, require to be revised whenever\nthey are applied to any other. They are inapplicable where the only\ncapitalists are the landlords, and the laborers are their property, as in\nslave countries. They are inapplicable where the almost universal landlord\nis the state, as in India. They are inapplicable where the agricultural\nlaborer is generally the owner both of the land itself and of the capital,\nas frequently in France, or of the capital only, as in Ireland.\u201d But\nthough it may often be very justly objected to the existing race of\npolitical economists \u201cthat they attempt to construct a permanent fabric\nout of transitory materials; that they take for granted the immutability\nof arrangements of society, many of which are in their nature fluctuating\nor progressive, and enunciate with as little qualification as if they were\nuniversal and absolute truths, propositions which are perhaps applicable\nto no state of society except the particular one in which the writer\nhappened to live;\u201d this does not take away the value of the propositions,\nconsidered with reference to the state of society from which they were\ndrawn. And even as applicable to other states of society, \u201cit must not be\nsupposed that the science is so incomplete and unsatisfactory as this\nmight seem to prove. Though many of its conclusions are only locally true,\nits method of investigation is applicable universally; and as whoever has\nsolved a certain number of algebraic equations, can without difficulty\nsolve all others of the same kind, so whoever knows the political economy\nof England, or even of Yorkshire, knows that of all nations, actual or\npossible, provided he have good sense enough not to expect the same\nconclusion to issue from varying premises.\u201d Whoever has mastered with the\ndegree of precision which is attainable the laws which, under free\ncompetition, determine the rent, profits, and wages, received by\nlandlords, capitalists, and laborers, in a state of society in which the\nthree classes are completely separate, will have no difficulty in\ndetermining the very different laws which regulate the distribution of the\nproduce among the classes interested in it in any of the states of\ncultivation and landed property set forth in the foregoing extract.(278)\n\n\u00a7 4. I would not here undertake to decide what other hypothetical or\nabstract sciences similar to Political Economy, may admit of being carved\nout of the general body of the social science; what other portions of the\nsocial phenomena are in a sufficiently close and complete dependence, in\nthe first resort, on a peculiar class of causes, to make it convenient to\ncreate a preliminary science of those causes; postponing the consideration\nof the causes which act through them, or in concurrence with them, to a\nlater period of the inquiry. There is, however, among these separate\ndepartments one which can not be passed over in silence, being of a more\ncomprehensive and commanding character than any of the other branches into\nwhich the social science may admit of being divided. Like them, it is\ndirectly conversant with the causes of only one class of social facts, but\na class which exercises, immediately or remotely, a paramount influence\nover the test. I allude to what may be termed Political Ethology, or the\ntheory of the causes which determine the type of character belonging to a\npeople or to an age. Of all the subordinate branches of the social\nscience, this is the most completely in its infancy. The causes of\nnational character are scarcely at all understood, and the effect of\ninstitutions or social arrangements upon the character of the people is\ngenerally that portion of their effects which is least attended to, and\nleast comprehended. Nor is this wonderful, when we consider the infant\nstate of the science of Ethology itself, from whence the laws must be\ndrawn, of which the truths of political ethology can be but results and\nexemplifications.\n\nYet, to whoever well considers the matter, it must appear that the laws of\nnational (or collective) character are by far the most important class of\nsociological laws. In the first place, the character which is formed by\nany state of social circumstances is in itself the most interesting\nphenomenon which that state of society can possibly present. Secondly, it\nis also a fact which enters largely into the production of all the other\nphenomena. And above all, the character, that is, the opinions, feelings,\nand habits, of the people, though greatly the results of the state of\nsociety which precedes them, are also greatly the causes of the state of\nsociety which follows them; and are the power by which all those of the\ncircumstances of society which are artificial, laws and customs for\ninstance, are altogether moulded: customs evidently, laws no less really,\neither by the direct influence of public sentiment upon the ruling powers,\nor by the effect which the state of national opinion and feeling has in\ndetermining the form of government and shaping the character of the\ngovernors.\n\nAs might be expected, the most imperfect part of those branches of social\ninquiry which have been cultivated as separate sciences, is the theory of\nthe manner in which their conclusions are affected by ethological\nconsiderations. The omission is no defect in them as abstract or\nhypothetical sciences, but it vitiates them in their practical application\nas branches of a comprehensive social science. In political economy, for\ninstance, empirical laws of human nature are tacitly assumed by English\nthinkers, which are calculated only for Great Britain and the United\nStates. Among other things, an intensity of competition is constantly\nsupposed, which, as a general mercantile fact, exists in no country in the\nworld except those two. An English political economist, like his\ncountrymen in general, has seldom learned that it is possible that men, in\nconducting the business of selling their goods over a counter, should care\nmore about their ease or their vanity than about their pecuniary gain. Yet\nthose who know the habits of the continent of Europe are aware how\napparently small a motive often outweighs the desire of money getting,\neven in the operations which have money getting for their direct object.\nThe more highly the science of ethology is cultivated, and the better the\ndiversities of individual and national character are understood, the\nsmaller, probably, will the number of propositions become, which it will\nbe considered safe to build on as universal principles of human nature.\n\nThese considerations show that the process of dividing off the social\nscience into compartments, in order that each may be studied separately,\nand its conclusions afterward corrected for practice by the modifications\nsupplied by the others, must be subject to at least one important\nlimitation. Those portions alone of the social phenomena can with\nadvantage be made the subjects, even provisionally, of distinct branches\nof science, into which the diversities of character between different\nnations or different times enter as influencing causes only in a secondary\ndegree. Those phenomena, on the contrary, with which the influences of the\nethological state of the people are mixed up at every step (so that the\nconnection of effects and causes can not be even rudely marked out without\ntaking those influences into consideration) could not with any advantage,\nnor without great disadvantage, be treated independently of political\nethology, nor, therefore, of all the circumstances by which the qualities\nof a people are influenced. For this reason (as well as for others which\nwill hereafter appear) there can be no separate Science of Government;\nthat being the fact which, of all others, is most mixed up, both as cause\nand effect, with the qualities of the particular people or of the\nparticular age. All questions respecting the tendencies of forms of\ngovernment must stand part of the general science of society, not of any\nseparate branch of it.\n\nThis general Science of Society, as distinguished from the separate\ndepartments of the science (each of which asserts its conclusions only\nconditionally, subject to the paramount control of the laws of the general\nscience) now remains to be characterized. And as will be shown presently,\nnothing of a really scientific character is here possible, except by the\ninverse deductive method. But before we quit the subject of those\nsociological speculations which proceed by way of direct deduction, we\nmust examine in what relation they stand to that indispensable element in\nall deductive sciences, Verification by Specific Experience\u2014comparison\nbetween the conclusions of reasoning and the results of observation.\n\n\u00a7 5. We have seen that, in most deductive sciences, and among the rest in\nEthology itself, which is the immediate foundation of the Social Science,\na preliminary work of preparation is performed on the observed facts, to\nfit them for being rapidly and accurately collated (sometimes even for\nbeing collated at all) with the conclusions of theory. This preparatory\ntreatment consists in finding general propositions which express concisely\nwhat is common to large classes of observed facts; and these are called\nthe empirical laws of the phenomena. We have, therefore, to inquire,\nwhether any similar preparatory process can be performed on the facts of\nthe social science; whether there are any empirical laws in history or\nstatistics.\n\nIn statistics, it is evident that empirical laws may sometimes be traced;\nand the tracing them forms an important part of that system of indirect\nobservation on which we must often rely for the data of the Deductive\nScience. The process of the science consists in inferring effects from\ntheir causes; but we have often no means of observing the causes, except\nthrough the medium of their effects. In such cases the deductive science\nis unable to predict the effects, for want of the necessary data; it can\ndetermine what causes are capable of producing any given effect, but not\nwith what frequency and in what quantities those causes exist. An instance\nin point is afforded by a newspaper now lying before me. A statement was\nfurnished by one of the official assignees in bankruptcy showing among the\nvarious bankruptcies which it had been his duty to investigate, in how\nmany cases the losses had been caused by misconduct of different kinds,\nand in how many by unavoidable misfortunes. The result was, that the\nnumber of failures caused by misconduct greatly preponderated over those\narising from all other causes whatever. Nothing but specific experience\ncould have given sufficient ground for a conclusion to this purport. To\ncollect, therefore, such empirical laws (which are never more than\napproximate generalizations) from direct observation, is an important part\nof the process of sociological inquiry.\n\nThe experimental process is not here to be regarded as a distinct road to\nthe truth, but as a means (happening accidentally to be the only, or the\nbest, available) for obtaining the necessary data for the deductive\nscience. When the immediate causes of social facts are not open to direct\nobservation, the empirical law of the effects gives us the empirical law\n(which in that case is all that we can obtain) of the causes likewise. But\nthose immediate causes depend on remote causes; and the empirical law,\nobtained by this indirect mode of observation, can only be relied on as\napplicable to unobserved cases, so long as there is reason to think that\nno change has taken place in any of the remote causes on which the\nimmediate causes depend. In making use, therefore, of even the best\nstatistical generalizations for the purpose of inferring (though it be\nonly conjecturally) that the same empirical laws will hold in any new\ncase, it is necessary that we be well acquainted with the remoter causes,\nin order that we may avoid applying the empirical law to cases which\ndiffer in any of the circumstances on which the truth of the law\nultimately depends. And thus, even where conclusions derived from specific\nobservation are available for practical inferences in new cases, it is\nnecessary that the deductive science should stand sentinel over the whole\nprocess; that it should be constantly referred to, and its sanction\nobtained to every inference.\n\nThe same thing holds true of all generalizations which can be grounded on\nhistory. Not only there are such generalizations, but it will presently be\nshown that the general science of society, which inquires into the laws of\nsuccession and co-existence of the great facts constituting the state of\nsociety and civilization at any time, can proceed in no other manner than\nby making such generalizations\u2014afterward to be confirmed by connecting\nthem with the psychological and ethological laws on which they must really\ndepend.\n\n\u00a7 6. But (reserving this question for its proper place) in those more\nspecial inquiries which form the subject of the separate branches of the\nsocial science, this twofold logical process and reciprocal verification\nis not possible; specific experience affords nothing amounting to\nempirical laws. This is particularly the case where the object is to\ndetermine the effect of any one social cause among a great number acting\nsimultaneously; the effect, for example, of corn laws, or of a prohibitive\ncommercial system generally. Though it may be perfectly certain, from\ntheory, what _kind_ of effects corn laws must produce, and in what general\ndirection their influence must tell upon industrial prosperity, their\neffect is yet of necessity so much disguised by the similar or contrary\neffects of other influencing agents, that specific experience can at most\nonly show that on the average of some great number of instances, the cases\nwhere there were corn laws exhibited the effect in a greater degree than\nthose where there were not. Now the number of instances necessary to\nexhaust the whole round of combinations of the various influential\ncircumstances, and thus afford a fair average, never can be obtained. Not\nonly we can never learn with sufficient authenticity the facts of so many\ninstances, but the world itself does not afford them in sufficient\nnumbers, within the limits of the given state of society and civilization\nwhich such inquiries always presuppose. Having thus no previous empirical\ngeneralizations with which to collate the conclusions of theory, the only\nmode of direct verification which remains is to compare those conclusions\nwith the result of an individual experiment or instance. But here the\ndifficulty is equally great. For in order to verify a theory by an\nexperiment, the circumstances of the experiment must be exactly the same\nwith those contemplated in the theory. But in social phenomena the\ncircumstances of no two cases are exactly alike. A trial of corn laws in\nanother country, or in a former generation, would go a very little way\ntoward verifying a conclusion drawn respecting their effect in this\ngeneration and in this country. It thus happens, in most cases, that the\nonly individual instance really fitted to verify the predictions of theory\nis the very instance for which the predictions were made; and the\nverification comes too late to be of any avail for practical guidance.\n\nAlthough, however, direct verification is impossible, there is an indirect\nverification, which is scarcely of less value, and which is always\npracticable. The conclusion drawn as to the individual case can only be\ndirectly verified in that case; but it is verified indirectly, by the\nverification of other conclusions, drawn in other individual cases from\nthe same laws. The experience which comes too late to verify the\nparticular proposition to which it refers, is not too late to help toward\nverifying the general sufficiency of the theory. The test of the degree in\nwhich the science affords safe ground for predicting (and consequently for\npractically dealing with) what has not yet happened, is the degree in\nwhich it would have enabled us to predict what has actually occurred.\nBefore our theory of the influence of a particular cause, in a given state\nof circumstances, can be entirely trusted, we must be able to explain and\naccount for the existing state of all that portion of the social phenomena\nwhich that cause has a tendency to influence. If, for instance, we would\napply our speculations in political economy to the prediction or guidance\nof the phenomena of any country, we must be able to explain all the\nmercantile or industrial facts of a general character, appertaining to the\npresent state of that country; to point out causes sufficient to account\nfor all of them, and prove, or show good ground for supposing, that these\ncauses have really existed. If we can not do this, it is a proof either\nthat the facts which ought to be taken into account are not yet completely\nknown to us, or that although we know the facts, we are not masters of a\nsufficiently perfect theory to enable us to assign their consequences. In\neither case we are not, in the present state of our knowledge, fully\ncompetent to draw conclusions, speculative or practical, for that country.\nIn like manner, if we would attempt to judge of the effect which any\npolitical institution would have, supposing that it could be introduced\ninto any given country, we must be able to show that the existing state of\nthe practical government of that country, and of whatever else depends\nthereon, together with the particular character and tendencies of the\npeople, and their state in respect to the various elements of social\nwell-being, are such as the institutions they have lived under, in\nconjunction with the other circumstances of their nature or of their\nposition, were calculated to produce.\n\nTo prove, in short, that our science, and our knowledge of the particular\ncase, render us competent to predict the future, we must show that they\nwould have enabled us to predict the present and the past. If there be any\nthing which we could not have predicted, this constitutes a residual\nphenomenon, requiring further study for the purpose of explanation; and we\nmust either search among the circumstances of the particular case until we\nfind one which, on the principles of our existing theory, accounts for the\nunexplained phenomenon, or we must turn back, and seek the explanation by\nan extension and improvement of the theory itself.\n\n\n\n\n                                Chapter X.\n\n\nOf The Inverse Deductive, Or Historical, Method.\n\n\n\u00a7 1. There are two kinds of sociological inquiry. In the first kind, the\nquestion proposed is, what effect will follow from a given cause, a\ncertain general condition of social circumstances being presupposed. As,\nfor example, what would be the effect of imposing or of repealing corn\nlaws, of abolishing monarchy or introducing universal suffrage, in the\npresent condition of society and civilization in any European country, or\nunder any other given supposition with regard to the circumstances of\nsociety in general, without reference to the changes which might take\nplace, or which may already be in progress, in those circumstances. But\nthere is also a second inquiry, namely, what are the laws which determine\nthose general circumstances themselves. In this last the question is, not\nwhat will be the effect of a given cause in a certain state of society,\nbut what are the causes which produce, and the phenomena which\ncharacterize, states of society generally. In the solution of this\nquestion consists the general Science of Society; by which the conclusions\nof the other and more special kind of inquiry must be limited and\ncontrolled.\n\n\u00a7 2. In order to conceive correctly the scope of this general science, and\ndistinguish it from the subordinate departments of sociological\nspeculation, it is necessary to fix the ideas attached to the phrase, \u201cA\nState of Society.\u201d What is called a state of society, is the simultaneous\nstate of all the greater social facts or phenomena. Such are: the degree\nof knowledge, and of intellectual and moral culture, existing in the\ncommunity, and in every class of it; the state of industry, of wealth and\nits distribution; the habitual occupations of the community; their\ndivision into classes, and the relations of those classes to one another;\nthe common beliefs which they entertain on all the subjects most important\nto mankind, and the degree of assurance with which those beliefs are held;\ntheir tastes, and the character and degree of their \u00e6sthetic development;\ntheir form of government, and the more important of their laws and\ncustoms. The condition of all these things, and of many more which will\nreadily suggest themselves, constitute the state of society, or the state\nof civilization, at any given time.\n\nWhen states of society, and the causes which produce them, are spoken of\nas a subject of science, it is implied that there exists a natural\ncorrelation among these different elements; that not every variety of\ncombination of these general social facts is possible, but only certain\ncombinations; that, in short, there exist Uniformities of Co-existence\nbetween the states of the various social phenomena. And such is the truth;\nas is indeed a necessary consequence of the influence exercised by every\none of those phenomena over every other. It is a fact implied in the\n_consensus_ of the various parts of the social body.\n\nStates of society are like different constitutions or different ages in\nthe physical frame; they are conditions not of one or a few organs or\nfunctions, but of the whole organism. Accordingly, the information which\nwe possess respecting past ages, and respecting the various states of\nsociety now existing in different regions of the earth, does, when duly\nanalyzed, exhibit uniformities. It is found that when one of the features\nof society is in a particular state, a state of many other features, more\nor less precisely determinate, always or usually co-exists with it.\n\nBut the uniformities of co-existence obtaining among phenomena which are\neffects of causes, must (as we have so often observed) be corollaries from\nthe laws of causation by which these phenomena are really determined. The\nmutual correlation between the different elements of each state of\nsociety, is, therefore, a derivative law, resulting from the laws which\nregulate the succession between one state of society and another; for the\nproximate cause of every state of society is the state of society\nimmediately preceding it. The fundamental problem, therefore, of the\nsocial science, is to find the laws according to which any state of\nsociety produces the state which succeeds it and takes its place. This\nopens the great and vexed question of the progressiveness of man and\nsociety; an idea involved in every just conception of social phenomena as\nthe subject of a science.\n\n\u00a7 3. It is one of the characters, not absolutely peculiar to the sciences\nof human nature and society, but belonging to them in a peculiar degree,\nto be conversant with a subject-matter whose properties are changeable. I\ndo not mean changeable from day to day, but from age to age; so that not\nonly the qualities of individuals vary, but those of the majority are not\nthe same in one age as in another.\n\nThe principal cause of this peculiarity is the extensive and constant\nreaction of the effects upon their causes. The circumstances in which\nmankind are placed, operating according to their own laws and to the laws\nof human nature, form the characters of the human beings; but the human\nbeings, in their turn, mould and shape the circumstances for themselves\nand for those who come after them. From this reciprocal action there must\nnecessarily result either a cycle or a progress. In astronomy also, every\nfact is at once effect and cause; the successive positions of the various\nheavenly bodies produce changes both in the direction and in the intensity\nof the forces by which those positions are determined. But in the case of\nthe solar system, these mutual actions bring around again, after a certain\nnumber of changes, the former state of circumstances; which, of course,\nleads to the perpetual recurrence of the same series in an unvarying\norder. Those bodies, in short, revolve in orbits: but there are (or,\nconformably to the laws of astronomy, there might be) others which,\ninstead of an orbit, describe a trajectory\u2014a course not returning into\nitself. One or other of these must be the type to which human affairs must\nconform.\n\nOne of the thinkers who earliest conceived the succession of historical\nevents as subject to fixed laws, and endeavored to discover these laws by\nan analytical survey of history, Vico, the celebrated author of the\n_Scienza Nuova_, adopted the former of these opinions. He conceived the\nphenomena of human society as revolving in an orbit; as going through\nperiodically the same series of changes. Though there were not wanting\ncircumstances tending to give some plausibility to this view, it would not\nbear a close scrutiny: and those who have succeeded Vico in this kind of\nspeculations have universally adopted the idea of a trajectory or\nprogress, in lieu of an orbit or cycle.\n\nThe words Progress and Progressiveness are not here to be understood as\nsynonymous with improvement and tendency to improvement. It is conceivable\nthat the laws of human nature might determine, and even necessitate, a\ncertain series of changes in man and society, which might not in every\ncase, or which might not on the whole, be improvements. It is my belief,\nindeed, that the general tendency is, and will continue to be, saving\noccasional and temporary exceptions, one of improvement; a tendency toward\na better and happier state. This, however, is not a question of the method\nof the social science, but a theorem of the science itself. For our\npurpose it is sufficient that there is a progressive change both in the\ncharacter of the human race and in their outward circumstances, so far as\nmoulded by themselves; that in each successive age the principal phenomena\nof society are different from what they were in the age preceding, and\nstill more different from any previous age: the periods which most\ndistinctly mark these successive changes being intervals of one\ngeneration, during which a new set of human beings have been educated,\nhave grown up from childhood, and taken possession of society.\n\nThe progressiveness of the human race is the foundation on which a method\nof philosophizing in the social science has been of late years erected,\nfar superior to either of the two modes which had previously been\nprevalent, the chemical or experimental, and the geometrical modes. This\nmethod, which is now generally adopted by the most advanced thinkers on\nthe Continent, consists in attempting, by a study and analysis of the\ngeneral facts of history, to discover (what these philosophers term) the\nlaw of progress: which law, once ascertained, must according to them\nenable us to predict future events, just as after a few terms of an\ninfinite series in algebra we are able to detect the principle, of\nregularity in their formation, and to predict the rest of the series to\nany number of terms we please. The principal aim of historical speculation\nin France, of late years, has been to ascertain this law. But while I\ngladly acknowledge the great services which have been rendered to\nhistorical knowledge by this school, I can not but deem them to be mostly\nchargeable with a fundamental misconception of the true method of social\nphilosophy. The misconception consists in supposing that the order of\nsuccession which we may be able to trace among the different states of\nsociety and civilization which history presents to us, even if that order\nwere more rigidly uniform than it has yet been proved to be, could ever\namount to a law of nature. It can only be an empirical law. The succession\nof states of the human mind and of human society can not have an\nindependent law of its own; it must depend on the psychological and\nethological laws which govern the action of circumstances on men and of\nmen on circumstances. It is conceivable that those laws might be such, and\nthe general circumstances of the human race such, as to determine the\nsuccessive transformations of man and society to one given and unvarying\norder. But even if the case were so, it can not be the ultimate aim of\nscience to discover an empirical law. Until that law could be connected\nwith the psychological and ethological laws on which it must depend, and,\nby the consilience of deduction _a priori_ with historical evidence, could\nbe converted from an empirical law into a scientific one, it could not be\nrelied on for the prediction of future events, beyond, at most, strictly\nadjacent cases. M. Comte alone, among the new historical school, has seen\nthe necessity of thus connecting all our generalizations from history with\nthe laws of human nature.\n\n\u00a7 4. But, while it is an imperative rule never to introduce any\ngeneralization from history into the social science unless sufficient\ngrounds can be pointed out for it in human nature, I do not think any one\nwill contend that it would have been possible, setting out from the\nprinciples of human nature and from the general circumstances of the\nposition of our species, to determine _a priori_ the order in which human\ndevelopment must take place, and to predict, consequently, the general\nfacts of history up to the present time. After the first few terms of the\nseries, the influence exercised, over each generation by the generations\nwhich preceded it, becomes, (as is well observed by the writer last\nreferred to) more and more preponderant over all other influences; until\nat length what we now are and do, is in a very small degree the result of\nthe universal circumstances of the human race, or even of our own\ncircumstances acting through the original qualities of our species, but\nmainly of the qualities produced in us by the whole previous history of\nhumanity. So long a series of actions and reactions between Circumstances\nand Man, each successive term being composed of an ever greater number and\nvariety of parts, could not possibly be computed by human faculties from\nthe elementary laws which produce it. The mere length of the series would\nbe a sufficient obstacle, since a slight error in any one of the terms\nwould augment in rapid progression at every subsequent step.\n\nIf, therefore, the series of the effects themselves did not, when examined\nas a whole, manifest any regularity, we should in vain attempt to\nconstruct a general science of society. We must in that case have\ncontented ourselves with that subordinate order of sociological\nspeculation formerly noticed, namely, with endeavoring to ascertain what\nwould be the effect of the introduction of any new cause, in a state of\nsociety supposed to be fixed\u2014a knowledge sufficient for the more common\nexigencies of daily political practice, but liable to fail in all cases in\nwhich the progressive movement of society is one of the influencing\nelements; and therefore more precarious in proportion as the case is more\nimportant. But since both the natural varieties of mankind, and the\noriginal diversities of local circumstances, are much less considerable\nthan the points of agreement, there will naturally be a certain degree of\nuniformity in the progressive development of the species and of its works.\nAnd this uniformity tends to become greater, not less, as society\nadvances; since the evolution of each people, which is at first determined\nexclusively by the nature and circumstances of that people, is gradually\nbrought under the influence (which becomes stronger as civilization\nadvances) of the other nations of the earth, and of the circumstances by\nwhich they have been influenced. History accordingly does, when\njudiciously examined, afford Empirical Laws of Society. And the problem of\ngeneral sociology is to ascertain these, and connect them with the laws of\nhuman nature, by deductions showing that such were the derivative laws\nnaturally to be expected as the consequences of those ultimate ones.\n\nIt is, indeed, hardly ever possible, even after history has suggested the\nderivative law, to demonstrate _a priori_ that such was the only order of\nsuccession or of co-existence in which the effects could, consistently\nwith the laws of human nature, have been produced. We can at most make out\nthat there were strong _a priori_ reasons for expecting it, and that no\nother order of succession or co-existence would have been so likely to\nresult from the nature of man and the general circumstances of his\nposition. Often we can not do even this; we can not even show that what\ndid take place was probable _a priori_, but only that it was possible.\nThis, however\u2014which, in the Inverse Deductive Method that we are now\ncharacterizing, is a real process of verification\u2014is as indispensable, as\nverification by specific experience has been shown to be, where the\nconclusion is originally obtained by the direct way of deduction. The\nempirical laws must be the result of but a few instances, since few\nnations have ever attained at all, and still fewer by their own\nindependent development, a high stage of social progress. If, therefore,\neven one or two of these few instances be insufficiently known, or\nimperfectly analyzed into their elements, and therefore not adequately\ncompared with other instances, nothing is more probable than that a wrong\nempirical law will emerge instead of the right one. Accordingly, the most\nerroneous generalizations are continually made from the course of history;\nnot only in this country, where history can not yet be said to be at all\ncultivated as a science, but in other countries where it is so cultivated,\nand by persons well versed in it. The only check or corrective is,\nconstant verification by psychological and ethological laws. We may add to\nthis, that no one but a person competently skilled in those laws is\ncapable of preparing the materials for historical generalization, by\nanalyzing the facts of history, or even by observing the social phenomena\nof his own time. No other will be aware of the comparative importance of\ndifferent facts, nor consequently know what facts to look for, or to\nobserve; still less will he be capable of estimating the evidence of facts\nwhich, as is the case with most, can not be ascertained by direct\nobservation or learned from testimony, but must be inferred from marks.\n\n\u00a7 5. The Empirical Laws of Society are of two kinds; some are uniformities\nof co-existence, some of succession. According as the science is occupied\nin ascertaining and verifying the former sort of uniformities or the\nlatter, M. Comte gives it the title of Social Statics, or of Social\nDynamics; conformably to the distinction in mechanics between the\nconditions of equilibrium and those of movement; or in biology, between\nthe laws of organization and those of life. The first branch of the\nscience ascertains the conditions of stability in the social union; the\nsecond, the laws of progress. Social Dynamics is the theory of Society\nconsidered in a state of progressive movement; while Social Statics is the\ntheory of the _consensus_ already spoken of as existing among the\ndifferent parts of the social organism; in other words, the theory of the\nmutual actions and reactions of contemporaneous social phenomena;\nmaking(279) provisionally, as far as possible, abstraction, for scientific\npurposes, of the fundamental movement which is at all times gradually\nmodifying the whole of them.\n\n\u201cIn this first point of view, the provisions of sociology will enable us\nto infer one from another (subject to ulterior verification by direct\nobservation) the various characteristic marks of each distinct mode of\nsocial existence, in a manner essentially analogous to what is now\nhabitually practiced in the anatomy of the physical body. This preliminary\naspect, therefore, of political science, of necessity supposes that\n(contrary to the existing habits of philosophers) each of the numerous\nelements of the social state, ceasing to be looked at independently and\nabsolutely, shall be always and exclusively considered relatively to all\nthe other elements, with the whole of which it is united by mutual\ninterdependence. It would be superfluous to insist here upon the great and\nconstant utility of this branch of sociological speculation. It is, in the\nfirst place, the indispensable basis of the theory of social progress. It\nmay, moreover, be employed, immediately, and of itself, to supply the\nplace, provisionally at least, of direct observation, which in many cases\nis not always practicable for some of the elements of society, the real\ncondition of which may, however, be sufficiently judged of by means of the\nrelations which connect them with others previously known. The history of\nthe sciences may give us some notion of the habitual importance of this\nauxiliary resource, by reminding us, for example, how the vulgar errors of\nmere erudition concerning the pretended acquirements of the ancient\nEgyptians in the higher astronomy were irrevocably dissipated (even before\nsentence had been passed on them by a sounder erudition) from the single\nconsideration of the inevitable connection between the general state of\nastronomy and that of abstract geometry, then evidently in its infancy. It\nwould be easy to cite a multitude of analogous cases, the character of\nwhich could admit of no dispute. In order to avoid exaggeration, however,\nit should be remarked, that these necessary relations among the different\naspects of society can not, from their very nature, be so simple and\nprecise that the results observed could only have arisen from some one\nmode of mutual co-ordination. Such a notion, already too narrow in the\nscience of life, would be completely at variance with the still more\ncomplex nature of sociological speculations. But the exact estimation of\nthese limits of variation, both in the healthy and in the morbid state,\nconstitutes, at least as much as in the anatomy of the natural body, an\nindispensable complement to every theory of Sociological Statics; without\nwhich the indirect exploration above spoken of would often lead into\nerror.\n\n\u201cThis is not the place for methodically demonstrating the existence of a\nnecessary relation among all the possible aspects of the same social\norganism; a point on which, in principle at least, there is now little\ndifference of opinion among sound thinkers. From whichever of the social\nelements we choose to set out, we may easily recognize that it has always\na connection, more or less immediate, with all the other elements, even\nwith those which at first sight appear the most independent of it. The\ndynamical consideration of the progressive development of civilized\nhumanity, affords, no doubt, a still more efficacious means of effecting\nthis interesting verification of the _consensus_ of the social phenomena,\nby displaying the manner in which every change in any one part, operates\nimmediately, or very speedily, upon all the rest. But this indication may\nbe preceded, or at all events followed, by a confirmation of a purely\nstatical kind; for, in politics as in mechanics, the communication of\nmotion from one object to another proves a connection between them.\nWithout descending to the minute interdependence of the different branches\nof any one science or art, is it not evident that among the different\nsciences, as well as among most of the arts, there exists such a\nconnection, that if the state of any one well-marked division of them is\nsufficiently known to us, we can with real scientific assurance infer,\nfrom their necessary correlation, the contemporaneous state of every one\nof the others? By a further extension of this consideration, we may\nconceive the necessary relation which exists between the condition of the\nsciences in general and that of the arts in general, except that the\nmutual dependence is less intense in proportion as it is more indirect.\nThe same is the case, when, instead of considering the aggregate of the\nsocial phenomena in some one people, we examine it simultaneously in\ndifferent contemporaneous nations; between which the perpetual reciprocity\nof influence, especially in modern times, can not be contested, though the\n_consensus_ must in this case be ordinarily of a less decided character,\nand must decrease gradually with the affinity of the cases and the\nmultiplicity of the points of contact, so as at last, in some cases, to\ndisappear almost entirely; as for, example, between Western Europe and\nEastern Asia, of which the various general states of society appear to\nhave been hitherto almost independent of one another.\u201d\n\nThese remarks are followed by illustrations of one of the most important,\nand until lately, most neglected, of the general principles which, in this\ndivision of the social science, may be considered as established; namely,\nthe necessary correlation between the form of government existing in any\nsociety and the contemporaneous state of civilization: a natural law which\nstamps the endless discussions and innumerable theories respecting forms\nof government in the abstract, as fruitless and worthless, for any other\npurpose than as a preparatory treatment of materials to be afterward used\nfor the construction of a better philosophy.\n\nAs already remarked, one of the main results of the science of social\nstatics would be to ascertain the requisites of stable political union.\nThere are some circumstances which, being found in all societies without\nexception, and in the greatest degree where the social union is most\ncomplete, may be considered (when psychological and ethological laws\nconfirm the indication) as conditions of the existence of the complex\nphenomena called a State. For example, no numerous society has ever been\nheld together without laws, or usages equivalent to them; without\ntribunals, and an organized force of some sort to execute their decisions.\nThere have always been public authorities whom, with more or less\nstrictness and in cases more or less accurately defined, the rest of the\ncommunity obeyed, or according to general opinion were bound to obey. By\nfollowing out this course of inquiry we shall find a number of requisites,\nwhich have been present in every society that has maintained a collective\nexistence, and on the cessation of which it has either merged in some\nother society, or reconstructed itself on some new basis, in which the\nconditions were conformed to. Although these results, obtained by\ncomparing different forms and states of society, amount in themselves only\nto empirical laws; some of them, when once suggested, are found to follow\nwith so much probability from general laws of human nature, that the\nconsilience of the two processes raises the evidence to proof, and the\ngeneralizations to the rank of scientific truths.\n\nThis seems to be affirmable (for instance) of the conclusions arrived at\nin the following passage, extracted, with some alterations, from a\ncriticism on the negative philosophy of the eighteenth century,(280) and\nwhich I quote, though (as in some former instances) from myself, because I\nhave no better way of illustrating the conception I have formed of the\nkind of theorems of which sociological statics would consist.\n\n\u201cThe very first element of the social union, obedience to a government of\nsome sort, has not been found so easy a thing to establish in the world.\nAmong a timid and spiritless race like the inhabitants of the vast plains\nof tropical countries, passive obedience may be of natural growth; though\neven there we doubt whether it has ever been found among any people with\nwhom fatalism, or in other words, submission to the pressure of\ncircumstances as a divine decree, did not prevail as a religious doctrine.\nBut the difficulty of inducing a brave and warlike race to submit their\nindividual _arbitrium_ to any common umpire, has always been felt to be so\ngreat, that nothing short of supernatural power has been deemed adequate\nto overcome it; and such tribes have always assigned to the first\ninstitution of civil society a divine origin. So differently did those\njudge who knew savage men by actual experience, from those who had no\nacquaintance with them except in the civilized state. In modern Europe\nitself, after the fall of the Roman empire, to subdue the feudal anarchy\nand bring the whole people of any European nation into subjection to\ngovernment (though Christianity in the most concentrated form of its\ninfluence was co-operating in the work) required thrice as many centuries\nas have elapsed since that time.\n\n\u201cNow if these philosophers had known human nature under any other type\nthan that of their own age, and of the particular classes of society among\nwhom they lived, it would have occurred to them, that wherever this\nhabitual submission to law and government has been firmly and durably\nestablished, and yet the vigor and manliness of character which resisted\nits establishment have been in any degree preserved, certain requisites\nhave existed, certain conditions have been fulfilled, of which the\nfollowing may be regarded as the principal.\n\n\u201cFirst: there has existed, for all who were accounted citizens\u2014for all who\nwere not slaves, kept down by brute force\u2014a system of _education_,\nbeginning with infancy and continued through life, of which whatever else\nit might include, one main and incessant ingredient was _restraining\ndiscipline_. To train the human being in the habit, and thence the power,\nof subordinating his personal impulses and aims to what were considered\nthe ends of society; of adhering, against all temptation, to the course of\nconduct which those ends prescribed; of controlling in himself all\nfeelings which were liable to militate against those ends, and encouraging\nall such as tended toward them; this was the purpose, to which every\noutward motive that the authority directing the system could command, and\nevery inward power or principle which its knowledge of human nature\nenabled it to evoke, were endeavored to be rendered instrumental. The\nentire civil and military policy of the ancient commonwealths was such a\nsystem of training; in modern nations its place has been attempted to be\nsupplied, principally, by religious teaching. And whenever and in\nproportion as the strictness of the restraining discipline was relaxed,\nthe natural tendency of mankind to anarchy re-asserted itself; the state\nbecame disorganized from within; mutual conflict for selfish ends,\nneutralized the energies which were required to keep up the contest\nagainst natural causes of evil; and the nation, after a longer or briefer\ninterval of progressive decline, became either the slave of a despotism,\nor the prey of a foreign invader.\n\n\u201cThe second condition of permanent political society has been found to be,\nthe existence, in some form or other, of the feeling of allegiance or\nloyalty. This feeling may vary in its objects, and is not confined to any\nparticular form of government; but whether in a democracy or in a\nmonarchy, its essence is always the same; viz., that there be in the\nconstitution of the state _something_ which is settled, something\npermanent, and not to be called in question; something which, by general\nagreement, has a right to be where it is, and to be secure against\ndisturbance, whatever else may change. This feeling may attach itself, as\namong the Jews (and in most of the commonwealths of antiquity), to a\ncommon God or gods, the protectors and guardians of their state. Or it may\nattach itself to certain persons, who are deemed to be, whether by divine\nappointment, by long prescription, or by the general recognition of their\nsuperior capacity and worthiness, the rightful guides and guardians of the\nrest. Or it may connect itself with laws; with ancient liberties or\nordinances. Or, finally, (and this is the only shape in which the feeling\nis likely to exist hereafter), it may attach itself to the principles of\nindividual freedom and political and social equality, as realized in\ninstitutions which as yet exist nowhere, or exist only in a rudimentary\nstate. But in all political societies which have had a durable existence,\nthere has been some fixed point: something which people agreed in holding\nsacred; which, wherever freedom of discussion was a recognized principle,\nit was of course lawful to contest in theory, but which no one could\neither fear or hope to see shaken in practice; which, in short (except\nperhaps during some temporary crisis), was in the common estimation placed\nbeyond discussion. And the necessity of this may easily be made evident. A\nstate never is, nor until mankind are vastly improved, can hope to be, for\nany long time exempt from internal dissension; for there neither is nor\nhas ever been any state of society in which collisions did not occur\nbetween the immediate interests and passions of powerful sections of the\npeople. What, then, enables nations to weather these storms, and pass\nthrough turbulent times without any permanent weakening of the securities\nfor peaceable existence? Precisely this\u2014that however important the\ninterests about which men fell out, the conflict did not affect the\nfundamental principle of the system of social union which happened to\nexist; nor threaten large portions of the community with the subversion of\nthat on which they had built their calculations, and with which their\nhopes and aims had become identified. But when the questioning of these\nfundamental principles is (not the occasional disease, or salutary\nmedicine, but) the habitual condition of the body politic, and when all\nthe violent animosities are called forth, which spring naturally from such\na situation, the state is virtually in a position of civil war; and can\nnever long remain free from it in act and fact.\n\n\u201cThe third essential condition of stability in political society, is a\nstrong and active principle of cohesion among the members of the same\ncommunity or state. We need scarcely say that we do not mean nationality,\nin the vulgar sense of the term; a senseless antipathy to foreigners;\nindifference to the general welfare of the human race, or an unjust\npreference of the supposed interests of our own country; a cherishing of\nbad peculiarities because they are national, or a refusal to adopt what\nhas been found good by other countries. We mean a principle of sympathy,\nnot of hostility; of union, not of separation. We mean a feeling of common\ninterest among those who live under the same government, and are contained\nwithin the same natural or historical boundaries. We mean, that one part\nof the community do not consider themselves as foreigners with regard to\nanother part; that they set a value on their connection\u2014feel that they are\none people, that their lot is cast together, that evil to any of their\nfellow-countrymen is evil to themselves, and do not desire selfishly to\nfree themselves from their share of any common inconvenience by severing\nthe connection. How strong this feeling was in those ancient commonwealths\nwhich attained any durable greatness, every one knows. How happily Rome,\nin spite of all her tyranny, succeeded in establishing the feeling of a\ncommon country among the provinces of her vast and divided empire, will\nappear when any one who has given due attention to the subject shall take\nthe trouble to point it out. In modern times the countries which have had\nthat feeling in the strongest degree have been the most powerful\ncountries: England, France, and, in proportion to their territory and\nresources, Holland and Switzerland; while England in her connection with\nIreland is one of the most signal examples of the consequences of its\nabsence. Every Italian knows why Italy is under a foreign yoke; every\nGerman knows what maintains despotism in the Austrian empire;(281) the\nevils of Spain flow as much from the absence of nationality among the\nSpaniards themselves, as from the presence of it in their relations with\nforeigners: while the completest illustration of all is afforded by the\nrepublics of South America, where the parts of one and the same state\nadhere so slightly together, that no sooner does any province think itself\naggrieved by the general government than it proclaims itself a separate\nnation.\u201d\n\n\u00a7 6. While the derivative laws of social statics are ascertained by\nanalyzing different states of society, and comparing them with one\nanother, without regard to the order of their succession, the\nconsideration of the successive order is, on the contrary, predominant in\nthe study of social dynamics, of which the aim is to observe and explain\nthe sequences of social conditions. This branch of the social science\nwould be as complete as it can be made, if every one of the leading\ngeneral circumstances of each generation were traced to its causes in the\ngeneration immediately preceding. But the _consensus_ is so complete\n(especially in modern history), that in the filiation of one generation\nand another, it is the whole which produces the whole, rather than any\npart a part. Little progress, therefore, can be made in establishing the\nfiliation, directly from laws of human nature, without having first\nascertained the immediate or derivative laws according to which social\nstates generate one another as society advances; the _axiomata media_ of\nGeneral Sociology.\n\nThe empirical laws which are most readily obtained by generalization from\nhistory do not amount to this. They are not the \u201cmiddle principles\u201d\nthemselves, but only evidence toward the establishment of such principles.\nThey consist of certain general tendencies which may be perceived in\nsociety; a progressive increase of some social elements, and diminution of\nothers, or a gradual change in the general character of certain elements.\nIt is easily seen, for instance, that as society advances, mental tend\nmore and more to prevail over bodily qualities, and masses over\nindividuals; that the occupation of all that portion of mankind who are\nnot under external restraint is at first chiefly military, but society\nbecomes progressively more and more engrossed with productive pursuits,\nand the military spirit gradually gives way to the industrial; to which\nmany similar truths might be added. And with generalizations of this\ndescription, ordinary inquirers, even of the historical school now\npredominant on the Continent, are satisfied. But these and all such\nresults are still at too great a distance from the elementary laws of\nhuman nature on which they depend\u2014too many links intervene, and the\nconcurrence of causes at each link is far too complicated\u2014to enable these\npropositions to be presented as direct corollaries from those elementary\nprinciples. They have, therefore, in the minds of most inquirers, remained\nin the state of empirical laws, applicable only within the bounds of\nactual observation; without any means of determining their real limits,\nand of judging whether the changes which have hitherto been in progress\nare destined to continue indefinitely, or to terminate, or even to be\nreversed.\n\n\u00a7 7. In order to obtain better empirical laws, we must not rest satisfied\nwith noting the progressive changes which manifest themselves in the\nseparate elements of society, and in which nothing is indicated but the\nrelation of fragments of the effect to corresponding fragments of the\ncause. It is necessary to combine the statical view of social phenomena\nwith the dynamical, considering not only the progressive changes of the\ndifferent elements, but the contemporaneous condition of each; and thus\nobtain empirically the law of correspondence not only between the\nsimultaneous states, but between the simultaneous changes, of those\nelements. This law of correspondence it is, which, duly verified _a\npriori_, would become the real scientific derivative law of the\ndevelopment of humanity and human affairs.\n\nIn the difficult process of observation and comparison which is here\nrequired, it would evidently be a great assistance if it should happen to\nbe the fact, that some one element in the complex existence of social man\nis pre-eminent over all others as the prime agent of the social movement.\nFor we could then take the progress of that one element as the central\nchain, to each successive link of which, the corresponding links of all\nthe other progressions being appended, the succession of the facts would\nby this alone be presented in a kind of spontaneous order, far more nearly\napproaching to the real order of their filiation than could be obtained by\nany other merely empirical process.\n\nNow, the evidence of history and that of human nature combine, by a\nstriking instance of consilience, to show that there really is one social\nelement which is thus predominant, and almost paramount, among the agents\nof the social progression. This is, the state of the speculative faculties\nof mankind; including the nature of the beliefs which by any means they\nhave arrived at, concerning themselves and the world by which they are\nsurrounded.\n\nIt would be a great error, and one very little likely to be committed, to\nassert that speculation, intellectual activity, the pursuit of truth, is\namong the more powerful propensities of human nature, or holds a\npredominating place in the lives of any, save decidedly exceptional,\nindividuals. But, notwithstanding the relative weakness of this principle\namong other sociological agents, its influence is the main determining\ncause of the social progress; all the other dispositions of our nature\nwhich contribute to that progress being dependent on it for the means of\naccomplishing their share of the work. Thus (to take the most obvious case\nfirst), the impelling force to most of the improvements effected in the\narts of life, is the desire of increased material comfort; but as we can\nonly act upon external objects in proportion to our knowledge of them, the\nstate of knowledge at any time is the limit of the industrial improvements\npossible at that time; and the progress of industry must follow, and\ndepend on, the progress of knowledge. The same thing may be shown to be\ntrue, though it is not quite so obvious, of the progress of the fine arts.\nFurther, as the strongest propensities of uncultivated or half-cultivated\nhuman nature (being the purely selfish ones, and those of a sympathetic\ncharacter which partake most of the nature of selfishness) evidently tend\nin themselves to disunite mankind, not to unite them\u2014to make them rivals,\nnot confederates, social existence is only possible by a disciplining of\nthose more powerful propensities, which consists in subordinating them to\na common system of opinions. The degree of this subordination is the\nmeasure of the completeness of the social union, and the nature of the\ncommon opinions determines its kind. But in order that mankind should\nconform their actions to any set of opinions, these opinions must exist,\nmust be believed by them. And thus, the state of the speculative\nfaculties, the character of the propositions assented to by the intellect,\nessentially determines the moral and political state of the community, as\nwe have already seen that it determines the physical.\n\nThese conclusions, deduced from the laws of human nature, are in entire\naccordance with the general facts of history. Every considerable change\nhistorically known to us in the condition of any portion of mankind, when\nnot brought about by external force, has been preceded by a change, of\nproportional extent, in the state of their knowledge, or in their\nprevalent beliefs. As between any given state of speculation, and the\ncorrelative state of every thing else, it was almost always the former\nwhich first showed itself; though the effects, no doubt, reacted potently\nupon the cause. Every considerable advance in material civilization has\nbeen preceded by an advance in knowledge: and when any great social change\nhas come to pass, either in the way of gradual development or of sudden\nconflict, it has had for its precursor a great change in the opinions and\nmodes of thinking of society. Polytheism, Judaism, Christianity,\nProtestantism, the critical philosophy of modern Europe, and its positive\nscience\u2014each of these has been a primary agent in making society what it\nwas at each successive period, while society was but secondarily\ninstrumental in making _them_, each of them (so far as causes can be\nassigned for its existence) being mainly an emanation not from the\npractical life of the period, but from the previous state of belief and\nthought. The weakness of the speculative propensity in mankind generally\nhas not, therefore, prevented the progress of speculation from governing\nthat of society at large; it has only, and too often, prevented progress\naltogether, where the intellectual progression has come to an early stand\nfor want of sufficiently favorable circumstances.\n\nFrom this accumulated evidence, we are justified in concluding, that the\norder of human progression in all respects will mainly depend on the order\nof progression in the intellectual convictions of mankind, that is, on the\nlaw of the successive transformations of human opinions. The question\nremains, whether this law can be determined; at first from history as an\nempirical law, then converted into a scientific theorem by deducing it _a\npriori_ from the principles of human nature. As the progress of knowledge\nand the changes in the opinions of mankind are very slow, and manifest\nthemselves in a well-defined manner only at long intervals, it can not be\nexpected that the general order of sequence should be discoverable from\nthe examination of less than a very considerable part of the duration of\nthe social progress. It is necessary to take into consideration the whole\nof past time, from the first recorded condition of the human race, to the\nmemorable phenomena of the last and present generations.\n\n\u00a7 8. The investigation which I have thus endeavored to characterize, has\nbeen systematically attempted, up to the present time, by M. Comte alone.\nHis work is hitherto the only known example of the study of social\nphenomena according to this conception of the Historical Method. Without\ndiscussing here the worth of his conclusions, and especially of his\npredictions and recommendations with respect to the Future of society,\nwhich appear to me greatly inferior in value to his appreciation of the\nPast, I shall confine myself to mentioning one important generalization,\nwhich M. Comte regards as the fundamental law of the progress of human\nknowledge. Speculation he conceives to have, on every subject of human\ninquiry, three successive stages; in the first of which it tends to\nexplain the phenomena by supernatural agencies, in the second by\nmetaphysical abstractions, and in the third or final state confines itself\nto ascertaining their laws of succession and similitude. This\ngeneralization appears to me to have that high degree of scientific\nevidence which is derived from the concurrence of the indications of\nhistory with the probabilities derived from the constitution of the human\nmind. Nor could it be easily conceived, from the mere enunciation of such\na proposition, what a flood of light it lets in upon the whole course of\nhistory, when its consequences are traced, by connecting with each of the\nthree states of human intellect which it distinguishes, and with each\nsuccessive modification of those three states, the correlative condition\nof other social phenomena.(282)\n\nBut whatever decision competent judges may pronounce on the results\narrived at by any individual inquirer, the method now characterized is\nthat by which the derivative laws of social order and of social progress\nmust be sought. By its aid we may hereafter succeed not only in looking\nfar forward into the future history of the human race, but in determining\nwhat artificial means may be used, and to what extent, to accelerate the\nnatural progress in so far as it is beneficial; to compensate for whatever\nmay be its inherent inconveniences or disadvantages; and to guard against\nthe dangers or accidents to which our species is exposed from the\nnecessary incidents of its progression. Such practical instructions,\nfounded on the highest branch of speculative sociology, will form the\nnoblest and most beneficial portion of the Political Art.\n\nThat of this science and art even the foundations are but beginning to be\nlaid, is sufficiently evident. But the superior minds are fairly turning\nthemselves toward that object. It has become the aim of really scientific\nthinkers to connect by theories the facts of universal history: it is\nacknowledged to be one of the requisites of a general system of social\ndoctrine, that it should explain, so far as the data exist, the main facts\nof history; and a Philosophy of History is generally admitted to be at\nonce the verification, and the initial form, of the Philosophy of the\nProgress of Society.\n\nIf the endeavors now making in all the more cultivated nations, and\nbeginning to be made even in England (usually the last to enter into the\ngeneral movement of the European mind) for the construction of a\nPhilosophy of History, shall be directed and controlled by those views of\nthe nature of sociological evidence which I have (very briefly and\nimperfectly) attempted to characterize; they can not fail to give birth to\na sociological system widely removed from the vague and conjectural\ncharacter of all former attempts, and worthy to take its place, at last,\namong the sciences. When this time shall come, no important branch of\nhuman affairs will be any longer abandoned to empiricism and unscientific\nsurmise: the circle of human knowledge will be complete, and it can only\nthereafter receive further enlargement by perpetual expansion from within.\n\n\n\n\n                               Chapter XI.\n\n\nAdditional Elucidations Of The Science Of History.\n\n\n\u00a7 1. The doctrine which the preceding chapters were intended to enforce\nand elucidate\u2014that the collective series of social phenomena, in other\nwords the course of history, is subject to general laws, which philosophy\nmay possibly detect\u2014has been familiar for generations to the scientific\nthinkers of the Continent, and has for the last quarter of a century\npassed out of their peculiar domain, into that of newspapers and ordinary\npolitical discussion. In our own country, however, at the time of the\nfirst publication of this Treatise, it was almost a novelty, and the\nprevailing habits of thought on historical subjects were the very reverse\nof a preparation for it. Since then a great change has taken place, and\nhas been eminently promoted by the important work of Mr. Buckle; who, with\ncharacteristic energy, flung down this great principle, together with many\nstriking exemplifications of it, into the arena of popular discussion, to\nbe fought over by a sort of combatants, in the presence of a sort of\nspectators, who would never even have been aware that there existed such a\nprinciple if they had been left to learn its existence from the\nspeculations of pure science. And hence has arisen a considerable amount\nof controversy, tending not only to make the principle rapidly familiar to\nthe majority of cultivated minds, but also to clear it from the confusions\nand misunderstandings by which it was but natural that it should for a\ntime be clouded, and which impair the worth of the doctrine to those who\naccept it, and are the stumbling-block of many who do not.\n\nAmong the impediments to the general acknowledgment, by thoughtful minds,\nof the subjection of historical facts to scientific laws, the most\nfundamental continues to be that which is grounded on the doctrine of Free\nWill, or, in other words, on the denial that the law of invariable\nCausation holds true of human volitions; for if it does not, the course of\nhistory, being the result of human volitions, can not be a subject of\nscientific laws, since the volitions on which it depends can neither be\nforeseen, nor reduced to any canon of regularity even after they have\noccurred. I have discussed this question, as far as seemed suitable to the\noccasion, in a former chapter; and I only think it necessary to repeat,\nthat the doctrine of the Causation of human actions, improperly called the\ndoctrine of Necessity, affirms no mysterious _nexus_, or overruling\nfatality: it asserts only that men\u2019s actions are the joint result of the\ngeneral laws and circumstances of human nature, and of their own\nparticular characters; those characters again being the consequence of the\nnatural and artificial circumstances that constituted their education,\namong which circumstances must be reckoned their own conscious efforts.\nAny one who is willing to take (if the expression may be permitted) the\ntrouble of thinking himself into the doctrine as thus stated, will find\nit, I believe, not only a faithful interpretation of the universal\nexperience of human conduct, but a correct representation of the mode in\nwhich he himself, in every particular case, spontaneously interprets his\nown experience of that conduct.\n\nBut if this principle is true of individual man, it must be true of\ncollective man. If it is the law of human life, the law must be realized\nin history. The experience of human affairs when looked at _en masse_,\nmust be in accordance with it if true, or repugnant to it if false. The\nsupport which this _a posteriori_ verification affords to the law, is the\npart of the case which has been most clearly and triumphantly brought out\nby Mr. Buckle.\n\nThe facts of statistics, since they have been made a subject of careful\nrecordation and study, have yielded conclusions, some of which have been\nvery startling to persons not accustomed to regard moral actions as\nsubject to uniform laws. The very events which in their own nature appear\nmost capricious and uncertain, and which in any individual case no\nattainable degree of knowledge would enable us to foresee, occur, when\nconsiderable numbers are taken into the account, with a degree of\nregularity approaching to mathematical. What act is there which all would\nconsider as more completely dependent on individual character, and on the\nexercise of individual free will, than that of slaying a fellow-creature?\nYet in any large country, the number of murders, in proportion to the\npopulation, varies (it has been found) very little from one year to\nanother, and in its variations never deviates widely from a certain\naverage. What is still more remarkable, there is a similar approach to\nconstancy in the proportion of these murders annually committed with every\nparticular kind of instrument. There is a like approximation to identity,\nas between one year and another, in the comparative number of legitimate\nand of illegitimate births. The same thing is found true of suicides,\naccidents, and all other social phenomena of which the registration is\nsufficiently perfect; one of the most curiously illustrative examples\nbeing the fact, ascertained by the registers of the London and Paris\npost-offices, that the number of letters posted which the writers have\nforgotten to direct, is nearly the same, in proportion to the whole number\nof letters posted, in one year as in another. \u201cYear after year,\u201d says Mr.\nBuckle, \u201cthe same proportion of letter-writers forget this simple act; so\nthat for each successive period we can actually foretell the number of\npersons whose memory will fail them in regard to this trifling, and as it\nmight appear, accidental occurrence.\u201d(283)\n\nThis singular degree of regularity _en masse_, combined with the extreme\nof irregularity in the cases composing the mass, is a felicitous\nverification _a posteriori_ of the law of causation in its application to\nhuman conduct. Assuming the truth of that law, every human action, every\nmurder, for instance, is the concurrent result of two sets of causes. On\nthe one part, the general circumstances of the country and its\ninhabitants; the moral, educational, economical, and other influences\noperating on the whole people, and constituting what we term the state of\ncivilization. On the other part, the great variety of influences special\nto the individual: his temperament, and other peculiarities of\norganization, his parentage, habitual associates, temptations, and so\nforth. If we now take the whole of the instances which occur within a\nsufficiently large field to exhaust all the combinations of these special\ninfluences, or, in other words, to eliminate chance; and if all these\ninstances have occurred within such narrow limits of time, that no\nmaterial change can have taken place in the general influences\nconstituting the state of civilization of the country; we may be certain,\nthat if human actions are governed by invariable laws, the aggregate\nresult will be something like a constant quantity. The number of murders\ncommitted within that space and time, being the effect partly of general\ncauses which have not varied, and partly of partial causes the whole round\nof whose variations has been included, will be, practically speaking,\ninvariable.\n\nLiterally and mathematically invariable it is not, and could not be\nexpected to be: because the period of a year is too short to include _all_\nthe possible combinations of partial causes, while it is, at the same\ntime, sufficiently long to make it probable that in some years at least,\nof every series, there will have been introduced new influences of a more\nor less general character; such as a more vigorous or a more relaxed\npolice; some temporary excitement from political or religious causes; or\nsome incident generally notorious, of a nature to act morbidly on the\nimagination. That in spite of these unavoidable imperfections in the data,\nthere should be so very trifling a margin of variation in the annual\nresults, is a brilliant continuation of the general theory.\n\n\u00a7 2. The same considerations which thus strikingly corroborate the\nevidence of the doctrine, that historical facts are the invariable effects\nof causes, tend equally to clear that doctrine from various\nmisapprehensions, the existence of which has been put in evidence by the\nrecent discussions. Some persons, for instance, seemingly imagine the\ndoctrine to imply, not merely that the total number of murders committed\nin a given space and time is entirely the effect of the general\ncircumstances of society, but that every particular murder is so too\u2014that\nthe individual murderer is, so to speak, a mere instrument in the hands of\ngeneral causes that he himself has no option, or, if he has, and chose to\nexercise it, some one else would be necessitated to take his place; that\nif any one of the actual murderers had abstained from the crime, some\nperson who would otherwise have remained innocent, would have committed an\nextra murder to make up the average. Such a corollary would certainly\nconvict any theory which necessarily led to it of absurdity. It is\nobvious, however, that each particular murder depends, not on the general\nstate of society only, but on that combined with causes special to the\ncase, which are generally much more powerful; and if these special causes,\nwhich have greater influence than the general ones in causing every\nparticular murder, have no influence on the number of murders in a given\nperiod, it is because the field of observation is so extensive as to\ninclude all possible combinations of the special causes\u2014all varieties of\nindividual character and individual temptation compatible with the general\nstate of society. The collective experiment, as it may be termed, exactly\nseparates the effect of the general from that of the special causes, and\nshows the net result of the former; but it declares nothing at all\nrespecting the amount of influence of the special causes, be it greater or\nsmaller, since the scale of the experiment extends to the number of cases\nwithin which the effects of the special causes balance one another, and\ndisappear in that of the general causes.\n\nI will not pretend that all the defenders of the theory have always kept\ntheir language free from this same confusion, and have shown no tendency\nto exalt the influence of general causes at the expense of special. I am\nof opinion, on the contrary, that they have done so in a very great\ndegree, and by so doing have encumbered their theory with difficulties,\nand laid it open to objections, which do not necessarily affect it. Some,\nfor example (among whom is Mr. Buckle himself), have inferred, or allowed\nit to be supposed that they inferred, from the regularity in the\nrecurrence of events which depend on moral qualities, that the moral\nqualities of mankind are little capable of being improved, or are of\nlittle importance in the general progress of society, compared with\nintellectual or economic causes. But to draw this inference is to forget\nthat the statistical tables, from which the invariable averages are\ndeduced, were compiled from facts occurring within narrow geographical\nlimits and in a small number of successive years; that is, from a field\nthe whole of which was under the operation of the same general causes, and\nduring too short a time to allow of much change therein. All moral causes\nbut those common to the country generally, have been eliminated by the\ngreat number of instances taken; and those which are common to the whole\ncountry have not varied considerably, in the short space of time comprised\nin the observations. If we admit the supposition that they have varied; if\nwe compare one age with another, or one country with another, or even one\npart of a country with another, differing in position and character as to\nthe moral elements, the crimes committed within a year give no longer the\nsame, but a widely different numerical aggregate. And this can not but be\nthe case: for, inasmuch as every single crime committed by an individual\nmainly depends on his moral qualities, the crimes committed by the entire\npopulation of the country must depend in an equal degree on their\ncollective moral qualities. To render this element inoperative upon the\nlarge scale, it would be necessary to suppose that the general moral\naverage of mankind does not vary from country to country or from age to\nage; which is not true, and, even if it were true, could not possibly be\nproved by any existing statistics. I do not on this account the less agree\nin the opinion of Mr. Buckle, that the intellectual element in mankind,\nincluding in that expression the nature of their beliefs, the amount of\ntheir knowledge, and the development of their intelligence, is the\npredominant circumstance in determining their progress. But I am of this\nopinion, not because I regard their moral or economical condition either\nas less powerful or less variable agencies, but because these are in a\ngreat degree the consequences of the intellectual condition, and are, in\nall cases, limited by it; as was observed in the preceding chapter. The\nintellectual changes are the most conspicuous agents in history, not from\ntheir superior force, considered in themselves, but because practically\nthey work with the united power belonging to all three.(284)\n\n\u00a7 3. There is another distinction often neglected in the discussion of\nthis subject, which it is extremely important to observe. The theory of\nthe subjection of social progress to invariable laws, is often held in\nconjunction with the doctrine, that social progress can not be materially\ninfluenced by the exertions of individual persons, or by the acts of\ngovernments. But though these opinions are often held by the same persons,\nthey are two very different opinions, and the confusion between them is\nthe eternally recurring error of confounding Causation with Fatalism.\nBecause whatever happens will be the effect of causes, human volitions\namong the rest, it does not follow that volitions, even those of peculiar\nindividuals, are not of great efficacy as causes. If any one in a storm at\nsea, because about the same number of persons in every year perish by\nshipwreck, should conclude that it was useless for him to attempt to save\nhis own life, we should call him a Fatalist; and should remind him that\nthe efforts of shipwrecked persons to save their lives are so far from\nbeing immaterial, that the average amount of those efforts is one of the\ncauses on which the ascertained annual number of deaths by shipwreck\ndepend. However universal the laws of social development may be, they can\nnot be more universal or more rigorous than those of the physical agencies\nof nature; yet human will can convert these into instruments of its\ndesigns, and the extent to which it does so makes the chief difference\nbetween savages and the most highly civilized people. Human and social\nfacts, from their more complicated nature, are not less, but more,\nmodifiable than mechanical and chemical facts; human agency, therefore,\nhas still greater power over them. And accordingly, those who maintain\nthat the evolution of society depends exclusively, or almost exclusively,\non general causes, always include among these the collective knowledge and\nintellectual development of the race. But if of the race, why not also of\nsome powerful monarch or thinker, or of the ruling portion of some\npolitical society, acting through its government? Though the varieties of\ncharacter among ordinary individuals neutralize one another on any large\nscale, exceptional individuals in important positions do not in any given\nage neutralize one another; there was not another Themistocles, or Luther,\nor Julius C\u00e6sar, of equal powers and contrary dispositions, who exactly\nbalanced the given Themistocles, Luther, and C\u00e6sar, and prevented them\nfrom having any permanent effect. Moreover, for aught that appears, the\nvolitions of exceptional persons, or the opinions and purposes of the\nindividuals who at some particular time compose a government, may be\nindispensable links in the chain of causation by which even the general\ncauses produce their effects; and I believe this to be the only tenable\nform of the theory.\n\nLord Macaulay, in a celebrated passage of one of his early essays (let me\nadd that it was one which he did not himself choose to reprint), gives\nexpression to the doctrine of the absolute inoperativeness of great men,\nmore unqualified, I should think, than has been given to it by any writer\nof equal abilities. He compares them to persons who merely stand on a\nloftier height, and thence receive the sun\u2019s rays a little earlier, than\nthe rest of the human race. \u201cThe sun illuminates the hills while it is\nstill below the horizon, and truth is discovered by the highest minds a\nlittle before it becomes manifest to the multitude. This is the extent of\ntheir superiority. They are the first to catch and reflect a light which,\nwithout their assistance, must in a short time be visible to those who lie\nfar beneath them.\u201d(285) If this metaphor is to be carried out, it follows\nthat if there had been no Newton, the world would not only have had the\nNewtonian system, but would have had it equally soon; as the sun would\nhave risen just as early to spectators in the plain if there had been no\nmountain at hand to catch still earlier rays. And so it would be, if\ntruths, like the sun, rose by their own proper motion, without human\neffort; but not otherwise. I believe that if Newton had not lived, the\nworld must have waited for the Newtonian philosophy until there had been\nanother Newton, or his equivalent. No ordinary man, and no succession of\nordinary men, could have achieved it. I will not go the length of saying\nthat what Newton did in a single life, might not have been done in\nsuccessive steps by some of those who followed him, each singly inferior\nto him in genius. But even the least of those steps required a man of\ngreat intellectual superiority. Eminent men do not merely see the coming\nlight from the hill-top, they mount on the hill-top and evoke it; and if\nno one had ever ascended thither, the light, in many cases, might never\nhave risen upon the plain at all. Philosophy and religion are abundantly\namenable to general causes; yet few will doubt that, had there been no\nSocrates, no Plato, and no Aristotle, there would have been no philosophy\nfor the next two thousand years, nor in all probability then; and that if\nthere had been no Christ, and no St. Paul, there would have been no\nChristianity.\n\nThe point in which, above all, the influence of remarkable individuals is\ndecisive, is in determining the celerity of the movement. In most states\nof society it is the existence of great men which decides even whether\nthere shall be any progress. It is conceivable that Greece, or that\nChristian Europe, might have been progressive in certain periods of their\nhistory through general causes only: but if there had been no Mohammed,\nwould Arabia have produced Avicenna or Averroes, or Caliphs of Bagdad or\nof Cordova? In determining, however, in what manner and order the progress\nof mankind shall take place if it take place at all, much less depends on\nthe character of individuals. There is a sort of necessity established in\nthis respect by the general laws of human nature\u2014by the constitution of\nthe human mind. Certain truths can not be discovered, nor inventions made,\nunless certain others have been made first; certain social improvements,\nfrom the nature of the case, can only follow, and not precede, others. The\norder of human progress, therefore, may to a certain extent have definite\nlaws assigned to it: while as to its celerity, or even as to its taking\nplace at all, no generalization, extending to the human species generally,\ncan possibly be made; but only some very precarious approximate\ngeneralizations, confined to the small portion of mankind in whom there\nhas been any thing like consecutive progress within the historical period,\nand deduced from their special position, or collected from their\nparticular history. Even looking to the _manner_ of progress, the order of\nsuccession of social states, there is need of great flexibility in our\ngeneralizations. The limits of variation in the possible development of\nsocial, as of animal life, are a subject of which little is yet\nunderstood, and are one of the great problems in social science. It is, at\nall events, a fact, that different portions of mankind, under the\ninfluence of different circumstances, have developed themselves in a more\nor less different manner and into different forms; and among these\ndetermining circumstances, the individual character of their great\nspeculative thinkers or practical organizers may well have been one. Who\ncan tell how profoundly the whole subsequent history of China may have\nbeen influenced by the individuality of Confucius? and of Sparta (and\nhence of Greece and the world) by that of Lycurgus?\n\nConcerning the nature and extent of what a great man under favorable\ncircumstances can do for mankind, as well as of what a government can do\nfor a nation, many different opinions are possible; and every shade of\nopinion on these points is consistent with the fullest recognition that\nthere are invariable laws of historical phenomena. Of course the degree of\ninfluence which has to be assigned to these more special agencies, makes a\ngreat difference in the precision which can be given to the general laws,\nand in the confidence with which predictions can be grounded on them.\nWhatever depends on the peculiarities of individuals, combined with the\naccident of the positions they hold, is necessarily incapable of being\nforeseen. Undoubtedly these casual combinations might be eliminated like\nany others, by taking a sufficiently large cycle: the peculiarities of a\ngreat historical character make their influence felt in history sometimes\nfor several thousand years, but it is highly probable that they will make\nno difference at all at the end of fifty millions. Since, however, we can\nnot obtain an average of the vast length of time necessary to exhaust all\nthe possible combinations of great men and circumstances, as much of the\nlaw of evolution of human affairs as depends upon this average, is and\nremains inaccessible to us; and within the next thousand years, which are\nof considerably more importance to us than the whole remainder of the\nfifty millions, the favorable and unfavorable combinations which will\noccur will be to us purely accidental. We can not foresee the advent of\ngreat men. Those who introduce new speculative thoughts or great practical\nconceptions into the world, can not have their epoch fixed beforehand.\nWhat science can do, is this. It can trace through past history the\ngeneral causes which had brought mankind into that preliminary state\nwhich, when the right sort of great man appeared, rendered them accessible\nto his influence. If this state continues, experience renders it tolerably\ncertain that in a longer or shorter period the great man will be produced;\nprovided that the general circumstances of the country and people are\n(which very often they are not) compatible with his existence; of which\npoint also, science can in some measure judge. It is in this manner that\nthe results of progress, except as to the celerity of their production,\ncan be, to a certain extent, reduced to regularity and law. And the belief\nthat they can be so, is equally consistent with assigning very great, or\nvery little efficacy, to the influence of exceptional men, or of the acts\nof governments. And the same may be said of all other accidents and\ndisturbing causes.\n\n\u00a7 4. It would nevertheless be a great error to assign only a trifling\nimportance to the agency of eminent individuals, or of governments. It\nmust not be concluded that the influence of either is small, because they\ncan not bestow what the general circumstances of society, and the course\nof its previous history, have not prepared it to receive. Neither thinkers\nnor governments effect all that they intend, but in compensation they\noften produce important results which they did not in the least foresee.\nGreat men, and great actions, are seldom wasted; they send forth a\nthousand unseen influences, more effective than those which are seen; and\nthough nine out of every ten things done, with a good purpose, by those\nwho are in advance of their age, produce no material effect, the tenth\nthing produces effects twenty times as great as any one would have dreamed\nof predicting from it. Even the men who for want of sufficiently favorable\ncircumstances left no impress at all upon their own age, have often been\nof the greatest value to posterity. Who could appear to have lived more\nentirely in vain than some of the early heretics? They were burned or\nmassacred, their writings extirpated, their memory anathematized, and\ntheir very names and existence left for seven or eight centuries in the\nobscurity of musty manuscripts\u2014their history to be gathered, perhaps, only\nfrom the sentences by which they were condemned. Yet the memory of these\nmen\u2014men who resisted certain pretensions or certain dogmas of the Church\nin the very age in which the unanimous assent of Christendom was afterward\nclaimed as having been given to them, and asserted as the ground of their\nauthority\u2014broke the chain of tradition, established a series of precedents\nfor resistance, inspired later Reformers with the courage, and armed them\nwith the weapons, which they needed when mankind were better prepared to\nfollow their impulse. To this example from men, let us add another from\ngovernments. The comparatively enlightened rule of which Spain had the\nbenefit during a considerable part of the eighteenth century, did not\ncorrect the fundamental defects of the Spanish people; and in consequence,\nthough it did great temporary good, so much of that good perished with it,\nthat it may plausibly be affirmed to have had no permanent effect. The\ncase has been cited as a proof how little governments can do in opposition\nto the causes which have determined the general character of the nation.\nIt does show how much there is which they can not do; but not that they\ncan do nothing. Compare what Spain was at the beginning of that\nhalf-century of liberal government, with what she had become at its close.\nThat period fairly let in the light of European thought upon the more\neducated classes; and it never afterward ceased to go on spreading.\nPrevious to that time the change was in an inverse direction; culture,\nlight, intellectual and even material activity, were becoming\nextinguished. Was it nothing to arrest this downward and convert it into\nan upward course? How much that Charles the Third and Aranda could not do,\nhas been the ultimate consequence of what they did! To that half-century\nSpain owes that she has got rid of the Inquisition, that she has got rid\nof the monks, that she now has parliaments and (save in exceptional\nintervals) a free press, and the feelings of freedom and citizenship, and\nis acquiring railroads and all the other constituents of material and\neconomical progress. In the Spain which preceded that era, there was not a\nsingle element at work which could have led to these results in any length\nof time, if the country had continued to be governed as it was by the last\nprinces of the Austrian dynasty, or if the Bourbon rulers had been from\nthe first what, both in Spain and in Naples, they afterward became.\n\nAnd if a government can do much, even when it seems to have done little,\nin causing positive improvement, still greater are the issues dependent on\nit in the way of warding off evils, both internal and external, which else\nwould stop improvement altogether. A good or a bad counselor, in a single\ncity at a particular crisis, has affected the whole subsequent fate of the\nworld. It is as certain as any contingent judgment respecting historical\nevents can be, that if there had been no Themistocles there would have\nbeen no victory of Salamis; and had there not, where would have been all\nour civilization? How different, again, would have been the issue if\nEpaminondas, or Timoleon, or even Iphicrates, instead of Chares and\nLysicles, had commanded at Ch\u00e6roneia. As is well said in the second of two\nEssays on the Study of History,(286) in my judgment the soundest and most\nphilosophical productions which the recent controversies on this subject\nhave called forth, historical science authorizes not absolute, but only\nconditional predictions. General causes count for much, but individuals\nalso \u201cproduce great changes in history, and color its whole complexion\nlong after their death.... No one can doubt that the Roman republic would\nhave subsided into a military despotism if Julius C\u00e6sar had never lived\u201d\n(thus much was rendered practically certain by general causes); \u201cbut is it\nat all clear that in that case Gaul would ever have formed a province of\nthe empire? Might not Varus have lost his three legions on the banks of\nthe Rhone? and might not that river have become the frontier instead of\nthe Rhine? This might well have happened if C\u00e6sar and Crassus had changed\nprovinces; and it is surely impossible to say that in such an event the\nvenue (as lawyers say) of European civilization might not have been\nchanged. The Norman Conquest in the same way was as much the act of a\nsingle man, as the writing of a newspaper article; and knowing as we do\nthe history of that man and his family, we can retrospectively predict\nwith all but infallible certainty, that no other person\u201d (no other in that\nage, I presume, is meant) \u201ccould have accomplished the enterprise. If it\nhad not been accomplished, is there any ground to suppose that either our\nhistory or our national character would have been what they are?\u201d\n\nAs is most truly remarked by the same writer, the whole stream of Grecian\nhistory, as cleared up by Mr. Grote, is one series of examples how often\nevents on which the whole destiny of subsequent civilization turned, were\ndependent on the personal character for good or evil of some one\nindividual. It must be said, however, that Greece furnishes the most\nextreme example of this nature to be found in history, and is a very\nexaggerated specimen of the general tendency. It has happened only that\nonce, and will probably never happen again, that the fortunes of mankind\ndepended upon keeping a certain order of things in existence in a single\ntown, or a country scarcely larger than Yorkshire; capable of being ruined\nor saved by a hundred causes, of very slight magnitude in comparison with\nthe general tendencies of human affairs. Neither ordinary accidents, nor\nthe characters of individuals, can ever again be so vitally important as\nthey then were. The longer our species lasts, and the more civilized it\nbecomes, the more, as Comte remarks, does the influence of past\ngenerations over the present, and of mankind _en masse_ over every\nindividual in it, predominate over other forces; and though the course of\naffairs never ceases to be susceptible of alteration both by accidents and\nby personal qualities, the increasing preponderance of the collective\nagency of the species over all minor causes, is constantly bringing the\ngeneral evolution of the race into something which deviates less from a\ncertain and preappointed track. Historical science, therefore, is always\nbecoming more possible; not solely because it is better studied, but\nbecause, in every generation, it becomes better adapted for study.\n\n\n\n\n                               Chapter XII.\n\n\nOf The Logic Of Practice, Or Art; Including Morality And Policy.\n\n\n\u00a7 1. In the preceding chapters we have endeavored to characterize the\npresent state of those among the branches of knowledge called Moral, which\nare sciences in the only proper sense of the term, that is, inquiries into\nthe course of nature. It is customary, however, to include under the term\nmoral knowledge, and even (though improperly) under that of moral science,\nan inquiry the results of which do not express themselves in the\nindicative, but in the imperative mood, or in periphrases equivalent to\nit; what is called the knowledge of duties; practical ethics, or morality.\n\nNow, the imperative mood is the characteristic of art, as distinguished\nfrom science. Whatever speaks in rules, or precepts, not in assertions\nrespecting matters of fact, is art; and ethics, or morality, is properly a\nportion of the art corresponding to the sciences of human nature and\nsociety.(287)\n\nThe Method, therefore, of Ethics, can be no other than that of Art, or\nPractice, in general; and the portion yet uncompleted of the task which we\nproposed to ourselves in the concluding Book, is to characterize the\ngeneral Method of Art, as distinguished from Science.\n\n\u00a7 2. In all branches of practical business there are cases in which\nindividuals are bound to conform their practice to a pre-established rule,\nwhile there are others in which it is part of their task to find or\nconstruct the rule by which they are to govern their conduct. The first,\nfor example, is the case of a judge, under a definite written code. The\njudge is not called upon to determine what course would be intrinsically\nthe most advisable in the particular case in hand, but only within what\nrule of law it falls; what the legislature has ordained to be done in the\nkind of case, and must therefore be presumed to have intended in the\nindividual case. The method must here be wholly and exclusively one of\nratiocination, or syllogism; and the process is obviously, what in our\nanalysis of the syllogism we showed that all ratiocination is, namely the\ninterpretation of a formula.\n\nIn order that our illustration of the opposite case may be taken from the\nsame class of subjects as the former, we will suppose, in contrast with\nthe situation of the judge, the position of the legislator. As the judge\nhas laws for his guidance, so the legislator has rules, and maxims of\npolicy; but it would be a manifest error to suppose that the legislator is\nbound by these maxims in the same manner as the judge is bound by the\nlaws, and that all he has to do is to argue down from them to the\nparticular case, as the judge does from the laws. The legislator is bound\nto take into consideration the reasons or grounds of the maxim; the judge\nhas nothing to do with those of the law, except so far as a consideration\nof them may throw light upon the intention of the law-maker, where his\nwords have left it doubtful. To the judge, the rule, once positively\nascertained, is final; but the legislator, or other practitioner, who goes\nby rules rather than by their reasons, like the old-fashioned German\ntacticians who were vanquished by Napoleon, or the physician who preferred\nthat his patients should die by rule rather than recover contrary to it,\nis rightly judged to be a mere pedant, and the slave of his formulas.\n\nNow, the reasons of a maxim of policy, or of any other rule of art, can be\nno other than the theorems of the corresponding science.\n\nThe relation in which rules of art stand to doctrines of science may be\nthus characterized. The art proposes to itself an end to be attained,\ndefines the end, and hands it over to the science. The science receives\nit, considers it as a phenomenon or effect to be studied, and having\ninvestigated its causes and conditions, sends it back to art with a\ntheorem of the combination of circumstances by which it could be produced.\nArt then examines these combinations of circumstances, and according as\nany of them are or are not in human power, pronounces the end attainable\nor not. The only one of the premises, therefore, which Art supplies, is\nthe original major premise, which asserts that the attainment of the given\nend is desirable. Science then lends to Art the proposition (obtained by a\nseries of inductions or of deductions) that the performance of certain\nactions will attain the end. From these premises Art concludes that the\nperformance of these actions is desirable, and finding it also\npracticable, converts the theorem into a rule or precept.\n\n\u00a7 3. It deserves particular notice, that the theorem or speculative truth\nis not ripe for being turned into a precept, until the whole, and not a\npart merely, of the operation which belongs to science, has been\nperformed. Suppose that we have completed the scientific process only up\nto a certain point; have discovered that a particular cause will produce\nthe desired effect, but have not ascertained all the negative conditions\nwhich are necessary, that is, all the circumstances which, if present,\nwould prevent its production. If, in this imperfect state of the\nscientific theory, we attempt to frame a rule of art, we perform that\noperation prematurely. Whenever any counteracting cause, overlooked by the\ntheorem, takes place, the rule will be at fault; we shall employ the means\nand the end will not follow. No arguing from or about the rule itself will\nthen help us through the difficulty; there is nothing for it but to turn\nback and finish the scientific process which should have preceded the\nformation of the rule. We must re-open the investigation to inquire into\nthe remainder of the conditions on which the effect depends; and only\nafter we have ascertained the whole of these are we prepared to transform\nthe completed law of the effect into a precept, in which those\ncircumstances or combinations of circumstances which the science exhibits\nas conditions are prescribed as means.\n\nIt is true that, for the sake of convenience, rules must be formed from\nsomething less than this ideally perfect theory: in the first place,\nbecause the theory can seldom be made ideally perfect; and next, because,\nif all the counteracting contingencies, whether of frequent or of rare\noccurrence, were included, the rules would be too cumbrous to be\napprehended and remembered by ordinary capacities, on the common occasions\nof life. The rules of art do not attempt to comprise more conditions than\nrequire to be attended to in ordinary cases; and are therefore always\nimperfect. In the manual arts, where the requisite conditions are not\nnumerous, and where those which the rules do not specify are generally\neither plain to common observation or speedily learned from practice,\nrules may often be safely acted on by persons who know nothing more than\nthe rule. But in the complicated affairs of life, and still more in those\nof states and societies, rules can not be relied on, without constantly\nreferring back to the scientific laws on which they are founded. To know\nwhat are the practical contingencies which require a modification of the\nrule, or which are altogether exceptions to it, is to know what\ncombinations of circumstances would interfere with, or entirely\ncounteract, the consequences of those laws; and this can only be learned\nby a reference to the theoretic grounds of the rule.\n\nBy a wise practitioner, therefore, rules of conduct will only be\nconsidered as provisional. Being made for the most numerous cases, or for\nthose of most ordinary occurrence, they point out the manner in which it\nwill be least perilous to act, where time or means do not exist for\nanalyzing the actual circumstances of the case, or where we can not trust\nour judgment in estimating them. But they do not at all supersede the\npropriety of going through, when circumstances permit, the scientific\nprocess requisite for framing a rule from the data of the particular case\nbefore us. At the same time, the common rule may very properly serve as an\nadmonition that a certain mode of action has been found by ourselves and\nothers to be well adapted to the cases of most common occurrence; so that\nif it be unsuitable to the case in hand, the reason of its being so will\nbe likely to arise from some unusual circumstance.\n\n\u00a7 4. The error is therefore apparent of those who would deduce the line of\nconduct proper to particular cases from supposed universal practical\nmaxims, overlooking the necessity of constantly referring back to the\nprinciples of the speculative science, in order to be sure of attaining\neven the specific end which the rules have in view. How much greater\nstill, then, must the error be, of setting up such unbending principles,\nnot merely as universal rules for attaining a given end, but as rules of\nconduct generally, without regard to the possibility, not only that some\nmodifying cause may prevent the attainment of the given end by the means\nwhich the rule prescribes, but that success itself may conflict with some\nother end, which may possibly chance to be more desirable.\n\nThis is the habitual error of many of the political speculators whom I\nhave characterized as the geometrical school; especially in France, where\nratiocination from rules of practice forms the staple commodity of\njournalism and political oratory\u2014a misapprehension of the functions of\nDeduction which has brought much discredit, in the estimation of other\ncountries, upon the spirit of generalization so honorably characteristic\nof the French mind. The commonplaces of politics in France are large and\nsweeping practical maxims, from which, as ultimate premises, men reason\ndownward to particular applications; and this they call being logical and\nconsistent. For instance, they are perpetually arguing that such and such\na measure ought to be adopted, because it is a consequence of the\nprinciple on which the form of government is founded; of the principle of\nlegitimacy, or the principle of the sovereignty of the people. To which it\nmay be answered, that if these be really practical principles, they must\nrest on speculative grounds; the sovereignty of the people, for example,\nmust be a right foundation for government, because a government thus\nconstituted tends to produce certain beneficial effects. Inasmuch,\nhowever, as no government produces all possible beneficial effects, but\nall are attended with more or fewer inconveniences, and since these can\nnot usually be combated by means drawn from the very causes which produce\nthem, it would be often a much stronger recommendation of some practical\narrangement, that it does not follow from what is called the general\nprinciple of the government, than that it does. Under a government of\nlegitimacy, the presumption is far rather in favor of institutions of\npopular origin; and in a democracy, in favor of arrangements tending to\ncheck the impetus of popular will. The line of augmentation so commonly\nmistaken in France for political philosophy, tends to the practical\nconclusion that we should exert our utmost efforts to aggravate, instead\nof alleviating, whatever are the characteristic imperfections of the\nsystem of institutions which we prefer, or under which we happen to live.\n\n\u00a7 5. The grounds, then, of every rule of art, are to be found in the\ntheorems of science. An art, or a body of art, consists of the rules,\ntogether with as much of the speculative propositions as comprises the\njustification of those rules. The complete art of any matter includes a\nselection of such a portion from the science as is necessary to show on\nwhat conditions the effects, which the art aims at producing, depend. And\nArt in general, consists of the truths of Science, arranged in the most\nconvenient order for practice, instead of the order which is the most\nconvenient for thought. Science groups and arranges its truths, so as to\nenable us to take in at one view as much as possible of the general order\nof the universe. Art, though it must assume the same general laws, follows\nthem only into such of their detailed consequences as have led to the\nformation of rules of conduct; and brings together from parts of the field\nof science most remote from one another, the truths relating to the\nproduction of the different and heterogeneous conditions necessary to each\neffect which the exigencies of practical life require to be produced.(288)\n\nScience, therefore, following one cause to its various effects, while art\ntraces one effect to its multiplied and diversified causes and conditions,\nthere is need of a set of intermediate scientific truths, derived from the\nhigher generalities of science, and destined to serve as the generalia or\nfirst principles of the various arts. The scientific operation of framing\nthese intermediate principles, M. Comte characterizes as one of those\nresults of philosophy which are reserved for futurity. The only complete\nexample which he points out as actually realized, and which can be held up\nas a type to be imitated in more important matters, is the general theory\nof the art of Descriptive Geometry, as conceived by M. Monge. It is not,\nhowever, difficult to understand what the nature of these intermediate\nprinciples must generally be. After framing the most comprehensive\npossible conception of the end to be aimed at, that is, of the effect to\nbe produced, and determining in the same comprehensive manner the set of\nconditions on which that effect depends, there remains to be taken, a\ngeneral survey of the resources which can be commanded for realizing this\nset of conditions; and when the result of this survey has been embodied in\nthe fewest and most extensive propositions possible, those propositions\nwill express the general relation between the available means and the end,\nand will constitute the general scientific theory of the art, from which\nits practical methods will follow as corollaries.\n\n\u00a7 6. But though the reasonings which connect the end or purpose of every\nart with its means belong to the domain of Science, the definition of the\nend itself belongs exclusively to Art, and forms its peculiar province.\nEvery art has one first principle, or general major premise, not borrowed\nfrom science; that which enunciates the object aimed at, and affirms it to\nbe a desirable object. The builder\u2019s art assumes that it is desirable to\nhave buildings; architecture, as one of the fine arts, that it is\ndesirable to have them beautiful or imposing. The hygienic and medical\narts assume, the one that the preservation of health, the other that the\ncure of disease, are fitting and desirable ends. These are not\npropositions of science. Propositions of science assert a matter of fact:\nan existence, a co-existence, a succession, or a resemblance. The\npropositions now spoken of do not assert that any thing is, but enjoin or\nrecommend that something should be. They are a class by themselves. A\nproposition of which the predicate is expressed by the words _ought_ or\n_should be_, is generically different from one which is expressed by _is_,\nor _will be_. It is true, that in the largest sense of the words, even\nthese propositions assert something as a matter of fact. The fact affirmed\nin them is, that the conduct recommended excites in the speaker\u2019s mind the\nfeeling of approbation. This, however, does not go to the bottom of the\nmatter; for the speaker\u2019s approbation is no sufficient reason why other\npeople should approve; nor ought it to be a conclusive reason even with\nhimself. For the purposes of practice, every one must be required to\njustify his approbation; and for this there is need of general premises,\ndetermining what are the proper objects of approbation, and what the\nproper order of precedence among those objects.\n\nThese general premises, together with the principal conclusions which may\nbe deduced from them, form (or rather might form) a body of doctrine,\nwhich is properly the Art of Life, in its three departments, Morality,\nPrudence or Policy, and \u00c6sthetics; the Right, the Expedient, and the\nBeautiful or Noble, in human conduct and works. To this art (which, in the\nmain, is unfortunately still to be created), all other arts are\nsubordinate; since its principles are those which must determine whether\nthe special aim of any particular art is worthy and desirable, and what is\nits place in the scale of desirable things. Every art is thus a joint\nresult of laws of nature disclosed by science, and of the general\nprinciples of what has been called Teleology, or the Doctrine of\nEnds;(289) which, borrowing the language of the German metaphysicians, may\nalso be termed, not improperly, the principles of Practical Reason.\n\nA scientific observer or reasoner, merely as such, is not an adviser for\npractice. His part is only to show that certain consequences follow from\ncertain causes, and that to obtain certain ends, certain means are the\nmost effectual. Whether the ends themselves are such as ought to be\npursued, and if so, in what cases and to how great a length, it is no part\nof his business as a cultivator of science to decide, and science alone\nwill never qualify him for the decision. In purely physical science, there\nis not much temptation to assume this ulterior office; but those who treat\nof human nature and society invariably claim it: they always undertake to\nsay, not merely what is, but what ought to be. To entitle them to do this,\na complete doctrine of Teleology is indispensable. A scientific theory,\nhowever perfect, of the subject-matter, considered merely as part of the\norder of nature, can in no degree serve as a substitute. In this respect\nthe various subordinate arts afford a misleading analogy. In them there is\nseldom any visible necessity for justifying the end, since in general its\ndesirableness is denied by nobody, and it is only when the question of\nprecedence is to be decided between that end and some other, that the\ngeneral principles of Teleology have to be called in; but a writer on\nMorals and Politics requires those principles at every step. The most\nelaborate and well-digested exposition of the laws of succession and\nco-existence among mental or social phenomena, and of their relation to\none another as causes and effects, will be of no avail toward the art of\nLife or of Society, if the ends to be aimed at by that art are left to the\nvague suggestions of the _intellectus sibi permissus_, or are taken for\ngranted without analysis or questioning.\n\n\u00a7 7. There is, then, a _philosophia prima_ peculiar to Art, as there is\none which belongs to Science. There are not only first principles of\nKnowledge, but first principles of Conduct. There must be some standard by\nwhich to determine the goodness or badness, absolute and comparative, of\nends, or objects of desire. And whatever that standard is, there can be\nbut one; for if there were several ultimate principles of conduct, the\nsame conduct might be approved by one of those principles and condemned by\nanother; and there would be needed some more general principle, as umpire\nbetween them.\n\nAccordingly, writers on Moral Philosophy have mostly felt the necessity\nnot only of referring all rules of conduct, and all judgments of praise\nand blame, to principles, but of referring them to some one principle;\nsome rule, or standard, with which all other rules of conduct were\nrequired to be consistent, and from which by ultimate consequence they\ncould all be deduced. Those who have dispensed with the assumption of such\na universal standard, have only been enabled to do so by supposing that a\nmoral sense, or instinct, inherent in our constitution, informs us, both\nwhat principles of conduct we are bound to observe, and also in what order\nthese should be subordinated to one another.\n\nThe theory of the foundations of morality is a subject which it would be\nout of place, in a work like this, to discuss at large, and which could\nnot to any useful purpose be treated incidentally. I shall content myself,\ntherefore, with saying, that the doctrine of intuitive moral principles,\neven if true, would provide only for that portion of the field of conduct\nwhich is properly called moral. For the remainder of the practice of life\nsome general principle, or standard, must still be sought; and if that\nprinciple be rightly chosen, it will be found, I apprehend, to serve quite\nas well for the ultimate principle of Morality, as for that of Prudence,\nPolicy, or Taste.\n\nWithout attempting in this place to justify my opinion, or even to define\nthe kind of justification which it admits of, I merely declare my\nconviction, that the general principle to which all rules of practice\nought to conform, and the test by which they should be tried, is that of\nconduciveness to the happiness of mankind, or rather, of all sentient\nbeings; in other words, that the promotion of happiness is the ultimate\nprinciple of Teleology.(290)\n\nI do not mean to assert that the promotion of happiness should be itself\nthe end of all actions, or even of all rules of action. It is the\njustification, and ought to be the controller, of all ends, but it is not\nitself the sole end. There are many virtuous actions, and even virtuous\nmodes of action (though the cases are, I think, less frequent than is\noften supposed), by which happiness in the particular instance is\nsacrificed, more pain being produced than pleasure. But conduct of which\nthis can be truly asserted, admits of justification only because it can be\nshown that, on the whole, more happiness will exist in the world, if\nfeelings are cultivated which will make people, in certain cases,\nregardless of happiness. I fully admit that this is true; that the\ncultivation of an ideal nobleness of will and conduct should be to\nindividual human beings an end, to which the specific pursuit either of\ntheir own happiness or of that of others (except so far as included in\nthat idea) should, in any case of conflict, give way. But I hold that the\nvery question, what constitutes this elevation of character, is itself to\nbe decided by a reference to happiness as the standard. The character\nitself should be, to the individual, a paramount end, simply because the\nexistence of this ideal nobleness of character, or of a near approach to\nit, in any abundance, would go farther than all things else toward making\nhuman life happy, both in the comparatively humble sense of pleasure and\nfreedom from pain, and in the higher meaning, of rendering life, not what\nit now is almost universally, puerile and insignificant, but such as human\nbeings with highly developed faculties can care to have.\n\n\u00a7 8. With these remarks we must close this summary view of the application\nof the general logic of scientific inquiry to the moral and social\ndepartments of science. Notwithstanding the extreme generality of the\nprinciples of method which I have laid down (a generality which, I trust,\nis not, in this instance, synonymous with vagueness), I have indulged the\nhope that to some of those on whom the task will devolve of bringing those\nmost important of all sciences into a more satisfactory state, these\nobservations may be useful, both in removing erroneous, and in clearing up\nthe true, conceptions of the means by which, on subjects of so high a\ndegree of complication, truth can be attained. Should this hope be\nrealized, what is probably destined to be the great intellectual\nachievement of the next two or three generations of European thinkers will\nhave been in some degree forwarded.\n\nTHE END.\n\n\n\n\nFOOTNOTES\n\n\n    1 In the later editions of Archbishop Whately\u2019s \u201cLogic,\u201d he states his\n      meaning to be, not that \u201crules\u201d for the ascertainment of truths by\n      inductive investigation can not be laid down, or that they may not\n      be \u201cof eminent service,\u201d but that they \u201cmust always be comparatively\n      vague and general, and incapable of being built up into a regular\n      demonstrative theory like that of the Syllogism.\u201d (Book iv., ch.\n      iv., \u00a7 3.) And he observes, that to devise a system for this\n      purpose, capable of being \u201cbrought into a scientific form,\u201d would be\n      an achievement which \u201che must be more sanguine than scientific who\n      expects.\u201d (Book iv., ch. ii., \u00a7 4.) To effect this, however, being\n      the express object of the portion of the present work which treats\n      of Induction, the words in the text are no overstatement of the\n      difference of opinion between Archbishop Whately and me on the\n      subject.\n\n    2 Now forming a chapter in his volume on \u201cThe Philosophy of\n      Discovery.\u201d\n\n    3 Archbishop Whately.\n\n    4 I use these terms indiscriminately, because, for the purpose in\n      view, there is no need for making any distinction between them. But\n      metaphysicians usually restrict the name Intuition to the direct\n      knowledge we are supposed to have of things external to our minds,\n      and Consciousness to our knowledge of our own mental phenomena.\n\n    5 This important theory has of late been called in question by a\n      writer of deserved reputation, Mr. Samuel Bailey; but I do not\n      conceive that the grounds on which it has been admitted as an\n      established doctrine for a century past, have been at all shaken by\n      that gentleman\u2019s objections. I have elsewhere said what appeared to\n      me necessary in reply to his arguments. (_Westminster Review_ for\n      October, 1842; reprinted in \u201cDissertations and Discussions,\u201d vol.\n      ii.)\n\n    6 The view taken in the text, of the definition and purpose of Logic,\n      stands in marked opposition to that of the school of philosophy\n      which, in this country, is represented by the writings of Sir\n      William Hamilton and of his numerous pupils. Logic, as this school\n      conceives it, is \u201cthe Science of the Formal Laws of Thought;\u201d a\n      definition framed for the express purpose of excluding, as\n      irrelevant to Logic, whatever relates to Belief and Disbelief, or to\n      the pursuit of truth as such, and restricting the science to that\n      very limited portion of its total province, which has reference to\n      the conditions, not of Truth, but of Consistency. What I have\n      thought it useful to say in opposition to this limitation of the\n      field of Logic, has been said at some length in a separate work,\n      first published in 1865, and entitled \u201cAn Examination of Sir William\n      Hamilton\u2019s Philosophy, and of the Principal Philosophical Questions\n      discussed in his Writings.\u201d For the purposes of the present\n      Treatise, I am content that the justification of the larger\n      extension which I give to the domain of the science, should rest on\n      the sequel of the Treatise itself. Some remarks on the relation\n      which the Logic of Consistency bears to the Logic of Truth, and on\n      the place which that particular part occupies in the whole to which\n      it belongs, will be found in the present volume (Book II., chap.\n      iii., \u00a7 9).\n\n_    7 Computation or Logic_, chap. ii.\n\n    8 In the original \u201chad, _or had not_.\u201d These last words, as involving\n      a subtlety foreign to our present purpose, I have forborne to quote.\n\n    9 Vide infra, note at the end of \u00a7 3, book ii., chap. ii.\n\n_   10 Notare_, to mark; _con_notare, to mark _along with_; to mark one\n      thing _with_ or _in addition to_ another.\n\n   11 Archbishop Whately, who, in the later editions of his _Elements of\n      Logic_, aided in reviving the important distinction treated of in\n      the text, proposes the term \u201cAttributive\u201d as a substitute for\n      \u201cConnotative\u201d (p. 22, 9th edit.). The expression is, in itself,\n      appropriate; but as it has not the advantage of being connected with\n      any verb, of so markedly distinctive a character as \u201cto connote,\u201d it\n      is not, I think, fitted to supply the place of the word Connotative\n      in scientific use.\n\n   12 A writer who entitles his book _Philosophy; or, the Science of\n      Truth_, charges me in his very first page (referring at the foot of\n      it to this passage) with asserting that _general_ names have\n      properly no signification. And he repeats this statement many times\n      in the course of his volume, with comments, not at all flattering,\n      thereon. It is well to be now and then reminded to how great a\n      length perverse misquotation (for, strange as it appears, I do not\n      believe that the writer is dishonest) can sometimes go. It is a\n      warning to readers when they see an author accused, with volume and\n      page referred to, and the apparent guarantee of inverted commas, of\n      maintaining something more than commonly absurd, not to give\n      implicit credence to the assertion without verifying the reference.\n\n   13 \u201cTake the familiar term Stone. It is applied to mineral and rocky\n      materials, to the kernels of fruit, to the accumulations in the\n      gall-bladder and in the kidney; while it is refused to polished\n      minerals (called gems), to rocks that have the cleavage suited for\n      roofing (slates), and to baked clay (bricks). It occurs in the\n      designation of the magnetic oxide of iron (loadstone), and not in\n      speaking of other metallic ores. Such a term is wholly unfit for\n      accurate reasoning, unless hedged round on every occasion by other\n      phrases; as building stone, precious stone, gall-stone, etc.\n      Moreover, the methods of definition are baffled for want of\n      sufficient community to ground upon. There is no quality uniformly\n      present in the cases where it is applied, and uniformly absent where\n      it is not applied; hence the definer would have to employ largely\n      the license of striking off existing applications, and taking in new\n      ones.\u201d\u2014BAIN, _Logic_, ii., 172.\n\n   14 Before quitting the subject of connotative names, it is proper to\n      observe, that the first writer who, in our times, has adopted from\n      the schoolmen the word _to connote_, Mr. James Mill, in his\n      _Analysis of the Phenomena of the Human Mind_, employs it in a\n      signification different from that in which it is here used. He uses\n      the word in a sense co-extensive with its etymology, applying it to\n      every case in which a name, while pointing directly to one thing\n      (which is consequently termed its signification), includes also a\n      tacit reference to some other thing. In the case considered in the\n      text, that of concrete general names, his language and mine are the\n      converse of one another. Considering (very justly) the signification\n      of the name to lie in the attribute, he speaks of the word as\n      _noting_ the attribute, and _connoting_ the things possessing the\n      attribute. And he describes abstract names as being properly\n      concrete names with their connotation dropped; whereas, in my view,\n      it is the _de_notation which would be said to be dropped, what was\n      previously connoted becoming the whole signification.\n\n      In adopting a phraseology at variance with that which so high an\n      authority, and one which I am less likely than any other person to\n      undervalue, has deliberately sanctioned, I have been influenced by\n      the urgent necessity for a term exclusively appropriated to express\n      the manner in which a concrete general name serves to mark the\n      attributes which are involved in its signification. This necessity\n      can scarcely be felt in its full force by any one who has not found\n      by experience how vain is the attempt to communicate clear ideas on\n      the philosophy of language without such a word. It is hardly an\n      exaggeration to say, that some of the most prevalent of the errors\n      with which logic has been infected, and a large part of the\n      cloudiness and confusion of ideas which have enveloped it, would, in\n      all probability, have been avoided, if a term had been in common use\n      to express exactly what I have signified by the term to connote. And\n      the schoolmen, to whom we are indebted for the greater part of our\n      logical language, gave us this also, and in this very sense. For\n      though some of their general expressions countenance the use of the\n      word in the more extensive and vague acceptation in which it is\n      taken by Mr. Mill, yet when they had to define it specifically as a\n      technical term, and to fix its meaning as such, with that admirable\n      precision which always characterizes their definitions, they clearly\n      explained that nothing was said to be connoted except _forms_, which\n      word may generally, in their writings, be understood as synonymous\n      with _attributes_.\n\n      Now, if the word _to connote_, so well suited to the purpose to\n      which they applied it, be diverted from that purpose by being taken\n      to fulfill another, for which it does not seem to me to be at all\n      required; I am unable to find any expression to replace it, but such\n      as are commonly employed in a sense so much more general, that it\n      would be useless attempting to associate them peculiarly with this\n      precise idea. Such are the words, to involve, to imply, etc. By\n      employing these, I should fail of attaining the object for which\n      alone the name is needed, namely, to distinguish this particular\n      kind of involving and implying from all other kinds, and to assure\n      to it the degree of habitual attention which its importance demands.\n\n   15 Professor Bain (_Logic_, i., 56) thinks that negative names are not\n      names of all things whatever except those denoted by the correlative\n      positive name, but only for all things of some particular class:\n      _not-white_, for instance, he deems not to be a name for every thing\n      in nature except white things, but only for every _colored_ thing\n      other than white. In this case, however, as in all others, the test\n      of what a name denotes is what it can be predicated of: and we can\n      certainly predicate of a sound, or a smell, that it is not white.\n      The affirmation and the negation of the same attribute can not but\n      divide the whole field of predication between them.\n\n   16 Or rather, all objects except itself and the percipient mind; for,\n      as we shall see hereafter, to ascribe any attribute to an object,\n      necessarily implies a mind to perceive it.\n\n      The simple and clear explanation given in the text, of relation and\n      relative names, a subject so long the opprobrium of metaphysics, was\n      given (as far as I know) for the first time, by Mr. James Mill, in\n      his Analysis of the Phenomena of the Human Mind.\n\n   17 On the preceding passage Professor Bain remarks (Logic, i., 265):\n      \u201cThe Categories do not seem to have been intended as a\n      classification of Namable Things, in the sense of \u2018an enumeration of\n      all kinds of Things which are capable of being made predicates, or\n      of having any thing predicated of them.\u2019 They seem to have been\n      rather intended as a generalization of predicates; an analysis of\n      the final import of predication. Viewed in this light, they are not\n      open to the objections offered by Mr. Mill. The proper question to\n      ask is not\u2014In what Category are we to place sensations or other\n      feelings or states of mind? but, Under what Categories can we\n      predicate regarding states of mind? Take, for example, Hope. When we\n      say that it is a state of mind, we predicate Substance: we may also\n      describe how great it is (Quantity), what is the quality of it,\n      pleasurable or painful (Quality), what it has reference to\n      (Relation). Aristotle seems to have framed the Categories on the\n      plan\u2014Here is an individual; what is the final analysis of all that\n      we can predicate about him?\u201d\n\n      This is doubtless a true statement of the leading idea in the\n      classification. The Category \u039f\u1f50\u03c3\u03af\u03b1 was certainly understood by\n      Aristotle to be a general name for all possible answers to the\n      question Quid sit? when asked respecting a concrete individual; as\n      the other Categories are names comprehending all possible answers to\n      the questions Quantum sit? Quale sit? etc. In Aristotle\u2019s\n      conception, therefore, the Categories may not have been a\n      classification of Things; but they were soon converted into one by\n      his Scholastic followers, who certainly regarded and treated them as\n      a classification of Things, and carried them out as such, dividing\n      down the Category Substance as a naturalist might do, into the\n      different classes of physical or metaphysical objects as\n      distinguished from attributes, and the other Categories into the\n      principal varieties of quantity, quality, relation, etc. It is,\n      therefore, a just subject of complaint against them, that they had\n      no Category of Feeling. Feeling is assuredly predicable as a summum\n      genus, of every particular kind of feeling, for instance, as in Mr.\n      Bain\u2019s example, of Hope: but it can not be brought within any of the\n      Categories as interpreted either by Aristotle or by his followers.\n\n_   18 Philosophy of the Inductive Sciences_, vol. i., p. 40.\n\n_   19 Discussions on Philosophy_, etc. Appendix I., pp. 643, 644.\n\n   20 It is to be regretted that Sir William Hamilton, though he often\n      strenuously insists on this doctrine, and though, in the passage\n      quoted, he states it with a comprehensiveness and force which leave\n      nothing to be desired, did not consistently adhere to his own\n      doctrine, but maintained along with it opinions with which it is\n      utterly irreconcilable. See the third and other chapters of _An\n      Examination of Sir William Hamilton\u2019s Philosophy_.\n\n   21 \u201cNous savons qu\u2019il existe quelque chose hors de nous, parceque nous\n      ne pouvons expliquer nos perceptions sans les rattacher \u00e0 des causes\n      distinctes de nous m\u00eames; nous savons de plus que ces causes, dont\n      nous ne connaissons pas d\u2019ailleurs l\u2019essence, produisent les effets\n      les plus variables, les plus divers, et m\u00eame les plus contraires,\n      selon qu\u2019elles rencontrent telle nature ou telle disposition du\n      sujet. Mais savons-nous quelque chose de plus? et m\u00eame, vu le\n      caract\u00e8re ind\u00e9termin\u00e9 des causes que nous concevons dans les corps,\n      y a-t-il quelque chose de plus \u00e0 savoir? Y a-t-il lieu de nous\n      enqu\u00e9rir si nous percevons les choses telles qu\u2019elles sont? Non\n      \u00e9videmment.... Je ne dis pas que le probl\u00e8me est insoluble, _je dis\n      qu\u2019il est absurde et enferme une contradiction_. Nous _ne savons pas\n      ce que ces causes sont en elles-m\u00eames_, et la raison nous d\u00e9fend de\n      chercher \u00e0 le conna\u00eetre: mais il est bien \u00e9vident _\u00e0 priori_,\n      qu\u2019_elles ne sont pas en elles-m\u00eames ce qu\u2019elles sont par rapport \u00e0\n      nous_, puisque la pr\u00e9sence du sujet modifie n\u00e9cessairement leur\n      action. Supprimez tout sujet sentant, il est certain que ces causes\n      agiraient encore puisqu\u2019elles continueraient d\u2019exister; mais elles\n      agiraient autrement; elles seraient encore des qualit\u00e9s et des\n      propri\u00e9t\u00e9s, mais qui ne ressembleraient \u00e0 rien de ce que nous\n      connaissons. Le feu ne manifesterait plus aucune des propri\u00e9t\u00e9s que\n      nous lui connaissons: que serait-il? C\u2019est ce que nous ne saurons\n      jamais. _C\u2019est d\u2019ailleurs peut-\u00eatre un probl\u00e8me qui ne r\u00e9pugne pas\n      seulement \u00e0 la nature de notre esprit, mais \u00e0 l\u2019essence m\u00eame des\n      choses._ Quand m\u00eame en effet on supprimerait par le pens\u00e9e tous les\n      sujets sentants, il faudrait encore admettre que nul corps ne\n      manifesterait ses propri\u00e9t\u00e9s autrement qu\u2019en relation avec un sujet\n      quelconque, et dans ce cas _ses propri\u00e9t\u00e9s ne seraient encore que\n      relatives_: en sorte qu\u2019il me para\u00eet fort raisonnable d\u2019admettre que\n      les propri\u00e9t\u00e9s d\u00e9termin\u00e9es des corps n\u2019existent pas ind\u00e9pendamment\n      d\u2019un sujet quelconque, et que quand on demande si les propri\u00e9t\u00e9s de\n      la matiere sont telles que nous les percevons, il faudrait voir\n      auparavant si elles sont en tant que d\u00e9termin\u00e9es, et dans quel sens\n      il est vrai de dire qu\u2019elles sont.\u201d\u2014_Cours d\u2019Histoire de la\n      Philosophie Morale au 18me si\u00e8cle_, 8me le\u00e7on.\n\n   22 An attempt, indeed, has been made by Reid and others, to establish\n      that although some of the properties we ascribe to objects exist\n      only in our sensations, others exist in the things themselves, being\n      such as can not possibly be copies of any impression upon the\n      senses; and they ask, from what sensations our notions of extension\n      and figure have been derived? The gauntlet thrown down by Reid was\n      taken up by Brown, who, applying greater powers of analysis than had\n      previously been applied to the notions of extension and figure,\n      pointed out that the sensations from which those notions are\n      derived, are sensations of touch, combined with sensations of a\n      class previously too little adverted to by metaphysicians, those\n      which have their seat in our muscular frame. His analysis, which was\n      adopted and followed up by James Mill, has been further and greatly\n      improved upon in Professor Bain\u2019s profound work, _The Senses and the\n      Intellect_, and in the chapters on \u201cPerception\u201d of a work of eminent\n      analytic power, Mr. Herbert Spencer\u2019s _Principles of Psychology_.\n\n      On this point M. Cousin may again be cited in favor of the better\n      doctrine. M. Cousin recognizes, in opposition to Reid, the essential\n      subjectivity of our conceptions of what are called the primary\n      qualities of matter, as extension, solidity, etc., equally with\n      those of color, heat, and the remainder of the so-called secondary\n      qualities.\u2014_Cours_, ut supra, 9me le\u00e7on.\n\n   23 This doctrine, which is the most complete form of the philosophical\n      theory known as the Relativity of Human Knowledge, has, since the\n      recent revival in this country of an active interest in metaphysical\n      speculation, been the subject of a greatly increased amount of\n      discussion and controversy; and dissentients have manifested\n      themselves in considerably greater number than I had any knowledge\n      of when the passage in the text was written. The doctrine has been\n      attacked from two sides. Some thinkers, among whom are the late\n      Professor Ferrier, in his _Institutes of Metaphysic_, and Professor\n      John Grote, in his _Exploratio Philosophica_, appear to deny\n      altogether the reality of Noumena, or Things in themselves\u2014of an\n      unknowable substratum or support for the sensations which we\n      experience, and which, according to the theory, constitute all our\n      knowledge of an external world. It seems to me, however, that in\n      Professor Grote\u2019s case at least, the denial of Noumena is only\n      apparent, and that he does not essentially differ from the other\n      class of objectors, including Mr. Bailey in his valuable _Letters on\n      the Philosophy of the Human Mind_, and (in spite of the striking\n      passage quoted in the text) also Sir William Hamilton, who contend\n      for a direct knowledge by the human mind of more than the\n      sensations\u2014of certain attributes or properties as they exist not in\n      us, but in the Things themselves.\n\n      With the first of these opinions, that which denies Noumena, I have,\n      as a metaphysician, no quarrel; but, whether it be true or false, it\n      is irrelevant to Logic. And since all the forms of language are in\n      contradiction to it, nothing but confusion could result from its\n      unnecessary introduction into a treatise, every essential doctrine\n      of which could stand equally well with the opposite and accredited\n      opinion. The other and rival doctrine, that of a direct perception\n      or intuitive knowledge of the outward object as it is in itself,\n      considered as distinct from the sensations we receive from it, is of\n      far greater practical moment. But even this question, depending on\n      the nature and laws of Intuitive Knowledge, is not within the\n      province of Logic. For the grounds of my own opinion concerning it,\n      I must content myself with referring to a work already mentioned\u2014_An\n      Examination of Sir William Hamilton\u2019s Philosophy_; several chapters\n      of which are devoted to a full discussion of the questions and\n      theories relating to the supposed direct perception of external\n      objects.\n\n   24 Professor Bain (_Logic_, i., 49) defines attributes as \u201cpoints of\n      community among classes.\u201d This definition expresses well one point\n      of view, but is liable to the objection that it applies only to the\n      attributes of classes; though an object, unique in its kind, may be\n      said to have attributes. Moreover, the definition is not ultimate,\n      since the points of community themselves admit of, and require,\n      further analysis; and Mr. Bain does analyze them into resemblances\n      in the sensations, or other states of consciousness excited by the\n      object.\n\n_   25 Analysis of the Human Mind_, i., 126 et seq.\n\n_   26 Logic_, i., 85.\n\n   27 Instead of Universal and Particular as applied to propositions,\n      Professor Bain proposes (_Logic_, i., 81) the terms Total and\n      Partial; reserving the former pair of terms for their inductive\n      meaning, \u201cthe contrast between a general proposition and the\n      particulars or individuals that we derive it from.\u201d This change in\n      nomenclature would be attended with the further advantage, that\n      Singular propositions, which in the Syllogism follow the same rules\n      as Universal, would be included along with them in the same class,\n      that of Total predications. It is not the Subject\u2019s denoting many\n      things or only one, that is of importance in reasoning, it is that\n      the assertion is made of the whole or a part only of what the\n      Subject denotes. The words Universal and Particular, however, are so\n      familiar and so well understood in both the senses mentioned by Mr.\n      Bain, that the double meaning does not produce any material\n      inconvenience.\n\n   28 It may, however, be considered as equivalent to a universal\n      proposition with a different predicate, viz.: \u201cAll wine is good\n      _qu\u00e2_ wine,\u201d or \u201cis good in respect of the qualities which\n      constitute it wine.\u201d\n\n_   29 Logic_, i., 82.\n\n   30 Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this\n      statement, and asks, \u201cAre we to say that a mole can not dig the\n      ground, except he has an idea of the ground, and of the snout and\n      paws with which he digs it?\u201d I do not know what passes in a mole\u2019s\n      mind, nor what amount of mental apprehension may or may not\n      accompany his instinctive actions. But a human being does not use a\n      spade by instinct; and he certainly could not use it unless he had\n      knowledge of a spade, and of the earth which he uses it upon.\n\n   31 Professor Bain remarks, in qualification of the statement in the\n      text (_Logic_, i., 50), that the word Class has two meanings; \u201cthe\n      class definite, and the class indefinite. The class definite is an\n      enumeration of actual individuals, as the Peers of the Realm, the\n      oceans of the globe, the known planets.... The class indefinite is\n      unenumerated. Such classes are stars, planets, gold-bearing rocks,\n      men, poets, virtuous.... In this last acceptation of the word, class\n      name and general name are identical. The class name denotes an\n      indefinite number of individuals, and connotes the points of\n      community or likeness.\u201d\n\n      The theory controverted in the text, tacitly supposes all classes to\n      be _definite_. I have assumed them to be indefinite; because, for\n      the purposes of Logic, definite classes, as such, are almost\n      useless; though often serviceable as means of abridged expression.\n      (Vide infra, book iii., chap. ii.)\n\n   32 \u201cFrom hence also this may be deduced, that the first truths were\n      arbitrarily made by those that first of all imposed names upon\n      things, or received them from the imposition of others. For it is\n      true (for example) that _man is a living creature_, but it is for\n      this reason, that it pleased men to impose both these names on the\n      same thing.\u201d\u2014_Computation or Logic_, chap. iii., sect. 8.\n\n   33 \u201cMen are subject to err not only in affirming and denying, but also\n      in perception, and in silent cogitation.... Tacit errors, or the\n      errors of sense and cogitation, are made by passing from one\n      imagination to the imagination of another different thing; or by\n      feigning that to be past, or future, which never was, nor ever shall\n      be; as when by seeing the image of the sun in water, we imagine the\n      sun itself to be there; or by seeing swords, that there has been, or\n      shall be, fighting, because it used to be so for the most part; or\n      when from promises we feign the mind of the promiser to be such and\n      such; or, lastly, when from any sign we vainly imagine something to\n      be signified which is not. And errors of this sort are common to all\n      things that have sense.\u201d\u2014_Computation or Logic_, chap. v., sect. 1.\n\n   34 Chap. iii., sect 3.\n\n   35 To the preceding statement it has been objected, that \u201cwe naturally\n      construe the subject of a proposition in its extension, and the\n      predicate (which therefore may be an adjective) in its intension\n      (connotation): and that consequently co-existence of attributes does\n      not, any more than the opposite theory of equation of groups,\n      correspond with the living processes of thought and language.\u201d I\n      acknowledge the distinction here drawn, which, indeed, I had myself\n      laid down and exemplified a few pages back (p. 77). But though it is\n      true that we naturally \u201cconstrue the subject of a proposition in its\n      extension,\u201d this extension, or in other words, the extent of the\n      class denoted by the name, is not apprehended or indicated directly.\n      It is both apprehended and indicated solely through the attributes.\n      In the \u201cliving processes of thought and language\u201d the extension,\n      though in this case really thought of (which in the case of the\n      predicate it is not), is thought of only through the medium of what\n      my acute and courteous critic terms the \u201cintension.\u201d\n\n      For further illustrations of this subject, see _Examination of Sir\n      William Hamilton\u2019s Philosophy_, chap. xxii.\n\n   36 Professor Bain, in his _Logic_ (i., 256), excludes Existence from\n      the list, considering it as a mere name. All propositions, he says,\n      which predicate mere existence \u201care more or less abbreviated, or\n      elliptical: when fully expressed they fall under either co-existence\n      or succession. When we say there _exists_ a conspiracy for a\n      particular purpose, we mean that at the present time a body of men\n      have formed themselves into a society for a particular object; which\n      is a complex affirmation, resolvable into propositions of\n      co-existence and succession (as causation). The assertion that the\n      dodo does not exist, points to the fact that this animal, once known\n      in a certain place, has disappeared or become extinct; is no longer\n      associated with the locality: all which may be better stated without\n      the use of the verb \u2018exist.\u2019 There is a debated question\u2014Does an\n      ether exist? but the concrete form would be this\u2014\u2018Are heat and light\n      and other radiant influences propagated by an ethereal medium\n      diffused in space;\u2019 which is a proposition of causation. In like\n      manner the question of the Existence of a Deity can not be discussed\n      in that form. It is properly a question as to the First _Cause_ of\n      the Universe, and as to the continued exertion of that Cause in\n      providential superintendence.\u201d (i., 407.)\n\n      Mr. Bain thinks it \u201cfictitious and unmeaning language\u201d to carry up\n      the classification of Nature to one _summum genus_, Being, or that\n      which Exists; since nothing can be perceived or apprehended but by\n      way of contrast with something else (of which important truth, under\n      the name of Law of Relativity, he has been in our time the principal\n      expounder and champion), and we have no other class to oppose to\n      Being, or fact to contrast with Existence.\n\n      I accept fully Mr. Bain\u2019s Law of Relativity, but I do not understand\n      by it that to enable us to apprehend or be conscious of any fact, it\n      is necessary that we should contrast it with some other positive\n      fact. The antithesis necessary to consciousness need not, I\n      conceive, be an antithesis between two positives; it may be between\n      one positive and its negative. Hobbes was undoubtedly right when he\n      said that a single sensation indefinitely prolonged would cease to\n      be felt at all; but simple intermission, without other change, would\n      restore it to consciousness. In order to be conscious of heat, it is\n      not necessary that we should pass to it from cold; it suffices that\n      we should pass to it from a state of no sensation, or from a\n      sensation of some other kind. The relative opposite of Being,\n      considered as a summum genus, is Nonentity, or Nothing; and we have,\n      now and then, occasion to consider and discuss things merely in\n      contrast with Nonentity.\n\n      I grant that the _decision_ of questions of Existence usually if not\n      always depends on a previous question of either Causation or\n      Co-existence. But Existence is nevertheless a different thing from\n      Causation or Co-existence, and can be predicated apart from them.\n      The meaning of the abstract name Existence, and the connotation of\n      the concrete name Being, consist, like the meaning of all other\n      names, in sensations or states of consciousness: their peculiarity\n      is that to exist, is to excite, or be capable of exciting, _any_\n      sensations or states of consciousness: no matter what, but it is\n      indispensable that there should be some. It was from overlooking\n      this that Hegel, finding that Being is an abstraction reached by\n      thinking away all particular attributes, arrived at the\n      self-contradictory proposition on which he founded all his\n      philosophy, that Being is the same as Nothing. It is really the name\n      of Something, taken in the most comprehensive sense of the word.\n\n   37 Book iv., chap. vii.\n\n_   38 Logic_, i., 103\u2013105.\n\n   39 The doctrines which prevented the real meaning of Essences from\n      being understood, had not assumed so settled a shape in the time of\n      Aristotle and his immediate followers, as was afterward given to\n      them by the Realists of the Middle Ages. Aristotle himself (in his\n      Treatise on the Categories) expressly denies that the \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03b1\u03b9\n      \u03bf\u1f54\u03c3\u03b9\u03b1\u03b9, or Substanti\u00e6 Secund\u00e6, inhere in a subject. They are only,\n      he says, predicated of it.\n\n   40 The always acute and often profound author of _An Outline of\n      Sematology_ (Mr. B. H. Smart) justly says, \u201cLocke will be much more\n      intelligible, if, in the majority of places, we substitute \u2018the\n      knowledge of\u2019 for what he calls \u2018the Idea of\u2019\u201d (p. 10). Among the\n      many criticisms on Locke\u2019s use of the word Idea, this is the one\n      which, as it appears to me, most nearly hits the mark; and I quote\n      it for the additional reason that it precisely expresses the point\n      of difference respecting the import of Propositions, between my view\n      and what I have spoken of as the Conceptualist view of them. Where a\n      Conceptualist says that a name or a proposition expresses our Idea\n      of a thing, I should generally say (instead of our Idea) our\n      Knowledge, or Belief, concerning the thing itself.\n\n   41 This distinction corresponds to that which is drawn by Kant and\n      other metaphysicians between what they term _analytic_ and\n      _synthetic_, judgments; the former being those which can be evolved\n      from the meaning of the terms used.\n\n   42 If we allow a differentia to what is not really a species. For the\n      distinction of Kinds, in the sense explained by us, not being in any\n      way applicable to attributes, it of course follows that although\n      attributes may be put into classes, those classes can be admitted to\n      be genera or species only by courtesy.\n\n   43 Professor Bain, in his Logic, takes a peculiar view of Definition.\n      He holds (i., 71) with the present work, that \u201cthe definition in its\n      full import, is the sum of all the properties connoted by the name;\n      it exhausts the meaning of a word.\u201d But he regards the meaning of a\n      general name as including, not indeed all the common properties of\n      the class named, but all of them that are ultimate properties, not\n      resolvable into one another. \u201cThe enumeration of the attributes of\n      oxygen, of gold, of man, should be an enumeration of the final (so\n      far as can be made out), the underivable, powers or functions of\n      each,\u201d and nothing less than this is a complete Definition (i., 75).\n      An independent property, not derivable from other properties, even\n      if previously unknown, yet as soon as discovered becomes, according\n      to him, part of the meaning of the term, and should be included in\n      the definition. \u201cWhen we are told that diamond, which we know to be\n      a transparent, glittering, hard, and high-priced substance, is\n      composed of carbon, and is combustible, we must put these additional\n      properties on the same level as the rest; to us they are henceforth\n      connoted by the name\u201d (i., 73). Consequently the propositions that\n      diamond is composed of carbon, and that it is combustible, are\n      regarded by Mr. Bain as merely verbal propositions. He carries this\n      doctrine so far as to say that unless mortality can be shown to be a\n      consequence of the ultimate laws of animal organization, mortality\n      is connoted by man, and \u201cMan is Mortal\u201d is a merely verbal\n      proposition. And one of the peculiarities (I think a disadvantageous\n      peculiarity) of his able and valuable treatise, is the large number\n      of propositions requiring proof, and learned by experience, which,\n      in conformity with this doctrine, he considers as not real, but\n      verbal, propositions.\n\n      The objection I have to this language is that it confounds, or at\n      least confuses, a much more important distinction than that which it\n      draws. The only reason for dividing Propositions into real and\n      verbal, is in order to discriminate propositions which convey\n      information about facts, from those which do not. A proposition\n      which affirms that an object has a given attribute, while\n      designating the object by a name which already signifies the\n      attribute, adds no information to that which was already possessed\n      by all who understood the name. But when this is said, it is implied\n      that, by the signification of a name, is meant the signification\n      attached to it in the common usage of life. I can not think we ought\n      to say that the meaning of a word includes matters of fact which are\n      unknown to every person who uses the word unless he has learned them\n      by special study of a particular department of Nature; or that\n      because a few persons are aware of these matters of fact, the\n      affirmation of them is a proposition conveying no information. I\n      hold that (special scientific connotation apart) a name means, or\n      connotes, only the properties which it is a mark of in the general\n      mind; and that in the case of any additional properties, however\n      uniformly found to accompany these, it remains possible that a thing\n      which did not possess the properties might still be thought entitled\n      to the name. Ruminant, according to Mr. Bain\u2019s use of language,\n      connotes cloven-hoofed, since the two properties are always found\n      together, and no connection has ever been discovered between them:\n      but ruminant does not mean cloven-hoofed; and were an animal to be\n      discovered which chews the cud, but has its feet undivided, I\n      venture to say that it would still be called ruminant.\n\n   44 In the fuller discussion which Archbishop Whately has given to this\n      subject in his later editions, he almost ceases to regard the\n      definitions of names and those of things as, in any important sense,\n      distinct. He seems (9th ed., p. 145) to limit the notion of a Real\n      Definition to one which \u201cexplains any thing _more_ of the nature of\n      the thing than is implied in the name;\u201d (including under the word\n      \u201cimplied,\u201d not only what the name connotes, but every thing which\n      can be deduced by reasoning from the attributes connoted). Even\n      this, as he adds, is usually called not a Definition, but a\n      Description; and (as it seems to me) rightly so called. A\n      Description, I conceive, can only be ranked among Definitions, when\n      taken (as in the case of the zoological definition of man) to\n      fulfill the true office of a Definition, by declaring the\n      connotation given to a word in some special use, as a term of\n      science or art: which special connotation of course would not be\n      expressed by the proper definition of the word in its ordinary\n      employment.\n\n      Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,\n      understands by a Real Definition one which contains _less_ than the\n      Nominal Definition, provided only that what it contains is\n      sufficient for distinction. \u201cBy _real_ definition I mean such an\n      explanation of the word, be it the whole of the meaning or only\n      part, as will be sufficient to separate the things contained under\n      that word from all others. Thus the following, I believe, is a\n      complete definition of an elephant: An animal which naturally drinks\n      by drawing the water into its nose, and then spurting it into its\n      mouth.\u201d\u2014_Formal Logic_, p. 36. Mr. De Morgan\u2019s general proposition\n      and his example are at variance; for the peculiar mode of drinking\n      of the elephant certainly forms no part of the meaning of the word\n      elephant. It could not be said, because a person happened to be\n      ignorant of this property, that he did not know what an elephant\n      means.\n\n   45 In the only attempt which, so far as I know, has been made to refute\n      the preceding argumentation, it is maintained that in the first form\n      of the syllogism,\n\n      A dragon is a thing which breathes flame,\n      A dragon is a serpent,\n      Therefore some serpent or serpents breathe flame,\n\n      \u201cthere is just as much truth in the conclusion as there is in the\n      premises, or rather, no more in the latter than in the former. If\n      the general name serpent includes both real and imaginary serpents,\n      there is no falsity in the conclusion; if not, there is falsity in\n      the minor premise.\u201d\n\n      Let us, then, try to set out the syllogism on the hypothesis that\n      the name serpent includes imaginary serpents. We shall find that it\n      is now necessary to alter the predicates; for it can not be asserted\n      that an imaginary creature breathes flame; in predicating of it such\n      a fact, we assert by the most positive implication that it is real,\n      and not imaginary. The conclusion must run thus, \u201cSome serpent or\n      serpents either do or are _imagined_ to breathe flame.\u201d And to prove\n      this conclusion by the instance of dragons, the premises must be, A\n      dragon is _imagined_ as breathing flame. A dragon is a (real or\n      imaginary) serpent: from which it undoubtedly follows, that there\n      are serpents which are imagined to breathe flame; but the major\n      premise is not a definition, nor part of a definition; which is all\n      that I am concerned to prove.\n\n      Let us now examine the other assertion\u2014that if the word serpent\n      stands for none but real serpents, the minor premise (a dragon is a\n      serpent) is false. This is exactly what I have myself said of the\n      premise, considered as a statement of fact: but it is not false as\n      part of the definition of a dragon; and since the premises, or one\n      of them, must be false (the conclusion being so), the real premise\n      can not be the definition, which is true, but the statement of fact,\n      which is false.\n\n   46 \u201cFew people\u201d (I have said in another place) \u201chave reflected how\n      great a knowledge of Things is required to enable a man to affirm\n      that any given argument turns wholly upon words. There is, perhaps,\n      not one of the leading terms of philosophy which is not used in\n      almost innumerable shades of meaning, to express ideas more or less\n      widely different from one another. Between two of these ideas a\n      sagacious and penetrating mind will discern, as it were intuitively,\n      an unobvious link of connection, upon which, though perhaps unable\n      to give a logical account of it, he will found a perfectly valid\n      argument, which his critic, not having so keen an insight into the\n      Things, will mistake for a fallacy turning on the double meaning of\n      a term. And the greater the genius of him who thus safely leaps over\n      the chasm, the greater will probably be the crowing and vainglory of\n      the mere logician, who, hobbling after him, evinces his own superior\n      wisdom by pausing on its brink, and giving up as desperate his\n      proper business of bridging it over.\u201d\n\n   47 The different cases of Equipollency, or \u201cEquivalent Propositional\n      Forms,\u201d are set forth with some fullness in Professor Bain\u2019s\n      _Logic_. One of the commonest of these changes of expression, that\n      from affirming a proposition to denying its negative, or _vic\u00e8\n      versa_, Mr. Bain designates, very happily, by the name Obversion.\n\n   48 As Sir William Hamilton has pointed out, \u201cSome A is not B\u201d may also\n      be converted in the following form: \u201cNo B is _some_ A.\u201d Some men are\n      not negroes; therefore, No negroes are _some_ men (_e.g._,\n      Europeans).\n\n   49 Contraries:\n      All  A is B\n      No   A is B\n\n      Subtraries:\n      Some A is B\n      Some A is not B\n\n      Contradictories:\n      All  A is B\n      Some A is not B\n\n      Also contradictories:\n      No A is B\n      Some A is B\n\n      Respectively subalternate:\n      All  A is B and No A is B\n      Some A is B and Some A is not B\n\n   50 Professor Bain denies the claim of Singular Propositions to be\n      classed, for the purposes of ratiocination, with Universal; though\n      they come within the designation which he himself proposes as an\n      equivalent for Universal, that of Total. He would even, to use his\n      own expression, banish them entirely from the syllogism. He takes as\n      an example,\n\n      Socrates is wise,\n      Socrates is poor, therefore\n      Some poor men are wise,\n\n      or more properly (as he observes) \u201cone poor man is wise.\u201d \u201cNow, if\n      wise, poor, and a man, are attributes belonging to the meaning of\n      the word Socrates, there is then no march of reasoning at all. We\n      have given in Socrates, _inter alia_, the facts wise, poor, and a\n      man, and we merely repeat the concurrence which is selected from the\n      whole aggregate of properties making up the whole, Socrates. The\n      case is one under the head \u2018Greater and Less Connotation\u2019 in\n      Equivalent Propositional Forms, or Immediate Inference.\n\n      \u201cBut the example in this form does not do justice to the syllogism\n      of singulars. We must suppose both propositions to be real, the\n      predicates being in no way involved in the subject. Thus\n\n      Socrates was the master of Plato,\n      Socrates fought at Delium,\n      The master of Plato fought at Delium.\n\n      \u201cIt may fairly be doubted whether the transitions, in this instance,\n      are any thing more than equivalent forms. For the proposition\n      \u2018Socrates was the master of Plato and fought at Delium,\u2019 compounded\n      out of the two premises, is obviously nothing more than a\n      grammatical abbreviation. No one can say that there is here any\n      change of meaning, or any thing beyond a verbal modification of the\n      original form. The next step is, \u2018The master of Plato fought at\n      Delium,\u2019 which is the previous statement cut down by the omission of\n      Socrates. It contents itself with reproducing a part of the meaning,\n      or saying less than had been previously said. The full equivalent of\n      the affirmation is, \u2018The master of Plato fought at Delium, and the\n      master of Plato was Socrates:\u2019 the new form omits the last piece of\n      information, and gives only the first. Now, we never consider that\n      we have made a real inference, a step in advance, when we repeat\n      _less_ than we are entitled to say, or drop from a complex statement\n      some portion not desired at the moment. Such an operation keeps\n      strictly within the domain of equivalence, or Immediate Inference.\n      In no way, therefore, can a syllogism with two singular premises be\n      viewed as a genuine syllogistic or deductive inference.\u201d (_Logic_,\n      i., 159.)\n\n      The first argument, as will have been seen, rests upon the\n      supposition that the name Socrates has a meaning; that man, wise,\n      and poor, are parts of this meaning; and that by predicating them of\n      Socrates we convey no information; a view of the signification of\n      names which, for reasons already given (Note to \u00a7 4 of the chapter\n      on Definition, _supra_, pp. 110, 111.), I can not admit, and which,\n      as applied to the class of names which Socrates belongs to, is at\n      war with Mr. Bain\u2019s own definition of a Proper Name (i., 148), \u201ca\n      single _meaningless_ mark or designation appropriated to the thing.\u201d\n      Such names, Mr. Bain proceeded to say, do not necessarily indicate\n      even human beings: much less then does the name Socrates include the\n      meaning of wise or poor. Otherwise it would follow that if Socrates\n      had grown rich, or had lost his mental faculties by illness, he\n      would no longer have been called Socrates.\n\n      The second part of Mr. Bain\u2019s argument, in which he contends that\n      even when the premises convey real information, the conclusion is\n      merely the premises with a part left out, is applicable, if at all,\n      as much to universal propositions as to singular. In every syllogism\n      the conclusion contains less than is asserted in the two premises\n      taken together. Suppose the syllogism to be\n\n      All bees are intelligent,\n      All bees are insects, therefore\n      Some insects are intelligent:\n\n      one might use the same liberty taken by Mr. Bain, of joining\n      together the two premises as if they were one\u2014\u201cAll bees are insects\n      and intelligent\u201d\u2014and might say that in omitting the middle term\n      _bees_ we make no real inference, but merely reproduce part of what\n      had been previously said. Mr. Bain\u2019s is really an objection to the\n      syllogism itself, or at all events to the third figure: it has no\n      special applicability to singular propositions.\n\n   51 His conclusions are, \u201cThe first figure is suited to the discovery or\n      proof of the properties of a thing; the second to the discovery or\n      proof of the distinctions between things; the third to the discovery\n      or proof of instances and exceptions; the fourth to the discovery,\n      or exclusion, of the different species of a genus.\u201d The reference of\n      syllogisms in the last three figures to the _dictum de omni et\n      nullo_ is, in Lambert\u2019s opinion, strained and unnatural: to each of\n      the three belongs, according to him, a separate axiom, co-ordinate\n      and of equal authority with that _dictum_, and to which he gives the\n      names of _dictum de diverso_ for the second figure, _dictum de\n      exemplo_ for the third, and _dictum de reciproco_ for the fourth.\n      See part i., or _Dianoiologie_, chap, iv., \u00a7 229 _et seqq._ Mr.\n      Bailey (_Theory of Reasoning_, 2d ed., pp. 70\u201374) takes a similar\n      view of the subject.\n\n   52 Since this chapter was written, two treatises have appeared (or\n      rather a treatise and a fragment of a treatise), which aim at a\n      further improvement in the theory of the forms of ratiocination: Mr.\n      De Morgan\u2019s \u201cFormal Logic; or, the Calculus of Inference, Necessary\n      and Probable;\u201d and the \u201cNew Analytic of Logical Forms,\u201d attached as\n      an Appendix to Sir William Hamilton\u2019s _Discussions on Philosophy_,\n      and at greater length, to his posthumous _Lectures on Logic_.\n\n      In Mr. De Morgan\u2019s volume\u2014abounding, in its more popular parts, with\n      valuable observations felicitously expressed\u2014the principal feature\n      of originality is an attempt to bring within strict technical rules\n      the cases in which a conclusion can be drawn from premises of a form\n      usually classed as particular. Mr. De Morgan observes, very justly,\n      that from the premises most Bs are Cs, most Bs are As, it may be\n      concluded with certainty that some As are Cs, since two portions of\n      the class B, each of them comprising more than half, must\n      necessarily in part consist of the same individuals. Following out\n      this line of thought, it is equally evident that if we knew exactly\n      what proportion the \u201cmost\u201d in each of the premises bear to the\n      entire class B, we could increase in a corresponding degree the\n      definiteness of the conclusion. Thus if 60 per cent. of B are\n      included in C, and 70 per cent. in A, 30 per cent. at least must be\n      common to both; in other words, the number of As which are Cs, and\n      of Cs which are As, must be at least equal to 30 per cent. of the\n      class B. Proceeding on this conception of \u201cnumerically definite\n      propositions,\u201d and extending it to such forms as these:\u2014\u201c45 Xs (or\n      more) are each of them one of 70 Ys,\u201d or \u201c45 Xs (or more) are no one\n      of them to be found among 70 Ys,\u201d and examining what inferences\n      admit of being drawn from the various combinations which may be made\n      of premises of this description, Mr. De Morgan establishes universal\n      formul\u00e6 for such inferences; creating for that purpose not only a\n      new technical language, but a formidable array of symbols analogous\n      to those of algebra.\n\n      Since it is undeniable that inferences, in the cases examined by Mr.\n      De Morgan, can legitimately be drawn, and that the ordinary theory\n      takes no account of them, I will not say that it was not worth while\n      to show in detail how these also could be reduced to formul\u00e6 as\n      rigorous as those of Aristotle. What Mr. De Morgan has done was\n      worth doing once (perhaps more than once, as a school exercise); but\n      I question if its results are worth studying and mastering for any\n      practical purpose. The practical use of technical forms of reasoning\n      is to bar out fallacies: but the fallacies which require to be\n      guarded against in ratiocination properly so called, arise from the\n      incautious use of the common forms of language; and the logician\n      must track the fallacy into that territory, instead of waiting for\n      it on a territory of his own. While he remains among propositions\n      which have acquired the numerical precision of the Calculus of\n      Probabilities, the enemy is left in possession of the only ground on\n      which he can be formidable. And since the propositions (short of\n      universal) on which a thinker has to depend, either for purposes of\n      speculation or of practice, do not, except in a few peculiar cases,\n      admit of any numerical precision; common reasoning can not be\n      translated into Mr. De Morgan\u2019s forms, which therefore can not serve\n      any purpose as a test of it.\n\n      Sir William Hamilton\u2019s theory of the \u201cquantification of the\n      predicate\u201d may be described as follows:\n\n      \u201cLogically\u201d (I quote his words) \u201cwe ought to take into account the\n      quantity, always understood in thought, but usually, for manifest\n      reasons, elided in its expression, not only of the subject, but also\n      of the predicate of a judgment.\u201d All A is B, is equivalent to all A\n      is _some_ B. No A is B, to No A is _any_ B. Some A is B, is\n      tantamount to some A is _some_ B. Some A is not B, to Some A is _not\n      any_ B. As in these forms of assertion the predicate is exactly\n      co-extensive with the subject, they all admit of simple conversion;\n      and by this we obtain two additional forms\u2014Some B is _all_ A, and No\n      B is _some_ A. We may also make the assertion All A is all B, which\n      will be true if the classes A and B are exactly co-extensive. The\n      last three forms, though conveying real assertions, have no place in\n      the ordinary classification of Propositions. All propositions, then,\n      being supposed to be translated into this language, and written each\n      in that one of the preceding forms which answers to its\n      signification, there emerges a new set of syllogistic rules,\n      materially different from the common ones. A general view of the\n      points of difference may be given in the words of Sir W. Hamilton\n      (_Discussions_, 2d ed., p. 651):\n\n      \u201cThe revocation of the two terms of a Proposition to their true\n      relation; a proposition being always an _equation_ of its subject\n      and its predicate.\n\n      \u201cThe consequent reduction of the Conversion of Propositions from\n      three species to one\u2014that of Simple Conversion.\n\n      \u201cThe reduction of all the _General Laws_ of Categorical Syllogisms\n      to a single Canon.\n\n      \u201cThe evolution from that one canon of all the Species and varieties\n      of Syllogisms.\n\n      \u201cThe abrogation of all the _Special Laws_ of Syllogism.\n\n      \u201cA demonstration of the exclusive possibility of Three Syllogistic\n      Figures; and (on new grounds) the scientific and final abolition of\n      the Fourth.\n\n      \u201cA manifestation that Figure is an unessential variation in\n      syllogistic form; and the consequent absurdity of Reducing the\n      syllogisms of the other figures to the first.\n\n      \u201cAn enouncement of _one Organic Principle_ for each Figure.\n\n      \u201cA determination of the true number of the Legitimate Moods; with\n\n      \u201cTheir amplification in number (thirty-six);\n\n      \u201cTheir numerical equality under all the figures; and\n\n      \u201cTheir relative equivalence, or virtual identity, throughout every\n      schematic difference.\n\n      \u201cThat, in the second and third figures, the extremes holding both\n      the same relation to the middle term, there is not, as in the first,\n      an opposition and subordination between a term major and a term\n      minor, mutually containing and contained, in the counter wholes of\n      Extension and Comprehension.\n\n      \u201cConsequently, in the second and third figures, there is no\n      determinate major and minor premises, and there are two indifferent\n      conclusions: whereas in the first the premises are determinate, and\n      there is a single proximate conclusion.\u201d\n\n      This doctrine, like that of Mr. De Morgan previously noticed, is a\n      real addition to the syllogistic theory; and has moreover this\n      advantage over Mr. De Morgan\u2019s \u201cnumerically definite Syllogism,\u201d\n      that the forms it supplies are really available as a test of the\n      correctness of ratiocination; since propositions in the common form\n      may always have their predicates quantified, and so be made amenable\n      to Sir W. Hamilton\u2019s rules. Considered, however, as a contribution\n      to the _Science_ of Logic, that is, to the analysis of the mental\n      processes concerned in reasoning, the new doctrine appears to me, I\n      confess, not merely superfluous, but erroneous; since the form in\n      which it clothes propositions does not, like the ordinary form,\n      express what is in the mind of the speaker when he enunciates the\n      proposition. I can not think Sir William Hamilton right in\n      maintaining that the quantity of the predicate is \u201calways understood\n      in thought.\u201d It is implied, but is not present to the mind of the\n      person who asserts the proposition. The quantification of the\n      predicate, instead of being a means of bringing out more clearly the\n      meaning of the proposition, actually leads the mind out of the\n      proposition, into another order of ideas. For when we say, All men\n      are mortal, we simply mean to affirm the attribute mortality of all\n      men; without thinking at all of the _class_ mortal in the concrete,\n      or troubling ourselves about whether it contains any other beings or\n      not. It is only for some artificial purpose that we ever look at the\n      proposition in the aspect in which the predicate also is thought of\n      as a class-name, either including the subject only, or the subject\n      and something more. (See above, p. 77, 78.)\n\n      For a fuller discussion of this subject, see the twenty-second\n      chapter of a work already referred to, \u201cAn Examination of Sir\n      William Hamilton\u2019s Philosophy.\u201d\n\n   53 Mr. Herbert Spencer (_Principles of Psychology_, pp. 125\u20137), though\n      his theory of the syllogism coincides with all that is essential of\n      mine, thinks it a logical fallacy to present the two axioms in the\n      text, as the regulating principles of syllogism. He charges me with\n      falling into the error pointed out by Archbishop Whately and myself,\n      of confounding exact likeness with literal identity; and maintains,\n      that we ought not to say that Socrates possesses _the same_\n      attributes which are connoted by the word Man, but only that he\n      possesses attributes _exactly like_ them: according to which\n      phraseology, Socrates, and the attribute mortality, are not two\n      things co-existing with the same thing, as the axiom asserts, but\n      two things coexisting with two different things.\n\n      The question between Mr. Spencer and me is merely one of language;\n      for neither of us (if I understand Mr. Spencer\u2019s opinions rightly)\n      believes an attribute to be a real thing, possessed of objective\n      existence; we believe it to be a particular mode of naming our\n      sensations, or our expectations of sensation, when looked at in\n      their relation to an external object which excites them. The\n      question raised by Mr. Spencer does not, therefore, concern the\n      properties of any really existing thing, but the comparative\n      appropriateness, for philosophical purposes, of two different modes\n      of using a name. Considered in this point of view, the phraseology I\n      have employed, which is that commonly used by philosophers, seems to\n      me to be the best. Mr. Spencer is of opinion that because Socrates\n      and Alcibiades are not the same man, the attribute which constitutes\n      them men should not be called the same attribute; that because the\n      humanity of one man and that of another express themselves to our\n      senses not by the same individual sensations but by sensations\n      exactly alike, humanity ought to be regarded as a different\n      attribute in every different man. But on this showing, the humanity\n      even of any one man should be considered as different attributes now\n      and half an hour hence; for the sensations by which it will then\n      manifest itself to my organs will not be a continuation of my\n      present sensations, but a repetition of them; fresh sensations, not\n      identical with, but only exactly like the present. If every general\n      conception, instead of being \u201cthe One in the Many,\u201d were considered\n      to be as many different conceptions as there are things to which it\n      is applicable, there would be no such thing as general language. A\n      name would have no general meaning if _man_ connoted one thing when\n      predicated of John, and another, though closely resembling, thing\n      when predicated of William. Accordingly a recent pamphlet asserts\n      the impossibility of general knowledge on this precise ground.\n\n      The meaning of any general name is some outward or inward\n      phenomenon, consisting, in the last resort, of feelings; and these\n      feelings, if their continuity is for an instant broken, are no\n      longer the same feelings, in the sense of individual identity. What,\n      then, is the common something which gives a meaning to the general\n      name? Mr. Spencer can only say, it is the similarity of the\n      feelings; and I rejoin, the attribute is precisely that similarity.\n      The names of attributes are in their ultimate analysis names for the\n      resemblances of our sensations (or other feelings). Every general\n      name, whether abstract or concrete, denotes or connotes one or more\n      of those resemblances. It will not, probably, be denied, that if a\n      hundred sensations are undistinguishably alike, their resemblance\n      ought to be spoken of as one resemblance, and not a hundred\n      resemblances which merely _resemble_ one another. The things\n      compared are many, but the something common to all of them must be\n      conceived as one, just as the name is conceived as one, though\n      corresponding to numerically different sensations of sound each time\n      it is pronounced. The general term _man_ does not connote the\n      sensations derived once from one man, which, once gone, can no more\n      occur again than the same flash of lightning. It connotes the\n      general type of the sensations derived always from all men, and the\n      power (always thought of as one) of producing sensations of that\n      type. And the axiom might be thus worded: Two _types of sensation_\n      each of which co-exists with a third type, co-exist with another; or\n      Two _powers_ each of which co-exists with a third power co-exist\n      with one another.\n\n      Mr. Spencer has misunderstood me in another particular. He supposes\n      that the co-existence spoken of in the axiom, of two things with the\n      same third thing, means simultaneousness in time. The co-existence\n      meant is that of being jointly attributes of the same subject. The\n      attribute of being born without teeth, and the attribute of having\n      thirty-two teeth in mature age, are in this sense co-existent, both\n      being attributes of man, though _ex vi termini_ never of the same\n      man at the same time.\n\n   54 Supra, p. 93.\n\n   55 Professor Bain (_Logic_, i., 157) considers the axiom (or rather\n      axioms) here proposed as a substitute for the _dictum de omni_, to\n      possess certain advantages, but to be \u201cunworkable as a basis of the\n      syllogism. The fatal defect consists in this, that it is ill-adapted\n      to bring out the difference between total and partial coincidence of\n      terms, the observation of which is the essential precaution in\n      syllogizing correctly. If all the terms were co-extensive, the axiom\n      would flow on admirably; A carries B, all B and none but B; B\n      carries C in the same manner; at once A carries C, without\n      limitation or reserve. But in point of fact, we know that while A\n      carries B, other things carry B also; whence a process of limitation\n      is required, in transferring A to C through B. A (in common with\n      other things) carries B; B (in common with other things) carries C;\n      whence A (in common with other things) carries C. The axiom provides\n      no means of making this limitation; if we were to follow A\n      literally, we should be led to suppose A and C co-extensive: for\n      such is the only obvious meaning of \u2018the attribute A coincides with\n      the attribute C.\u2019\u201d\n\n      It is certainly possible that a careless learner here and there may\n      suppose that if A carries B, it follows that B carries A. But if any\n      one is so incautious as to commit this mistake, the very earliest\n      lesson in the logic of inference, the Conversion of propositions,\n      will correct it. The first of the two forms in which I have stated\n      the axiom, is in some degree open to Mr. Bain\u2019s criticism: when B is\n      said to co-exist with A (it must be by a _lapsus calami_ that Mr.\n      Bain uses the word _coincide_), it is possible, in the absence of\n      warning, to suppose the meaning to be that the two things are only\n      found together. But this misinterpretation is excluded by the other,\n      or practical, form of the maxim; _Nota not\u0153 est nota rei ipsius._ No\n      one would be in any danger of inferring that because _a_ is a mark\n      of _b, b_ can never exist without _a_; that because being in a\n      confirmed consumption is a mark of being about to die, no one dies\n      who is not in a consumption; that because being coal is a mark of\n      having come out of the earth, nothing can come out of the earth\n      except coal. Ordinary knowledge of English seems a sufficient\n      protection against these mistakes, since in speaking of a mark of\n      any thing we are never understood as implying reciprocity.\n\n      A more fundamental objection is stated by Mr. Bain in a subsequent\n      passage (p. 158). \u201cThe axiom does not accommodate itself to the type\n      of Deductive Reasoning as contrasted with Induction\u2014the application\n      of a general principle to a special case. Any thing that fails to\n      make prominent this circumstance is not adapted as a foundation for\n      the syllogism.\u201d But though it may be proper to limit the term\n      Deduction to the application of a general principle to a special\n      case, it has never been held that Ratiocination or Syllogism is\n      subject to the same limitation; and the adoption of it would exclude\n      a great amount of valid and conclusive syllogistic reasoning.\n      Moreover, if the _dictum de omni_ makes prominent the fact of the\n      application of a general principle to a particular case, the axiom I\n      propose makes prominent the condition which alone makes that\n      application a real inference.\n\n      I conclude, therefore, that both forms have their value, and their\n      place in Logic. The _dictum de omni_ should be retained as the\n      fundamental axiom of the logic of mere consistency, often called\n      Formal Logic; nor have I ever quarreled with the use of it in that\n      character, nor proposed to banish it from treatises on Formal Logic.\n      But the other is the proper axiom for the logic of the pursuit of\n      truth by way of Deduction; and the recognition of it can alone show\n      how it is possible that deductive reasoning can be a road to truth.\n\n_   56 Logic_, p. 239 (9th ed.).\n\n   57 It is hardly necessary to say, that I am not contending for any such\n      absurdity as that we _actually_ \u201cought to have known\u201d and considered\n      the case of every individual man, past, present, and future, before\n      affirming that all men are mortal: although this interpretation has\n      been, strangely enough, put upon the preceding observations. There\n      is no difference between me and Archbishop Whately, or any other\n      defender of the syllogism, on the practical part of the matter; I am\n      only pointing out an inconsistency in the logical theory of it, as\n      conceived by almost all writers. I do not say that a person who\n      affirmed, before the Duke of Wellington was born, that all men are\n      mortal, _knew_ that the Duke of Wellington was mortal; but I do say\n      that he _asserted_ it; and I ask for an explanation of the apparent\n      logical fallacy, of adducing in proof of the Duke of Wellington\u2019s\n      mortality, a general statement which presupposes it. Finding no\n      sufficient resolution of this difficulty in any of the writers on\n      Logic, I have attempted to supply one.\n\n   58 The language of ratiocination would, I think, be brought into closer\n      agreement with the real nature of the process, if the general\n      propositions employed in reasoning, instead of being in the form All\n      men are mortal, or Every man is mortal, were expressed in the form\n      Any man is mortal. This mode of expression, exhibiting as the type\n      of all reasoning from experience \u201cThe men A, B, C, etc., are so and\n      so, therefore _any_ man is so and so,\u201d would much better manifest\n      the true idea\u2014that inductive reasoning is always, at bottom,\n      inference from particulars to particulars, and that the whole\n      function of general propositions in reasoning, is to vouch for the\n      legitimacy of such inferences.\n\n   59 Review of Quetelet on Probabilities, _Essays_, p. 367.\n\n_   60 Philosophy of Discovery_, p. 289.\n\n_   61 Theory of Reasoning_, chap. iv., to which I may refer for an able\n      statement and enforcement of the grounds of the doctrine.\n\n   62 On a recent careful reperusal of Berkeley\u2019s whole works, I have been\n      unable to find this doctrine in them. Sir John Herschel probably\n      meant that it is implied in Berkeley\u2019s argument against abstract\n      ideas. But I can not find that Berkeley saw the implication, or had\n      ever asked himself what bearing his argument had on the theory of\n      the syllogism. Still less can I admit that the doctrine is (as has\n      been affirmed by one of my ablest and most candid critics) \u201camong\n      the standing marks of what is called the empirical philosophy.\u201d\n\n_   63 Logic_, book iv., chap. i., sect. 1.\n\n   64 See the important chapter on Belief, in Professor Bain\u2019s great\n      treatise, _The Emotions and the Will_, pp. 581\u20134.\n\n   65 A writer in the \u201cBritish Quarterly Review\u201d (August, 1846), in a\n      review of this treatise, endeavors to show that there is no _petitio\n      principii_ in the syllogism, by denying that the proposition, All\n      men are mortal, asserts or assumes that Socrates is mortal. In\n      support of this denial, he argues that we may, and in fact do, admit\n      the general proposition that all men are mortal, without having\n      particularly examined the case of Socrates, and even without knowing\n      whether the individual so named is a man or something else. But this\n      of course was never denied. That we can and do draw conclusions\n      concerning cases specifically unknown to us, is the datum from which\n      all who discuss this subject must set out. The question is, in what\n      terms the evidence, or ground, on which we draw these conclusions,\n      may best be designated\u2014whether it is most correct to say, that the\n      unknown case is proved by known cases, or that it is proved by a\n      general proposition including both sets of cases, the unknown and\n      the known? I contend for the former mode of expression. I hold it an\n      abuse of language to say, that the proof that Socrates is mortal, is\n      that all men are mortal. Turn it in what way we will, this seems to\n      me to be asserting that a thing is the proof of itself. Whoever\n      pronounces the words, All men are mortal, has affirmed that Socrates\n      is mortal, though he may never have heard of Socrates; for since\n      Socrates, whether known to be so or not, really is a man, he is\n      included in the words, All men, and in every assertion of which they\n      are the subject. If the reviewer does not see that there is a\n      difficulty here, I can only advise him to reconsider the subject\n      until he does: after which he will be a better judge of the success\n      or failure of an attempt to remove the difficulty. That he had\n      reflected very little on the point when he wrote his remarks, is\n      shown by his oversight respecting the _dictum de omni et nullo_. He\n      acknowledges that this maxim as commonly expressed\u2014\u201cWhatever is true\n      of a class, is true of every thing included in the class,\u201d is a mere\n      identical proposition, since the class _is_ nothing but the things\n      included in it. But he thinks this defect would be cured by wording\n      the maxim thus\u2014\u201cWhatever is true of a class, is true of every thing\n      which _can be shown_ to be a member of the class:\u201d as if a thing\n      could \u201cbe shown\u201d to be a member of the class without being one. If a\n      class means the sum of all the things included in the class, the\n      things which can \u201cbe shown\u201d to be included in it are part of the\n      sum, and the _dictum_ is as much an identical proposition with\n      respect to them as to the rest. One would almost imagine that, in\n      the reviewer\u2019s opinion, things are not members of a class until they\n      are called up publicly to take their place in it\u2014that so long, in\n      fact, as Socrates is not known to be a man, he _is not_ a man, and\n      any assertion which can be made concerning men does not at all\n      regard him, nor is affected as to its truth or falsity by any thing\n      in which he is concerned.\n\n      The difference between the reviewer\u2019s theory and mine may be thus\n      stated. Both admit that when we say, All men are mortal, we make an\n      assertion reaching beyond the sphere of our knowledge of individual\n      cases; and that when a new individual, Socrates, is brought within\n      the field of our knowledge by means of the minor premise, we learn\n      that we have already made an assertion respecting Socrates without\n      knowing it: our own general formula being, to that extent, for the\n      first time _interpreted_ to us. But according to the reviewer\u2019s\n      theory, the smaller assertion is proved by the larger: while I\n      contend, that both assertions are proved together, by the same\n      evidence, namely, the grounds of experience on which the general\n      assertion was made, and by which it must be justified.\n\n      The reviewer says, that if the major premise included the\n      conclusion, \u201cwe should be able to affirm the conclusion without the\n      intervention of the minor premise; but every one sees that that is\n      impossible.\u201d A similar argument is urged by Mr. De Morgan (_Formal\n      Logic_, p. 259): \u201cThe whole objection tacitly assumes the\n      superfluity of the minor; that is, tacitly assumes we know Socrates\n      (Mr. De Morgan says \u2018Plato,\u2019 but to prevent confusion I have kept to\n      my own _exemplum_.) to be a man as soon as we know him to be\n      Socrates.\u201d The objection would be well grounded if the assertion\n      that the major premise includes the conclusion, meant that it\n      individually specifies all it includes. As, however, the only\n      indication it gives is a description by marks, we have still to\n      compare any new individual with the marks; and to show that this\n      comparison has been made, is the office of the minor. But since, by\n      supposition, the new individual has the marks, whether we have\n      ascertained him to have them or not; if we have affirmed the major\n      premise, we have asserted him to be mortal. Now my position is that\n      this assertion can not be a necessary part of the argument. It can\n      not be a necessary condition of reasoning that we should begin by\n      making an assertion, which is afterward to be employed in proving a\n      part of itself. I can conceive only one way out of this difficulty,\n      viz., that what really forms the proof is _the other_ part of the\n      assertion: the portion of it, the truth of which has been\n      ascertained previously: and that the unproved part is bound up in\n      one formula with the proved part in mere anticipation, and as a\n      memorandum of the nature of the conclusions which we are prepared to\n      prove.\n\n      With respect to the minor premise in its formal shape, the minor as\n      it stands in the syllogism, predicating of Socrates a definite class\n      name, I readily admit that it is no more a necessary part of\n      reasoning than the major. When there is a major, doing its work by\n      means of a class name, minors are needed to interpret it: but\n      reasoning can be carried on without either the one or the other.\n      They are not the conditions of reasoning, but a precaution against\n      erroneous reasoning. The only minor premise necessary to reasoning\n      in the example under consideration, is, Socrates is _like_ A, B, C,\n      and the other individuals who are known to have died. And this is\n      the only universal type of that step in the reasoning process which\n      is represented by the minor. Experience, however, of the uncertainty\n      of this loose mode of inference, teaches the expediency of\n      determining beforehand what _kind_ of likeness to the cases\n      observed, is necessary to bring an unobserved case within the same\n      predicate; and the answer to this question is the major. The minor\n      then identifies the precise kind of likeness possessed by Socrates,\n      as being the kind required by the formula. Thus the syllogistic\n      major and the syllogistic minor start into existence together, and\n      are called forth by the same exigency. When we conclude from\n      personal experience without referring to any record\u2014to any general\n      theorems, either written, or traditional, or mentally registered by\n      ourselves as conclusions of our own drawing\u2014we do not use, in our\n      thoughts, either a major or a minor, such as the syllogism puts into\n      words. When, however, we revise this rough inference from\n      particulars to particulars, and substitute a careful one, the\n      revision consists in selecting two syllogistic premises. But this\n      neither alters nor adds to the evidence we had before; it only puts\n      us in a better position for judging whether our inference from\n      particulars to particulars is well grounded.\n\n   66 Infra, book iii., chap. ii.\n\n   67 Infra, book iii., ch. iv., \u00a7 3, and elsewhere.\n\n   68 It is justly remarked by Professor Bain (_Logic_, ii., 134) that the\n      word Hypothesis is here used in a somewhat peculiar sense. An\n      hypothesis, in science, usually means a supposition not proved to be\n      true, but surmised to be so, because if true it would account for\n      certain known facts; and the final result of the speculation may be\n      to prove its truth. The hypotheses spoken of in the text are of a\n      different character; they are known not to be literally true, while\n      as much of them as is true is not hypothetical, but certain. The two\n      cases, however, resemble in the circumstance that in both we reason,\n      not from a truth, but from an assumption, and the truth therefore of\n      the conclusions is conditional, not categorical. This suffices to\n      justify, in point of logical propriety, Stewart\u2019s use of the term.\n      It is of course needful to bear in mind that the hypothetical\n      element in the definitions of geometry is the assumption that what\n      is very nearly true is exactly so. This unreal exactitude might be\n      called a fiction, as properly as an hypothesis; but that\n      appellation, still more than the other, would fail to point out the\n      close relation which exists between the fictitious point or line and\n      the points and lines of which we have experience.\n\n_   69 Mechanical Euclid_, pp. 149 _et seqq._\n\n   70 We might, it is true, insert this property into the definition of\n      parallel lines, framing the definition so as to require, both that\n      when produced indefinitely they shall never meet, and also that any\n      straight line which intersects one of them shall, if prolonged, meet\n      the other. But by doing this we by no means get rid of the\n      assumption; we are still obliged to take for granted the geometrical\n      truth, that all straight lines in the same plane, which have the\n      former of these properties, have also the latter. For if it were\n      possible that they should not, that is, if any straight lines in the\n      same plane, other than those which are parallel according to the\n      definition, had the property of never meeting although indefinitely\n      produced, the demonstrations of the subsequent portions of the\n      theory of parallels could not be maintained.\n\n   71 Some persons find themselves prevented from believing that the\n      axiom, Two straight lines can not inclose a space, could ever become\n      known to us through experience, by a difficulty which may be stated\n      as follows: If the straight lines spoken of are those contemplated\n      in the definition\u2014lines absolutely without breadth and absolutely\n      straight\u2014that such are incapable of inclosing a space is not proved\n      by experience, for lines such as these do not present themselves in\n      our experience. If, on the other hand, the lines meant are such\n      straight lines as we do meet with in experience, lines straight\n      enough for practical purposes, but in reality slightly zigzag, and\n      with some, however trifling, breadth; as applied to these lines the\n      axiom is not true, for two of them may, and sometimes do, inclose a\n      small portion of space. In neither case, therefore, does experience\n      prove the axiom.\n\n      Those who employ this argument to show that geometrical axioms can\n      not be proved by induction, show themselves unfamiliar with a common\n      and perfectly valid mode of inductive proof; proof by approximation.\n      Though experience furnishes us with no lines so unimpeachably\n      straight that two of them are incapable of inclosing the smallest\n      space, it presents us with gradations of lines possessing less and\n      less either of breadth or of flexure, of which series the straight\n      line of the definition is the ideal limit. And observation shows\n      that just as much, and as nearly, as the straight lines of\n      experience approximate to having no breadth or flexure, so much and\n      so nearly does the space-inclosing power of any two of them approach\n      to zero. The inference that if they had no breadth or flexure at\n      all, they would inclose no space at all, is a correct inductive\n      inference from these facts, conformable to one of the four Inductive\n      Methods hereinafter characterized, the Method of Concomitant\n      Variations; of which the mathematical Doctrine of Limits presents\n      the extreme case.\n\n   72 Whewell\u2019s _History of Scientific Ideas_, i., 140.\n\n   73 Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it\n      unreasonable to contend that we know by experience, that our idea of\n      a line exactly resembles a real line. \u201cIt does not appear,\u201d he says,\n      \u201chow we can compare our ideas with the realities, since we know the\n      realities only by our ideas.\u201d We know the realities by our\n      sensations. Dr. Whewell surely does not hold the \u201cdoctrine of\n      perception by means of ideas,\u201d which Reid gave himself so much\n      trouble to refute. If Dr. Whewell doubts whether we compare our\n      ideas with the corresponding sensations, and assume that they\n      resemble, let me ask on what evidence do we judge that a portrait of\n      a person not present is like the original. Surely because it is like\n      our idea, or mental image of the person, and because our idea is\n      like the man himself.\n\n      Dr. Whewell also says, that it does not appear why this resemblance\n      of ideas to the sensations of which they are copies, should be\n      spoken of as if it were a peculiarity of one class of ideas, those\n      of space. My reply is, that I do not so speak of it. The peculiarity\n      I contend for is only one of degree. All our ideas of sensation of\n      course resemble the corresponding sensations, but they do so with\n      very different degrees of exactness and of reliability. No one, I\n      presume, can recall in imagination a color or an odor with the same\n      distinctness and accuracy with which almost every one can mentally\n      reproduce an image of a straight line or a triangle. To the extent,\n      however, of their capabilities of accuracy, our recollections of\n      colors or of odors may serve as subjects of experimentation, as well\n      as those of lines and spaces, and may yield conclusions which will\n      be true of their external prototypes. A person in whom, either from\n      natural gift or from cultivation, the impressions of color were\n      peculiarly vivid and distinct, if asked which of two blue flowers\n      was of the darkest tinge, though he might never have compared the\n      two, or even looked at them together, might be able to give a\n      confident answer on the faith of his distinct recollection of the\n      colors; that is, he might examine his mental pictures, and find\n      there a property of the outward objects. But in hardly any case\n      except that of simple geometrical forms, could this be done by\n      mankind generally, with a degree of assurance equal to that which is\n      given by a contemplation of the objects themselves. Persons differ\n      most widely in the precision of their recollection, even of forms:\n      one person, when he has looked any one in the face for half a\n      minute, can draw an accurate likeness of him from memory; another\n      may have seen him every day for six months, and hardly know whether\n      his nose is long or short. But every body has a perfectly distinct\n      mental image of a straight line, a circle, or a rectangle. And every\n      one concludes confidently from these mental images to the\n      corresponding outward things. The truth is, that we may, and\n      continually do, study nature in our recollections, when the objects\n      themselves are absent; and in the case of geometrical forms we can\n      perfectly, but in most other cases only imperfectly, trust our\n      recollections.\n\n_   74 Logic_, i., 222.\n\n   75 Ibid., 226.\n\n_   76 History of Scientific Ideas_, i., 65\u201367.\n\n   77 Ibid., i., 60.\n\n   78 Ibid., 58, 59.\n\n   79 \u201cIf all mankind had spoken one language, we can not doubt that there\n      would have been a powerful, perhaps a universal, school of\n      philosophers, who would have believed in the inherent connection\n      between names and things, who would have taken the sound _man_ to be\n      the mode of agitating the air which is essentially communicative of\n      the ideas of reason, cookery, bipedality, etc.\u201d\u2014De Morgan, _Formal\n      Logic_, p. 246.\n\n   80 It would be difficult to name a man more remarkable at once for the\n      greatness and the wide range of his mental accomplishments, than\n      Leibnitz. Yet this eminent man gave as a reason for rejecting\n      Newton\u2019s scheme of the solar system, that God _could not_ make a\n      body revolve round a distant centre, unless either by some impelling\n      mechanism, or by miracle: \u201cTout ce qui n\u2019est pas explicable,\u201d says\n      he in a letter to the Abb\u00e9 Conti, \u201cpar la nature des cr\u00e9atures, est\n      miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de\n      nature; donc la chose est naturelle. Il faut que la loi soit\n      ex\u00e9cutable par les natures des cr\u00e9atures. Si Dien donnait cette loi,\n      par exemple, \u00e0 un corps libre, de tourner \u00e0 l\u2019entour d\u2019un certain\n      centre, _il faudrait ou qu\u2019il y joign\u00eet d\u2019autres corps qui par leur\n      impulsion l\u2019obligeassent de rester toujours dans son orbite\n      circulaire, ou qu\u2019il m\u00eet un ange \u00e0 ses trousses, ou enfin il\n      faudrait qu\u2019il y concour\u00fbt extraordinairement_; car naturellement il\n      s\u2019\u00e9cartera par la tangente.\u201d\u2014_Works of Leibnitz_, ed. Dutens, iii.,\n      446.\n\n_   81 Novum Organum Renovatum_, pp. 32, 33.\n\n_   82 History of Scientific Ideas_, i., 264.\n\n   83 Ibid., i., 263.\n\n   84 Ibid., 240.\n\n_   85 Hist. Scientific Ideas_, ii., 25, 26.\n\n_   86 Phil. of Disc._, p. 339.\n\n_   87 Phil. of Disc._, p. 338.\n\n   88 Ibid., p. 463.\n\n_   89 Phil. of Disc._, pp. 472, 473.\n\n   90 The _Quarterly Review_ for June, 1841, contained an article of great\n      ability on Dr. Whewell\u2019s two great works (since acknowledged and\n      reprinted in Sir John Herschel\u2019s Essays) which maintains, on the\n      subject of axioms, the doctrine advanced in the text, that they are\n      generalizations from experience, and supports that opinion by a line\n      of argument strikingly coinciding with mine. When I state that the\n      whole of the present chapter (except the last four pages, added in\n      the fifth edition) was written before I had seen the article (the\n      greater part, indeed, before it was published), it is not my object\n      to occupy the reader\u2019s attention with a matter so unimportant as the\n      degree of originality which may or may not belong to any portion of\n      my own speculations, but to obtain for an opinion which is opposed\n      to reigning doctrines, the recommendation derived from a striking\n      concurrence of sentiment between two inquirers entirely independent\n      of one another. I embrace the opportunity of citing from a writer of\n      the extensive acquirements in physical and metaphysical knowledge\n      and the capacity of systematic thought which the article evinces,\n      passages so remarkably in unison with my own views as the following:\n\n      \u201cThe truths of geometry are summed up and embodied in its\n      definitions and axioms.... Let us turn to the axioms, and what do we\n      find? A string of propositions concerning magnitude in the abstract,\n      which are equally true of space, time, force, number, and every\n      other magnitude susceptible of aggregation and subdivision. Such\n      propositions, where they are not mere definitions, as some of them\n      are, carry their inductive origin on the face of their\n      enunciation.... Those which declare that two straight lines can not\n      inclose a space, and that two straight lines which cut one another\n      can not both be parallel to a third, are in reality the only ones\n      which express characteristic properties of space, and these it will\n      be worth while to consider more nearly. Now the only clear notion we\n      can form of straightness is uniformity of direction, for space in\n      its ultimate analysis is nothing but an assemblage of distances and\n      directions. And (not to dwell on the notion of continued\n      contemplation, _i.e._, mental experience, as included in the very\n      idea of uniformity; nor on that of transfer of the contemplating\n      being from point to point, and of experience, during such transfer,\n      of the homogeneity of the interval passed over) we can not even\n      propose the proposition in an intelligible form to any one whose\n      experience ever since he was born has not assured him of the fact.\n      The unity of direction, or that we can not march from a given point\n      by more than one path direct to the same object, is matter of\n      practical experience long before it can by possibility become matter\n      of abstract thought. _We can not attempt mentally to exemplify the\n      conditions of the assertion in an imaginary case opposed to it,\n      without violating our habitual recollection of this experience, and\n      defacing our mental picture of space as grounded on it._ What but\n      experience, we may ask, can possibly assure us of the homogeneity of\n      the parts of distance, time, force, and measurable aggregates in\n      general, on which the truth of the other axioms depends? As regards\n      the latter axiom, after what has been said it must be clear that the\n      very same course of remarks equally applies to its case, and that\n      its truth is quite as much forced on the mind as that of the former\n      by daily and hourly experience, ... _including always, be it\n      observed, in our notion of experience, that which is gained by\n      contemplation of the inward picture which the mind forms to itself\n      in any proposed case, or which it arbitrarily selects as an\n      example\u2014such picture, in virtue of the extreme simplicity of these\n      primary relations, being called up by the imagination with as much\n      vividness and clearness as could be done by any external impression,\n      which is the only meaning we can attach to the word intuition, as\n      applied to such relations_.\u201d\n\n      And again, of the axioms of mechanics: \u201cAs we admit no such\n      propositions, other than as truths inductively collected from\n      observation, even in geometry itself, it can hardly be expected\n      that, in a science of obviously contingent relations, we should\n      acquiesce in a contrary view. Let us take one of these axioms and\n      examine its evidence: for instance, that equal forces\n      perpendicularly applied at the opposite ends of equal arms of a\n      straight lever will balance each other. What but experience, we may\n      ask, in the first place, can possibly inform us that a force so\n      applied will have any tendency to turn the lever on its centre at\n      all? or that force can be so transmitted along a rigid line\n      perpendicular to its direction, as to act elsewhere in space than\n      along its own line of action? Surely this is so far from being\n      self-evident that it has even a paradoxical appearance, which is\n      only to be removed by giving our lever thickness, material\n      composition, and molecular powers. Again, we conclude, that the two\n      forces, being equal and applied under precisely similar\n      circumstances, must, if they exert any effort at all to turn the\n      lever, exert equal and opposite efforts: but what _a priori_\n      reasoning can possibly assure us that they _do_ act under precisely\n      similar circumstances? that points which differ in place _are_\n      similarly circumstanced as regards the exertion of force? that\n      universal space may not have relations to universal force\u2014or, at all\n      events, that the organization of the material universe may not be\n      such as to place that portion of space occupied by it in such\n      relations to the forces exerted in it, as may invalidate the\n      absolute similarity of circumstances assumed? Or we may argue, what\n      have we to do with the notion of angular movement in the lever at\n      all? The case is one of rest, and of quiescent destruction of force\n      by force. Now how is this destruction effected? Assuredly by the\n      counter-pressure which supports the fulcrum. But would not this\n      destruction equally arise, and by the same amount of counteracting\n      force, if each force simply pressed its own half of the lever\n      against the fulcrum? And what can assure us that it is not so,\n      except removal of one or other force, and consequent tilting of the\n      lever? The other fundamental axiom of statics, that the pressure on\n      the point of support is the sum of the weights ... is merely a\n      scientific transformation and more refined mode of stating a coarse\n      and obvious result of universal experience, viz., that the weight of\n      a rigid body is the same, handle it or suspend it in what position\n      or by what point we will, and that whatever sustains it sustains its\n      total weight. Assuredly, as Mr. Whewell justly remarks, \u2018No one\n      probably ever made a trial for the purpose of showing that the\n      pressure on the support is equal to the sum of the weights.\u2019 ... But\n      it is precisely because in every action of his life from earliest\n      infancy he has been continually making the trial, and seeing it made\n      by every other living being about him, that he never dreams of\n      staking its result on one additional attempt made with scientific\n      accuracy. This would be as if a man should resolve to decide by\n      experiment whether his eyes were useful for the purpose of seeing,\n      by hermetically sealing himself up for half an hour in a metal\n      case.\u201d\n\n      On the \u201cparadox of universal propositions obtained by experience,\u201d\n      the same writer says: \u201cIf there be necessary and universal truths\n      expressible in propositions of axiomatic simplicity and obviousness,\n      and having for their subject-matter the elements of all our\n      experience and all our knowledge, surely these are the truths which,\n      if experience suggest to us any truths at all, it ought to suggest\n      most readily, clearly, and unceasingly. If it were a truth,\n      universal and necessary, that a net is spread over the whole surface\n      of every planetary globe, we should not travel far on our own\n      without getting entangled in its meshes, and making the necessity of\n      some means of extrication an axiom of locomotion.... There is,\n      therefore, nothing paradoxical, but the reverse, in our being led by\n      observation to a recognition of such truths, as _general_\n      propositions, co-extensive at least with all human experience. That\n      they pervade all the objects of experience, must insure their\n      continual suggestion _by_ experience; that they are true, must\n      insure that consistency of suggestion, that iteration of\n      uncontradicted assertion, which commands implicit assent, and\n      removes all occasion of exception; that they are simple, and admit\n      of no misunderstanding, must secure their admission by every mind.\u201d\n\n      \u201cA truth, necessary and universal, relative to any object of our\n      knowledge, must verify itself in every instance where that object is\n      before our contemplation, and if at the same time it be simple and\n      intelligible, its verification must be obvious. _The sentiment of\n      such a truth can not, therefore, but be present to our minds\n      whenever that object is contemplated, and must therefore make a part\n      of the mental picture or idea of that object which we may on any\n      occasion summon before our imagination.... All propositions,\n      therefore, become not only untrue but inconceivable_, if ... axioms\n      be violated in their enunciation.\u201d\n\n      Another eminent mathematician had previously sanctioned by his\n      authority the doctrine of the origin of geometrical axioms in\n      experience. \u201cGeometry is thus founded likewise on observation; but\n      of a kind so familiar and obvious, that the primary notions which it\n      furnishes might seem intuitive.\u201d\u2014_Sir John Leslie_, quoted by Sir\n      William Hamilton, _Discourses_, etc., p. 272.\n\n   91 Principles of Psychology.\n\n   92 Mr. Spencer is mistaken in supposing me to claim any peculiar\n      \u201cnecessity\u201d for this axiom as compared with others. I have corrected\n      the expressions which led him into that misapprehension of my\n      meaning.\n\n   93 Mr. Spencer, in recently returning to the subject (Principles of\n      Psychology, new edition, chap. xii.: \u201cThe Test of Relative\n      Validity\u201d), makes two answers to the preceding remarks. One is:\n\n      \u201cWere an argument formed by repeating the same proposition over and\n      over again, it would be true that any intrinsic fallibility of the\n      postulate would not make the conclusion more untrustworthy than the\n      first step. But an argument consists of unlike propositions. Now,\n      since Mr. Mill\u2019s criticism on the Universal Postulate is that in\n      some cases, which he names, it has proved to be an untrustworthy\n      test; it follows that in any argument consisting of heterogeneous\n      propositions, there is a risk, increasing as the number of\n      propositions increases, that some one of them belongs to this class\n      of cases, and is wrongly accepted because of the inconceivableness\n      of its negation.\u201d\n\n      No doubt: but this supposes new _premises_ to be taken in. The point\n      we are discussing is the fallibility not of the premises, but of the\n      reasoning, as distinguished from the premises. Now the validity of\n      the reasoning depends always upon the same axiom, repeated (in\n      thought) \u201cover and over again,\u201d viz., that whatever has a mark, has\n      what it is a mark of. Even, therefore, on the assumption that this\n      axiom rests ultimately on the Universal Postulate, and that, the\n      Postulate not being wholly trustworthy, the axiom may be one of the\n      cases of its failure; all the risk there is of this is incurred at\n      the very first step of the reasoning, and is not added to, however\n      long may be the series of subsequent steps.\n\n      I am here arguing, of course, from Mr. Spencer\u2019s point of view. From\n      my own the case is still clearer; for, in my view, the truth that\n      whatever has a mark has what it is a mark of, is wholly trustworthy,\n      and derives none of its evidence from so very untrustworthy a test\n      as the inconceivability of the negative.\n\n      Mr. Spencer\u2019s second answer is valid up to a certain point; it is,\n      that every prolongation of the process involves additional chances\n      of casual error, from carelessness in the reasoning operation. This\n      is an important consideration in the private speculations of an\n      individual reasoner; and even with respect to mankind at large, it\n      must be admitted that, though mere oversights in the syllogistic\n      process, like errors of addition in an account, are special to the\n      individual, and seldom escape detection, confusion of thought\n      produced (for example) by ambiguous terms has led whole nations or\n      ages to accept fallacious reasoning as valid. But this very fact\n      points to causes of error so much more dangerous than the mere\n      length of the process, as quite to vitiate the doctrine that the\n      \u201ctest of the relative validities of conflicting conclusions\u201d is the\n      number of times the fundamental postulate is involved. On the\n      contrary, the subjects on which the trains of reasoning are longest,\n      and the assumption, therefore, oftenest repeated, are in general\n      those which are best fortified against the really formidable causes\n      of fallacy; as in the example already given of mathematics.\n\n   94 Mr. Spencer makes a distinction between conceiving myself looking\n      into darkness, and conceiving _that I am_ then and there looking\n      into darkness. To me it seems that this change of the expression to\n      the form _I am_, just marks the transition from conception to\n      belief, and that the phrase \u201cto conceive that _I am_,\u201d or \u201cthat any\n      thing _is_,\u201d is not consistent with using the word conceive in its\n      rigorous sense.\n\n   95 I have myself accepted the contest, and fought it out on this\n      battle-ground, in the eleventh chapter of _An Examination of Sir\n      William Hamilton\u2019s Philosophy._\n\n   96 Chap. xi.\n\n   97 In one of the three cases, Mr. Spencer, to my no small surprise,\n      thinks that the belief of mankind \u201ccan not be rightly said to have\n      undergone\u201d the change I allege. Mr. Spencer himself still thinks we\n      are unable to conceive gravitation acting through empty space. \u201cIf\n      an astronomer avowed that he could conceive gravitative force as\n      exercised through space absolutely void, my private opinion would be\n      that he mistook the nature of conception. Conception implies\n      representation. Here the elements of the representation are the two\n      bodies and an agency by which either affects the other. To conceive\n      this agency is to represent it in some terms derived from our\n      experiences\u2014that is, from our sensations. As this agency gives us no\n      sensations, we are obliged (if we try to conceive it) to use symbols\n      idealized from our sensations\u2014imponderable units forming a medium.\u201d\n\n      If Mr. Spencer means that the action of gravitation gives us no\n      sensations, the assertion is one than which I have not seen, in the\n      writings of philosophers, many more startling. What other sensation\n      do we need than the sensation of one body moving toward another?\n      \u201cThe elements of the representation\u201d are not two bodies and an\n      \u201cagency,\u201d but two bodies and an effect; viz., the fact of their\n      approaching one another. If we are able to conceive a vacuum, is\n      there any difficulty in conceiving a body falling to the earth\n      through it?\n\n_   98 Discussions_, etc., 2d ed., p. 624.\n\n   99 Professor Bain (_Logic_, i., 16) identifies the Principle of\n      Contradiction with his Law of Relativity, viz., that \u201cevery thing\n      that can be thought of, every affirmation that can be made, has an\n      opposite or counter notion or affirmation;\u201d a proposition which is\n      one of the general results of the whole body of human experience.\n      For further considerations respecting the axioms of Contradiction\n      and Excluded Middle, see the twenty-first chapter of _An Examination\n      of Sir William Hamilton\u2019s Philosophy_.\n\n  100 Dr. Whewell thinks it improper to apply the term Induction to any\n      operation not terminating in the establishment of a general truth.\n      Induction, he says (_Philosophy of Discovery_, p. 245), \u201cis not the\n      same thing as experience and observation. Induction is experience or\n      observation _consciously_ looked at in a _general_ form. This\n      consciousness and generality are necessary parts of that knowledge\n      which is science.\u201d And he objects (p. 241) to the mode in which the\n      word Induction is employed in this work, as an undue extension of\n      that term \u201cnot only to the cases in which the general induction is\n      consciously applied to a particular instance, but to the cases in\n      which the particular instance is dealt with by means of experience\n      in that rude sense in which experience can be asserted of brutes,\n      and in which of course we can in no way imagine that the law is\n      possessed or understood as a general proposition.\u201d This use of the\n      term he deems a \u201cconfusion of knowledge with practical tendencies.\u201d\n\n      I disclaim, as strongly as Dr. Whewell can do, the application of\n      such terms as induction, inference, or reasoning, to operations\n      performed by mere instinct, that is, from an animal impulse, without\n      the exertion of any intelligence. But I perceive no ground for\n      confining the use of those terms to cases in which the inference is\n      drawn in the forms and with the precautions required by scientific\n      propriety. To the idea of Science, an express recognition and\n      distinct apprehension of general laws as such, is essential: but\n      nine-tenths of the conclusions drawn from experience in the course\n      of practical life, are drawn without any such recognition: they are\n      direct inferences from known cases, to a case supposed to be\n      similar. I have endeavored to show that this is not only as\n      legitimate an operation, but substantially the same operation, as\n      that of ascending from known cases to a general proposition; except\n      that the latter process has one great security for correctness which\n      the former does not possess. In science, the inference must\n      necessarily pass through the intermediate stage of a general\n      proposition, because Science wants its conclusions for record, and\n      not for instantaneous use. But the inferences drawn for the guidance\n      of practical affairs, by persons who would often be quite incapable\n      of expressing in unexceptionable terms the corresponding\n      generalizations, may and frequently do exhibit intellectual powers\n      quite equal to any which have ever been displayed in science; and if\n      these inferences are not inductive, what are they? The limitation\n      imposed on the term by Dr. Whewell seems perfectly arbitrary;\n      neither justified by any fundamental distinction between what he\n      includes and what he desires to exclude, nor sanctioned by usage, at\n      least from the time of Reid and Stewart, the principal legislators\n      (as far as the English language is concerned) of modern metaphysical\n      terminology.\n\n  101 Supra, p. 145.\n\n_  102 Novum Organum Renovatum_, pp. 72, 73.\n\n_  103 Novum Organum Renovatum_, p. 32.\n\n_  104 Cours de Philosophie Positive_, vol. ii., p. 202.\n\n  105 Dr. Whewell, in his reply, contests the distinction here drawn, and\n      maintains, that not only different descriptions, but different\n      explanations of a phenomenon, may all be true. Of the three theories\n      respecting the motions of the heavenly bodies, he says (_Philosophy\n      of Discovery_, p. 231): \u201cUndoubtedly all these explanations may be\n      true and consistent with each other, and would be so if each had\n      been followed out so as to show in what manner it could be made\n      consistent with the facts. And this was, in reality, in a great\n      measure done. The doctrine that the heavenly bodies were moved by\n      vortices was successfully modified, so that it came to coincide in\n      its results with the doctrine of an inverse-quadratic centripetal\n      force.... When this point was reached, the vortex was merely a\n      machinery, well or ill devised, for producing such a centripetal\n      force, and therefore did not contradict the doctrine of a\n      centripetal force. Newton himself does not appear to have been\n      averse to explaining gravity by impulse. So little is it true that\n      if one theory be true the other must be false. The attempt to\n      explain gravity by the impulse of streams of particles flowing\n      through the universe in all directions, which I have mentioned in\n      the _Philosophy_, is so far from being inconsistent with the\n      Newtonian theory, that it is founded entirely upon it. And even with\n      regard to the doctrine, that the heavenly bodies move by an inherent\n      virtue; if this doctrine had been maintained in any such way that it\n      was brought to agree with the facts, the inherent virtue must have\n      had its laws determined; and then it would have been found that the\n      virtue had a reference to the central body; and so, the \u2018inherent\n      virtue\u2019 must have coincided in its effect with the Newtonian force;\n      and then, the two explanations would agree, except so far as the\n      word \u2018inherent\u2019 was concerned. And if such a part of an earlier\n      theory as this word _inherent_ indicates, is found to be untenable,\n      it is of course rejected in the transition to later and more exact\n      theories, in Inductions of this kind, as well as in what Mr. Mill\n      calls Descriptions. There is, therefore, still no validity\n      discoverable in the distinction which Mr. Mill attempts to draw\n      between descriptions like Kepler\u2019s law of elliptical orbits, and\n      other examples of induction.\u201d\n\n      If the doctrine of vortices had meant, not that vortices existed,\n      but only that the planets moved _in the same manner_ as if they had\n      been whirled by vortices; if the hypothesis had been merely a mode\n      of representing the facts, not an attempt to account for them; if,\n      in short, it had been only a Description; it would, no doubt, have\n      been reconcilable with the Newtonian theory. The vortices, however,\n      were not a mere aid to conceiving the motions of the planets, but a\n      supposed physical agent, actively impelling them; a material fact,\n      which might be true or not true, but could not be both true and not\n      true. According to Descartes\u2019s theory it was true, according to\n      Newton\u2019s it was not true. Dr. Whewell probably means that since the\n      phrases, centripetal and projectile force, do not declare the nature\n      but only the direction of the forces, the Newtonian theory does not\n      absolutely contradict any hypothesis which may be framed respecting\n      the mode of their production. The Newtonian theory, regarded as a\n      mere _description_ of the planetary motions, does not; but the\n      Newtonian theory as an _explanation_ of them does. For in what does\n      the explanation consist? In ascribing those motions to a general law\n      which obtains between all particles of matter, and in identifying\n      this with the law by which bodies fall to the ground. If the planets\n      are kept in their orbits by a force which draws the particles\n      composing them toward every other particle of matter in the solar\n      system, they are not kept in those orbits by the impulsive force of\n      certain streams of matter which whirl them round. The one\n      explanation absolutely excludes the other. Either the planets are\n      not moved by vortices, or they do not move by a law common to all\n      matter. It is impossible that both opinions can be true. As well\n      might it be said that there is no contradiction between the\n      assertions, that a man died because somebody killed him, and that he\n      died a natural death.\n\n      So, again, the theory that the planets move by a virtue inherent in\n      their celestial nature, is incompatible with either of the two\n      others: either that of their being moved by vortices, or that which\n      regards them as moving by a property which they have in common with\n      the earth and all terrestrial bodies. Dr. Whewell says that the\n      theory of an inherent virtue agrees with Newton\u2019s when the word\n      inherent is left out, which of course it would be (he says) if\n      \u201cfound to be untenable.\u201d But leave that out, and where is the\n      theory? The word inherent _is_ the theory. When that is omitted,\n      there remains nothing except that the heavenly bodies move \u201cby a\n      virtue,\u201d _i.e._, by a power of some sort; or by virtue of their\n      celestial nature, which directly contradicts the doctrine that\n      terrestrial bodies fall by the same law.\n\n      If Dr. Whewell is not yet satisfied, any other subject will serve\n      equally well to test his doctrine. He will hardly say that there is\n      no contradiction between the emission theory and the undulatory\n      theory of light; or that there can be both one and two\n      electricities; or that the hypothesis of the production of the\n      higher organic forms by development from the lower, and the\n      supposition of separate and successive acts of creation, are quite\n      reconcilable; or that the theory that volcanoes are fed from a\n      central fire, and the doctrines which ascribe them to chemical\n      action at a comparatively small depth below the earth\u2019s surface, are\n      consistent with one another, and all true as far as they go.\n\n      If different explanations of the same fact can not both be true,\n      still less, surely, can different predictions. Dr. Whewell quarrels\n      (on what ground it is not necessary here to consider) with the\n      example I had chosen on this point, and thinks an objection to an\n      illustration a sufficient answer to a theory. Examples not liable to\n      his objection are easily found, if the proposition that conflicting\n      predictions can not both be true, can be made clearer by many\n      examples. Suppose the phenomenon to be a newly-discovered comet, and\n      that one astronomer predicts its return once in every 300\n      years\u2014another once in every 400: can they both be right? When\n      Columbus predicted that by sailing constantly westward he should in\n      time return to the point from which he set out, while others\n      asserted that he could never do so except by turning back, were both\n      he and his opponents true prophets? Were the predictions which\n      foretold the wonders of railways and steamships, and those which\n      averred that the Atlantic could never be crossed by steam\n      navigation, nor a railway train propelled ten miles an hour, both\n      (in Dr. Whewell\u2019s words) \u201ctrue, and consistent with one another?\u201d\n\n      Dr. Whewell sees no distinction between holding contradictory\n      opinions on a question of fact, and merely employing different\n      analogies to facilitate the conception of the same fact. The case of\n      different Inductions belongs to the former class, that of different\n      Descriptions to the latter.\n\n_  106 Phil. of Discov._, p. 256.\n\n_  107 Essays on the Pursuit of Truth._\n\n  108 In the first edition a note was appended at this place, containing\n      some criticism on Archbishop Whately\u2019s mode of conceiving the\n      relation between Syllogism and Induction. In a subsequent issue of\n      his _Logic_, the Archbishop made a reply to the criticism, which\n      induced me to cancel part of the note, incorporating the remainder\n      in the text. In a still later edition, the Archbishop observes in a\n      tone of something like disapprobation, that the objections,\n      \u201cdoubtless from their being fully answered and found untenable, were\n      silently suppressed,\u201d and that hence he might appear to some of his\n      readers to be combating a shadow. On this latter point, the\n      Archbishop need give himself no uneasiness. His readers, I make bold\n      to say, will fully credit his mere affirmation that the objections\n      have actually been made.\n\n      But as he seems to think that what he terms the suppression of the\n      objections ought not to have been made \u201csilently,\u201d I now break that\n      silence, and state exactly what it is that I suppressed, and why. I\n      suppressed that alone which might be regarded as personal criticism\n      on the Archbishop. I had imputed to him the having omitted to ask\n      himself a particular question. I found that he had asked himself the\n      question, and could give it an answer consistent with his own\n      theory. I had also, within the compass of a parenthesis, hazarded\n      some remarks on certain general characteristics of Archbishop\n      Whately as a philosopher. These remarks, though their tone, I hope,\n      was neither disrespectful nor arrogant, I felt, on reconsideration,\n      that I was hardly entitled to make; least of all, when the instance\n      which I had regarded as an illustration of them, failed, as I now\n      saw, to bear them out. The real matter at the bottom of the whole\n      dispute, the different view we take of the function of the major\n      premise, remains exactly where it was; and so far was I from\n      thinking that my opinion had been fully \u201canswered\u201d and was\n      \u201cuntenable,\u201d that in the same edition in which I canceled the note,\n      I not only enforced the opinion by further arguments, but answered\n      (though without naming him) those of the Archbishop.\n\n      For not having made this statement before, I do not think it needful\n      to apologize. It would be attaching very great importance to one\u2019s\n      smallest sayings, to think a formal retractation requisite every\n      time that one falls into an error. Nor is Archbishop Whately\u2019s\n      well-earned fame of so tender a quality as to require that in\n      withdrawing a slight criticism on him I should have been bound to\n      offer a public _amende_ for having made it.\n\n  109 But though it is a condition of the validity of every induction that\n      there be uniformity in the course of nature, it is not a necessary\n      condition that the uniformity should pervade all nature. It is\n      enough that it pervades the particular class of phenomena to which\n      the induction relates. An induction concerning the motions of the\n      planets, or the properties of the magnet, would not be vitiated\n      though we were to suppose that wind and weather are the sport of\n      chance, provided it be assumed that astronomical and magnetic\n      phenomena are under the dominion of general laws. Otherwise the\n      early experience of mankind would have rested on a very weak\n      foundation; for in the infancy of science it could not be known that\n      _all_ phenomena are regular in their course.\n\n      Neither would it be correct to say that every induction by which we\n      infer any truth, implies the general fact of uniformity _as\n      foreknown_, even in reference to the kind of phenomena concerned. It\n      implies, _either_ that this general fact is already known, _or_ that\n      we may now know it: as the conclusion, the Duke of Wellington is\n      mortal, drawn from the instances A, B, and C, implies either that we\n      have already concluded all men to be mortal, or that we are now\n      entitled to do so from the same evidence. A vast amount of confusion\n      and paralogism respecting the grounds of Induction would be\n      dispelled by keeping in view these simple considerations.\n\n  110 Infra, chap. xxi.\n\n  111 Infra, chap. xxi., xxii.\n\n  112 In strictness, wherever the present constitution of space exists;\n      which we have ample reason to believe that it does in the region of\n      the fixed stars.\n\n  113 Dr. Whewell (_Phil. of Discov._, p. 246) will not allow these and\n      similar erroneous judgments to be called inductions; inasmuch as\n      such superstitious fancies \u201cwere not collected from the facts by\n      seeking a law of their occurrence, but were suggested by an\n      imagination of the anger of superior powers, shown by such\n      deviations from the ordinary course of nature.\u201d I conceive the\n      question to be, not in what manner these notions were at first\n      suggested, but by what evidence they have, from time to time, been\n      supposed to be substantiated. If the believers in these erroneous\n      opinions had been put on their defense, they would have referred to\n      experience: to the comet which preceded the assassination of Julius\n      C\u00e6sar, or to oracles and other prophecies known to have been\n      fulfilled. It is by such appeals to facts that all analogous\n      superstitions, even in our day, attempt to justify themselves; the\n      supposed evidence of experience is necessary to their hold on the\n      mind. I quite admit that the influence of such coincidences would\n      not be what it is, if strength were not lent to it by an antecedent\n      presumption; but this is not peculiar to such cases; preconceived\n      notions of probability form part of the explanation of many other\n      cases of belief on insufficient evidence. The _a priori_ prejudice\n      does not prevent the erroneous opinion from being sincerely regarded\n      as a legitimate conclusion from experience; though it improperly\n      predisposes the mind to that interpretation of experience.\n\n      Thus much in defense of the sort of examples objected to. But it\n      would be easy to produce instances, equally adapted to the purpose,\n      and in which no antecedent prejudice is at all concerned. \u201cFor many\n      ages,\u201d says Archbishop Whately, \u201call farmers and gardeners were\n      firmly convinced\u2014and convinced of their knowing it by\n      experience\u2014that the crops would never turn out good unless the seed\n      were sown during the increase of the moon.\u201d This was induction, but\n      bad induction; just as a vicious syllogism is reasoning, but bad\n      reasoning.\n\n  114 The assertion, that any and every one of the conditions of a\n      phenomenon may be and is, on some occasions and for some purposes,\n      spoken of as the cause, has been disputed by an intelligent reviewer\n      of this work in the _Prospective Review_ (the predecessor of the\n      justly esteemed _National Review_), who maintains that \u201cwe always\n      apply the word cause rather to that element in the antecedents which\n      exercises _force_, and which would _tend_ at all times to produce\n      the same or a similar effect to that which, under certain\n      conditions, it would actually produce.\u201d And he says, that \u201cevery one\n      would feel\u201d the expression, that the cause of a surprise was the\n      sentinel\u2019s being off his post, to be incorrect; but that the\n      \u201callurement or force which _drew_ him off his post, might be so\n      called, because in doing so it removed a resisting power which would\n      have prevented the surprise.\u201d I can not think that it would be wrong\n      to say, that the event took place because the sentinel was absent,\n      and yet right to say that it took place because he was bribed to be\n      absent. Since the only direct effect of the bribe was his absence,\n      the bribe could be called the remote cause of the surprise, only on\n      the supposition that the absence was the proximate cause; nor does\n      it seem to me that any one (who had not a theory to support) would\n      use the one expression and reject the other.\n\n      The reviewer observes, that when a person dies of poison, his\n      possession of bodily organs is a necessary condition, but that no\n      one would ever speak of it as the cause. I admit the fact; but I\n      believe the reason to be, that the occasion could never arise for so\n      speaking of it; for when in the inaccuracy of common discourse we\n      are led to speak of some one condition of a phenomenon as its cause,\n      the condition so spoken of is always one which it is at least\n      possible that the hearer may require to be informed of. The\n      possession of bodily organs is a known condition, and to give that\n      as the answer, when asked the cause of a person\u2019s death, would not\n      supply the information sought. Once conceive that a doubt could\n      exist as to his having bodily organs, or that he were to be compared\n      with some being who had them not, and cases may be imagined in which\n      it might be said that his possession of them was the cause of his\n      death. If Faust and Mephistopheles together took poison, it might be\n      said that Faust died because he was a human being, and had a body,\n      while Mephistopheles survived because he was a spirit.\n\n      It is for the same reason that no one (as the reviewer remarks)\n      \u201ccalls the cause of a leap, the muscles or sinews of the body,\n      though they are necessary conditions; nor the cause of a\n      self-sacrifice, the knowledge which was necessary for it; nor the\n      cause of writing a book, that a man has time for it, which is a\n      necessary condition.\u201d These conditions (besides that they are\n      antecedent _states_, and not proximate antecedent _events_, and are\n      therefore never the conditions in closest apparent proximity to the\n      effect) are all of them so obviously implied, that it is hardly\n      possible there should exist that necessity for insisting on them,\n      which alone gives occasion for speaking of a single condition as if\n      it were the cause. Wherever this necessity exists in regard to some\n      one condition, and does not exist in regard to any other, I conceive\n      that it is consistent with usage, when scientific accuracy is not\n      aimed at, to apply the name cause to that one condition. If the only\n      condition which can be supposed to be unknown is a negative\n      condition, the negative condition may be spoken of as the cause. It\n      might be said that a person died for want of medical advice: though\n      this would not be likely to be said, unless the person was already\n      understood to be ill, and in order to indicate that this negative\n      circumstance was what made the illness fatal, and not the weakness\n      of his constitution, or the original virulence of the disease. It\n      might be said that a person was drowned because he could not swim;\n      the positive condition, namely, that he fell into the water, being\n      already implied in the word drowned. And here let me remark, that\n      his falling into the water is in this case the only positive\n      condition: all the conditions not expressly or virtually included in\n      this (as that he could not swim, that nobody helped him, and so\n      forth) are negative. Yet, if it were simply said that the cause of a\n      man\u2019s death was falling into the water, there would be quite as\n      great a sense of impropriety in the expression, as there would be if\n      it were said that the cause was his inability to swim; because,\n      though the one condition is positive and the other negative, it\n      would be felt that neither of them was sufficient, without the\n      other, to produce death.\n\n      With regard to the assertion that nothing is termed the cause,\n      except the element which exerts active force; I waive the question\n      as to the meaning of active force, and accepting the phrase in its\n      popular sense, I revert to a former example, and I ask, would it be\n      more agreeable to custom to say that a man fell because his foot\n      slipped in climbing a ladder, or that he fell because of his weight?\n      for his weight, and not the motion of his foot, was the active force\n      which determined his fall. If a person walking out in a frosty day,\n      stumbled and fell, it might be said that he stumbled because the\n      ground was slippery, or because he was not sufficiently careful: but\n      few people, I suppose, would say, that he stumbled because he\n      walked. Yet the only active force concerned was that which he\n      exerted in walking: the others were mere negative conditions; but\n      they happened to be the only ones which there could be any necessity\n      to state; for he walked, most likely, in exactly his usual manner,\n      and the negative conditions made all the difference. Again, if a\n      person were asked why the army of Xerxes defeated that of Leonidas,\n      he would probably say, because they were a thousand times the\n      number; but I do not think he would say, it was because they fought,\n      though that was the element of active force. To borrow another\n      example, used by Mr. Grove and by Mr. Baden Powell, the opening of\n      flood-gates is said to be the cause of the flow of water; yet the\n      active force is exerted by the water itself, and opening the\n      flood-gates merely supplies a negative condition. The reviewer adds,\n      \u201cThere are some conditions absolutely passive, and yet absolutely\n      necessary to physical phenomena, viz., the relations of space and\n      time; and to these no one ever applies the word cause without being\n      immediately arrested by those who hear him.\u201d Even from this\n      statement I am compelled to dissent. Few persons would feel it\n      incongruous to say (for example) that a secret became known because\n      it was spoken of when A. B. was within hearing; which is a condition\n      of space: or that the cause why one of two particular trees is\n      taller than the other, is that it has been longer planted; which is\n      a condition of time.\n\n  115 There are a few exceptions; for there are some properties of objects\n      which seem to be purely preventive; as the property of opaque\n      bodies, by which they intercept the passage of light. This, as far\n      as we are able to understand it, appears an instance not of one\n      cause counteracting another by the same law whereby it produces its\n      own effects, but of an agency which manifests itself in no other way\n      than in defeating the effects of another agency. If we knew on what\n      other relations to light, or on what peculiarities of structure,\n      opacity depends, we might find that this is only an apparent, not a\n      real, exception to the general proposition in the text. In any case\n      it needs not affect the practical application. The formula which\n      includes all the negative conditions of an effect in the single one\n      of the absence of counteracting causes, is not violated by such\n      cases as this; though, if all counteracting agencies were of this\n      description, there would be no purpose served by employing the\n      formula.\n\n  116 I mean by this expression, the ultimate laws of nature (whatever\n      they may be) as distinguished from the derivative laws and from the\n      collocations. The diurnal revolution of the earth (for example) is\n      not a part of the constitution of things, because nothing can be so\n      called which might possibly be terminated or altered by natural\n      causes.\n\n  117 I use the words \u201cstraight line\u201d for brevity and simplicity. In\n      reality the line in question is not exactly straight, for, from the\n      effect of refraction, we actually see the sun for a short interval\n      during which the opaque mass of the earth is interposed in a direct\n      line between the sun and our eyes; thus realizing, though but to a\n      limited extent, the coveted desideratum of seeing round a corner.\n\n_  118 Second Burnett Prize Essay_, by Principal Tulloch, p. 25.\n\n_  119 Letters on the Philosophy of the Human Mind_, First Series, p. 219.\n\n_  120 Essays_, pp. 206\u2013208.\n\n  121 To the universality which mankind are agreed in ascribing to the Law\n      of Causation, there is one claim of exception, one disputed case,\n      that of the Human Will; the determinations of which, a large class\n      of metaphysicians are not willing to regard as following the causes\n      called motives, according to as strict laws as those which they\n      suppose to exist in the world of mere matter. This controverted\n      point will undergo a special examination when we come to treat\n      particularly of the Logic of the Moral Sciences (Book vi., chap. 2).\n      In the mean time, I may remark that these metaphysicians, who, it\n      must be observed, ground the main part of their objection on the\n      supposed repugnance of the doctrine in question to our\n      consciousness, seem to me to mistake the fact which consciousness\n      testifies against. What is really in contradiction to consciousness,\n      they would, I think, on strict self-examination, find to be, the\n      application to human actions and volitions of the ideas involved in\n      the common use of the term Necessity; which I agree with them in\n      objecting to. But if they would consider that by saying that a\n      person\u2019s actions _necessarily_ follow from his character, all that\n      is really meant (for no more is meant in any case whatever of\n      causation) is that he invariably _does_ act in conformity to his\n      character, and that any one who thoroughly knew his character could\n      certainly predict how he would act in any supposable case; they\n      probably would not find this doctrine either contrary to their\n      experience or revolting to their feelings. And no more than this is\n      contended for by any one but an Asiatic fatalist.\n\n  122 I believe, however, the accredited authorities do suppose that\n      molecular motion, equivalent in amount to that which will be\n      manifested in the combustion of the coal, is actually taking place\n      during the whole of the long interval, if not in the coal, yet in\n      the oxygen which will then combine with it. But how purely\n      hypothetical this supposition is, need hardly be remarked; I venture\n      to say, unnecessarily and extravagantly hypothetical.\n\n_  123 Lectures on Metaphysics_, vol. ii., Lect. xxxix., pp. 391\u20132.\n\n      I regret that I can not invoke the authority of Sir William Hamilton\n      in favor of my own opinions on Causation, as I can against the\n      particular theory which I am now combating. But that acute thinker\n      has a theory of Causation peculiar to himself, which has never yet,\n      as far as I know, been analytically examined, but which, I venture\n      to think, admits of as complete refutation as any one of the false\n      or insufficient psychological theories which strew the ground in\n      such numbers under his potent metaphysical scythe. (Since examined\n      and controverted in the sixteenth chapter of _An Examination of Sir\n      William Hamilton\u2019s Philosophy_.)\n\n  124 Unless we are to consider as such the following statement, by one of\n      the writers quoted in the text: \u201cIn the case of mental exertion, the\n      result to be accomplished is _preconsidered_ or meditated, and is\n      therefore known _a priori_, or before experience.\u201d\u2014(Bowen\u2019s _Lowell\n      Lectures on the Application of Metaphysical and Ethical Science to\n      the Evidence of Religion_. Boston, 1849.) This is merely saying that\n      when we will a thing we have an idea of it. But to have an idea of\n      what we wish to happen, does not imply a prophetic knowledge that it\n      will happen. Perhaps it will be said that the _first time_ we\n      exerted our will, when we had of course no experience of any of the\n      powers residing in us, we nevertheless must already have known that\n      we possessed them, since we can not will that which we do not\n      believe to be in our power. But the impossibility is perhaps in the\n      words only, and not in the facts; for we may _desire_ what we do not\n      know to be in our power; and finding by experience that our bodies\n      move according to our _desire_, we may then, and only then, pass\n      into the more complicated mental state which is termed will.\n\n      After all, even if we had an instinctive knowledge that our actions\n      would follow our will, this, as Brown remarks, would prove nothing\n      as to the nature of Causation. Our knowing, previous to experience,\n      that an antecedent will be followed by a certain consequent, would\n      not prove the relation between them to be any thing more than\n      antecedence and consequence.\n\n  125 Reid\u2019s _Essays on the Active Powers_, Essay iv., chap. 3.\n\n_  126 Prospective Review_ for February, 1850.\n\n  127 Vide supra, p. 178, note.\n\n_  128 Westminster Review_ for October, 1855.\n\n  129 See the whole doctrine in Aristotle _de \u00c1nim\u00e2_, where the \u03b8\u03c1\u03b5\u03c0\u03c4\u03b9\u03ba\u1f74\n      \u03c8\u03c5\u03c7\u1f74 is treated as exactly equivalent to \u03b8\u03c1\u03b5\u03c0\u03c4\u03b9\u03ba\u1f74 \u03b4\u03cd\u03bd\u03b1\u03bc\u03b9\u03c2.\n\n  130 It deserves notice that the parts of nature which Aristotle regards\n      as representing evidence of design, are the Uniformities: the\n      phenomena in so far as reducible to law. \u03a4\u03cd\u03c7\u03b7 and \u03c4\u1f78 \u03b1\u1f50\u03c4\u03bf\u03bc\u03ac\u03c4\u03bf\u03bd\n      satisfy him as explanations of the variable element in phenomena,\n      but their occurring according to a fixed rule can only, to his\n      conceptions, be accounted for by an Intelligent Will. The common, or\n      what may be called the instinctive, religious interpretation of\n      nature, is the reverse of this. The events in which men\n      spontaneously see the hand of a supernatural being, are those which\n      can not, as they think, be reduced to a physical law. What they can\n      distinctly connect with physical causes, and especially what they\n      can predict, though of course ascribed to an Author of Nature, if\n      they already recognize such an author, might be conceived, they\n      think, to arise from a blind fatality, and in any case do not appear\n      to them to bear so obviously the mark of a divine will. And this\n      distinction has been countenanced by eminent writers on Natural\n      Theology, in particular by Dr. Chalmers, who thinks that though\n      design is present everywhere, the irresistible evidence of it is to\n      be found not in the _laws_ of nature but in the collocations,\n      _i.e._, in the part of nature in which it is impossible to trace any\n      law. A few properties of dead matter might, he thinks, conceivably\n      account for the regular and invariable succession of effects and\n      causes; but that the different kinds of matter have been so placed\n      as to promote beneficent ends, is what he regards as the proof of a\n      Divine Providence. Mr. Baden Powell, in his Essay entitled\n      \u201cPhilosophy of Creation,\u201d has returned to the point of view of\n      Aristotle and the ancients, and vigorously re-asserts the doctrine\n      that the indication of design in the universe is not special\n      adaptations, but Uniformity and Law, these being the evidences of\n      mind, and not what appears to us to be a provision for our uses.\n      While I decline to express any opinion here on this _vexata\n      qu\u00e6stio_, I ought not to mention Mr. Powell\u2019s volume without the\n      acknowledgment due to the philosophic spirit which pervades\n      generally the three Essays composing it, forming in the case of one\n      of them (the \u201cUnity of Worlds\u201d) an honorable contrast with the other\n      dissertations, so far as they have come under my notice, which have\n      appeared on either side of that controversy.\n\n  131 In the words of Fontenelle, another celebrated Cartesian, \u201cles\n      philosophes aussi bien que le peuple avaient cru que l\u2019\u00e2me et le\n      corps agissaient r\u00e9ellement et physiquement l\u2019un sur l\u2019autre.\n      Descartes vint, qui prouva que leur nature ne permettait point cette\n      sorte de communication v\u00e9ritable, et qu\u2019ils n\u2019en pouvaient avoir\n      qu\u2019une apparente, dont Dieu \u00e9tait le M\u00e9diateur.\u201d\u2014(_\u0152uvres de\n      Fontenelle_, ed. 1767, tom. v., p. 534.)\n\n  132 I omit, for simplicity, to take into account the effect, in this\n      latter case, of the diminution of pressure, in diminishing the flow\n      of water through the drain; which evidently in no way affects the\n      truth or applicability of the principle, since when the two causes\n      act simultaneously the conditions of that diminution of pressure do\n      not arise.\n\n  133 Professor Bain adds several other well-established chemical\n      generalizations: \u201cThe laws that simple substances exhibit the\n      strongest affinities; that compounds are more fusible than their\n      elements; that combination tends to a lower state of matter from gas\n      down to solid;\u201d and some general propositions concerning the\n      circumstances which facilitate or resist chemical combination.\n      (Logic, ii., 254.)\n\n  134 Professor Bain (Logic, ii., 39) points out a class of cases, other\n      than that spoken of in the text, which he thinks must be regarded as\n      an exception to the Composition of Causes. \u201cCauses that merely make\n      good the collocation for bringing a prime mover into action, or that\n      release a potential force, do not follow any such rule. One man may\n      direct a gun upon a fort as well as three: two sparks are not more\n      effectual than one in exploding a barrel of gunpowder. In medicine\n      there is a certain dose that answers the end; and adding to it does\n      no more good.\u201d\n\n      I am not sure that these cases are really exceptions. The law of\n      Composition of Causes, I think, is really fulfilled, and the\n      appearance to the contrary is produced by attending to the remote\n      instead of the immediate effect of the causes. In the cases\n      mentioned, the immediate effect of the causes in action is a\n      collocation, and the duplication of the cause does double the\n      quantity of collocation. Two men could raise the gun to the required\n      angle twice as quickly as one, though one is enough. Two sparks put\n      two sets of particles of the gunpowder into the state of intestine\n      motion which makes them explode, though one is sufficient. It is the\n      collocation itself that does not, by being doubled, always double\n      the effect; because in many cases a certain collocation, once\n      obtained, is all that is required for the production of the whole\n      amount of effect which can be produced at all at the given time and\n      place. Doubling the collocation with difference of time and place,\n      as by pointing two guns, or exploding a second barrel after the\n      first, does double the effect. This remark applies still more to Mr.\n      Bain\u2019s third example, that of a double dose of medicine; for a\n      double dose of an aperient does purge more violently, and a double\n      dose of laudanum does produce longer and sounder sleep. But a double\n      purging, or a double amount of narcotism, may have remote effects\n      different in kind from the effect of the smaller amount, reducing\n      the case to that of heteropathic laws, discussed in the text.\n\n  135 Unless, indeed, the consequent was generated, not by the antecedent,\n      but by the means employed to produce the antecedent. As, however,\n      these means are under our power, there is so far a probability that\n      they are also sufficiently within our knowledge to enable us to\n      judge whether that could be the case or not.\n\n_  136 Discourse on the Study of Natural Philosophy_, p. 179.\n\n  137 For this speculation, as for many other of my scientific\n      illustrations, I am indebted to Professor Bain, whose subsequent\n      treatise on Logic abounds with apt illustrations of all the\n      inductive methods.\n\n  138 This view of the necessary co-existence of opposite excitements\n      involves a great extension of the original doctrine of two\n      electricities. The early theorists assumed that, when amber was\n      rubbed, the amber was made positive and the rubber negative to the\n      same degree; but it never occurred to them to suppose that the\n      existence of the amber charge was dependent on an opposite charge in\n      the bodies with which the amber was contiguous, while the existence\n      of the negative charge on the rubber was equally dependent on a\n      contrary state of the surfaces that might accidentally be confronted\n      with it; that, in fact, in a case of electrical excitement by\n      friction, four charges were the minimum that could exist. But this\n      double electrical action is essentially implied in the explanation\n      now universally adopted in regard to the phenomena of the common\n      electric machine.\n\n  139 Pp. 110, 111.\n\n  140 Infra, book iv., chap. ii., On Abstraction.\n\n  141 I must, however, remark, that this example, which seems to militate\n      against the assertion we made of the comparative inapplicability of\n      the Method of Difference to cases of pure observation, is really one\n      of those exceptions which, according to a proverbial expression,\n      prove the general rule. For in this case, in which Nature, in her\n      experiment, seems to have imitated the type of the experiments made\n      by man, she has only succeeded in producing the likeness of man\u2019s\n      most imperfect experiments; namely, those in which, though he\n      succeeds in producing the phenomenon, he does so by employing\n      complex means, which he is unable perfectly to analyze, and can\n      form, therefore, no sufficient judgment what portion of the effects\n      may be due, not to the supposed cause, but to some unknown agency of\n      the means by which that cause was produced. In the natural\n      experiment which we are speaking of, the means used was the clearing\n      off a canopy of clouds; and we certainly do not know sufficiently in\n      what this process consists, or on what it depends, to be certain _a\n      priori_ that it might not operate upon the deposition of dew\n      independently of any thermometric effect at the earth\u2019s surface.\n      Even, therefore, in a case so favorable as this to Nature\u2019s\n      experimental talents, her experiment is of little value except in\n      corroboration of a conclusion already attained through other means.\n\n  142 In his subsequent work, _Outlines of Astronomy_ (\u00a7 570), Sir John\n      Herschel suggests another possible explanation of the acceleration\n      of the revolution of a comet.\n\n  143 Discourse, pp. 156\u20138, and 171.\n\n  144 Outlines of Astronomy, \u00a7 856.\n\n_  145 Philosophy of Discovery_, pp. 263, 264.\n\n  146 See, on this point, the second chapter of the present book.\n\n  147 Ante, chap. vii., \u00a7 1.\n\n  148 It seems hardly necessary to say that the word _impinge_, as a\n      general term to express collision of forces, is here used by a\n      figure of speech, and not as expressive of any theory respecting the\n      nature of force.\n\n_  149 Essays on some Unsettled Questions of Political Economy_, Essay V.\n\n  150 It is justly remarked by Professor Bain, that though the Methods of\n      Agreement and Difference are not applicable to these cases, they are\n      not wholly inaccessible to the Method of Concomitant Variations. \u201cIf\n      a cause happens to vary alone, the effect will also vary alone: a\n      cause and effect may be thus singled out under the greatest\n      complications. Thus, when the appetite for food increases with the\n      cold, we have a strong evidence of connection between these two\n      facts, although other circumstances may operate in the same\n      direction. The assigning of the respective parts of the sun and moon\n      in the action of the tides may be effected, to a certain degree of\n      exactness, by the variations of the amount according to the\n      positions of the two attractive bodies. By a series of experiments\n      of Concomitant Variations, directed to ascertain the elimination of\n      nitrogen from the human body under varieties of muscular exercise,\n      Dr. Parkes obtained the remarkable conclusion, that a muscle grows\n      during exercise, and loses bulk during the subsequent rest.\u201d\n      (_Logic_, ii., 83.)\n\n      It is, no doubt, often possible to single out the influencing causes\n      from among a great number of mere concomitants, by noting what are\n      the antecedents, a variation in which is followed by a variation in\n      the effect. But when there are many influencing causes, no one of\n      them greatly predominating over the rest, and especially when some\n      of these are continually changing, it is scarcely ever possible to\n      trace such a relation between the variations of the effect and those\n      of any one cause as would enable us to assign to that cause its real\n      share in the production of the effect.\n\n  151 Bain\u2019s _Logic_, ii., 360.\n\n  152 What is said in the text on the applicability of the experimental\n      methods to resolve particular questions of medical treatment, does\n      not detract from their efficacy in ascertaining the general laws of\n      the animal or human system. The functions, for example, of the\n      different classes of nerves have been discovered, and probably could\n      only have been discovered, by experiments on living animals.\n      Observation and experiment are the ultimate basis of all knowledge:\n      from them we obtain the elementary laws of life, as we obtain all\n      other elementary truths. It is in dealing with the complex\n      combinations that the experimental methods are for the most part\n      illusory, and the deductive mode of investigation must be invoked to\n      disentangle the complexity.\n\n  153 Professor Bain, though concurring generally in the views expressed\n      in this chapter, seems to estimate more highly than I do the scope\n      for specific experimental evidence in politics. (_Logic_, ii.,\n      333\u2013337.) There are, it is true, as he remarks (p. 336), some cases\n      \u201cwhen an agent suddenly introduced is almost instantaneously\n      followed by some other changes, as when the announcement of a\n      diplomatic rupture between two nations is followed the same day by a\n      derangement of the money-market.\u201d But this experiment would be quite\n      inconclusive merely as an experiment. It can only serve, as any\n      experiment may, to verify the conclusion of a deduction. Unless we\n      already knew by our knowledge of the motives which act on business\n      men, that the prospect of war _tends_ to derange the money-market,\n      we should never have been able to prove a connection between the two\n      facts, unless after having ascertained historically that the one\n      followed the other in too great a number of instances to be\n      consistent with their having been recorded with due precautions.\n      Whoever has carefully examined any of the attempts continually made\n      to prove economic doctrines by such a recital of instances, knows\n      well how futile they are. It always turns out that the circumstances\n      of scarcely any of the cases have been fully stated; and that cases,\n      in equal or greater numbers, have been omitted which would have\n      tended to an opposite conclusion.\n\n  154 Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, \u201cOn Liquid\n      Diffusion applied to Analysis,\u201d in the _Philosophical Transactions_\n      for 1862, reprinted in the _Journal of the Chemical Society_, and\n      also separately as a pamphlet.\n\n  155 It was an old generalization in surgery, that tight bandaging had a\n      tendency to prevent or dissipate local inflammation. This sequence,\n      being, in the progress of physiological knowledge, resolved into\n      more general laws, led to the important surgical invention made by\n      Dr. Arnott, the treatment of local inflammation and tumors by means\n      of an equable pressure, produced by a bladder partially filled with\n      air. The pressure, by keeping back the blood from the part, prevents\n      the inflammation, or the tumor, from being nourished: in the case of\n      inflammation, it removes the stimulus, which the organ is unfit to\n      receive; in the case of tumors, by keeping back the nutritive fluid,\n      it causes the absorption of matter to exceed the supply, and the\n      diseased mass is gradually absorbed and disappears.\n\n  156 Since acknowledged and reprinted in Mr. Martineau\u2019s _Miscellanies_.\n\n_  157 Dissertations and Discussions_, vol. i., fourth paper.\n\n  158 Written before the rise of the new views respecting the relation of\n      heat to mechanical force; but confirmed rather than contradicted by\n      them.\n\n  159 As is well remarked by Professor Bain, in the very valuable chapter\n      of his Logic which treats of this subject (ii., 121), \u201cscientific\n      explanation and inductive generalization being the same thing, the\n      limits of Explanation are the limits of Induction,\u201d and \u201cthe limits\n      to inductive generalization are the limits to the agreement or\n      community of facts. Induction supposes similarity among phenomena;\n      and when such similarity is discovered, it reduces the phenomena\n      under a common statement. The similarity of terrestrial gravity to\n      celestial attraction enables the two to be expressed as one\n      phenomenon. The similarity between capillary attraction, solution,\n      the operation of cements, etc., leads to their being regarded not as\n      a plurality, but as a unity, a single causative link, the operation\n      of a single agency.... If it be asked whether we can merge gravity\n      itself in some still higher law, the answer must depend upon the\n      facts. Are there any other forces, at present held distinct from\n      gravity, that we may hope to make fraternize with it, so as to join\n      in constituting a higher unity? Gravity is an attractive force; and\n      another great attractive force is cohesion, or the force that binds\n      together the atoms of solid matter. Might we, then, join these two\n      in a still higher unity, expressed under a more comprehensive law?\n      Certainly we might, but not to any advantage. The two kinds of force\n      agree in the one point, attraction, but they agree in no other;\n      indeed, in the manner of the attraction, they differ widely; so\n      widely that we should have to state totally distinct laws for each.\n      Gravity is common to all matter, and equal in amount in equal masses\n      of matter, whatever be the kind; it follows the law of the diffusion\n      of space from a point (the inverse square of the distance); it\n      extends to distances unlimited; it is indestructible and invariable.\n      Cohesion is special for each separate substance; it decreases\n      according to distance much more rapidly than the inverse square,\n      vanishing entirely at very small distances. Two such forces have not\n      sufficient kindred to be generalized into one force; the\n      generalization is only illusory; the statement of the difference\n      would still make two forces; while the consideration of one would\n      not in any way simplify the phenomena of the other, as happened in\n      the generalization of gravity itself.\u201d\n\n      To the impassable limit of the explanation of laws of nature, set\n      forth in the text, must therefore be added a further limitation.\n      Although, when the phenomena to be explained are not, in their own\n      nature, generically distinct, the attempt to refer them to the same\n      cause is scientifically legitimate; yet to the success of the\n      attempt it is indispensable that the cause should be shown to be\n      capable of producing them according to the same law. Otherwise the\n      unity of cause is a mere guess, and the generalization only a\n      nominal one, which, even if admitted, would not diminish the number\n      of ultimate laws of nature.\n\n_  160 Cours de Philosophie Positive_, ii., 656.\n\n  161 Vide supra, book iii., chap. xi.\n\n_  162 Philosophy of Discovery_, p. 185 et seq.\n\n  163 Comte, _Philosophie Positive_, ii., 434\u2013437.\n\n  164 As an example of legitimate hypothesis according to the test here\n      laid down, has been justly cited that of Broussais, who, proceeding\n      on the very rational principle that every disease must originate in\n      some definite part or other of the organism, boldly assumed that\n      certain fevers, which not being known to be local were called\n      constitutional, had their origin in the mucous membrane of the\n      alimentary canal. The supposition was, indeed, as is now generally\n      admitted, erroneous; but he was justified in making it, since by\n      deducing the consequences of the supposition, and comparing them\n      with the facts of those maladies, he might be certain of disproving\n      his hypothesis if it was ill founded, and might expect that the\n      comparison would materially aid him in framing another more\n      conformable to the phenomena.\n\n      The doctrine now universally received that the earth is a natural\n      magnet, was originally an hypothesis of the celebrated Gilbert.\n\n      Another hypothesis, to the legitimacy of which no objection can lie,\n      and which is well calculated to light the path of scientific\n      inquiry, is that suggested by several recent writers, that the brain\n      is a voltaic pile, and that each of its pulsations is a discharge of\n      electricity through the system. It has been remarked that the\n      sensation felt by the hand from the beating of a brain, bears a\n      strong resemblance to a voltaic shock. And the hypothesis, if\n      followed to its consequences, might afford a plausible explanation\n      of many physiological facts, while there is nothing to discourage\n      the hope that we may in time sufficiently understand the conditions\n      of voltaic phenomena to render the truth of the hypothesis amenable\n      to observation and experiment.\n\n      The attempt to localize, in different regions of the brain, the\n      physical organs of our different mental faculties and propensities,\n      was, on the part of its original author, a legitimate example of a\n      scientific hypothesis; and we ought not, therefore, to blame him for\n      the extremely slight grounds on which he often proceeded, in an\n      operation which could only be tentative, though we may regret that\n      materials barely sufficient for a first rude hypothesis should have\n      been hastily worked up into the vain semblance of a science. If\n      there be really a connection between the scale of mental endowments\n      and the various degrees of complication in the cerebral system, the\n      nature of that connection was in no other way so likely to be\n      brought to light as by framing, in the first instance, an hypothesis\n      similar to that of Gall. But the verification of any such hypothesis\n      is attended, from the peculiar nature of the phenomena, with\n      difficulties which phrenologists have not shown themselves even\n      competent to appreciate, much less to overcome.\n\n      Mr. Darwin\u2019s remarkable speculation on the Origin of Species is\n      another unimpeachable example of a legitimate hypothesis. What he\n      terms \u201cnatural selection\u201d is not only a _vera causa_, but one proved\n      to be capable of producing effects of the same kind with those which\n      the hypothesis ascribes to it; the question of possibility is\n      entirely one of degree. It is unreasonable to accuse Mr. Darwin (as\n      has been done) of violating the rules of Induction. The rules of\n      Induction are concerned with the conditions of Proof. Mr. Darwin has\n      never pretended that his doctrine was proved. He was not bound by\n      the rules of Induction, but by those of Hypothesis. And these last\n      have seldom been more completely fulfilled. He has opened a path of\n      inquiry full of promise, the results of which none can foresee. And\n      is it not a wonderful feat of scientific knowledge and ingenuity to\n      have rendered so bold a suggestion, which the first impulse of every\n      one was to reject at once, admissible and discussible, even as a\n      conjecture?\n\n  165 Whewell\u2019s _Phil. of Discovery_, pp. 275, 276.\n\n  166 What has most contributed to accredit the hypothesis of a physical\n      medium for the conveyance of light, is the certain fact that light\n      _travels_ (which can not be proved of gravitation); that its\n      communication is not instantaneous, but requires time; and that it\n      is intercepted (which gravitation is not) by intervening objects.\n      These are analogies between its phenomena and those of the\n      mechanical motion of a solid or fluid substance. But we are not\n      entitled to assume that mechanical motion is the only power in\n      nature capable of exhibiting those attributes.\n\n_  167 Phil. of Discovery_, p. 274.\n\n  168 P. 271.\n\n  169 P. 251 and the whole of Appendix G.\n\n  170 In Dr. Whewell\u2019s latest version of his theory (_Philosophy of\n      Discovery_, p. 331) he makes a concession respecting the medium of\n      the transmission of light, which, taken in conjunction with the rest\n      of his doctrine on the subject, is not, I confess, very intelligible\n      to me, but which goes far toward removing, if it does not actually\n      remove, the whole of the difference between us. He is contending,\n      against Sir William Hamilton, that all matter has weight. Sir\n      William, in proof of the contrary, cited the luminiferous ether, and\n      the calorific and electric fluids, \u201cwhich,\u201d he said, \u201cwe can neither\n      denude of their character of substance, nor clothe with the\n      attribute of weight.\u201d \u201cTo which,\u201d continues Dr. Whewell, \u201cmy reply\n      is, that precisely because I can not clothe these agents with the\n      attribute of Weight, I _do_ denude them of the character of\n      Substance. They are not substances, but agencies. These Imponderable\n      Agents are not properly called Imponderable Fluids. This I conceive\n      that I have proved.\u201d Nothing can be more philosophical. But if the\n      luminiferous ether is not matter, and fluid matter, too, what is the\n      meaning of its undulations? Can an agency undulate? Can there be\n      alternate motion forward and backward of the particles of an agency?\n      And does not the whole mathematical theory of the undulations imply\n      them to be material? Is it not a series of deductions from the known\n      properties of elastic fluids? _This_ opinion of Dr. Whewell reduces\n      the undulations to a figure of speech, and the undulatory theory to\n      the proposition which all must admit, that the transmission of light\n      takes place according to laws which present a very striking and\n      remarkable agreement with those of undulations. If Dr. Whewell is\n      prepared to stand by this doctrine, I have no difference with him on\n      the subject.\n\n  171 Thus water, of which eight-ninths in weight are oxygen, dissolves\n      most bodies which contain a high proportion of oxygen, such as all\n      the nitrates (which have more oxygen than any others of the common\n      salts), most of the sulphates, many of the carbonates, etc. Again,\n      bodies largely composed of combustible elements, like hydrogen and\n      carbon, are soluble in bodies of similar composition; resin, for\n      instance, will dissolve in alcohol, tar in oil of turpentine. This\n      empirical generalization is far from being universally true; no\n      doubt because it is a remote, and therefore easily defeated, result\n      of general laws too deep for us at present to penetrate; but it will\n      probably in time suggest processes of inquiry, leading to the\n      discovery of those laws.\n\n  172 Or, according to Laplace\u2019s theory, the sun and the sun\u2019s rotation.\n\n  173 Supra, book iii., chap. v., \u00a7 7.\n\n  174 Supra, book iii., chap. x., \u00a7 2\n\n  175 In the preceding discussion, the _mean_ is spoken of as if it were\n      exactly the same thing with the _average_. But the mean, for\n      purposes of inductive inquiry, is not the average, or arithmetical\n      mean, though in a familiar illustration of the theory the difference\n      may be disregarded. If the deviations on one side of the average are\n      much more numerous than those on the other (these last being fewer\n      but greater), the effect due to the invariable cause, as distinct\n      from the variable ones, will not coincide with the average, but will\n      be either below or above the average, the deviation being toward the\n      side on which the greatest number of the instances are found. This\n      follows from a truth, ascertained both inductively and deductively,\n      that small deviations from the true central point are greatly more\n      frequent than large ones. The mathematical law is, \u201cthat the most\n      probable determination of one or more invariable elements from\n      observation is that in which the _sum of the squares_ of the\n      individual aberrations,\u201d or deviations, \u201c_shall be the least\n      possible_.\u201d See this principle stated, and its grounds popularly\n      explained, by Sir John Herschel, in his review of Quetelet on\n      Probabilities, _Essays_, p. 395 _et seq._\n\n_  176 Essai Philosophique sur les Probabilit\u00e9s_, fifth Paris edition, p.\n      7.\n\n  177 It even appears to me that the calculation of chances, where there\n      are no data grounded either on special experience or on special\n      inference, must, in an immense majority of cases, break down, from\n      sheer impossibility of assigning any principle by which to be guided\n      in setting out the list of possibilities. In the case of the colored\n      balls we have no difficulty in making the enumeration, because we\n      ourselves determine what the possibilities shall be. But suppose a\n      case more analogous to those which occur in nature: instead of three\n      colors, let there be in the box all possible colors, we being\n      supposed ignorant of the comparative frequency with which different\n      colors occur in nature, or in the productions of art. How is the\n      list of cases to be made out? Is every distinct shade to count as a\n      color? If so, is the test to be a common eye, or an educated eye\u2014a\n      painter\u2019s, for instance? On the answer to these questions would\n      depend whether the chances against some particular color would be\n      estimated at ten, twenty, or perhaps five hundred to one. While if\n      we knew from experience that the particular color occurs on an\n      average a certain number of times in every hundred or thousand, we\n      should not require to know any thing either of the frequency or of\n      the number of the other possibilities.\n\n_  178 Prospective Review_ for February, 1850.\n\n  179 \u201cIf this be not so, why do we feel so much more probability added by\n      the first instance than by any single subsequent instance? Why,\n      except that the first instance gives us its possibility (a cause\n      _adequate_ to it), while every other only gives us the frequency of\n      its conditions? If no reference to a cause be supposed, possibility\n      would have no meaning; yet it is clear that, antecedent to its\n      happening, we might have supposed the event impossible, _i.e._, have\n      believed that there was no physical energy really existing in the\n      world equal to producing it.... After the first time of happening,\n      which is, then, more important to the whole probability than any\n      other single instance (because proving the possibility), the\n      _number_ of times becomes important as an index to the intensity or\n      extent of the cause, and its independence of any particular time. If\n      we took the case of a tremendous leap, for instance, and wished to\n      form an estimate of the probability of its succeeding a certain\n      number of times; the first instance, by showing its possibility\n      (before doubtful) is of the most importance; but every succeeding\n      leap shows the power to be more perfectly under control, greater and\n      more invariable, and so increases the probability; and no one would\n      think of reasoning in this case straight from one instance to the\n      next, without referring to the physical energy which each leap\n      indicated. Is it not, then, clear that we do not ever\u201d (let us\n      rather say, that we do not in an advanced state of our knowledge)\n      \u201cconclude directly from the happening of an event to the probability\n      of its happening again; but that we refer to the cause, regarding\n      the past cases as an index to the cause, and the cause as our guide\n      to the future?\u201d\u2014_Ibid._\n\n  180 The writer last quoted says that the valuation of chances by\n      comparing the number of cases in which the event occurs with the\n      number in which it does not occur, \u201cwould generally be wholly\n      erroneous,\u201d and \u201cis not the true theory of probability.\u201d It is at\n      least that which forms the foundation of insurance, and of all those\n      calculations of chances in the business of life which experience so\n      abundantly verifies. The reason which the reviewer gives for\n      rejecting the theory is, that it \u201cwould regard an event as certain\n      which had hitherto never failed; which is exceedingly far from the\n      truth, even for a very large number of constant successes.\u201d This is\n      not a defect in a particular theory, but in any theory of chances.\n      No principle of evaluation can provide for such a case as that which\n      the reviewer supposes. If an event has never once failed, in a\n      number of trials sufficient to eliminate chance, it really has all\n      the certainty which can be given by an empirical law; it _is_\n      certain during the continuance of the same collocation of causes\n      which existed during the observations. If it ever fails, it is in\n      consequence of some change in that collocation. Now, no theory of\n      chances will enable us to infer the future probability of an event\n      from the past, if the causes in operation, capable of influencing\n      the event, have intermediately undergone a change.\n\n  181 Pp. 18, 19. The theorem is not stated by Laplace in the exact terms\n      in which I have stated it; but the identity of import of the two\n      modes of expression is easily demonstrable.\n\n  182 For a fuller treatment of the many interesting questions raised by\n      the theory of probabilities, I may now refer to a recent work by Mr.\n      Venn, Fellow of Caius College, Cambridge, \u201cThe Logic of Chance;\u201d one\n      of the most thoughtful and philosophical treatises on any subject\n      connected with Logic and Evidence which have been produced, to my\n      knowledge, for many years. Some criticisms contained in it have been\n      very useful to me in revising the corresponding chapters of the\n      present work. In several of Mr. Venn\u2019s opinions, however, I do not\n      agree. What these are will be obvious to any reader of Mr. Venn\u2019s\n      work who is also a reader of this.\n\n  183 Hartley\u2019s _Observations on Man_, vol. i., p. 16. The passage is not\n      in Priestley\u2019s curtailed edition.\n\n  184 I am happy to be able to quote the following excellent passage from\n      Mr. Baden Powell\u2019s _Essay on the Inductive Philosophy_, in\n      confirmation, both in regard to history and to doctrine, of the\n      statement made in the text. Speaking of the \u201cconviction of the\n      universal and permanent uniformity of nature,\u201d Mr. Powell says (pp.\n      98\u2013100):\n\n      \u201cWe may remark that this idea, in its proper extent, is by no means\n      one of popular acceptance or natural growth. Just so far as the\n      daily experience of every one goes, so far indeed he comes to\n      embrace a certain persuasion of this kind, but merely to this\n      limited extent, that what is going on around him at present, in his\n      own narrow sphere of observation, will go on in like manner in\n      future. The peasant believes that the sun which rose to-day will\n      rise again to-morrow; that the seed put into the ground will be\n      followed in due time by the harvest this year as it was last year,\n      and the like; but has no notion of such inferences in subjects\n      beyond his immediate observation. And it should be observed that\n      each class of persons, in admitting this belief within the limited\n      range of his own experience, though he doubt or deny it in every\n      thing beyond, is, in fact, bearing unconscious testimony to its\n      universal truth. Nor, again, is it only among the _most_ ignorant\n      that this limitation is put upon the truth. There is a very general\n      propensity to believe that every thing beyond common experience, or\n      especially ascertained laws of nature, is left to the dominion of\n      chance or fate or arbitrary intervention; and even to object to any\n      attempted explanation by physical causes, if conjecturally thrown\n      out for an apparently unaccountable phenomenon.\n\n      \u201cThe precise doctrine of the _generalization_ of this idea of the\n      uniformity of nature, so far from being obvious, natural, or\n      intuitive, is utterly beyond the attainment of the many. In all the\n      extent of its universality it is characteristic of the philosopher.\n      It is clearly the result of philosophic cultivation and training,\n      and by no means the spontaneous offspring of any primary principle\n      naturally inherent in the mind, as some seem to believe. It is no\n      mere vague persuasion taken up without examination, as a common\n      prepossession to which we are always accustomed; on the contrary,\n      all common prejudices and associations are against it. It is\n      pre-eminently _an acquired idea_. It is not attained without deep\n      study and reflection. The best informed philosopher is the man who\n      most firmly believes it, even in opposition to received notions; its\n      acceptance depends on the extent and profoundness of his inductive\n      studies.\u201d\n\n  185 Supra, book iii., chap. iii., \u00a7 1\n\n  186 It deserves remark, that these early generalizations did not, like\n      scientific inductions, presuppose causation. What they did\n      presuppose, was _uniformity_ in physical facts. But the observers\n      were as ready to presume uniformity in the co-existence of facts as\n      in the sequences. On the other hand, they never thought of assuming\n      that this uniformity was a principle pervading all nature: their\n      generalizations did not imply that there was uniformity in every\n      thing, but only that as much uniformity as existed within their\n      observation, existed also beyond it. The induction, fire burns, does\n      not require for its validity that all nature should observe uniform\n      laws, but only that there should be uniformity in one particular\n      class of natural phenomena; the effects of fire on the senses and on\n      combustible substances. And uniformity to this extent was not\n      assumed, anterior to the experience, but proved by the experience.\n      The same observed instances which proved the narrower truth, proved\n      as much of the wider one as corresponded to it. It is from losing\n      sight of this fact, and considering the law of causation in its full\n      extent as necessarily presupposed in the very earliest\n      generalizations, that persons have been led into the belief that the\n      law of causation is known _a priori_, and is not itself a conclusion\n      from experience.\n\n  187 Book ii., chap. iii.\n\n  188 One of the most rising thinkers of the new generation in France, M.\n      Taine (who has given, in the _Revue des Deux Mondes_, the most\n      masterly analysis, at least in one point of view, ever made of the\n      present work), though he rejects, on this and similar points of\n      psychology, the intuition theory in its ordinary form, nevertheless\n      assigns to the law of causation, and to some other of the most\n      universal laws, that certainty beyond the bounds of human\n      experience, which I have not been able to accord to them. He does\n      this on the faith of our faculty of abstraction, in which he seems\n      to recognize an independent source of evidence, not indeed\n      disclosing truths not contained in our experience, but affording an\n      assurance which experience can not give, of the universality of\n      those which it does contain. By abstraction M. Taine seems to think\n      that we are able, not merely to analyze that part of nature which we\n      see, and exhibit apart the elements which pervade it, but to\n      distinguish such of them as are elements of the system of nature\n      considered as a whole, not incidents belonging to our limited\n      terrestrial experience. I am not sure that I fully enter into M.\n      Taine\u2019s meaning; but I confess I do not see how any mere abstract\n      conception, elicited by our minds from our experience, can be\n      evidence of an objective fact in universal Nature, beyond what the\n      experience itself bears witness of; or how, in the process of\n      interpreting in general language the testimony of experience, the\n      limitations of the testimony itself can be cast off.\n\n      Dr. Ward, in an able article in the _Dublin Review_ for October,\n      1871, contends that the uniformity of nature can not be proved from\n      experience, but from \u201ctranscendental considerations\u201d only, and that,\n      consequently, all physical science would be deprived of its basis,\n      if such transcendental proof were impossible.\n\n      When physical science is said to depend on the assumption that the\n      course of nature is invariable, all that is meant is that the\n      conclusions of physical science are not known as _absolute_ truths:\n      the truth of them is _conditional_ on the uniformity of the course\n      of nature; and all that the most conclusive observations and\n      experiments can prove, is that the result arrived at will be true\n      if, and as long as, the present laws of nature are valid. But this\n      is all the assurance we require for the guidance of our conduct. Dr.\n      Ward himself does not think that his transcendental proofs make it\n      practically greater; for he believes, as a Catholic, that the course\n      of nature not only has been, but frequently and even daily is,\n      suspended by supernatural intervention.\n\n      But though this conditional conclusiveness of the evidence of\n      experience, which is sufficient for the purposes of life, is all\n      that I was necessarily concerned to prove, I have given reasons for\n      thinking that the uniformity, as itself a part of experience, is\n      sufficiently proved to justify undoubting reliance on it. This Dr.\n      Ward contests, for the following reasons:\n\n      First (p. 315), supposing it true that there has hitherto been no\n      well authenticated case of a breach in the uniformity of nature;\n      \u201cthe number of natural agents constantly at work is incalculably\n      large; and the observed cases of uniformity in their action must be\n      immeasurably fewer than one thousandth of the whole. Scientific men,\n      we assume for the moment, have discovered that in a certain\n      proportion of instances\u2014immeasurably fewer than one thousandth of\n      the whole\u2014a certain fact has prevailed; the fact of uniformity; and\n      they have not found a single instance in which that fact does _not_\n      prevail. Are they justified, we ask, in inferring from these\n      premises that the fact is universal? Surely the question answers\n      itself. Let us make a very grotesque supposition, in which, however,\n      the conclusion would really be tried according to the arguments\n      adduced. In some desert of Africa there is an enormous connected\n      edifice, surrounding some vast space, in which dwell certain\n      reasonable beings, who are unable to leave the inclosure. In this\n      edifice are more than a thousand chambers, which some years ago were\n      entirely locked up, and the keys no one knew where. By constant\n      diligence twenty-five keys have been found, out of the whole number;\n      and the corresponding chambers, situated promiscuously throughout\n      the edifice, have been opened. Each chamber, when examined, is found\n      to be in the precise shape of a dodecahedron. Are the inhabitants\n      justified on that account in holding with certitude that the\n      remaining 975 chambers are built on the same plan?\u201d\n\n      Not with perfect certitude, but (if the chambers to which the keys\n      have been found are really \u201csituated promiscuously\u201d) with so high a\n      degree of probability that they would be justified in acting upon\n      the presumption until an exception appeared.\n\n      Dr. Ward\u2019s argument, however, does not touch mine as it stands in\n      the text. My argument is grounded on the fact that the uniformity of\n      the course of nature as a whole, is constituted by the uniform\n      sequences of special effects from special natural agencies; that the\n      number of these natural agencies in the part of the universe known\n      to us is not incalculable, nor even extremely great; that we have\n      now reason to think that at least the far greater number of them, if\n      not separately, at least in some of the combinations into which they\n      enter, have been made sufficiently amenable to observation, to have\n      enabled us actually to ascertain some of their fixed laws; and that\n      this amount of experience justifies the same degree of assurance\n      that the course of nature is uniform throughout, which we previously\n      had of the uniformity of sequence among the phenomena best known to\n      us. This view of the subject, if correct, destroys the force of Dr.\n      Ward\u2019s first argument.\n\n      His second argument is, that many or most persons, both scientific\n      and unscientific, believe that there _are_ well authenticated cases\n      of breach in the uniformity of nature, namely, miracles. Neither\n      does this consideration touch what I have said in the text. I admit\n      no other uniformity in the events of nature than the law of\n      Causation; and (as I have explained in the chapter of this volume\n      which treats of the Grounds of Disbelief) a miracle is no exception\n      to that law. In every case of alleged miracle, a _new antecedent_ is\n      affirmed to exist; a _counteracting cause_, namely, the volition of\n      a supernatural being. To all, therefore, to whom beings with\n      superhuman power over nature are a _vera causa_, a miracle is a\n      _case_ of the Law of Universal Causation, not a deviation from it.\n\n      Dr. Ward\u2019s last, and as he says, strongest argument, is the familiar\n      one of Reid, Stewart, and their followers\u2014that whatever knowledge\n      experience gives us of the past and present, it gives us none of the\n      future. I confess that I see no force whatever in this argument.\n      Wherein does a future fact differ from a present or a past fact,\n      except in their merely momentary relation to the human beings at\n      present in existence? The answer made by Priestley, in his\n      _Examination of Reid_, seems to me sufficient, viz., that though we\n      have had no experience of what _is_ future, we have had abundant\n      experience of what _was_ future. The \u201cleap in the dark\u201d (as\n      Professor Bain calls it) from the past to the future, is exactly as\n      much in the dark and no more, as the leap from a past which we have\n      personally observed, to a past which we have not. I agree with Mr.\n      Bain in the opinion that the resemblance of what we have not\n      experienced to what we have, is, by a law of our nature, presumed\n      through the mere energy of the idea, before experience has proved\n      it. This _psychological_ truth, however, is not, as Dr. Ward when\n      criticising Mr. Bain appears to think, inconsistent with the\n      _logical_ truth that experience does prove it. The proof comes after\n      the presumption, and consists in its invariable _verification_ by\n      experience when the experience arrives. The fact which while it was\n      future could not be observed, having as yet no existence, is always,\n      when it becomes present and _can_ be observed, found conformable to\n      the past.\n\n      Dr. M\u2019Cosh maintains (_Examination of Mr. J. S. Mill\u2019s Philosophy_,\n      p. 257) that the uniformity of the course of nature is a different\n      thing from the law of causation; and while he allows that the former\n      is only proved by a long continuance of experience, and that it is\n      not inconceivable nor necessarily incredible that there may be\n      worlds in which it does not prevail, he considers the law of\n      causation to be known intuitively. There is, however, no other\n      uniformity in the events of nature than that which arises from the\n      law of causation: so long therefore as there remained any doubt that\n      the course of nature was uniform throughout, at least when not\n      modified by the intervention of a new (supernatural) cause, a doubt\n      was necessarily implied, not indeed of the reality of causation, but\n      of its universality. If the uniformity of the course of nature has\n      any exceptions\u2014if any events succeed one another without fixed\n      laws\u2014to that extent the law of causation fails; there are events\n      which do not depend on causes.\n\n  189 Book i., chap. vii.\n\n  190 In some cases, a Kind is sufficiently identified by some one\n      remarkable property: but most commonly several are required; each\n      property considered singly, being a joint property of that and of\n      other Kinds. The color and brightness of the diamond are common to\n      it with the paste from which false diamonds are made; its octohedral\n      form is common to it with alum, and magnetic iron ore; but the color\n      and brightness and the form together, identify its Kind: that is,\n      are a mark to us that it is combustible; that when burned it\n      produces carbonic acid; that it can not be cut with any known\n      substance; together with many other ascertained properties, and the\n      fact that there exist an indefinite number still unascertained.\n\n  191 This doctrine of course assumes that the allotropic forms of what is\n      chemically the same substance are so many different Kinds; and such,\n      in the sense in which the word Kind is used in this treatise, they\n      really are.\n\n  192 Professor Bain (Logic, ii., 13) mentions two empirical laws, which\n      he considers to be, with the exception of the law connecting Gravity\n      with Resistance to motion, \u201cthe two most widely operating laws as\n      yet discovered whereby two distinct properties are conjoined\n      throughout substances generally.\u201d The first is, \u201ca law connecting\n      Atomic Weight and Specific Heat by an inverse proportion. For equal\n      weights of the simple bodies, the atomic weight multiplied by a\n      number expressing the specific heat, gives a nearly uniform product.\n      The products, for all the elements, are near the constant number 6.\u201d\n      The other is a law which obtains \u201cbetween the specific gravity of\n      substances in the gaseous state, and the atomic weights. The\n      relationship of the two numbers is in some instances equality; in\n      other instances the one is a multiple of the other.\u201d\n\n      Neither of these generalizations has the smallest appearance of\n      being an ultimate law. They point unmistakably to higher laws. Since\n      the heat necessary to raise to a given temperature the same weight\n      of different substances (called their specific heat) is inversely as\n      their atomic weight, that is, directly as the number of atoms in a\n      given weight of the substance, it follows that a single atom of\n      every substance requires the same amount of heat to raise it to a\n      given temperature; a most interesting and important law, but a law\n      of causation. The other law mentioned by Mr. Bain points to the\n      conclusion, that in the gaseous state all substances contain, in the\n      same space, the same number of atoms; which, as the gaseous state\n      suspends all cohesive force, might naturally be expected, though it\n      could not have been positively assumed. This law may also be a\n      result of the mode of action of causes, namely, of molecular\n      motions. The cases in which one of the numbers is not identical with\n      the other, but a multiple of it, may be explained on the nowise\n      unlikely supposition, that in our present estimate of the atomic\n      weights of some substances, we mistake two, or three, atoms for one,\n      or one for several.\n\n  193 Dr. M\u2019Cosh (p. 324 of his book) considers the laws of the chemical\n      composition of bodies as not coming under the principle of\n      Causation; and thinks it an omission in this work not to have\n      provided special canons for their investigation and proof. But every\n      case of chemical composition is, as I have explained, a case of\n      causation. When it is said that water is composed of hydrogen and\n      oxygen, the affirmation is that hydrogen and oxygen, by the action\n      on one another which they exert under certain conditions, _generate_\n      the properties of water. The Canons of Induction, therefore, as laid\n      down in this treatise, are applicable to the case. Such special\n      adaptations as the Inductive methods may require in their\n      application to chemistry, or any other science, are a proper subject\n      for any one who treats of the logic of the special sciences, as\n      Professor Bain has done in the latter part of his work; but they do\n      not appertain to General Logic.\n\n      Dr. M\u2019Cosh also complains (p. 325) that I have given no canons for\n      those sciences in which \u201cthe end sought is not the discovery of\n      Causes or of Composition, but of Classes; that is, Natural Classes.\u201d\n      Such canons could be no other than the principles and rules of\n      Natural Classification, which I certainly thought that I had\n      expounded at considerable length. But this is far from the only\n      instance in which Dr. M\u2019Cosh does not appear to be aware of the\n      contents of the books he is criticising.\n\n  194 Mr. De Morgan, in his _Formal Logic_, makes the just remark, that\n      from two such premises as Most A are B, and Most A are C, we may\n      infer with certainty that some B are C. But this is the utmost limit\n      of the conclusions which can be drawn from two approximate\n      generalizations, when the precise degree of their approximation to\n      universality is unknown or undefined.\n\n_  195 Rationale of Judicial Evidence_, vol. iii., p. 224.\n\n  196 The evaluation of the chances in this statement has been objected to\n      by a mathematical friend. The correct mode, in his opinion, of\n      setting out the possibilities is as follows. If the thing (let us\n      call it T) which is both an A and a C, is a B, something is true\n      which is only true twice in every thrice, and something else which\n      is only true thrice in every four times. The first fact being true\n      eight times in twelve, and the second being true six times in every\n      eight, and consequently six times in those eight; both facts will be\n      true only six times in twelve. On the other hand, if T, although it\n      is both an A and a C, is not a B, something is true which is only\n      true once in every thrice, and something else which is only true\n      once in every four times. The former being true four times out of\n      twelve, and the latter once in every four, and therefore once in\n      those four; both are only true in one case out of twelve. So that T\n      is a B six times in twelve, and T is not a B, only once: making the\n      comparative probabilities, not eleven to one, as I had previously\n      made them, but six to one.\n\n      In the last edition I accepted this reasoning as conclusive. More\n      attentive consideration, however, has convinced me that it contains\n      a fallacy.\n\n      The objector argues, that the fact of A\u2019s being a B is true eight\n      times in twelve, and the fact of C\u2019s being a B six times in eight,\n      and consequently six times in those eight; both facts, therefore,\n      are true only six times in every twelve. That is, he concludes that\n      because among As taken indiscriminately only eight out of twelve are\n      Bs and the remaining four are not, it must equally hold that four\n      out of twelve are not Bs when the twelve are taken from the select\n      portion of As which are also Cs. And by this assumption he arrives\n      at the strange result, that there are fewer Bs among things which\n      are both As and Cs than there are among either As or Cs taken\n      indiscriminately; so that a thing which has both chances of being a\n      B, is less likely to be so than if it had only the one chance or\n      only the other.\n\n      The objector (as has been acutely remarked by another correspondent)\n      applies to the problem under consideration, a mode of calculation\n      only suited to the reverse problem. Had the question been\u2014If two of\n      every three Bs are As and three out of every four Bs are Cs, how\n      many Bs will be both As and Cs, his reasoning would have been\n      correct. For the Bs that are both As and Cs must be fewer than\n      either the Bs that are As or the Bs that are Cs, and to find their\n      number we must abate either of these numbers in the ratio due to the\n      other. But when the problem is to find, not how many Bs are both As\n      and Cs, but how many things that are both As and Cs are Bs, it is\n      evident that among these the proportion of Bs must be not less, but\n      greater, than among things which are only A, or among things which\n      are only B.\n\n      The true theory of the chances is best found by going back to the\n      scientific grounds on which the proportions rest. The degree of\n      frequency of a coincidence depends on, and is a measure of, the\n      frequency, combined with the efficacy, of the causes in operation\n      that are favorable to it. If out of every twelve As taken\n      indiscriminately eight are Bs and four are not, it is implied that\n      there are causes operating on A which tend to make it a B, and that\n      these causes are sufficiently constant and sufficiently powerful to\n      succeed in eight out of twelve cases, but fail in the remaining\n      four. So if of twelve Cs, nine are Bs and three are not, there must\n      be causes of the same tendency operating on C, which succeed in nine\n      cases and fail in three. Now suppose twelve cases which are both As\n      and Cs. The whole twelve are now under the operation of both sets of\n      causes. One set is sufficient to prevail in eight of the twelve\n      cases, the other in nine. The analysis of the cases shows that six\n      of the twelve will be Bs through the operation of both sets of\n      causes; two more in virtue of the causes operating on A; and three\n      more through those operating on C, and that there will be only one\n      case in which all the causes will be inoperative. The total number,\n      therefore, which are Bs will be eleven in twelve, and the evaluation\n      in the text is correct.\n\n  197 Supra, book i., chap. v.\n\n  198 Supra, book i., chap. v., \u00a7 1, and book ii., chap, v., \u00a7 5.\n\n  199 The axiom, \u201cEquals subtracted from equals leave equal differences,\u201d\n      may be demonstrated from the two axioms in the text. If A = _a_ and\n      B = _b_, A-B = _a-b_. For if not, let A-B = _a-b+c_. Then since B =\n      _b_, adding equals to equals, A = _a+c_. But A = _a_. Therefore _a =\n      a+c_, which is impossible.\n\n      This proposition having been demonstrated, we may, by means of it,\n      demonstrate the following: \u201cIf equals be added to unequals, the sums\n      are unequal.\u201d If A = _a_ and B not = _b_, A+B is not = _a+b_. For\n      suppose it to be so. Then, since A = _a_ and A+B = _a+b_,\n      subtracting equals from equals, B = _b_; which is contrary to the\n      hypothesis.\n\n      So again, it may be proved that two things, one of which is equal\n      and the other unequal to a third thing, are unequal to one another.\n      If A = _a_ and A not = B, neither is _a_ = B. For suppose it to be\n      equal. Then since A = _a_ and _a_ = B, and since things equal to the\n      same thing are equal to one another A = B; which is contrary to the\n      hypothesis.\n\n  200 Geometers have usually preferred to define parallel lines by the\n      property of being in the same plane and never meeting. This,\n      however, has rendered it necessary for them to assume, as an\n      additional axiom, some other property of parallel lines; and the\n      unsatisfactory manner in which properties for that purpose have been\n      selected by Euclid and others has always been deemed the opprobrium\n      of elementary geometry. Even as a verbal definition, equidistance is\n      a fitter property to characterize parallels by, since it is the\n      attribute really involved in the signification of the name. If to be\n      in the same plane and never to meet were all that is meant by being\n      parallel, we should feel no incongruity in speaking of a curve as\n      parallel to its asymptote. The meaning of parallel lines is, lines\n      which pursue exactly the same direction, and which, therefore,\n      neither draw nearer nor go farther from one another; a conception\n      suggested at once by the contemplation of nature. That the lines\n      will never meet is of course included in the more comprehensive\n      proposition that they are everywhere equally distant. And that any\n      straight lines which are in the same plane and not equidistant will\n      certainly meet, may be demonstrated in the most rigorous manner from\n      the fundamental property of straight lines assumed in the text,\n      viz., that if they set out from the same point, they diverge more\n      and more without limit.\n\n_  201 Philosophie Positive_, iii., 414\u2013416.\n\n  202 See the two remarkable notes (A) and (F), appended to his _Inquiry\n      into the Relation of Cause and Effect_.\n\n  203 Supra, p. 413.\n\n  204 A writer to whom I have several times referred, gives as the\n      definition of an impossibility, that which there exists in the world\n      no cause adequate to produce. This definition does not take in such\n      impossibilities as these\u2014that two and two should make five; that two\n      straight lines should inclose a space; or that any thing should\n      begin to exist without a cause. I can think of no definition of\n      impossibility comprehensive enough to include all its varieties,\n      except the one which I have given: viz., An impossibility is that,\n      the truth of which would conflict with a complete induction, that\n      is, with the most conclusive evidence which we possess of universal\n      truth.\n\n      As to the reputed impossibilities which rest on no other grounds\n      than our ignorance of any cause capable of producing the supposed\n      effects; very few of them are certainly impossible, or permanently\n      incredible. The facts of traveling seventy miles an hour, painless\n      surgical operations, and conversing by instantaneous signals between\n      London and New York, held a high place, not many years ago, among\n      such impossibilities.\n\n  205 Not, however, as might at first sight appear, 999 times as much. A\n      complete analysis of the cases shows that (always assuming the\n      veracity of the witness to be \u2079\u2044\u2081\u2080) in 10,000 drawings, the drawing\n      of No. 79 will occur nine times, and be announced incorrectly once;\n      the credibility, therefore, of the announcement of No. 79 is \u2079\u2044\u2081\u2080;\n      while the drawing of a white ball will occur nine times, and be\n      announced incorrectly 999 times. The credibility, therefore, of the\n      announcement of white is \u2079\u2044\u2081\u2080\u2080\u2088, and the ratio of the two 1008:10;\n      the one announcement being thus only about a hundred times more\n      credible than the other, instead of 999 times.\n\n  206 Supra, book iii., chap. ii., \u00a7 3, 4, 5.\n\n  207 Mr. Bailey has given the best statement of this theory. \u201cThe general\n      name,\u201d he says, \u201craises up the image sometimes of one individual of\n      the class formerly seen, sometimes of another, not unfrequently of\n      many individuals in succession; and it sometimes suggests an image\n      made up of elements from several different objects, by a latent\n      process of which I am not conscious.\u201d (Letters on the Philosophy of\n      the Human Mind, 1st series, letter 22.) But Mr. Bailey must allow\n      that we carry on inductions and ratiocinations respecting the class,\n      by means of this idea or conception of some one individual in it.\n      This is all I require. The name of a class calls up some idea,\n      through which we can, to all intents and purposes, think of the\n      class as such, and not solely of an individual member of it.\n\n  208 I have entered rather fully into this question in chap. xvii. of _An\n      Examination of Sir William Hamilton\u2019s Philosophy_, headed \u201cThe\n      Doctrine of Concepts or General Notions,\u201d which contains my last\n      views on the subject.\n\n  209 Other examples of inappropriate conceptions are given by Dr. Whewell\n      (_Phil. Ind. Sc._ ii., 185) as follows: \u201cAristotle and his followers\n      endeavored in vain to account for the mechanical relation of forces\n      in the lever, by applying the _inappropriate_ geometrical\n      conceptions of the properties of the circle: they failed in\n      explaining the _form_ of the luminous spot made by the sun shining\n      through a hole, because they applied the _inappropriate_ conception\n      of a circular _quality_ in the sun\u2019s light: they speculated to no\n      purpose about the elementary composition of bodies, because they\n      assumed the _inappropriate_ conception of _likeness_ between the\n      elements and the compound, instead of the genuine notion of elements\n      merely _determining_ the qualities of the compound.\u201d But in these\n      cases there is more than an inappropriate conception; there is a\n      false conception; one which has no prototype in nature, nothing\n      corresponding to it in facts. This is evident in the last two\n      examples, and is equally true in the first; the \u201cproperties of the\n      circle\u201d which were referred to, being purely fantastical. There is,\n      therefore, an error beyond the wrong choice of a principle of\n      generalization; there is a false assumption of matters of fact. The\n      attempt is made to resolve certain laws of nature into a more\n      general law, that law not being one which, though real, is\n      inappropriate, but one wholly imaginary.\n\n  210 Professor Bain.\n\n  211 This sentence having been erroneously understood as if I had meant\n      to assert that belief is nothing but an irresistible association, I\n      think it necessary to observe that I express no theory respecting\n      the ultimate analysis either of reasoning or of belief, two of the\n      most obscure points in analytical psychology. I am speaking not of\n      the powers themselves, but of the previous conditions necessary to\n      enable those powers to exert themselves: of which conditions I am\n      contending that language is not one, senses and association being\n      sufficient without it. The irresistible association theory of\n      belief, and the difficulties connected with the subject, have been\n      discussed at length in the notes to the new edition of Mr. James\n      Mill\u2019s _Analysis of the Phenomena of the Human Mind_.\n\n  212 Mr. Bailey agrees with me in thinking that whenever \u201cfrom something\n      actually present to my senses, conjoined with past experience, I\n      feel satisfied that something has happened, or will happen, or is\n      happening, beyond the sphere of my personal observation,\u201d I may with\n      strict propriety be said to reason: and of course to reason\n      inductively, for demonstrative reasoning is excluded by the\n      circumstances of the case. (_The Theory of Reasoning_, 2d ed., p.\n      27.)\n\n_  213 Novum Organum Renovatum_, pp. 35\u201337.\n\n_  214 Novum Organum Renovatum_, pp. 39, 40.\n\n  215 P. 217, 4to edition.\n\n  216 \u201cE, ex, extra, extraneus, \u00e9tranger, stranger.\u201d\n\n      Another etymological example sometimes cited is the derivation of\n      the English _uncle_ from the Latin _avus_. It is scarcely possible\n      for two words to bear fewer outward marks of relationship, yet there\n      is but one step between them, _avus_, _avunculus_, _uncle_. So\n      _pilgrim_, from _ager_: _per agrum_, _peragrinus_, _peregrinus_,\n      _pellegrino_, _pilgrim_. Professor Bain gives some apt examples of\n      these transitions of meaning. \u201cThe word \u2018damp\u2019 primarily signified\n      moist, humid, wet. But the property is often accompanied with the\n      feeling of cold or chilliness, and hence the idea of cold is\n      strongly suggested by the word. This is not all. Proceeding upon the\n      superadded meaning, we speak of damping a man\u2019s ardor, a metaphor\n      where the cooling is the only circumstance concerned; we go on still\n      further to designate the iron slide that shuts off the draft of a\n      stove, \u2018the damper,\u2019 the primary meaning being now entirely dropped.\n      \u2018Dry,\u2019 in like manner, through signifying the absence of moisture,\n      water, or liquidity, is applied to sulphuric acid containing water,\n      although not thereby ceasing to be a moist, wet, or liquid\n      substance.\u201d So in the phrases, dry sherry, or Champagne.\n\n      \u201c\u2018Street,\u2019 originally a paved way, with or without houses, has been\n      extended to roads lined with houses, whether paved or unpaved.\n      \u2018Impertinent\u2019 signified at first irrelevant, alien to the purpose in\n      hand: through which it has come to mean, meddling, intrusive,\n      unmannerly, insolent.\u201d (_Logic_, ii., 173, 174.)\n\n  217 Pp. 226, 227.\n\n_  218 Essays_, p. 214.\n\n_  219 Essays_, p. 215.\n\n  220 Though no such evil consequences as take place in these instances\n      are likely to arise from the modern freak of writing _sanatory_\n      instead of sanitary, it deserves notice as a charming specimen of\n      pedantry ingrafted upon ignorance. Those who thus undertake to\n      correct the spelling of the classical English writers, are not aware\n      that the meaning of _sanatory_, if there were such a word in the\n      language, would have reference not to the preservation of health,\n      but to the cure of disease.\n\n_  221 Historical Introduction_, vol. i., pp. 66\u201368.\n\n_  222 History of Scientific Ideas_, ii., 110, 111.\n\n_  223 History of Scientific Ideas_, ii., 111\u2013113.\n\n_  224 Nov. Org. Renov._, pp. 286, 287.\n\n_  225 History of Scientific Ideas_, ii., 120\u2013122.\n\n_  226 Nov. Org. Renov._, p. 274.\n\n_  227 Hist. Sc. Id._, i. 133.\n\n  228 Dr. Whewell, in his reply (_Philosophy of Discovery_, p. 270) says\n      that he \u201cstopped short of, or rather passed by, the doctrine of a\n      series of organized beings,\u201d because he \u201cthought it bad and narrow\n      philosophy.\u201d If he did, it was evidently without understanding this\n      form of the doctrine; for he proceeds to quote a passage from his\n      \u201cHistory,\u201d in which the doctrine he condemns is designated as that\n      of \u201ca mere linear progression in nature, which would place each\n      genus in contact only with the preceding and succeeding ones.\u201d Now\n      the series treated of in the text agrees with this linear\n      progression in nothing whatever but in being a progression.\n\n  229 Supra, p. 137.\n\n_  230 Vulgar Errors_, book v., chap. 21.\n\n_  231 Pharmacologia_, Historical Introduction, p. 16.\n\n  232 The author of one of the Bridgewater Treatises has fallen, as it\n      seems to me, into a similar fallacy when, after arguing in rather a\n      curious way to prove that matter may exist without any of the known\n      properties of matter, and may therefore be changeable, he concludes\n      that it can not be eternal, because \u201ceternal (passive) existence\n      necessarily involves incapability of change.\u201d I believe it would be\n      difficult to point out any other connection between the facts of\n      eternity and unchangeableness, than a strong association between the\n      two ideas. Most of the _a priori_ arguments, both religious and\n      anti-religious, on the origin of things, are fallacies drawn from\n      the same source.\n\n  233 Supra, book ii., chap. v., \u00a7 6, and chap. vii., \u00a7 1, 2, 3, 4. See\n      also _Examination of Sir William Hamilton\u2019s Philosophy_, chap. vi.\n      and elsewhere.\n\n  234 It seems that this doctrine was, before the time I have mentioned,\n      disputed by some thinkers. Dr. Ward mentions Scotus, Vasquez, Biel,\n      Francis Lugo, and Valentia.\n\n  235 I quote this passage from Playfair\u2019s celebrated _Dissertation on the\n      Progress of Mathematical and Physical Science_.\n\n  236 This statement I must now correct, as too unqualified. The maxim in\n      question was maintained with full conviction by no less an authority\n      than Sir William Hamilton. See my _Examination_, chap. xxiv.\n\n_  237 Nouveaux Essais sur l\u2019Entendement Humain\u2014Avant-propos._ (\u0152uvres,\n      Paris ed., 1842, vol. i., p. 19.)\n\n  238 This doctrine also was accepted as true, and conclusions were\n      grounded on it, by Sir William Hamilton. See _Examination_, chap.\n      xxiv.\n\n  239 Not that of Leibnitz, but the principle commonly appealed to under\n      that name by mathematicians.\n\n_  240 Dissertation_, p. 27.\n\n_  241 Hist. Ind. Sc._, Book i., chap. i.\n\n_  242 Novum Organum_, Aph. 75.\n\n  243 Supra, book iii., chap. vii., \u00a7 4.\n\n  244 It is hardly needful to remark that nothing is here intended to be\n      said against the possibility at some future period of making gold\u2014by\n      first discovering it to be a compound, and putting together its\n      different elements or ingredients. But this is a totally different\n      idea from that of the seekers of the grand arcanum.\n\n_  245 Pharmacologia_, pp. 43\u201345.\n\n  246 Vol. i., chap. 8.\n\n_  247 Nov. Org._, Aph. 46.\n\n  248 Playfair\u2019s _Dissertation_, sect. 4.\n\n_  249 Nov. Org. Renov._, p. 61.\n\n_  250 Pharmacologia_, p. 21.\n\n_  251 Pharmacologia_, pp. 23, 24.\n\n  252 Ibid., p. 28.\n\n  253 Ibid., p. 62.\n\n  254 Ibid., pp. 61, 62.\n\n_  255 Supra_, p. 450.\n\n_  256 Elements of the Philosophy of the Mind_, vol. ii., chap. 4, sect.\n      5.\n\n  257 \u201cThus Fourcroy,\u201d says Dr. Paris, \u201cexplained the operation of mercury\n      by its specific gravity, and the advocates of this doctrine favored\n      the general introduction of the preparations of iron, especially in\n      scirrhus of the spleen or liver, upon the same hypothetical\n      principle; for, say they, whatever is most forcible in removing the\n      obstruction must be the most proper instrument of cure: such is\n      steel, which, besides the attenuating power with which it is\n      furnished, has still a greater force in this case from the gravity\n      of its particles, which, being seven times specifically heavier than\n      any vegetable, acts in proportion with a stronger impulse, and\n      therefore is a more powerful deobstruent. This may be taken as a\n      specimen of the style in which these mechanical physicians reasoned\n      and practiced.\u201d\u2014_Pharmacologia_, pp. 38, 39.\n\n_  258 Pharmacologia_, pp. 39, 40.\n\n  259 I quote from Dr. Whewell\u2019s _Hist. Ind. Sc._, 3d ed., i., 129.\n\n_  260 Hist. Ind. Sc._, i., 52.\n\n_  261 Nov. Org._, Aph. 60.\n\n  262 \u201cAn advocate,\u201d says Mr. De Morgan (_Formal Logic_, p. 270), \u201cis\n      sometimes guilty of the argument _\u00e0 dicto secundum quid ad dictum\n      simpliciter_: it is his business to do for his client all that his\n      client might _honestly_ do for himself. Is not the word in italics\n      frequently omitted? _Might_ any man honestly try to do for himself\n      all that counsel frequently try to do for him? We are often reminded\n      of the two men who stole the leg of mutton; one could swear he had\n      not got it, the other that he had not taken it. The counsel is doing\n      his duty by his client, the client has left the matter to his\n      counsel. Between the unexecuted intention of the client, and the\n      unintended execution of the counsel, there may be a wrong done, and,\n      if we are to believe the usual maxims, no wrong-doer.\u201d\n\n      The same writer justly remarks (p. 251) that there is a converse\n      fallacy, _\u00e0 dicto simpliciter ad dictum secundum quid_, called by\n      the scholastic logicians _fallacia accidentis_; and another which\n      may be called _\u00e0 dicto secundum quid ad dictum secundum alterum\n      quid_ (p. 265). For apt instances of both, I must refer the reader\n      to Mr. De Morgan\u2019s able chapter on Fallacies.\n\n  263 An example of this fallacy is the popular error that _strong_ drink\n      must be a cause of _strength_. There is here fallacy within fallacy;\n      for granting that the words \u201cstrong\u201d and \u201cstrength\u201d were not (as\n      they are) applied in a totally different sense to fermented liquors\n      and to the human body, there would still be involved the error of\n      supposing that an effect must be like its cause; that the conditions\n      of a phenomenon are likely to resemble the phenomenon itself; which\n      we have already treated of as an _a priori_ fallacy of the first\n      rank. As well might it be supposed that a strong poison will make\n      the person who takes it strong.\n\n  264 In his later editions, Archbishop Whately confines the name of\n      Petitio Principii \u201cto those cases in which one of the premises\n      either is manifestly the same in sense with the conclusion, or is\n      actually proved from it, or is such as the persons you are\n      addressing are not likely to know, or to admit, except as an\n      inference from the conclusion; as, _e.g._, if any one should infer\n      the authenticity of a certain history, from its recording such and\n      such facts, the reality of which rests on the evidence of that\n      history.\u201d\n\n  265 No longer even a probable hypothesis, since the establishment of the\n      atomic theory; it being now certain that the integral particles of\n      different substances gravitate unequally. It is true that these\n      particles, though real _minima_ for the purposes of chemical\n      combination, may not be the ultimate particles of the substance; and\n      this doubt alone renders the hypothesis admissible, even as an\n      hypothesis.\n\n_  266 Hist. Ind. Sc._, i., 34.\n\n  267 \u201cAnd coxcombs vanquish Berkeley with a grin.\u201d\n\n  268 Some arguments and explanations, supplementary to those in the text,\n      will be found in _An Examination of Sir William Hamilton\u2019s\n      Philosophy_, chap. xxvi.\n\n_  269 Supra_, p. 424.\n\n  270 When this chapter was written, Professor Bain had not yet published\n      even the first part (\u201cThe Senses and the Intellect\u201d) of his profound\n      Treatise on the Mind. In this the laws of association have been more\n      comprehensively stated and more largely exemplified than by any\n      previous writer; and the work, having been completed by the\n      publication of \u201cThe Emotions and the Will,\u201d may now be referred to\n      as incomparably the most complete analytical exposition of the\n      mental phenomena, on the basis of a legitimate Induction, which has\n      yet been produced. More recently still, Mr. Bain has joined with me\n      in appending to a new edition of the \u201cAnalysis,\u201d notes intended to\n      bring up the analytic science of Mind to its latest improvements.\n\n      Many striking applications of the laws of association to the\n      explanation of complex mental phenomena are also to be found in Mr.\n      Herbert Spencer\u2019s \u201cPrinciples of Psychology.\u201d\n\n  271 In the case of the moral sentiments the place of direct experiment\n      is to a considerable extent supplied by historical experience, and\n      we are able to trace with a tolerable approach to certainty the\n      particular associations by which those sentiments are engendered.\n      This has been attempted, so far as respects the sentiment of\n      justice, in a little work by the present author, entitled\n      _Utilitarianism_.\n\n  272 The most favorable cases for making such approximate generalizations\n      are what may be termed collective instances; where we are\n      fortunately enabled to see the whole class respecting which we are\n      inquiring in action at once, and, from the qualities displayed by\n      the collective body, are able to judge what must be the qualities of\n      the majority of the individuals composing it. Thus the character of\n      a nation is shown in its acts as a nation; not so much in the acts\n      of its government, for those are much influenced by other causes;\n      but in the current popular maxims, and other marks of the general\n      direction of public opinion; in the character of the persons or\n      writings that are held in permanent esteem or admiration; in laws\n      and institutions, so far as they are the work of the nation itself,\n      or are acknowledged and supported by it; and so forth. But even here\n      there is a large margin of doubt and uncertainty. These things are\n      liable to be influenced by many circumstances; they are partially\n      determined by the distinctive qualities of that nation or body of\n      persons, but partly also by external causes which would influence\n      any other body of persons in the same manner. In order, therefore,\n      to make the experiment really complete, we ought to be able to try\n      it without variation upon other nations: to try how Englishmen would\n      act or feel if placed in the same circumstances in which we have\n      supposed Frenchmen to be placed; to apply, in short, the Method of\n      Differences as well as that of Agreement. Now these experiments we\n      can not try, nor even approximate to.\n\n  273 \u201cTo which,\u201d says Dr. Whewell, \u201cwe may add, that it is certain, from\n      the history of the subject, that in that case the hypothesis would\n      never have been framed at all.\u201d\n\n      Dr. Whewell (_Philosophy of Discovery_, pp. 277\u2013282) defends Bacon\u2019s\n      rule against the preceding strictures. But his defense consists only\n      in asserting and exemplifying a proposition which I had myself\n      stated, viz., that though the largest generalizations may be the\n      earliest made, they are not at first seen in their entire\n      generality, but acquire it by degrees, as they are found to explain\n      one class after another of phenomena. The laws of motion, for\n      example, were not known to extend to the celestial regions, until\n      the motions of the celestial bodies had been deduced from them.\n      This, however, does not in any way affect the fact, that the middle\n      principles of astronomy, the central force, for example, and the law\n      of the inverse square, could not have been discovered, if the laws\n      of motion, which are so much more universal, had not been known\n      first. On Bacon\u2019s system of step-by-step generalization, it would be\n      impossible in any science to ascend higher than the empirical laws;\n      a remark which Dr. Whewell\u2019s own Inductive Tables, referred to by\n      him in support of his argument, amply bear out.\n\n_  274 Supra_, page 317 to the end of the chapter.\n\n_  275 Biographia Literaria_, i., 214.\n\n_  276 Supra_, p. 321.\n\n_  277 Essays on some Unsettled Questions of Political Economy_, pp.\n      137\u2013140.\n\n  278 The quotations in this paragraph are from a paper written by the\n      author, and published in a periodical in 1834.\n\n_  279 Cours de Philosophie Positive_, iv., 325\u201329.\n\n  280 Since reprinted entire in _Dissertations and Discussions_, as the\n      concluding paper of the first volume.\n\n  281 Written and first published in 1840.\n\n  282 This great generalization is often unfavorably criticised (as by Dr.\n      Whewell, for instance) under a misapprehension of its real import.\n      The doctrine, that the theological explanation of phenomena belongs\n      only to the infancy of our knowledge of them, ought not to be\n      construed as if it was equivalent to the assertion, that mankind, as\n      their knowledge advances, will necessarily cease to believe in any\n      kind of theology. This was M. Comte\u2019s opinion; but it is by no means\n      implied in his fundamental theorem. All that is implied is, that in\n      an advanced state of human knowledge, no other Ruler of the World\n      will be acknowledged than one who rules by universal laws, and does\n      not at all, or does not unless in very peculiar cases, produce\n      events by special interpositions. Originally all natural events were\n      ascribed to such interpositions. At present every educated person\n      rejects this explanation in regard to all classes of phenomena of\n      which the laws have been fully ascertained; though some have not yet\n      reached the point of referring all phenomena to the idea of Law, but\n      believe that rain and sunshine, famine and pestilence, victory and\n      defeat, death and life, are issues which the Creator does not leave\n      to the operation of his general laws, but reserves to be decided by\n      express acts of volition. M. Comte\u2019s theory is the negation of this\n      doctrine.\n\n      Dr. Whewell equally misunderstands M. Comte\u2019s doctrine respecting\n      the second or metaphysical stage of speculation. M. Comte did not\n      mean that \u201cdiscussions concerning ideas\u201d are limited to an early\n      stage of inquiry, and cease when science enters into the positive\n      stage. (_Philosophy of Discovery_, pp. 226 et seq.) In all M.\n      Comte\u2019s speculations as much stress is laid on the process of\n      clearing up our conceptions as on the ascertainment of facts. When\n      M. Comte speaks of the metaphysical stage of speculation, he means\n      the stage in which men speak of \u201cNature\u201d and other abstractions as\n      if they were active forces, producing effects; when Nature is said\n      to do this, or forbid that; when Nature\u2019s horror of a vacuum,\n      Nature\u2019s non-admission of a break, Nature\u2019s _vis medicatrix_, were\n      offered as explanations of phenomena; when the qualities of things\n      were mistaken for real entities dwelling in the things; when the\n      phenomena of living bodies were thought to be accounted for by being\n      referred to a \u201cvital force;\u201d when, in short, the abstract names of\n      phenomena were mistaken for the causes of their existence. In this\n      sense of the word it can not be reasonably denied that the\n      metaphysical explanation of phenomena, equally with the theological,\n      gives way before the advance of real science.\n\n      That the final, or positive stage, as conceived by M. Comte, has\n      been equally misunderstood, and that, notwithstanding some\n      expressions open to just criticism, M. Comte never dreamed of\n      denying the legitimacy of inquiry into all causes which are\n      accessible to human investigation, I have pointed out in a former\n      place.\n\n  283 Buckle\u2019s _History of Civilization_, i., 30.\n\n  284 I have been assured by an intimate friend of Mr. Buckle that he\n      would not have withheld his assent from these remarks, and that he\n      never intended to affirm or imply that mankind are not progressive\n      in their moral as well as in their intellectual qualities. \u201cIn\n      dealing with his problem, he availed himself of the artifice\n      resorted to by the Political Economist, who leaves out of\n      consideration the generous and benevolent sentiments, and founds his\n      science on the proposition that mankind are actuated by acquisitive\n      propensities alone,\u201d not because such is the fact, but because it is\n      necessary to begin by treating the principal influence as if it was\n      the sole one, and make the due corrections afterward. \u201cHe desired to\n      make abstraction of the intellect as the determining and dynamical\n      element of the progression, eliminating the more dependent set of\n      conditions, and treating the more active one as if it were an\n      entirely independent variable.\u201d\n\n      The same friend of Mr. Buckle states that when he used expressions\n      which seemed to exaggerate the influence of general at the expense\n      of special causes, and especially at the expense of the influence of\n      individual minds, Mr. Buckle really intended no more than to affirm\n      emphatically that the greatest men can not effect great changes in\n      human affairs unless the general mind has been in some considerable\n      degree prepared for them by the general circumstances of the age; a\n      truth which, of course, no one thinks of denying. And there\n      certainly are passages in Mr. Buckle\u2019s writings which speak of the\n      influence exercised by great individual intellects in as strong\n      terms as could be desired.\n\n  285 Essay on Dryden, in Miscellaneous Writings, i., 186.\n\n  286 In the _Cornhill Magazine_ for June and July, 1861.\n\n  287 It is almost superfluous to observe, that there is another meaning\n      of the word Art, in which it may be said to denote the poetical\n      department or aspect of things in general, in contradistinction to\n      the scientific. In the text, the word is used in its older, and I\n      hope, not yet obsolete sense.\n\n  288 Professor Bain and others call the selection from the truths of\n      science made for the purposes of an art, a Practical Science, and\n      confine the name Art to the actual rules.\n\n  289 The word Teleology is also, but inconveniently and improperly,\n      employed by some writers as a name for the attempt to explain the\n      phenomena of the universe from final causes.\n\n  290 For an express discussion and vindication of this principle, see the\n      little volume entitled \u201cUtilitarianism.\u201d","title":"A System of Logic, Ratiocinative and Inductive","tradition":"philosophy-ethics","translated_text":null,"word_count":410426}