{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_26495/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_26495","id":"gutenberg_26495","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/26495","summary":null,"tags":["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                             In Two Volumes.\n\n                                 Vol. I.\n\n                              Third Edition.\n\n                                 London:\n\n                        John Parker, West Strand.\n\n                                M DCCC LI.\n\n\n\n\n\nCONTENTS\n\n\nPREFACE TO THE FIRST EDITION.\nPREFACE TO THE THIRD EDITION.\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      I. Feelings, or States of Consciousness.\n      II. Substances.\n      III. Attributes: and, first, Qualities.\n      IV. Relations.\n      V. Quantity.\n      VI. Attributes Concluded.\n      VII. General Results.\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. OF 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.\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. OF THE COMPOSITION OF CAUSES.\n   CHAPTER VII. OF 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.\nFootnotes\n\n\n\n\n\n\nPREFACE TO THE FIRST EDITION.\n\n\nThis book makes no pretence 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 embody\nand systematize, the best ideas which have been either promulgated on its\nsubject by speculative writers, or conformed to by accurate thinkers in\ntheir 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; although the scientific theory on which its defence 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\nthe writings of its later teachers; and it appeared desirable both to\nrevive these, and to reform and rationalize the philosophical foundation\non which they 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\nat a very recent period, eminent writers (among whom it is sufficient to\nname Archbishop Whately, and the author of a celebrated article on Bacon\nin the _Edinburgh Review_) have not scrupled to pronounce it\nimpossible.(1) The author has endeavoured to combat their theory in the\nmanner in which Diogenes confuted the sceptical reasonings against the\npossibility of motion; remembering that Diogenes\u2019 argument would have been\nequally conclusive, though his individual perambulations might not have\nextended beyond 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 endeavoured 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_History of the Inductive Sciences_, the corresponding portion of this\nwork would probably not have been written.\n\nThe concluding Book is an attempt to contribute towards 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: viz. 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\n\nPREFACE TO THE THIRD EDITION.\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.\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 cancelled\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 favourable for\nplacing my own conclusions, and the grounds of them, more clearly and\ncompletely before the reader. Truth, on these subjects, is militant, and\ncan only establish itself by means of conflict. The most opposite opinions\ncan make a plausible show of evidence while each has the statement of its\nown case; and it is only possible to ascertain which of them is in the\nright, after hearing and comparing what each can say against the other,\nand what the other can urge in its defence.\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 arguments 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\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 favour.\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 a thing, until there is agreement about the thing\nitself. To define a thing, is to select from among the whole of its\nproperties those which shall be understood to be designated and declared\nby its 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 anything which can be called a science,\nthe definition we set out with is seldom that which a more extensive\nknowledge of the subject shows to be the most appropriate. Until we know\nthe particulars themselves, we cannot fix upon the most correct and\ncompact mode of circumscribing them by a general description. It was not\ntill 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 imperfections; 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 these volumes.\n\n\u00a7 2. Logic has often been called the Art of Reasoning. A writer(2) who has\ndone more than any other living person to restore this study to the rank\nfrom which it had fallen in the estimation of the cultivated class in our\nown country, 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 the\nscience on which it rests, it is only because several sciences are often\nnecessary to form the groundwork of a single art. Such is the complication\nof human affairs, that to enable one thing to be _done_, it is often\nrequisite 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.\nProfessedly, indeed, these previous topics were introduced only on account\nof their connexion 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 to\nthe Art of Thinking. Nor is this acceptation confined to books, and\nscientific inquirers. 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 premisses. 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 premisses; 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; the latter, of Inference. The\ntruths known by intuition are the original premisses from which all others\nare inferred. Our assent to the conclusion being grounded on the truth of\nthe premisses, 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 premisses 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 premisses 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 cannot\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. Newton saw\nthe truth of many propositions of geometry without reading the\ndemonstrations, but not, we may be sure, without their flashing through\nhis mind. A truth, or supposed truth, which is really the result of a very\nrapid inference, may seem to be apprehended intuitively. It has long been\nagreed by thinkers of the most opposite schools, that this mistake is\nactually made in so familiar an instance as that of the eyesight. There is\nnothing of which we appear to ourselves to be more directly conscious,\nthan the distance of an object from us. Yet it has long been ascertained,\nthat what is perceived by the eye, is at most nothing more than a\nvariously coloured surface; that when we fancy we see distance, all we\nreally see is certain variations of apparent size, and degrees of\nfaintness of colour; and that our estimate of the object\u2019s distance from\nus is the result of a comparison (made with so much rapidity that we are\nunconscious of making it) between the size and colour of the object as\nthey appear at the time, and the size and colour of the same or of similar\nobjects as they appeared when close at hand, or when their degree of\nremoteness was known by other evidence. The perception of distance by the\neye, which seems so like intuition, is thus, in reality, an inference\ngrounded on experience; an inference, too, which we learn to make; and\nwhich we make with more and more correctness as our experience increases;\nthough in familiar cases it takes place, so rapidly as to appear exactly\non a par with those perceptions of sight which are really intuitive, our\nperceptions of colour.(3)\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\n_in_ them. For in the present state of the discussion on these topics, it\nis almost universally allowed that the existence of matter or of spirit,\nof space or of time, is, in its nature, unsusceptible of being proved; and\nthat if anything is known of them, it must be by immediate intuition. To\nthe same 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 analysing 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,\nare realities, the existence of which is manifest to us \u00e0 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, that is, without evidence in the\nproper sense of the word, logic 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 afterwards apply certain rules, either devised by\nthemselves, or prescribed for their guidance by others; and as they do\nthis well or ill, so they discharge well or ill the duties of their\nseveral callings. It is the only occupation in which the mind never ceases\nto be engaged; and is the subject, not of logic, but of knowledge in\ngeneral.\n\nLogic, however, is not the same thing with knowledge, though the field of\nlogic is coextensive 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 fulfils these conditions, or whether facts\ncan be found which fulfil them in a given case, belongs exclusively to the\nparticular art or science, or to our knowledge of the particular subject.\n\nIt is in this sense that logic is, what Bacon so expressively called it,\n_ars artium_; the science of science itself. All science consists of data\nand conclusions from those data, of proofs and what they prove: now logic\npoints out what relations must subsist between data and whatever can be\nconcluded from them, between proof and everything which it can prove. If\nthere be any such indispensable relations, and if these can be precisely\ndetermined, every particular branch of science, as well as every\nindividual in the guidance of his conduct, is bound to conform to those\nrelations, under the penalty of making false inferences, of drawing\nconclusions which are not grounded in the realities of things. Whatever\nhas at any time been concluded justly, whatever knowledge has been\nacquired otherwise than by immediate intuition, depended on the observance\nof the laws which it is the province of logic to investigate. If the\nconclusions are just, and the knowledge real, those laws, whether known or\nnot, have been observed.\n\n\u00a7 6. We need not, therefore, seek any farther 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 may, by\nextraordinary genius, anticipate the results of science; but the bulk of\nmankind require either to understand the theory of what they are doing, or\nto have rules laid down for them by those who have understood the theory.\nIn the progress of science from its easiest to its more difficult\nproblems, each great step in advance has usually had either as its\nprecursor, or as its accompaniment and necessary condition, a\ncorresponding improvement in the notions and principles of logic received\namong the most advanced thinkers. And if several of the more difficult\nsciences are still in so defective a state; if not only so little is\nproved, but disputation has not terminated even about the little which\nseemed to be so; the reason perhaps is, that men\u2019s logical notions have\nnot yet acquired the degree of extension, or of accuracy, requisite for\nthe estimation of the evidence proper to those particular departments of\nknowledge.\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 proceeding 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 marshalling 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 connexion 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\ntogether or frame a set of rules or canons for testing the sufficiency of\nany given evidence 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 towards an\nanalysis holds good and has an independent value, though we should never\nbe able to make a second. The results of analytical chemistry are not the\nless valuable, though it should be discovered that all which we now call\nsimple substances are really compounds. All other things are at any rate\ncompounded of those elements: whether the elements themselves admit of\ndecomposition, is an important inquiry, but does not affect the certainty\nof the science up to that point.\n\nI shall, accordingly, attempt to analyse 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,\nanalyse 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 analyse\nthe mental processes with which Logic is concerned. Any ulterior and\nminuter analysis must be left to metaphysics; which in this, as in other\nparts of our mental nature, decides what are ultimate facts, and what are\nresolvable into other facts. And I believe it will be found that the\nconclusions arrived at in this work have no necessary connexion with any\nparticular views respecting the ulterior analysis. Logic is common ground\non which the partisans of Hartley and of Reid, of Locke and of Kant, may\nmeet and join hands. Particular and detached opinions of all these\nthinkers will no doubt occasionally be controverted, since all of them\nwere logicians as well as metaphysicians; but the field on which their\nprincipal battles have been fought, lies beyond the boundaries of our\nscience.\n\nIt cannot, 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 favourable to the adoption of some one opinion on these\ncontroverted subjects rather than another. For metaphysics, in\nendeavouring 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 all the other\nsciences. And I can conscientiously affirm, that no one proposition laid\ndown in this work has been adopted for the sake of establishing, or with\nany reference to its fitness for being employed in establishing,\npreconceived opinions in any department of knowledge or of inquiry on\nwhich the speculative world is still undecided.\n\n\n\n\n\nBOOK I. OF 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\n\n\nCHAPTER I. OF 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 make himself an astronomical observer, having never\nlearned to adjust the focal distance of his optical instruments so as to\nsee distinctly.\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 fertile source of error; unless they taught\ntheir pupil to put away the glasses which distort the object, and to use\nthose which are adapted to his purpose in such a manner as to assist, not\nperplex his vision; he would not be in a condition to practise 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 cannot 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\nquestions are conceivable? what inquiries are there, to which mankind have\neither obtained, or been able to imagine it possible that they should\nobtain, an answer? This point is best ascertained by a survey and analysis\nof Propositions.\n\n\u00a7 2. The answer to every question which it is possible to frame, is\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 apprize 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\nwhich something is affirmed or denied of something_. Thus, in the\nproposition, Gold is yellow, the quality _yellow_ is affirmed of the\nsubstance _gold_. In the proposition, Franklin was not born in England,\nthe fact expressed by the words _born in England_ is denied of the man\nFranklin.\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; brings\ntogether two names, in a particular manner. This is already a first step\ntowards 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: two names, to say\nthe least; and (since the names must be names of something) two _nameable\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 a part of what takes place) in the\nact of belief, consists in bringing (as it is often expressed) one of\nthese ideas under the other. But this we are not yet in a condition to\nsay: whether such be the correct mode of describing the phenomenon, is an\nafter consideration. The result with which for the present we must be\ncontented, is, that in every act of belief _two_ objects are in some\nmanner taken cognizance of; that there can be no belief claimed, or\nquestion propounded, which does not embrace two distinct (either material\nor intellectual) 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 cannot exist. When I say, \u201cthe sun,\u201d \u201cmy\nfather,\u201d or a \u201cround square,\u201d I call upon the hearer for no belief or\ndisbelief, 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\nanalyse 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\nlabours 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 recognised 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 recognised, 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 where\nthere were only distinctions in the manner of naming them. But we are not\nentitled to assume this in the commencement. We must begin by recognising\nthe distinctions made by ordinary language. If some of these appear, on a\nclose examination, not to be fundamental, the enumeration of the different\nkinds of realities may be abridged accordingly. But to impose upon the\nfacts in the first instance the yoke of a theory, while the grounds of the\ntheory are reserved for discussion in a subsequent stage, is not a course\nwhich a logician can reasonably adopt.\n\n\n\n\nCHAPTER II. OF NAMES.\n\n\n\u00a7 1. \u201cA name,\u201d says Hobbes,(4) \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(5) 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,\ncannot 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 cannot\nbe denied. Nevertheless, there seems good reason for adhering to the\ncommon usage, and calling the word _sun_ the name of the sun, and not the\nname of our idea of the sun. For names are not intended only to make the\nhearer conceive what we conceive, but also to inform him what we believe.\nNow, when I use a name for the purpose of expressing a belief, it is a\nbelief concerning the thing itself, not concerning my idea of it. When I\nsay, \u201cthe sun is the cause of day,\u201d I do not mean that my idea of the sun\ncauses or excites in me the idea of day; or in other words, that thinking\nof the sun makes me think of day. I mean, that a certain physical fact,\nwhich is called the sun\u2019s presence (and which, in the ultimate analysis,\nresolves itself into sensations, not ideas) causes another physical fact,\nwhich is called day. It seems proper to consider a word as the _name_ of\nthat which we intend to be understood by it when we use it; of that which\nany fact that we assert of it is to be understood of; that, in short,\nconcerning which, when we employ the word, we intend to give information.\nNames, therefore, shall always be spoken of in this work as the names of\nthings themselves, and 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_;(6) and\neven adjectives, as _large_, _heavy_. These words do not express things of\nwhich anything can be affirmed or denied. We cannot say, Heavy fell, or A\nheavy 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, viz. 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 cannot 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 colour. The adjective\nis often said to be so used by a grammatical ellipsis: Snow is white,\ninstead of Snow is a white object; White is an agreeable colour, instead\nof, A white colour, or, The colour white, is agreeable. The Greeks and\nRomans were allowed, by the rules of their language, to employ this\nellipsis universally in the subject as well as in the predicate of a\nproposition. In English this cannot, generally speaking, be done. We may\nsay, The earth is round; but we cannot say, Round is easily moved; we must\nsay, A round 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, without\nscruple, speak of adjectives as names, whether in their own right, or as\nrepresentative 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, cannot 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,\nalthough the only object of which they can both be used at the given\nmoment, consistently with their signification, may be the one of which I\nwish to speak.\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, Peter, George,\nMary, and other persons without assignable limit: and it is affirmed of\nall of them in the same sense; for the word man expresses certain\nqualities, and when we predicate it of those persons, we assert that they\nall possess those qualities. But _John_ is only capable of being truly\naffirmed of one single person, at least in the same sense. For although\nthere are many persons who bear that name, it is not conferred upon them\nto indicate any qualities, or anything which belongs to them in common;\nand cannot be said to be affirmed of them in any _sense_ at all,\nconsequently not in the same sense. \u201cThe present queen of England\u201d is also\nan individual name. For, that there never can be more than one person at a\ntime of whom it can be truly affirmed, is implied in the meaning of the\nwords.\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 cannot be predicated of each separately, but\nonly of all taken together. \u201cThe 76th regiment of foot,\u201d which is a\ncollective name, is not a general but an individual name; for although it\ncan be predicated of a multitude of individual soldiers taken jointly, it\ncannot be predicated of them severally. We may say, Jones is a soldier,\nand Thompson is a soldier, and Smith is a soldier, but we cannot say,\nJones is the 76th regiment, and Thompson is the 76th regiment, and Smith\nis the 76th regiment. We can only say, Jones, and Thompson, and Smith, and\nBrown, and so forth, (enumerating all the soldiers,) are the 76th\nregiment.\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\nis composed.\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 unrivalled 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\nhim in this abuse of language, until there is now some difficulty in\nrestoring the word to its original signification. A more wanton alteration\nin the meaning of a word is rarely to be met with; for the expression\n_general name_, 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 mean the opposite of\n_concrete_: by an abstract name, the name of an attribute; by a concrete\nname, 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 _colour_, which is a name common to whiteness, redness,\n&c. Such is even the word whiteness, in respect of the different shades of\nwhiteness to which it is applied in common; the word magnitude, in respect\nof the various degrees of magnitude and the various dimensions of space;\nthe word weight, in respect of the various degrees of weight. Such also is\nthe word _attribute_ itself, the common name of all particular attributes.\nBut when only one attribute, neither variable in degree nor in kind, is\ndesignated by the name; as visibleness; tangibleness; equality;\nsquareness; milkwhiteness; then the name can hardly be considered general;\nfor though it denotes an attribute of many different objects, the\nattribute itself is always conceived as one, not many. The question is,\nhowever, of no moment, and perhaps the best way of deciding it would be to\nconsider these names as neither general nor individual, but to place them\nin a class apart.\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 colour, 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 colour. We mean that they are things having the\ncolour. The reverse is the case with the word whiteness; what we affirm to\n_be_ whiteness is not snow but the colour of snow. Whiteness, therefore,\nis the name of the colour exclusively: white is a name of all things\nwhatever having the colour; a name, not of the quality whiteness, but of\nevery white object. It is true, this name was given to all those various\nobjects on account of the quality; and we may therefore say, without\nimpropriety, that the quality forms part of its signification; but a name\ncan only be said to stand for, or to be a name of, the things of which it\ncan be predicated. We shall presently see that all names which can be said\nto have 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 anything 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, &c., and implies, or as it was termed by\nthe schoolmen, _connotes_,(7) the attribute _whiteness_. The word white is\nnot predicated of the attribute, but of the subjects, snow, &c.; but when\nwe predicate it of them, we imply, or connote, 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 undefined 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 anything 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 Houyhnhms were\nnot so called. Or if such newly-discovered beings possessed the form of\nman without any vestige of reason, it is probable that some other name\nthan that of man would be found for them. How it happens that there can be\nany 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\nname.\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;\nJames, Mary, 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.(8)\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. It is thus, for example, with\nsuch a word as _fault_; equivalent to _bad_ or _hurtful quality_. This\nword is a name common to many attributes, and connotes hurtfulness, an\nattribute of those various attributes. When, for example, we say that\nslowness, in a horse, is a fault, we do not mean that the slow movement,\nthe actual change of place of the slow horse, is a thing to be avoided,\nbut that the property or peculiarity of the horse, from which it derives\nthat name, the quality of being a slow mover, is an undesirable\npeculiarity.\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, becomes independent of\nthe reason. A man may have been named John, because that was the name of\nhis father; a town may have been named Dartmouth, because it is situated\nat the mouth of the Dart. But 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, that is, predicable only of one object, are really connotative.\nFor, although we may give to an individual a name utterly unmeaning, which\nwe call a proper name,\u2014a word which answers the purpose of showing what\nthing it is we are talking about, but not of telling anything about it;\nyet a name peculiar to an individual is not necessarily of this\ndescription. It may be significant of some attribute, or some union of\nattributes, which being possessed by no object but one, determines the\nname exclusively to that individual. \u201cThe sun\u201d is a name of this\ndescription; \u201cGod,\u201d when used by a monotheist, is another. These, however,\nare scarcely examples of what we are now attempting to illustrate, being,\nin strictness of language, general, and not individual names: for, however\nthey may be _in fact_ predicable only of one object, there is nothing in\nthe meaning of the words themselves which implies this: and, accordingly,\nwhen we are imagining and not affirming, we may speak of many suns; and\nthe majority of mankind have believed, and still believe, that there are\nmany gods. But it is easy to produce words which are real instances of\nconnotative individual names. It may be part of the meaning of the\nconnotative name itself, that there exists but one individual possessing\nthe attribute which it connotes; as, for instance, \u201cthe _only_ son of John\nStiles;\u201d \u201cthe _first_ emperor of Rome.\u201d Or the attribute connoted may be a\nconnexion with some determinate event, and the connexion may be of such a\nkind as only one individual could have; or may at least be such as only\none individual 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, although 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 word\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\nafterwards limited by the word _present_, to such individuals as possess\nthe attributes at one indivisible point of time, it becomes applicable\nonly to one individual. And as this appears from the meaning of the name,\nwithout any extrinsic proof, it is strictly an individual name.\n\nFrom the preceding observations it will easily be collected, that whenever\nthe names given to objects convey any information, that is, whenever they\nhave properly any meaning, the 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.\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 anything 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\nsight of 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 anything 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 hearer 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 anything 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 names of Sophroniscus, not indeed of him alone, but of him and each of\nan indefinite number of other human beings. Each of these names is applied\nto Sophroniscus for a different reason, and by each whoever understands\nits meaning is apprised of a distinct fact or number of facts concerning\nhim; but those who knew nothing about the names except that they were\napplicable to Sophroniscus, would be altogether ignorant of their meaning.\nIt is even conceivable that I might know every single individual of whom a\ngiven name could be with truth affirmed, and yet could not be said to know\nthe meaning of the name. A child knows who are its brothers and sisters,\nlong before it has any definite conception of the nature of the facts\nwhich are involved in the signification of those words.\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\nabout the 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 of which he is but imperfectly\nconscious, 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.(9) 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 small stock of names serve with but little augmentation to\nexpress a constantly increasing number of objects and distinctions, and,\nconsequently, to express them in a manner progressively more and more\nimperfect.\n\nTo what 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 reflected\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 analyse, 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 recognised 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.(10)\n\n\u00a7 6. The fourth principal division of names, is into _positive_ and\n_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-many_,\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.\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, that 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, in short, the opposite of any\npositive word 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 filiation. 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 cannot, 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, although the objects _de_noted by the\nnames are different, they both, in a certain sense, connote the same\nthing. They cannot, indeed, be said to connote the same _attribute_; to be\na father, is not the same thing as to be a son. But when we call one man a\nfather, another his son, what we mean to affirm is a set of facts, which\nare exactly the same in both cases. To predicate of A that he is the\nfather of B, and of B that he is the son of A, is to assert one and the\nsame fact in different words. The two propositions are exactly equivalent:\nneither of them asserts more or asserts less than the other. The paternity\nof A and the filiety of B are not two facts, but two modes of expressing\nthe same fact. That fact, when analysed, consists of a series of physical\nevents or phenomena, in which both A and B are parties concerned, and from\nwhich they both derive names. What those names really connote, is this\nseries of events: that is the meaning, and the whole meaning, which either\nof them is intended to convey. The series of events may be said to\n_constitute_ the relation; the schoolmen called it the foundation of the\nrelation, _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\ncannot be explained but by mentioning another. Or we may state it\nthus\u2014when the name cannot 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 all objects\nbesides that one were annihilated;(11) 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_;\nbut it is \u00e6quivocal, or applied \u00e6quivocally, as respects those things of\nwhich it is predicated in different senses. It is scarcely necessary to\ngive instances 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_\nstanding for an iron instrument, and _file_ standing for a line of\nsoldiers, have no more title to be considered one word, because written\nalike, than _grease_ and _Greece_ have, because they are pronounced alike.\nThey are one sound, appropriated 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\nCHAPTER III. OF 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 everything which is capable\neither of being made a subject of affirmation or denial, or of being\nitself affirmed or denied of a subject. We have accordingly, in the\npreceding chapter, reviewed the various kinds of Names, in order to\nascertain what is signified by each of them. And we have now carried this\nsurvey far enough to be able to take an account of its results, and to\nexhibit an enumeration of all the kinds of Things which are capable of\nbeing made predicates, or of having anything predicated of them: after\nwhich to determine the import of Predication, that is, of Propositions,\ncan 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 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 intended by him\nand his followers as an enumeration of all things capable of being named;\nan enumeration by the _summa genera_, _i.e._ the most extensive classes\ninto which things could be distributed; which, therefore, were so many\nhighest Predicates, one or other of which was supposed capable of being\naffirmed with truth of every nameable thing whatsoever. The following are\nthe classes into which, according to this school of philosophy, Things in\ngeneral might be reduced:\u2014\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\u03b9, Situs.\n      \u0395\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 anything\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 counted among realities, but they\ncannot be reckoned either among substances or attributes.\n\n\u00a7 2. Before recommencing, under better auspices, the attempt made with\nsuch imperfect success by the great founder of the science of logic, we\nmust take notice of an unfortunate ambiguity in all the concrete names\nwhich correspond to the most general of all abstract terms, the word\nExistence. When we have occasion for a name which shall be capable of\ndenoting whatever exists, as contradistinguished from non-entity or\nNothing, there is hardly a word applicable to the purpose which is not\nalso, and even more familiarly, taken in a sense in which it denotes only\nsubstances. But substances are not all that exist; attributes, if such\nthings are to be spoken of, must be said to exist; feelings also exist.\nYet when we speak of an _object_, or of a _thing_, we are almost always\nsupposed to mean a substance. There seems a kind of contradiction in using\nsuch an expression as that one _thing_ is merely an attribute of another\nthing. And the announcement of a Classification of Things would, I\nbelieve, prepare most readers for an enumeration like those in natural\nhistory, beginning with the great divisions of animal, vegetable, and\nmineral, and subdividing them into classes and orders. If, rejecting the\nword Thing, we endeavour to find another of a more general import, or at\nleast more exclusively confined to that general import, a word denoting\nall that exists, and connoting only simple existence; no word might be\npresumed fitter for such a purpose than _being_: originally the present\nparticiple of a verb which in one of its meanings is exactly equivalent to\nthe verb _exist_; and therefore suitable, even by its grammatical\nformation, to be the concrete of the abstract _existence_. But this word,\nstrange as the fact may appear, is still more completely spoiled for the\npurpose which it seemed expressly made for, than the word Thing. _Being_\nis, by custom, exactly synonymous with substance; except that it is free\nfrom a slight taint of a second ambiguity; being applied impartially to\nmatter and to mind, while substance, though originally and in strictness\napplicable to both, is apt to suggest in preference the idea of matter.\nAttributes are never called Beings; nor are Feelings. A Being is that\nwhich excites feelings, and which possesses attributes. The soul is called\na Being; God and angels are called Beings; but if we were to say,\nextension, colour, wisdom, virtue are beings, we should perhaps be\nsuspected of thinking with some of the ancients, that the cardinal virtues\nare animals; or, at the least, of holding with the Platonic school the\ndoctrine of self-existent Ideas, or with the followers of Epicurus that of\nSensible Forms, which detach themselves in every direction from bodies,\nand by coming in contact with our organs, cause our perceptions. We should\nbe supposed, in short, to believe 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 enclosed 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 very names which, for want of\nbetter, I am necessitated to employ. It must now be the writer\u2019s endeavour\nso to employ them as in no case to leave the meaning doubtful or obscure.\nNo one of the above terms being altogether unambiguous, I shall not\nconfine myself to any one, but shall employ on each occasion the word\nwhich seems least likely in the particular case to lead to\nmisunderstanding; nor do I pretend to use either these or any other words\nwith a rigorous adherence to one single sense. To do so would often leave\nus without a word to express what is signified by a known word in some one\nor other of its senses: unless authors had an unlimited licence to coin\nnew words, together with (what it would be more difficult to assume)\nunlimited power of making their readers adopt them. Nor would it be wise\nin a writer, on a subject involving so much of abstraction, to deny\nhimself the advantage derived from even an improper use of a term, when,\nby means of it, some familiar association is called up which brings the\nmeaning home to the mind, 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 nameable things; the term\nFeeling being of course understood in its most enlarged sense.\n\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: everything is a feeling of which the\nmind is conscious; everything 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\ncolour without having it before our eyes, to the most recondite thoughts\nof a philosopher or poet. Be it remembered, however, that by a thought is\nto be understood what passes in the mind itself, and not any object\nexternal to the mind, which the person is commonly said to be thinking of.\nHe may be thinking of the sun, or of God, but the sun and God are not\nthoughts; his mental image, however, of the sun, and his idea of God, are\nthoughts; states of his mind, not of the objects themselves: and so also\nis his belief of the existence of the sun, or of God; or his disbelief, if\nthe case be so. Even imaginary objects, (which are said to exist only in\nour ideas,) are to be distinguished from our ideas of them. I may think of\na hobgoblin, as I may think of the loaf which was eaten yesterday, or of\nthe flower which will bloom to-morrow. But the hobgoblin which never\nexisted is not the same thing with my idea of a hobgoblin, any more than\nthe loaf which once existed is the same thing with my idea of a loaf, or\nthe flower which does not yet exist, but which will exist, is the same\nwith my idea of a flower. They are all, not thoughts, but objects of\nthought; though at the present time all the objects are alike\nnon-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 anything 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\nthe absence of any object whatever. We need only shut our eyes and listen\nto music, to have a conception of an 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_colour_ stands for the sensations of white, red, &c., but also for the\nquality in the coloured object. We talk of the colours 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 colour blue, is a feeling of blue colour,\nwhich is one thing; the picture on my retina, or the phenomenon of\nhitherto mysterious nature which takes place in my optic nerve or in my\nbrain, is another thing, of which I am not at all conscious, and which\nscientific investigation alone could have apprised me of. These are states\nof my body; but the sensation of blue, which is the consequence of these\nstates of body, is not a state of body: that which perceives and is\nconscious is called Mind. When sensations are called bodily feelings, it\nis only as being the class of feelings which are immediately occasioned by\nbodily states; whereas the other kinds of feelings, thoughts, for\ninstance, or emotions, are immediately excited not by anything acting upon\nthe bodily organs, but by sensations, or by previous thoughts. This,\nhowever, is a distinction not in our feelings, but in the agency which\nproduces our feelings: all of them when actually produced are states of\nmind.\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 sensation the mind is passive,\nbeing merely acted upon by the outward object. And according to some\nmetaphysicians it is by an act of the mind, similar to perception, except\nin not being preceded by any sensation, that the existence of God, the\nsoul, and other hyperphysical objects is recognised.\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(12)) 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 when 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\n_actions_ 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 nameable things, viz. Feelings or\nStates of Consciousness, we began by recognising three sub-divisions;\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. Without\nseeking to prejudge the metaphysical question whether any mental state or\nphenomenon can be found which is not included in one or other of these\nfour species, it appears to me that the amount of illustration bestowed\nupon these may, so far as we are concerned, suffice for the whole genus.\nWe shall, therefore, proceed to the two remaining classes of nameable\nthings; all things which are external to the mind being considered as\nbelonging either to the class of Substances or to that of Attributes.\n\n\n\nII. Substances.\n\n\nLogicians have endeavoured 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:\ncolour, for example, must be the colour _of_ something; goodness must be\nthe goodness _of_ something: and if this something should cease to exist,\nor should 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_ anything; the moon is not the moon _of_\nanything, 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, although 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 anything else. And\nas for the self-existence of substances, it is very true that a substance\nmay be conceived to exist without any other substance, but so also may an\nattribute without any other attribute: and we can no more imagine a\nsubstance without attributes than we can imagine attributes without a\nsubstance.\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. When\nI see and touch a piece of gold, I am conscious of a sensation of yellow\ncolour, and sensations of hardness and weight; and by varying the mode of\nhandling, I may add to these sensations many others completely distinct\nfrom them. The sensations are all of which I am directly conscious; but I\nconsider them as produced by something not only existing independently of\nmy will, but external to my bodily organs and to my mind. This external\nsomething 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 cause whatever,\nunless, indeed, a First Cause. Though we have no concern here with this\ncontroversy, nor with the metaphysical niceties on which it turns, one of\nthe best ways of showing what is meant by Substance is, to consider what\nposition it is necessary to take up, in order to maintain its existence\nagainst opponents.\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 colour, 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 take an\norange, and conceive it to be divested of its natural colour without\nacquiring any new one; to lose its softness without becoming hard, its\nroundness without becoming square or pentagonal, or of any other regular\nor irregular figure whatever; to be deprived of size, of weight, of taste,\nof smell; to lose all its mechanical and all its chemical properties, and\nacquire no new ones; to become, in short, invisible, intangible,\nimperceptible not only by all our senses, but by the senses of all other\nsentient beings, real or possible; nothing, say these thinkers, would\nremain. For of what nature, they ask, could be the residuum? and by what\ntoken could it manifest its presence? To the unreflecting its existence\nseems to rest on the evidence of the senses. But to the senses nothing is\napparent except the sensations. We know, indeed, that these sensations are\nbound together by some law; they do not come together at random, but\naccording to a systematic order, which is part of the order established in\nthe universe. When we experience one of these sensations, we usually\nexperience the others also, or know that we have it in our power to\nexperience them. But a fixed law of connexion, making the sensations occur\ntogether, does not, say these philosophers, necessarily require what is\ncalled a substratum to support them. The conception of a substratum is but\none of many possible forms in which that connexion presents itself to our\nimagination; a mode of, as it were, realizing the idea. If there be such a\nsubstratum, suppose it this instant miraculously annihilated, and let the\nsensations continue to occur in the same order, and how would the\nsubstratum be missed? By what signs should we be able to discover that its\nexistence had terminated? should we not have as much reason to believe\nthat it still existed as we now have? and if we should not then be\nwarranted in believing it, how can we be so now? A body, therefore,\naccording to these metaphysicians, is not anything intrinsically different\nfrom the sensations which the body is said to produce in us; it is, in\nshort, a set of sensations joined together according 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 connexion, 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 could 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\nan 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\nus.(13) There is not the slightest reason for believing that what we call\nthe sensible qualities of the object are a type of anything 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 these objects upon our senses?(14) And if not on the\nprinciple of resemblance, on what other principle can the manner in which\nobjects affect us through our senses afford us any insight into the\ninherent nature of those objects? It may therefore safely be laid down as\na truth both obvious in itself, and admitted by all whom it is at present\nnecessary to take into consideration, that, of the outward world, we know\nand can know absolutely nothing, except the sensations which we experience\nfrom it. Those, however, who still look upon Ontology as a possible\nscience, and think, not only that bodies have an essential constitution of\ntheir own, lying deeper than our perceptions, but that this essence or\nnature is accessible to human investigation, cannot expect to find their\nrefutation here. The question depends on the nature and laws of Intuitive\nKnowledge, and is not within the province of logic.\n\n\u00a7 8. Body having now been defined the external cause, and (according to\nthe more reasonable opinion) the _hidden_ external cause, to which we\nrefer our sensations; it remains to frame a definition of Mind. Nor, after\nthe preceding observations, will this be difficult. For, as our conception\nof a 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 the\nmysterious something which excites the mind to feel, so mind is the\nmysterious something which feels, and thinks. It is unnecessary to give in\nthe case of mind, as we gave in the case of matter, a particular statement\nof the sceptical system by which its existence as a Thing in itself,\ndistinct from the series of what are denominated its states, is called in\nquestion. But it is necessary to remark, that on the inmost nature of the\nthinking principle, as well as on the inmost nature of matter, we are, and\nwith our faculties must always remain, entirely in the dark. All which we\nare aware of, even in our own minds, is (in the words of Mr. Mill) a\ncertain \u201cthread of consciousness;\u201d a series of feelings, that is, of\nsensations, thoughts, emotions, and volitions, more or less numerous and\ncomplicated. There is a something I call Myself, or, by another form of\nexpression, my mind, which I consider as distinct from these sensations,\nthoughts, &c.; a something which I conceive to be not the thoughts, but\nthe being that has the thoughts, and which I can conceive as existing for\never in a state of quiescence, without any thoughts at all. But what this\nbeing is, although it is myself, I have no knowledge, other than the\nseries of its states of consciousness. As bodies manifest themselves to me\nonly through the sensations of which I regard them as the causes, so the\nthinking principle, or mind, in my own nature, makes itself known to me\nonly by the feelings of which it is conscious. I know nothing about\nmyself, save my capacities of feeling or being conscious (including, of\ncourse, thinking and willing): and were I to learn anything new concerning\nmy own nature, I cannot with my present faculties conceive this new\ninformation to be anything else, than that I have some additional\ncapacities, as yet unknown 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 German sense of the term) of\nall 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 anything; and if anything, logic has nothing to do with it,\nor with the manner in which the knowledge is acquired. With this result we\nmay conclude this portion of our subject, and pass to the third and only\nremaining class or division of Nameable Things.\n\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 cannot know,\nanything of bodies but the sensations which they excite in us or 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 denoted 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 colour 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 our receiving\nthe sensation, but something in the object itself; a _power_ inherent in\nit; something _in virtue_ of which the object produces the sensation. And\nwhen we affirm that snow possesses the attribute whiteness, we do not\nmerely assert that the presence of snow produces in us that sensation, but\nthat it 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, which is as much as to say under\ndifferent suppositions as to surrounding circumstances. Because _quality_\nand _sensation_ cannot be put indiscriminately one for the other, it is\nsupposed that they cannot both signify the same thing, namely, the\nimpression or feeling with which we are affected through our senses by the\npresence of an object; although there is at least no absurdity in\nsupposing that this identical impression or feeling may be called a\nsensation when considered merely in itself, and a quality when regarded as\nemanating from any one of the numerous objects, the presence of which to\nour organs excites in our minds that among various other sensations or\nfeelings. And if this be admissible as a supposition, it rests with those\nwho contend for an entity _per se_ called a quality, to show that their\nopinion is preferable, or is anything in fact but a lingering remnant of\nthe scholastic doctrine of occult causes; the very absurdity which Moli\u00e8re\nso happily ridiculed when he made one of his pedantic physicians account\nfor the fact that \u201cl\u2019opium endormit,\u201d by the maxim \u201cparcequ\u2019il a une vertu\nsoporifique.\u201d\n\nIt is evident that when the physician stated that opium had \u201cune vertu\nsoporifique,\u201d he did not account for, but merely asserted over again, the\nfact that it _endormit_. 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\ncannot 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 cannot 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\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 oneself or to\nsomebody else. There is no part of what the names expressive of the\nrelation imply, that is not resolvable into states of consciousness;\noutward objects being, no doubt, supposed throughout as the causes by\nwhich some of those states of consciousness are excited, and minds as the\nsubjects by which all of them are experienced, but neither the external\nobjects nor the minds making their existence known otherwise than by the\nstates 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 analyse the matter any farther.\n\n\u00a7 11. In a somewhat similar position are two other sorts of relation,\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 colours be a third state of consciousness, which I have _after_\nhaving the two sensations of colour, 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\nfrom being capable of analysis, that they are presupposed in every attempt\nto analyse any of our other feelings. Likeness and unlikeness, therefore,\nas well 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, although likeness or unlikeness cannot be resolved into anything\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. Of how\nvast a variety of resemblances of parts must that resemblance be composed,\nwhich induces us to say that a portrait, or a landscape, is like its\noriginal. If one person mimics another with any success, of how many\nsimple likenesses must the general or complex likeness be compounded:\nlikeness in a succession of bodily postures; likeness in voice, or in the\naccents and intonations of the voice; likeness in the choice of words, and\nin the thoughts or sentiments expressed, whether by word, countenance, or\ngesture.\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 portion at least of these 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 cannot\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\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 the province of Logic to\nanalyse it; nor to decide whether it is susceptible of analysis or not.\nFor us the following considerations are sufficient. It is evident that the\nsensations I receive from the gallon of water, and those I receive from\nthe gallon of wine, are not the same, that is, not precisely alike;\nneither 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. Everybody 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\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\nrecognise 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 cannot, 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\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 made themselves 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. If there\nbe any other kind of mental state not included under these subdivisions,\nwe did not think it necessary or proper in this place to discuss its\nexistence, or the rank which ought to be assigned to it.\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 very generally agreed, that all we can know of Matter is\nthe 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 Nameable Things is Attributes; and these are\nof three kinds, Quality, Relation, and Quantity. Qualities, like\nsubstances, are known to us no otherwise than by the sensations or other\nstates of consciousness which they excite: and while, in compliance with\ncommon usage, we have continued to speak of them as a distinct class of\nThings, we showed that in predicating them no one means to predicate\nanything but those sensations or states of consciousness, on which they\nmay be said to be grounded, and by which alone they can be defined or\ndescribed. Relations, except the simple cases of likeness and unlikeness,\nsuccession and simultaneity, are similarly grounded on some fact or\nphenomenon, that is, on some series of sensations or states of\nconsciousness, more or less complicated. The third species of attribute,\nQuantity, is also manifestly grounded on something in our sensations or\nstates of feeling, since there is an indubitable difference in the\nsensations excited by a larger and a smaller bulk, or by a greater or a\nless degree of intensity, in any object of sense or of consciousness. All\nattributes, therefore, are to us nothing but either our sensations and\nother states of feeling, or something inextricably involved therein; and\nto this even the peculiar and simple relations just adverted to are not\nexceptions. Those peculiar relations, however, are so important, and, even\nif they might in strictness be classed among states of consciousness, are\nso fundamentally distinct from any other of those states, that it would be\na vain subtlety to confound them under that common head, and it is\nnecessary that they should be classed apart.\n\nAs the result, therefore, of our analysis, we obtain the following as an\nenumeration and classification of all Nameable Things:\u2014\n\n1st. Feelings, or States of Consciousness.\n\n2nd. The Minds which experience those feelings.\n\n3rd. The Bodies, or external objects, which excite certain of those\nfeelings, together with the powers or properties whereby they excite them;\nthese being included rather in compliance with common opinion, and because\ntheir existence is taken for granted in the common language from which I\ncannot prudently deviate, than because the recognition of such powers or\nproperties as real existences appears to me warranted by a sound\nphilosophy.\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\nabortive Classification of Existences, termed the Categories of Aristotle.\nThe practical application of it will appear when we commence the inquiry\ninto the Import of Propositions; in other words, when we inquire what it\nis which the mind actually believes, when it gives what is called its\nassent to a proposition.\n\nThese four classes comprising, if the classification be correct, all\nNameable 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\ncorresponds to it,) except as a name for the unknown and inscrutable\nprocess by which that subjective or psychological fact is brought to pass.\n\n\n\n\nCHAPTER IV. OF 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\ncannot conclude from merely seeing two names put together, that they are a\npredicate 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\nproposition, Socrates is just, it may seem to be implied not only that the\nquality _just_ can be affirmed of Socrates, but moreover that Socrates\n_is_, that is to say, exists. This, however, only shows that there is an\nambiguity in the word _is_; a word which not only performs the function of\nthe copula in affirmations, but has also a meaning of its own, in virtue\nof which it may itself be made the predicate of a proposition. That the\nemployment of it as a copula does not necessarily include the affirmation\nof existence, appears from such a proposition as this, A centaur is a\nfiction of the poets; where it cannot possibly be implied that a centaur\nexists, since the proposition itself expressly asserts that the thing has\nno real existence.\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 words _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\nnon-entity, 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 labour not only unprofitably but mischievously, (as was\nfrequently done by the two philosophers just mentioned,) on vain attempts\nto discover in what this common nature consists. But, the habit once\nformed, intellects much inferior are capable of detecting even ambiguities\nwhich are common to many languages: and it is surprising that the one now\nunder consideration, though it exists in the modern languages as well as\nin the ancient, should have been overlooked by almost all authors. The\nquantity of futile speculation which had been caused by a misapprehension\nof the nature of the copula, was hinted at by Hobbes; but Mr. Mill(15)\nwas, I believe, the first who distinctly characterized the ambiguity, and\npointed out how many errors in the received systems of philosophy it has\nhad to answer 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 recognise 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\nanything _is_, but that something is _not_; to express which operation no\nword seems 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 truth as if it were only a difference between two kinds of words.\nTo put things together, and to put them or keep them asunder, will remain\ndifferent 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\nthe designations 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 cannot 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 anything 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. A\nsimple proposition is that in which one predicate is affirmed or denied of\none subject. A complex proposition is that in which there is more than one\npredicate, or more 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 proposition is often not a proposition at all, but\nseveral propositions, held together by a conjunction. Such, for example,\nis this: C\u00e6sar is dead, and Brutus is alive: or even this, C\u00e6sar is dead,\n_but_ Brutus is alive. There are here two distinct assertions; and we\nmight as well call a street a complex house, as these two propositions a\ncomplex proposition. It is true that the syncategorematic words _and_ and\n_but_ have a meaning; but that meaning is so far from making the two\npropositions one, that it adds a third proposition to them. All particles\nare abbreviations, and generally abbreviations of propositions; a kind of\nshort-hand, whereby that which, to be expressed fully, would have required\na proposition or a series of propositions, is suggested to the mind at\nonce. Thus the words, C\u00e6sar is dead and Brutus is alive, are equivalent to\nthese: C\u00e6sar is dead; Brutus is alive; it is desired that the two\npreceding propositions should be thought of together. If the words were,\nC\u00e6sar is dead _but_ Brutus is alive, the sense would be equivalent to the\nsame three propositions together with a fourth; \u201cbetween the two preceding\npropositions there exists a contrast:\u201d viz., either between the two facts\nthemselves, or between the feelings with which it is desired that they\nshould be regarded.\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. As has been well remarked by\nArchbishop Whately and others, the disjunctive form is resolvable into the\nconditional; every disjunctive proposition being equivalent to two or more\nconditional ones. \u201cEither A is B or C is D,\u201d means, \u201cif A is not B, C is\nD; and if C is not D, A is B.\u201d All hypothetical propositions, therefore,\nthough disjunctive in form, are conditional in meaning; and the words\nhypothetical and conditional may be, as indeed they generally are, used\nsynonymously. Propositions in which the assertion is not dependent on a\ncondition, are said, in the language of logicians, to be _categorical_.\n\nAn hypothetical proposition is not, like the pretended complex\npropositions which we previously considered, a mere aggregation of simple\npropositions. The simple propositions which form part of the words in\nwhich it is couched, form no part of the assertion which it conveys. When\nwe say, If the Koran comes from God, Mahomet is the prophet of God, we do\nnot intend to affirm either that the Koran does come from God, or that\nMahomet is really his prophet. Neither of these simple propositions may be\ntrue, and yet the truth of the hypothetical proposition may be\nindisputable. What is asserted is not the truth of either of the\npropositions, but the inferribility of the one from the other. What, then,\nis the subject, and what the predicate, of the hypothetical proposition?\n\u201cThe Koran\u201d is not the subject of it, nor is \u201cMahomet:\u201d for nothing is\naffirmed or denied either of the Koran or of Mahomet. The real subject of\nthe predication is the entire proposition, \u201cMahomet is the prophet of\nGod;\u201d and the affirmation is, that this is a legitimate inference from the\nproposition, \u201cThe Koran comes from God.\u201d The subject and predicate,\ntherefore, of an hypothetical proposition are names of propositions. The\nsubject is some one proposition. The predicate is a general relative name\napplicable to propositions; of this form\u2014\u201can inference from so and so.\u201d A\nfresh instance is here afforded of the remark, that all particles are\nabbreviations; since \u201c_If_ A is B, C is D,\u201d is found to be an abbreviation\nof the following: \u201cThe proposition C is D, is a legitimate inference from\nthe proposition A is 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 an hypothetical proposition, is that of\nbeing an inference from a certain other proposition. But this is only one\nof many 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\u2014                      Universal.\n_Some men_ are mortal\u2014                     Particular.\n_Man_ is mortal\u2014                           Indefinite.\n_Julius C\u00e6sar_ is mortal\u2014                  Singular.\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 non-assignable portion of them\nonly, it is particular. Thus, All men are mortal; Every man is mortal; are\nuniversal propositions. No man is immortal, is also an 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 an 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.\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\ncommonly called Indefinite; but this, as Archbishop Whately observes, is a\nsolecism, of the same nature as that committed by some grammarians when in\ntheir list of genders they enumerate the _doubtful_ gender. The speaker\nmust mean to assert the proposition either as an universal or as a\nparticular proposition, though he has failed to declare which: and it\noften happens that though the words do not show which of the two he\nintends, the context, or the custom of speech, supplies the deficiency.\nThus, when it is affirmed that \u201cMan is mortal,\u201d nobody doubts that the\nassertion is intended of all human beings, and the word indicative of\nuniversality is commonly omitted, only because the meaning is evident\nwithout it. In the proposition, \u201cWine is good,\u201d it is understood with\nequal readiness, though for somewhat different reasons, that the assertion\nis not intended to be universal, but particular.\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 an universal and a particular proposition. An 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\nCHAPTER V. OF THE IMPORT OF PROPOSITIONS.\n\n\n\u00a7 1. An inquiry into the nature of propositions must have one of two\nobjects: to analyse the state of mind called Belief, or to analyse what is\nbelieved. All language recognises a difference between a doctrine or\nopinion, and the act of entertaining the opinion; between assent, and what\nis 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 downwards, 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 analyse 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 Mahomet was an apostle of God, we must\nput the idea of Mahomet 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 where the mind itself is the\nsubject treated of) are not assertions respecting our ideas of things, but\nassertions respecting the things themselves. In order to believe that gold\nis yellow, I must, indeed, have the idea of gold, and the idea of yellow,\nand something having reference to those ideas must take place in my mind;\nbut my belief has not reference to the ideas, it has reference to the\nthings. What I believe is a fact relating to the outward thing, gold, and\nto the impression made by that outward thing upon the human organs; not a\nfact relating to my conception of gold, which would be a fact in my mental\nhistory, not a fact of external nature. It is true, that in order to\nbelieve this fact in external nature, another fact must take place in my\nmind, a process must be performed upon my ideas; but so it must in\neverything else that I do. I cannot dig the ground unless I have the idea\nof the ground, and of a spade, and of all the other things I am operating\nupon, and unless I put those ideas together.(16) But it would be a very\nridiculous description of digging the ground to say that it is putting one\nidea into another. Digging is an operation which is performed upon the\nthings themselves, although it cannot be performed unless I have in my\nmind the ideas of them. And so, in like manner, believing is an act which\nhas for its subject the facts themselves, although 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 anything 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\n_phenomena_ which they respectively express,) seems to me one of the most\nfatal errors ever introduced into the philosophy of Logic; and the\nprincipal cause why the theory of the science has made such inconsiderable\nprogress during the last two centuries. The treatises on Logic, and on the\nbranches of Mental Philosophy connected with Logic, which have been\nproduced since the intrusion of this cardinal error, though sometimes\nwritten by men of extraordinary abilities and attainments, almost always\ntacitly imply a theory that the investigation of truth consists in\ncontemplating and handling our ideas, or conceptions of things, instead of\nthe things themselves: a doctrine tantamount to the assertion, that the\nonly mode of acquiring knowledge of nature is to study it at second hand,\nas represented in our own minds. Meanwhile, inquiries into every kind of\nnatural phenomena were incessantly establishing great and fruitful truths\non the 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 come at, should deem a science futile,\nwhich consisted chiefly of such speculations. What has been done for the\nadvancement of Logic since these doctrines came into vogue, has been done\nnot by professed logicians, but by discoverers in the other sciences; in\nwhose methods of investigation many principles of logic, not previously\nthought of, have successively come forth into light, but who have\ngenerally committed the error of supposing that nothing whatever was known\nof the art of philosophizing by the old logicians, because their modern\ninterpreters 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 everything of which _man_ is a\nname. All men are six feet high, is not true, because _six feet high_ is\nnot a name of everything (though it is of some things) of which _man_ is a\nname.\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-coloured, 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-coloured. If it be\ntrue that all oxen ruminate, it must be true that all the individuals\ndenoted by the name ox are also among those denoted by the name\nruminating; and whoever asserts that all oxen ruminate, undoubtedly does\nassert that this relation 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 farther; 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 much more.\n\nThe only propositions of which Hobbes\u2019 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 analysing\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 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 John, Jane, and the remainder of the individuals. The\nword _mortal_, in like manner connotes a certain attribute or attributes;\nand when we say, All men are mortal, the meaning of the proposition is,\nthat all beings which possess the one set of attributes, possess also the\nother. If, in our experience, the attributes connoted by _man_ are always\naccompanied by the attribute connoted by _mortal_, it will follow as a\nconsequence, that the class _man_ will be wholly included in the class\n_mortal_, and that _mortal_ will be a name of all things of which _man_ is\na name: but why? Those objects are brought under the name, by possessing\nthe attributes connoted by it: but their possession of the attributes is\nthe real condition on which the truth of the proposition depends; not\ntheir being called by the name. Connotative names do not precede, but\nfollow, the attributes which they connote. If one attribute happens to be\nalways found in conjunction with another attribute, the concrete names\nwhich answer to those attributes will of course be predicable of the same\nsubjects, and may be said, in Hobbes\u2019 language, (in the propriety of which\non this occasion I fully concur,) to be two names for the same things. But\nthe possibility of a concurrent application of the two names, is a mere\nconsequence of the conjunction between the two attributes, and was, in\nmost cases, never thought of when the names were invented and their\nsignification fixed. That the diamond is combustible, was a proposition\ncertainly not dreamt of when the words Diamond and Combustible first\nreceived their meaning; and could not have been discovered by the most\ningenious and refined analysis of the signification of those words. It was\nfound out by a very different process, namely, by exerting the senses, and\nlearning from them, that the attribute of combustibility existed in all\nthose diamonds upon which the experiment was tried; the number and\ncharacter of the experiments being such, that what was true of those\nindividuals might be concluded to be true of all substances \u201ccalled by the\nname,\u201d that is, of all substances possessing the attributes which the name\nconnotes. The assertion, therefore, when analysed, is, that wherever we\nfind certain attributes, there will be found a certain other attribute:\nwhich is not a question of the signification of names, but of laws of\nnature; the order existing among phenomena.\n\n\u00a7 3. Although Hobbes\u2019 theory of Predication has not, in the terms in which\nhe stated it, met with a very favourable 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 anything 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 everything 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 also are 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 cannot 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, made\nthem up into parcels or lists, and gave to the objects of each list a\ncommon name, repeating this operation _toties quoties_ until they had\ninvented all the general names of which language consists; which having\nbeen 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 will 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.\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\u2019 theory of Predication, according to the\nwell-known remark of Leibnitz, and the avowal of Hobbes himself,(17)\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, that is, he may believe as matters\nof fact what are not really so. This last admission cannot be made in\nstronger terms than it is by Hobbes himself;(18) 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 anything works upon our senses, but by most men they are\ncalled _accidents_.\u201d(19) It is strange that having gone so far, he should\nnot have gone one step farther, 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 farther 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, &c., 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.\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 one, we have assurance of the existence of the other. Thus, in\nthe proposition, All men are mortal, the word man connotes the attributes\nwhich we ascribe to a certain kind of living creatures, on the ground of\ncertain phenomena which they exhibit, and which are partly physical\nphenomena, namely the impressions made on our senses by their bodily form\nand structure, and partly mental phenomena, namely the sentient and\nintellectual life which they have of their own. All this is understood\nwhen we utter the word man, by any one to whom the meaning of the word is\nknown. Now, when we say, Man is mortal, we mean that wherever these\nvarious 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 farther than to the\noccurrence of the phenomenon at some time or other, leaving the precise\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 anything more than the meaning of words, is generally, as\nin the cases which we have examined, either the coexistence 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 coexistence. 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 honour.\nWho would expect to recognize here a case of coexistence 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 honour, admits\nof a similar analysis. Honour, as here used, means a state of approving\nand admiring emotion, followed on occasion by corresponding outward acts.\n\u201cWorthy of honour\u201d connotes all this, together with our approval of the\nact of showing honour. All these are phenomena; states of internal\nconsciousness, accompanied or followed by physical facts. When we say, A\ngenerous person is worthy of honour, we affirm coexistence 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, honour, 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\nvery 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 coexistence of one such phenomenon with another; or the succession\nof one such phenomenon to another: their _conjunction_, in short, so that\nwhere the one is found, we may calculate on finding both.\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 coexistences 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\ncotemporary 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 does not assert that alone; it asserts that the Thing in\nitself, the _noumenon_ Socrates, was existing, and doing or experiencing\nthose various facts, during the same time. Coexistence and sequence,\ntherefore, may be affirmed or denied not only between phenomena, but\nbetween noumena, or between a noumenon and phenomena. And both of noumena\nand of phenomena we may affirm simple existence. But what is a noumenon?\nAn unknown cause. In affirming, therefore, the existence of a noumenon, we\naffirm causation. Here, therefore, are two additional kinds of fact,\ncapable of being asserted in a proposition. Besides the propositions which\nassert Sequence or Coexistence, there are some which assert simple\nExistence; and others assert Causation, which, subject to the explanations\nwhich will follow in the Third Book, must be considered provisionally as a\ndistinct 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 analyse; for which no _fundamentum_, distinct from the\nobjects themselves, could be assigned. Besides propositions which assert a\nsequence or coexistence between two phenomena, there are therefore also\npropositions which assert resemblance between them: as, This colour is\nlike that colour;\u2014The heat of to-day is _equal_ to the heat of yesterday.\nIt is true that such an assertion might with some plausibility be brought\nwithin the description of an affirmation of sequence, by considering it as\nan assertion that the simultaneous contemplation of the two colours is\n_followed_ by a specific feeling termed the feeling of resemblance. But\nthere would be nothing gained by encumbering ourselves, especially in this\nplace, with a generalization which may be looked upon as strained. Logic\ndoes not undertake to analyse 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 coexistence.\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,\neverything 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,(20)) 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. As, for instance, there are substances\ncalled metals which have very few of the properties by which metals are\ncommonly recognised; and almost every great family of plants or animals\nhas a few anomalous genera or species on its borders, which are admitted\ninto it by a sort of courtesy, and concerning which it has been matter of\ndiscussion to what family they properly belonged. Now when the class-name\nis predicated of any object of this description, we do, by so predicating\nit, affirm 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\na 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 unanalysable 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\ncolour I saw yesterday was a white colour, or, The sensation I feel is one\nof tightness, in both cases the attribute I affirm of the colour 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, Coexistence, Sequence, Causation, Resemblance: one or other of\nthese is asserted (or denied) in every proposition without exception. This\nfive-fold division is an exhaustive classification of matters-of-fact; of\nall things that can be believed or tendered for belief; of all questions\nthat can be propounded, and all answers that can be returned to them.\nInstead of Coexistence and Sequence, we shall sometimes say, for greater\nparticularity, Order in Place, and Order in Time: Order in Place being one\nof the modes of coexistence, not necessary to be more particularly\nanalysed here; while the mere fact of coexistence, or simultaneousness,\nmay be classed, 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 analyse _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 analysed 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\nanything 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 anything a concrete name, the\nattribute is what we in reality predicate of it. But it has now been shown\nthat in all propositions of which the predicate is a concrete name, what\nis really predicated is one of five things: Existence, Coexistence,\nCausation, Sequence, or Resemblance. An attribute, therefore, is\nnecessarily either an existence, a coexistence, 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 anything 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 Coexistence, or of\nCausation, or of Sequence, or of Resemblance.\n\nIt is impossible to imagine any proposition expressed in abstract terms,\nwhich cannot 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,\u2014\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 colour;\u201d or \u201cThe\ncolour 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 colour,\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 honour,\u201d thus, \u201cAll courageous persons\nare deserving of honour _in so far_ as they are courageous;\u201d which is\nequivalent to this\u2014\u201cAll courageous persons deserve an addition to the\nhonour, 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:\u2014\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 analyse the antecedent. Prudence is an\nattribute; and, in connexion 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\nacceptable to any good being. Is it upon prudential _conduct_, then, that\ndivine approbation and benefit to mankind are supposed to be invariably\nconsequent? Neither is this the assertion meant when it is said that\nprudence is a virtue; except with the same reservation as before, and for\nthe same reason, namely, that prudential conduct, although in _so far as_\nit is prudential it is beneficial to society, may yet, by reason of some\nother of its qualities, be productive of an injury outweighing the\nbenefit, and deserve a displeasure exceeding the approbation which would\nbe due to the prudence. Neither the substance, therefore, (viz., the\nperson,) nor the phenomenon, (the conduct,) is an antecedent on which the\nother term of the sequence is universally consequent. But the proposition,\n\u201cPrudence is a virtue,\u201d is an universal proposition. What is it, then,\nupon which the proposition affirms the effects in question to be\nuniversally consequent? Upon that _in_ the person, and in the conduct,\nwhich causes them to be called prudent, and which is equally in them when\nthe action, though prudent, is wicked; namely, a correct foresight of\nconsequences, a just estimation of their importance to the object in view,\nand repression of any unreflecting impulse at variance with the deliberate\npurpose. These, which are states of the person\u2019s mind, are the real\nantecedent in the sequence, the real cause in the causation, asserted by\nthe proposition. But these are also the real ground, or foundation, of the\nattribute Prudence; since wherever these states of mind exist we may\npredicate prudence, even before we know whether any conduct has followed.\nAnd in this manner every assertion respecting an attribute may be\ntransformed into an assertion exactly equivalent respecting the fact or\nphenomenon which is the ground of the attribute. And no case can be\nassigned, where that which is predicated of the fact or phenomenon, does\nnot belong to one or other of the five species formerly enumerated: it is\neither simple Existence, or it is some Sequence, Coexistence, Causation,\nor 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 coexist 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 coexistent: \u201cSome\nbirds are not web-footed,\u201d asserts that there are other instances in which\nthis coexistence does not have place. Any further explanation of a thing\nwhich, if the previous exposition has been assented to, is so obvious, may\nhere be spared.\n\n\n\n\nCHAPTER VI. OF 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\nNominalists, that it is the expression of an agreement or disagreement\nbetween the meanings of two names. We decided that, as general theories,\nboth of these are erroneous; and that, although propositions may be made\nboth respecting names and respecting ideas, neither the one nor the other\nare the subject-matter of Propositions considered generally. We then\nexamined the different kinds of Propositions, and found that, with the\nexception of those which are merely verbal, they assert five different\nkinds of matters of fact, namely, Existence, Order in Place, Order in\nTime, Causation, and Resemblance; that in every proposition one of these\nfive is either affirmed, or denied, of some fact or phenomenon, or of some\nobject the unknown source of a fact or phenomenon.\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\u2019 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 were 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 connexion may\nbe traced between this distinction, which originated with the schoolmen,\nand the well known dogmas of _substanti\u00e6 secund\u00e6_ or general substances,\nand _substantial forms_, doctrines which under varieties of language\npervaded alike the Aristotelian and the Platonic schools, and of which\nmore of the spirit has come down to modern times than might be conjectured\nfrom the disuse of the phraseology. The false views of the nature of\nclassification and generalization which prevailed among the schoolmen, and\nof which these dogmas were the technical expression, afford the only\nexplanation which can be given of their having misunderstood the real\nnature of those Essences which held so conspicuous a place in their\nphilosophy. They said, truly, that _man_ cannot be conceived without\nrationality. But though _man_ cannot, 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 cannot be conceived without rationality, is\nonly, that if he had not rationality, he would not be reputed a man. There\nis no impossibility in conceiving the _thing_, nor, for aught we know, in\nits existing: the impossibility is in the conventions of language, which\nwill not allow the thing, even if it exist, to be called by the name which\nis reserved for rational beings. Rationality, in short, is involved in the\nmeaning of the word man; is one of the attributes connoted by the name.\nThe essence of man, simply means the whole of the attributes connoted by\nthe word; and any one of those attributes taken singly, is an essential\nproperty of man.\n\nThe doctrines which prevented the real meaning of Essences from being\nunderstood, not having assumed so settled a shape in the time of Aristotle\nand his immediate followers as was afterwards given to them by the\nRealists of the middle ages, we find a nearer approach to a rational view\nof the subject in the writings of the ancient Aristotelians than in their\nmore modern followers. Porphyry, in his _Isagoge_, approached so near to\nthe true conception of essences, that only one step remained to be taken,\nbut this step, so easy in appearance, was reserved for the Nominalists of\nmodern times. By altering any property, not of the essence of the thing,\nyou merely, according to Porphyry, made a difference in it; you made it\n\u1f00\u03bb\u03bb\u03bf\u1fd6\u03bf\u03bd: but by altering any property which was of its essence, you made\nit _another thing_, \u1f04\u03bb\u03bb\u03bf.(21) To a modern it is obvious that between the\nchange which only makes a thing different, and the change which makes it\n_another thing_, the only distinction is that in the one case, though\nchanged, it is still called by the same name. Thus, pound ice in a mortar,\nand being still called ice, it is only made \u1f00\u03bb\u03bb\u03bf\u1fd6\u03bf\u03bd: melt it, and it\nbecomes \u1f04\u03bb\u03bb\u03bf, another thing, namely, water. Now it is really the same\nthing, _i.e._ the same particles of matter, in both cases; and you cannot\nso change anything that it shall cease to be the same thing in this sense.\nThe identity which it can be deprived of is merely that of the name: when\nthe thing ceases to be called ice, it becomes _another thing_; its\nessence, what constituted it ice, is gone; while, as long as it continues\nto be so called, nothing is gone except some of its accidents. But these\nreflections, so easy to us, would have been difficult to persons who\nthought, as most of the Aristotelians did, that objects were made what\nthey were called, that ice (for instance) was made ice, not by the\npossession of certain properties to which mankind have chosen to attach\nthat name, but by participation in the nature of a certain _general\nsubstance_, called _Ice in general_, which substance, together with all\nthe properties that belonged to it, _inhered_ in every individual piece of\nice. As they did not consider these universal substances to be attached to\nall general names, but only to some, they thought that an object borrowed\nonly a part of its properties from an universal substance, and that the\nrest belonged to it individually: the former they called its essence, and\nthe latter its accidents. The scholastic doctrine of essences long\nsurvived 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.(22)\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\nonly the result of an imperfection of language. It arises from the\nambiguity of the copula, which, in addition to its proper office of a mark\nto show that an assertion is made, is also, as we have formerly remarked,\na concrete word connoting existence. The actual existence of the subject\nof the proposition is therefore only apparently, not really, implied in\nthe predication, 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\nobject 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\nretains a footing in some remote fastness after it has been driven from\nthe open country. 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 anything wanting to render\nthe third book of Locke\u2019s Essay a nearly unexceptionable 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, although not necessarily connected with the thoughts,\ncontained in that immortal Third Book.(23) But, besides nominal essences,\nhe admitted real essences, or essences of individual objects, which he\nsupposed to be the causes of the sensible properties of those objects. We\nknow not (said he) what these are; (and this acknowledgment rendered the\nfiction comparatively innocuous;) but if we did, we could, from them\nalone, demonstrate the sensible properties of the object, as the\nproperties of the triangle are demonstrated from the definition of the\ntriangle. I shall have occasion to revert to this theory in treating of\nDemonstration, and of the conditions under which one property of a thing\nadmits of being demonstrated from another property. It is enough here to\nremark that according to this definition, the real essence of an object\nhas, in the progress of physics, come to be conceived as nearly\nequivalent, in the case of bodies, to their corpuscular structure: what it\nis now supposed to mean in the case of any other entities, I would not\ntake upon myself to define.\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,\nsome fact 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.\n\nNothing has probably contributed more to the opinion so commonly prevalent\nof the 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 of the syllogism, consist of essential propositions. They\nwere usually taken either from the branches or from the main trunk of the\nPredicamental Tree, which included nothing but what was of the _essence_\nof the species: _Omne corpus est substantia_, _Omne animal est corpus_,\n_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\npremisses 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 supposed to belong to\na god are not there; that where the former are, we need not expect to find\nthe 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\nCHAPTER VII. OF 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 be\napplicable, or whether there be any at all. God is as much a general term\nto the Christian or the 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\npredicating the name we predicate only the attributes; and the fact of\nbelonging to a class does not, in ordinary cases, come into view at all.\n\nAlthough, however, Predication does not presuppose Classification, and\nalthough the theory of Names and of Propositions is not cleared up, but\nonly encumbered, by intruding the idea of classification into it, there is\nnevertheless a close connexion 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_, &c., are as much the expression of\nattributes as if those names had preceded, instead of growing 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 process\nsubservient to the investigation of truth, cannot be discussed to any\npurpose until a much later stage of our inquiry. But, of classification as\nresulting from, and implied in, the fact of employing general language, we\ncannot forbear to treat here, without leaving the theory of general names,\nand of their employment in predication, mutilated and 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 five-fold 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:\u2014\n\nA _genus_ of the thing (\u03b3\u03ad\u03bd\u03bf\u03c2).\nA _species_ (\u03b5\u1f34\u03b4\u03bf\u03c2).\nA _differentia_ (\u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u1f70).\nA _proprium_ (\u1f30\u03b4\u03b9\u03cc\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, &c., 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 _de_notes, 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, &c. _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, &c. are species. _Virtue_ is a genus; justice, prudence,\ncourage, fortitude, generosity, &c. 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, &c., 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 that\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; and man and brute co-ordinate species under that genus: _biped_\nwould not have been admitted to be a genus with reference to man, but a\n_proprium_ or _accidens_ only. It was requisite, according to their\ntheory, that genus and species should be of the _essence_ of the subject.\n_Animal_ 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\nconnexion with the exploded tenets of the Realists; and what the schoolmen\nchose to call the essence of an individual, was simply the essence of the\nclass to which that individual was most familiarly referred.\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 by 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 of 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 characterise 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 colour, 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 (although 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 not\noptional but imperative to recognise this difference as the foundation of\na 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, are the only classes which, by the\nAristotelian logicians, were considered as genera or species. Differences\nwhich extended only to a certain property or properties, and there\nterminated, they considered as differences only in the _accidents_ of\nthings; but where any class differed from other things by an infinite\nseries of differences, known and unknown, they considered the distinction\nas one of _kind_, and spoke of it as being an _essential_ difference,\nwhich is also one of the usual meanings of that vague expression at the\npresent 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, Sir Isaac Newton would be said to be of the species man. There\nare indeed numerous sub-classes included in the class man, to which Newton\nalso belongs; as, for example, Christian, and Englishman, and\nMathematician. But these, though distinct classes, are not, in our sense\nof the term, distinct Kinds of men. A Christian, for example, differs from\nother human beings; but he differs only in the attribute which the word\nexpresses, namely, belief in Christianity, and whatever else that implies,\neither as involved in the fact itself, or connected with it through some\nlaw of cause and effect. We should never think of inquiring what\nproperties, unconnected with Christianity either as cause or effect, are\ncommon to all 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 cannot.\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, maybe 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,\n&c., 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 afterwards 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, &c., 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 very different signification in\nlogic and in natural history. By the naturalist, organized beings are\nnever said to be of different species, if it is supposed that they could\npossibly have descended from the same stock. That, however, is a sense\nartificially given to the word, for the technical purposes of a particular\nscience. To the logician, if a negro and a white man differ in the same\nmanner (however less in degree) as a horse and a camel do, that is, if\ntheir differences are inexhaustible, and not referrible to any common\ncause, they 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 special difference in structure, they are not,\nin 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 any 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, cannot 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\nquadruped, bird, &c., or quadruped into various species of quadrupeds) is\na genus 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\nwhether we use the concrete or the abstract form) is generally assigned by\nlogicians as the Differentia; and doubtless this attribute serves the\npurpose of distinction: but it has also been remarked of man, that he is a\ncooking animal; the only animal that dresses its food. This, therefore, is\nanother of the attributes by which the species man is distinguished from\nother species of the same genus: would this attribute serve equally well\nfor a differentia? The Aristotelians say No; having laid it down that the\ndifferentia must, like the genus and species, be of the _essence_ of the\nsubject.\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 anything which caused it to have them.\nLogicians, however, not liking to admit this, and being unable to detect\nwhat made the thing to be what it was, satisfied themselves with what made\nit to be what it was called. Of the innumerable properties, known and\nunknown, that are common to the class man, a portion only, and of course a\nvery small portion, are connoted by its name; these few, however, will\nnaturally have been thus distinguished from the rest either for their\ngreater obviousness, or for greater supposed importance. These properties,\nthen, which were connoted by the name, logicians seized upon, and called\nthem the essence of the species; and not stopping there, they affirmed\nthem, in the case of the _infima species_, to be the essence of the\nindividual 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 founded 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\nHouyhnhms 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, although 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\nthinks it desirable that our ideas should arrange themselves. With this\nview he finds it advisable that one of his fundamental divisions should be\ninto warm-blooded and cold-blooded animals; or into animals which breathe\nwith lungs 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\nsome of Cuvier\u2019s families are founded. In doing this, the naturalist\ncreates so 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 those 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; although not commonly considered\nas ambiguous, 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 be, who adhere to the Linn\u00e6an classification;\nand the question would arise, whether the word should continue to be used\nin two senses, or the classification be given up, and the technical sense\nof 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 colours, and desire to justify, or even merely to point\nout, the particular place assigned to whiteness in our arrangement, we may\ndefine it \u201cthe colour 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.(24)\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\nconnexion 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 connexion.\n\nA Proprium, therefore, of the species, may be defined, any attribute which\nbelongs to all the individuals included in the species, and which,\nalthough not connoted by the specific name, (either ordinarily if the\nclassification we are considering be for ordinary purposes, or specially\nif it be for a special purpose,) yet follows from some attribute which the\nname either ordinarily 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\npremisses, 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, it _cannot but_ follow, consistently with\nsome 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 connexion 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 connexion 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 colour of an 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, although 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\nCHAPTER VIII. OF 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 cannot 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, cannot 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 cannot 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 usually been esteemed one of the modes of\ndefinition.\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 may be done either\ndirectly or indirectly. The direct mode would be by a proposition in this\nform: \u201cMan\u201d (or whatsover the word may be) \u201cis a name connoting such and\nsuch attributes,\u201d or \u201cis a name which, when predicated of anything,\nsignifies the possession of such and such attributes by that thing.\u201d Or\nthus: Man is everything which possesses such and such attributes: Man is\neverything 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 and pedantic for\ncommon discourse. The more usual mode of declaring the connotation of a\nname, is to predicate of it another name or names of known signification,\nwhich connote the same aggregation of attributes. This may be done either\nby predicating of the name intended to be defined, another connotative\nname exactly 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 may employ names which connote several of\nthe attributes 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 premisses; 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 an 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 one, 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, and 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 coexistent or in succession. To obtain a definition of the\nattribute, we must analyse 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 analyse, 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 cannot 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, we\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. Anything, therefore, is to\nthem a sufficient definition of a term, which will serve as a correct\nindex to what the term _de_notes; although 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; namely,\nEssential but incomplete Definitions, and Accidental Definitions, or\nDescriptions. In the former, a connotative name is defined by a part only\nof its connotation; 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\nfollowing:\u2014Man is a rational animal. It is impossible to consider this as\na complete definition of the word Man, since (as before remarked) if we\nadhered to it we should be obliged to call the Houyhnhms men; but as there\nhappen to be no Houyhnhms, this imperfect definition is sufficient to mark\nout and distinguish from all other things, the objects at present denoted\nby \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\nanything which, whether it expounds the meaning of the name or not,\nenables us to discriminate the things denoted by the name from all other\nthings, and consequently to employ the term in predication without\ndeviating from established usage. This purpose is duly answered by stating\nany (no matter what) of the attributes which are common to the whole of\nthe class, and peculiar to it; or any combination of attributes which may\nhappen to be peculiar to it, though separately each of those attributes\nmay be common to it with some other things. It is only necessary that the\ndefinition (or description) thus formed, should be _convertible_ with the\nname which it professes to define; that is, should be exactly co-extensive\nwith it, being predicable of everything of which it is predicable, and of\nnothing of which it is not predicable; although the attributes specified\nmay have no connexion with those which mankind had in view when they\nformed or recognised the class, and gave it a name. The following are\ncorrect definitions of Man, according to this test: Man is a mammiferous\nanimal, having (by nature) two hands (for the human species answers to\nthis description, and no other animal does): Man is an animal who cooks\nhis food: 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, although the definition is still a declaration of\nthe meaning which in the particular instance the name is appointed to\nconvey, it cannot be said that to state the meaning of the word is the\npurpose of the definition. The purpose is not to expound a name, but to\nhelp to expound a classification. The special meaning which Cuvier\nassigned to the word Man, (quite foreign to its ordinary meaning, though\ninvolving no change in the denotation of the word,) was incidental to a\nplan of arranging animals into classes on a certain principle, that is,\naccording to a certain set of distinctions. And since the definition of\nMan according to the ordinary connotation of the word, though it would\nhave answered every other purpose of a definition, would not have pointed\nout the place which the species ought to occupy in that particular\nclassification; he gave the word a special connotation, that he might be\nable to define it by the kind of attributes on which, for reasons of\nscientific convenience, he had resolved to found his division of animated\nnature.\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, &c. 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\ncannot 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\nScientific men are still seeking, and may be long ere they find, a\nsuitable definition of one of the earliest words in the vocabulary of the\nhuman race, and one of those of which the popular sense is plainest and\nbest understood. The word I mean is Heat; and the source of the difficulty\nis the imperfect state of our scientific knowledge, which has shown to us\nmultitudes of phenomena certainly connected with the same power which\ncauses what our senses recognise as heat, but has not yet taught us the\nlaws of those phenomena with sufficient accuracy to admit of our\ndetermining under what characteristics the whole of those phenomena shall\nultimately be embodied as a class: which characteristics would of course\nbe so many differenti\u00e6 for the definition of the power itself. We have\nadvanced far enough to know that one of the attributes connoted must be\nthat of operating as a repulsive force; but this is certainly not all\nwhich must ultimately be included in the scientific definition of heat.\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\nthe Introductory 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 any one 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 cannot therefore be set forth in words, even by implication,\notherwise than by enumerating them all: and all are not known, nor ever\nwill be so. It is idle, therefore, to look to this as one of the purposes\nof a definition: while, if it be only required that the definition of a\nKind should indicate what Kinds include it or are included by it, any\ndefinitions which expound the connotation of the names will do this: for\nthe name of each class must necessarily connote enough of its properties\nto fix the boundaries of the class. If the definition, therefore, be a\nfull statement of the connotation, it is all that a definition can be\nrequired to be.\n\n\u00a7 5. Of the two incomplete or unscientific modes of definition, and in\nwhat they differ from the complete or scientific 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 deservedly popular work,\nArchbishop Whately\u2019s _Logic_.(25) In a review of that work published by me\nin the _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, cannot, as it appears to\nus, be maintained. We apprehend that no definition is ever intended to\n\u2018explain and unfold the nature of the thing.\u2019 It is some confirmation of\nour opinion, 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, cannot 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 &c., the sense would remain unchanged: in the second \u2018A triangle\nmeans,\u2019 &c., the meaning would be altered, since it would be obviously\nimpossible to deduce any of the truths of geometry from a proposition\nexpressive only of the manner in which we intend to employ a particular\nsign.\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 real existence of Things possessing the combination of\nattributes set forth in the definition; and this, if true, may be\nfoundation sufficient on which to build a whole fabric of scientific\ntruth.\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 afterwards, in their own philosophy,\nnumerous propositions which could only have a rational meaning as part of\na Realistic 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 anything 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 premisses 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 premisses 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 premisses in\nEuclid\u2019s Elements; the definition, let us say, of a circle. This, being\nanalysed, 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 BCD.\u201d Here is an assumption, that a figure, such as the definition\nexpresses, _may_ be described; which is no other than the postulate, or\ncovert assumption, involved in the so-called definition. But whether that\nfigure be called a circle or not is quite immaterial. The purpose would be\nas well 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 premisses 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 premisses in any of our reasonings, except such as relate to\nwords only. If this supposition were true, we might argue correctly from\ntrue premisses, and arrive at a false conclusion. We should only have to\nassume as a premiss 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\nA dragon is a serpent breathing flame.\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 premisses of the following syllogism:\n\nA dragon is a thing which breathes flame:\nA dragon is a serpent:\n\nFrom which the conclusion is,\n\nTherefore some serpent or serpents breathe flame:\u2014\n\nan unexceptionable syllogism in the first mode of the third figure, in\nwhich both premisses are true and yet the conclusion false; which every\nlogician knows to be an absurdity. The conclusion being false and the\nsyllogism correct, the premisses cannot be true. But the premisses,\nconsidered as parts of a definition, are true. Therefore, the premisses\nconsidered as parts of a definition cannot be the real ones. The real\npremisses must be\u2014\n\nA dragon is a _really existing_ thing which breathes flame:\nA dragon is a _really existing_ serpent:\n\nwhich implied premisses being false, the falsity of the conclusion\npresents no absurdity.\n\nIf we would determine what conclusion follows from the same ostensible\npremisses when the tacit assumption of real existence is left out, let us,\naccording to the recommendation in the Westminster Review, substitute\n_means_ for _is_. We then have\u2014\n\nDragon is _a word meaning_ a thing which breathes flame:\nDragon is _a word meaning_ a serpent:\n\nFrom which the conclusion is,\n\nSome _word or words which mean_ a serpent, also mean a thing which\n            breathes flame:\n\nwhere the conclusion (as well as the premisses) 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\nThe _idea of_ a dragon is _an idea of_ a thing which breathes flame:\nThe _idea of_ a dragon is _an idea of_ a serpent:\n\nTherefore, there is _an idea of_ a serpent, which is _an idea of_ a thing\nbreathing flame.\n\nHere the conclusion is true, and also the premisses; but the premisses 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.(26)\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 premiss, 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 realised by art. People had a difficulty, therefore, in\nconceiving that the most certain of all conclusions could rest on\npremisses which, instead of being certainly true, are certainly not true\nto the full extent asserted. This apparent paradox will be examined when\nwe come to treat of Demonstration; where we shall be able to show that as\nmuch of the postulate is true, as is required to support as much as is\ntrue of the conclusion. Philosophers however to whom this view had not\noccurred, or whom it did not satisfy, have thought it indispensable that\nthere should be found in definitions something _more_ certain, or at least\nmore accurately true, than the implied postulate of the real existence of\na corresponding 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 made up by the\nmind, out of the materials in nature. The definition (it is said) is a\ndefinition of this mental line, not of any actual line: and it is only of\nthe mental line, not of any line existing in nature, that the theorems of\ngeometry are accurately true.\n\nAllowing this doctrine respecting the nature of demonstrative truth to be\ncorrect, (which, in a subsequent place, I shall endeavour 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 cannot form any such\nnotion; it cannot conceive length without breadth; it can only, in\ncontemplating objects, _attend_ to their length, exclusively of their\nother sensible qualities, and so determine what properties may be\npredicated of them in virtue of their length alone. If this be true, the\npostulate involved in the geometrical definition of a line, is the real\nexistence, not of length without breadth, but merely of length, that is,\nof long objects. This is quite enough to support all the truths of\ngeometry, since every property of a geometrical line is really a property\nof all physical objects 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_: although, 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 cannot 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\nobject, knew, no doubt, very well what quality he intended to predicate,\nand had a perfectly distinct conception in his mind of the attribute\nsignified by the 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 easily\ndiscriminated, and referred each to its true source; it often happens that\nnames are applied to nameable objects, with no distinct connotation\npresent to the minds of those who apply them. They are only influenced by\na general resemblance between the new object and all or some of the old\nfamiliar objects which they have been accustomed to call by that name.\nThis, as we have seen, is the law which even the mind of the philosopher\nmust follow, in giving names to the simple elementary feelings of our\nnature: 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\ncannot be brought before the tribunal of the outward senses to be\nidentified and discriminated, connote little more than a vague gross\nresemblance to the things which they were earliest, or have been most,\naccustomed to call by those names. When, for instance, ordinary persons\npredicate the words _just_ or _unjust_ of any action, _noble_ or _mean_ of\nany sentiment, expression, or demeanour, _statesman_ or _charlatan_ of any\npersonage figuring in politics, do they mean to affirm of those various\nsubjects any determinate attributes, of whatever kind? No: they merely\nrecognise, as they think, some likeness, more or less vague and loose,\nbetween these and some other things which they have been accustomed to\ndenominate or to hear denominated 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,)\na name 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 always require to be, by the hands of the\nlogician, are often in themselves excellently suited to his purposes. When\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, though it may be founded only on\na gross and 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 connexions 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.(27)\n\nWhenever the inquiry into the definition of the name of any real object\nconsists of anything 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\nendeavour 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\nBOOK II. OF 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\u1f70 \u03c4\u03af\u03bd\u03c9\u03bd, \u03ba\u03b1\u1f76 \u03c0\u03cc\u03c4\u03b5, \u03ba\u03b1\u1f76 \u03c0\u1ff6\u03c2 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9\n\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. \u03a0\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03bd \u03b3\u1f70\u03c1 \u03c0\u03b5\u03c1\u1f76\n\u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u1fe6 \u03bb\u03b5\u03ba\u03c4\u03ad\u03bf\u03bd, \u1f23 \u03c0\u03b5\u03c1\u1f76 \u1f00\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c9\u03c2, \u03b4\u03b9\u1f70 \u03c4\u1f78 \u03ba\u03b1\u03b8\u03cc\u03bb\u03bf\u03c5 \u03bc\u1fb6\u03bb\u03bb\u03bf\u03bd \u03b5\u1f30\u03bd\u03b1\u1f76 \u03c4\u1f78\u03bd\n\u03c3\u03c5\u03bb\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03bd. \u1f29 \u03bc\u1f72\u03bd \u03b3\u1f70\u03c1 \u1f00\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b9\u03c2, \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\u1f50\n\u03c0\u1fb6\u03c2, \u1f00\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b9\u03c2.\n\nARIST. _Analyt. Prior._ 1. i. cap. 4.\n\n\n\n\nCHAPTER I. OF 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 analysed\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 recognises 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 analysed 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,\nand from which they are said to be _inferred_. To infer a proposition from\na previous 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\nearly 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 \u00e6quipollency 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 an 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; demonstrations in form, of conclusions\nto which whoever understands the terms used in the statement of the data,\nhas already, and consciously, assented.\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 cannot be inferred that All B is A; though all\nwater 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 an\nuniversal proposition into a particular, is termed conversion _per\naccidens_. From the proposition, Some A is not B, we cannot 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 legitimate conversion,\nif such it can be called, of a particular negative proposition, is in the\nform, Some A is not B, therefore, something which is not B is A; and this\nis termed conversion by contraposition. In this case, however, the\npredicate and subject are not merely reversed, but one of them is altered.\nInstead of [A] and [B], the terms of the new proposition are [a thing\nwhich is not B], and [A]. The original proposition, Some A _is not_ B, is\nfirst changed into a proposition \u00e6quipollent with it, Some A _is_ \u201ca thing\nwhich is not B\u201d; and the proposition, being now no longer a particular\nnegative, but a particular affirmative, admits of conversion in the first\nmode, or, as it is called, _simple_ conversion.\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\npremisses, and obvious to whoever apprehends them. The fact asserted in\nthe conclusion is either the very same fact, or part of the fact, asserted\nin the original proposition. This follows from our previous analysis of\nthe Import 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 coexist 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 coexist 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 coexist, 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 cannot be inferred. In order to reassert, 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 \u00e6quipollency of propositions. For, although\nthat cannot be called reasoning or inference which is a mere reassertion\nin different 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\ncannot both be true; that sub-contrary propositions may both be true, but\ncannot 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 _vice\nvers\u00e2_(28); 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 premisses,\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 premisses. 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 are said to form its\nbasis. A principle ascertained by experience, is more than a mere summing\nup of what has been specifically observed in the individual cases which\nhave been 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, so 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\nCHAPTER II. OF 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 afterwards 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 premisses. It is essential that there should be\nthree, and no more than three, terms, namely, the subject and predicate of\nthe conclusion, and another called the middleterm, which must be found in\nboth premisses, 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 premisses, together with the\nmiddleterm which is in them both. The premiss which contains the\nmiddleterm and the major term is called the major premiss; that which\ncontains the middle term and the minor term is called the minor premiss.\n\nSyllogisms are divided by some logicians into three _figures_, by others\ninto four, according to the position of the middleterm, which may either\nbe the subject in both premisses, the predicate in both, or the subject in\none and the predicate in the other. The most common case is that in which\nthe middleterm is the subject of the major premiss and the predicate of\nthe minor. This is reckoned as the first figure. When the middleterm is\nthe predicate in both premisses, the syllogism belongs to the second\nfigure; when it is the subject in both, to the third. In the fourth figure\nthe middleterm is the subject of the minor premiss 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 _modes_, 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 modes, that is, all those in which the\nconclusion correctly follows from the premisses. A is the minor term, C\nthe major, B the middleterm.\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 C    No B is C    Some B is C   All B is C    Some B is    No B is C\n                                                       not C\nAll B is A    All B is A   All B is A    Some B is A   All B is A   Some B is A\ntherefore     therefore    therefore     therefore     therefore    therefore\nSome A is C   Some A is    Some A is C   Some A is C   Some A is    Some A is\n              not 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 of 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 mode of\nthe first figure.\n\nThe reasons why syllogisms in any of the above forms are legitimate, that\nis, why, if the premisses be true, the conclusion must necessarily be so,\nand why this is not the case in any other possible _mode_, (that is, in\nany other combination of universal and particular, affirmative and\nnegative propositions,) any person taking interest in these inquiries may\nbe presumed to have either learnt from the common school books of the\nsyllogistic logic, or to be capable of divining 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 mode and figure.\n\nAlthough 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 premisses. Thus an argument in the first mode of the\nsecond figure, 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 an 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:\u2014\n\nNo B is C\nAll A is B\ntherefore\nNo A is C,\n\nwhich is a good syllogism in the second mode of the first figure. Again,\nan argument in the first mode of the third figure must resemble the\nfollowing:\u2014\n\nAll B is C\nAll B is A\ntherefore\nSome A is C,\n\nwhere the minor premiss, 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 mode of the first\nfigure:\u2014\n\nAll B is C\nSome A is B,\nfrom which it obviously follows, that\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 mode of the second, third, and fourth figures\nmay be reduced to some one of the four modes 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 premisses, 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:\u2014\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:\u2014\n\nTo prove an affirmative, the argument must admit of being stated in this\nform:\u2014\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:\u2014\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\nAlthough 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 ever yet made of the syllogistic doctrine, has\nexpressly examined what sorts of arguments fall most naturally and\nsuitably into each of the four figures; and his solution is characterized\nby great ingenuity and clearness of thought.(29) The argument, however, is\none and the same, in whichever figure it is expressed; since, as we have\nalready seen, the premisses of a syllogism in the second, third, or fourth\nfigure, and those of the syllogism in the first figure to which it may be\nreduced, are the same premisses in everything except language, or, at\nleast, as much of them as contributes to the proof of the conclusion is\nthe same. We are therefore at liberty, in conformity with the general\nopinion of logicians, to consider the two elementary forms of the first\nfigure as the universal types of all correct ratiocination; the one, when\nthe conclusion to be proved is affirmative, the other, when it is\nnegative; even though certain arguments may have a tendency to clothe\nthemselves in the forms of the second, third, and fourth figures; which,\nhowever, cannot possibly happen with the only class of arguments which are\nof first-rate scientific importance, those in which the conclusion is an\nuniversal affirmative, such conclusions being susceptible of proof in the\nfirst figure alone.\n\n\u00a7 2. On examining, then, these two general formul\u00e6, we find that in both\nof them, one premiss, the major, is an universal proposition; and\naccording as this is affirmative or negative, the conclusion is so too.\nAll ratiocination, therefore, starts from a _general_ proposition,\nprinciple, or assumption: a proposition in which a predicate is affirmed\nor denied of an entire class; that is, in which some attribute, or the\nnegation of some attribute, is asserted of an indefinite number of objects\ndistinguished by a common characteristic, and designated, in consequence,\nby a common name.\n\nThe other premiss 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 premiss. It follows that the attribute affirmed or\ndenied of the entire class may (if there was truth in that affirmation or\ndenial) be affirmed or denied of the object or objects alleged to be\nincluded in the class: and this is precisely the assertion made in the\nconclusion.\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 everything 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\nrevival. So long as what were termed Universals were regarded as a\npeculiar kind of substances, having an objective existence distinct from\nthe individual objects classed under them, the _dictum de omni_ conveyed\nan important meaning; because it expressed the intercommunity of nature,\nwhich it was necessary on that theory that we should suppose to exist\nbetween those general substances and the particular substances which were\nsubordinated to them. That everything predicable of the universal was\npredicable of the various individuals contained under it, was then no\nidentical proposition, but a statement of what was conceived as a\nfundamental law of the universe. The assertion that the entire nature and\nproperties of the _substantia secunda_ formed part of the properties of\neach of the individual substances called by the same name; that the\nproperties of Man, for example, were properties of all men; was a\nproposition of real significance when man did not _mean_ all men, but\nsomething inherent in men, and vastly superior to them in dignity. Now,\nhowever, when it is known that a class, an universal, a genus or species,\nis not an entity _per se_, but neither more nor less than the individual\nsubstances themselves which are placed in the class, and that there is\nnothing real in the matter except those objects, a common name given to\nthem, and common attributes indicated by the name; what, I should be glad\nto know, do we learn by being told, that whatever can be affirmed of a\nclass, may be affirmed of every object contained in the class? The class\n_is_ nothing but the objects contained in it: and the _dictum de omni_\nmerely amounts to the identical proposition, that whatever is true of\ncertain objects, is true of each of those objects. If all ratiocination\nwere no more than the application of this maxim to particular cases, the\nsyllogism would indeed be, what it has so often been declared to be,\nsolemn trifling. The _dictum de omni_ is on a par with another truth,\nwhich in its time was also reckoned of great importance, \u201cWhatever is,\nis;\u201d and not to be compared in point of significance to the cognate\naphorism, \u201cIt is impossible for the same thing to be and not to be;\u201d since\nthis is, at the lowest, equivalent to the logical axiom that contradictory\npropositions cannot both be true. To give any real meaning to the _dictum\nde omni_, we must consider it not as an axiom, but as a definition; we\nmust look upon it as intended to explain, in a circuitous and paraphrastic\nmanner, 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 Kantians, has never\nceased 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 premisses fairly put together were likely, if\nhe was 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 supposed to derive irresistible confirmation from the example\nof algebra. 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 anything, 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\nlearnt 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 cannot 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 anything 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 premiss\nasserted nothing more than that something belongs to a class, and if the\nmajor premiss 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 artificial classification. It\nasserts that a given object does or does not possess a given attribute; or\nit asserts that two attributes, or sets of attributes, do or do not\n(constantly or occasionally) coexist. 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 recognise this import of propositions, cannot, we may be sure, be the\ntrue one.\n\nApplying this view of propositions to the two premisses of a syllogism, we\nobtain the following results. The major premiss, 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 premiss asserts that\nthe thing or set of things which are the subject of that premiss, 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 premiss are connotative terms,\ndenoting objects and connoting attributes. The assertion in the major\npremiss 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\npremiss 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 premisses are general propositions, as\n\nAll men are mortal,\nAll kings are men,\ntherefore\nAll kings are mortal,\n\nthe minor premiss 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 premiss 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 premiss, it is concluded, that the same\nincompatibility exists between the attribute omnipotence and those\nconstituting a king. In a similar manner we might analyse 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 anything 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 coexist with the same thing, coexist with one another. The\nsecond is the principle of negative syllogisms, and is to this effect:\nthat a thing which coexists with another thing, with which other a third\nthing does not coexist, is not coexistent 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.\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(30) 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:\u2014\n\nAttribute A is a mark of attribute B,\nA 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:\u2014\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\nthat attribute.)\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\npossesses any mark, possesses that which it is a mark of. Or, when the\nminor premiss as well as the major is universal, we may state it thus:\nWhatever is a mark of any mark, is a mark of that which this last is a\nmark of. To trace the identity of these axioms with those previously laid\ndown, may be left to the intelligent reader. We shall find, as we proceed,\nthe great convenience of the phraseology into which we have last thrown\nthem, and which is better adapted than any I am acquainted with, to\nexpress with precision and force what is aimed at, and actually\naccomplished, in every case of the ascertainment of a truth by\nratiocination.\n\n\n\n\nCHAPTER III. OF 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 anything more in the conclusion than was assumed in the premisses. 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\npremisses. Yet the acknowledgment so explicitly made, has not prevented\none set of writers from continuing to represent the syllogism as the\ncorrect analysis of what the mind actually performs in discovering and\nproving the larger half of the truths, whether of science or of daily\nlife, which we believe; while those who have avoided this inconsistency,\nand followed out the general theorem respecting the logical value of the\nsyllogism to its legitimate corollary, have been led to impute uselessness\nand frivolity to the syllogistic theory itself, on the ground of the\n_petitio principii_ which they allege to be inherent in every syllogism.\nAs I believe both these opinions to be fundamentally erroneous, I must\nrequest the attention of the reader to certain considerations, without\nwhich any just appreciation of the true character of the syllogism, and\nthe functions it performs in philosophy, appears to me impossible; but\nwhich seem to have been either overlooked, or insufficiently adverted to,\nboth by the defenders 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 cannot 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 you 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, cannot 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 anything: since from a general principle you cannot 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 _bon\u00e2 fide_ a new truth? Is it not matter of daily experience\nthat truths previously undreamt of, facts which have not been, and cannot\nbe, 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, since he is not dead. If we were asked how, this being\nthe case, we know the duke to be mortal, we should probably answer,\nBecause all men are so. Here, therefore, we arrive at the knowledge of a\ntruth not (as yet) susceptible of observation, by a reasoning which admits\nof being exhibited in the following syllogism:\u2014\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; although none of them has cleared up the difficulty which arises\nfrom the inconsistency between that assertion, and the principle, that if\nthere be anything in the conclusion which was not already asserted in the\npremisses, 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 premisses, and being\ndirectly asserted in them. When Archbishop Whately, for example, says,(31)\nthat the object of reasoning is \u201cmerely to expand and unfold the\nassertions wrapt up, as it were, and implied in those with which we set\nout, and to bring a person to perceive and acknowledge the full force of\nthat which he has admitted,\u201d he does not, I think, meet the real\ndifficulty requiring to be explained, namely, how it happens that a\nscience, like geometry, _can_ be all \u201cwrapt up\u201d in a few definitions and\naxioms. Nor does this defence of the syllogism differ much from what its\nassailants urge against it as an accusation, when they charge it with\nbeing of no use except to those who seek to press the consequences of an\nadmission into which a person has been entrapped without having considered\nand understood its full force. When you admitted the major premiss, you\nasserted the conclusion; but, says Archbishop Whately, you asserted it by\nimplication merely: this, however, can here only mean that you asserted it\nunconsciously; that you did not know you were asserting it; but, if so,\nthe difficulty revives in this shape\u2014Ought you not to have known? Were you\nwarranted in asserting the general proposition without having satisfied\nyourself of the truth of everything which it fairly includes? And if not,\nwhat then is the syllogistic art but a contrivance for catching you in a\ntrap, and holding you fast in it?(32)\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 the two parts of the process of philosophizing, the inferring\npart, and the registering part; and ascribing to the latter the functions\nof the former. The mistake is that of referring a person to his own notes\nfor the origin of his knowledge. If a person is asked a question, and is\nat the moment unable to answer it, he may refresh his memory by turning to\na memorandum which he carries about with him. But if he were asked, how\nthe fact came to his knowledge, he would scarcely answer, because it was\nset down in his note-book: unless the book was written, like the Koran,\nwith a quill 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 afterwards is merely decyphering our\nown notes.\n\nArchbishop Whately has contended that syllogising, 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 cannot help thinking that the vulgar notion\nis, in this case, the more correct. If, from our experience of John,\nThomas, &c., who once were living, but are now dead, we are entitled to\nconclude that all human beings are mortal, we might surely without any\nlogical inconsequence have concluded at once from those instances, that\nthe Duke of Wellington is mortal. The mortality of John, Thomas, and\ncompany is, after all, the whole evidence we have for the mortality of the\nDuke of Wellington. Not one iota is added to the proof by interpolating a\ngeneral proposition. Since the individual cases are all the evidence we\ncan possess, evidence which no logical form into which we choose to throw\nit can make greater than it is; and since that evidence is either\nsufficient in itself, or, if insufficient for the one purpose, cannot be\nsufficient for the other; I am unable to see why we should be forbidden to\ntake the shortest cut from these sufficient premisses to the conclusion,\nand constrained to travel the \u201chigh priori road,\u201d by the arbitrary fiat of\nlogicians. I cannot perceive why it should be impossible to journey from\none place to another unless we \u201cmarch up a hill, and then march down\nagain.\u201d It may be the safest road, and there may be a resting place at the\ntop of the hill, affording a commanding view of the surrounding country;\nbut for the mere purpose of arriving at our journey\u2019s end, our taking that\nroad is perfectly optional; it is a question 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 burnt his fingers, avoids to thrust them again into\nthe fire, has reasoned or inferred, though he has never thought of the\ngeneral maxim, Fire burns. He knows from memory that he has been burnt,\nand on this evidence believes, when he sees a candle, that if he puts his\nfinger into the flame of it, he will be burnt again. He believes this in\nevery case which happens to arise; but without looking, in each instance,\nbeyond the present case. He is not generalizing; he is inferring a\nparticular 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 burnt child, but the burnt 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 having known the\nfeelings and conduct of the same person in some previous instance, or from\nconsidering 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\nneighbour\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 practising the habit of stating to oneself\nor to others the corresponding general propositions. An old warrior, on a\nrapid glance at the outlines of the ground, is able at once to give the\nnecessary orders for a skilful arrangement of his troops; though if he has\nreceived little theoretical instruction, and has seldom been called upon\nto answer to other people for his conduct, he may never have had in his\nmind a single general theorem respecting the relation between ground and\narray. But his experience of encampments, in circumstances more or less\nsimilar, has left a number of vivid, unexpressed, ungeneralized analogies\nin his mind, the most appropriate of which, instantly suggesting itself,\ndetermines 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, &c., 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 colours, 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 connexion in his mind between fine effects of\ncolour, 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\ncourt 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\nstored with 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 our 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 A B is equal to C D because each of them is equal to E F,\nthe most 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 stopt 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 premisses, 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 pit of darkness, and not seeing\nthat this is equally true in every other case of generalization, he\ncontended that axioms are in their nature barren of consequences, and that\nthe really fruitful truths, the real first principles of geometry, are the\ndefinitions; that the definition, for example, of the circle is to the\nproperties of the circle, what the laws of equilibrium and of the pressure\nof the atmosphere are to the rise of the mercury in the Torricellian tube.\nYet all that he had asserted respecting the function to which the axioms\nare confined in the demonstrations of geometry, holds equally true of the\ndefinitions. Every demonstration in Euclid might be carried on without\nthem. This is apparent from the ordinary process of proving a proposition\nof geometry by means of a diagram. What assumption, in fact, do we set out\nfrom, to demonstrate by a diagram any of the properties of the circle? Not\nthat in all circles the radii are equal, but only that they are so in the\ncircle ABC. As our warrant for assuming this, we appeal, it is true, to\nthe definition of a circle in general; but it is only necessary that the\nassumption be granted in the case of the particular circle supposed. From\nthis, which is not a general but a singular proposition, combined with\nother propositions of a similar kind, some of which _when generalized_ are\ncalled definitions, and others axioms, we prove that a certain conclusion\nis true, not of all circles, but of the particular circle ABC; or at least\nwould be so, if the facts precisely accorded with our assumptions. The\nenunciation, as it is called, that is, the general theorem which stands at\nthe head of the demonstration, is not the proposition actually\ndemonstrated. One instance only is demonstrated: but the process by which\nthis is done, is a process which, when we consider its nature, we perceive\nmight be exactly copied in an indefinite number of other instances; in\nevery instance which conforms to certain conditions. The contrivance of\ngeneral language furnishing us with terms which connote these conditions,\nwe are able to assert this indefinite multitude of truths in a single\nexpression, and this expression is the general theorem. By dropping the\nuse of diagrams, and substituting, in the demonstrations, general phrases\nfor the letters of the alphabet, we might prove the general theorem\ndirectly, that is, we might demonstrate all the cases at once; and to do\nthis we must, of course, employ as our premisses, the axioms and\ndefinitions in their general form. But this only means, that if we can\nprove an individual conclusion by assuming an individual fact, then in\nwhatever case we are warranted in making an exactly similar assumption, we\nmay draw an exactly similar conclusion. The definition is a sort of notice\nto ourselves and others, what assumptions we think ourselves entitled to\nmake. And so in all cases, the general propositions, whether called\ndefinitions, axioms, or laws of nature, which we lay down at the beginning\nof our reasonings, are merely abridged statements, in a kind of\nshort-hand, of the particular facts, which, as occasion arises, we either\nthink we may proceed on as proved, or intend to assume. In any one\ndemonstration it is enough if we assume for a particular case suitably\nselected, what by the statement of the definition or principle we announce\nthat we intend to assume in all cases which may arise. The definition of\nthe circle, therefore, is to one of Euclid\u2019s demonstrations, exactly what,\naccording to Stewart, the axioms are; that is, the demonstration does not\ndepend on it, but yet if we deny it the demonstration fails. The proof\ndoes not rest on the general assumption, but on a similar assumption\nconfined to the particular case: that case, however, being chosen as a\nspecimen or paradigm of the whole class of cases included in the theorem,\nthere can be no ground for making the assumption in that case which does\nnot exist in every other; and if you deny the assumption as a general\ntruth, you deny the right to make it in the 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\nunpractised 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 premiss 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 premisses, 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 given\ninference. 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\nensure 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\nfavourable 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 travelling from premisses 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 a certain description, 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 the generalization may not be,\nin the ordinary sense, an assertion at all, but a command; a law, not in\nthe philosophical, but in the moral and political sense of the term: an\nexpression of the desire of a superior, that we, or any number of other\npersons, shall conform our conduct to certain general instructions. So far\nas this asserts a fact, namely, a volition of the legislator, that fact is\nan individual fact, and the proposition, therefore, is not a general\nproposition. But the description therein contained of the conduct which it\nis the will of the legislator that his subjects should observe, is\ngeneral. The proposition asserts, not that all men _are_ anything, but\nthat all men _shall_ do something.\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 premisses 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 premisses\nare derived from observation, the function of Reasoning is to ascertain\nwhat we (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 anything, 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 premisses 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 cotemporary with them, have died.\nThose facts are the real premisses of the reasoning. But we are not led to\ninfer the conclusion from those premisses, by the necessity of avoiding\nany verbal inconsistency. There is no contradiction in supposing that all\nthose persons have died, and that the Duke of Wellington may,\nnotwithstanding, live for ever. But there would be a contradiction if we\nfirst, on the ground of those same premisses, 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 clearly shown, that,\nalthough there is always a process of reasoning or inference where a\nsyllogism is used, the syllogism is not a correct analysis of that process\nof reasoning or inference; which is, on the contrary, (when not a mere\ninference from testimony,) an inference from particulars to particulars;\nauthorized by a previous inference from particulars to generals, and\nsubstantially the same with it; of the nature, therefore, of Induction.\nBut, while these conclusions appear to me undeniable, I must yet enter a\nprotest, as strong as that of Archbishop Whately himself; against the\ndoctrine that the syllogistic art is useless for the purposes of\nreasoning. The reasoning lies in the act of generalization, not in\ninterpreting the record of that act; but the syllogistic form is an\nindispensable collateral security for the correctness of the\ngeneralization 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 a 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 anything.\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 inferrible from our premisses, if that one\nparticular conclusion is so; there is then a considerable likelihood that\nif the premisses 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 what the schoolmen termed a _reductio ad\nimpossibile_.\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\nconclude that Commodus would be a just ruler; supposing him to stop there,\nhe might only have been undeceived by sad experience. But if he reflected\nthat this conclusion could not be justifiable unless from the same\nevidence he was also warranted in concluding some general proposition, as,\nfor instance, that all Roman emperors are just rulers; he would\nimmediately have thought of Nero, Domitian, and other instances, which,\nshowing the falsity of the general conclusion, and therefore the\ninsufficiency of the premisses, would have warned him that those premisses\ncould not prove in the instance of Commodus, what they were inadequate to\nprove in any collection of cases in which 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.\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 afterwards 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 deduction from the\nimmense advantages 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, or the same minds without the same pre-eminent\nadvantages of personal experience, are quite helpless without the aid of\ngeneral 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 premiss, 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 premisses 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 one of the\nphilosophers to whom mental science is most indebted, but who, though a\nvery penetrating, was a very hasty thinker, and whose want of due\ncircumspection rendered him fully as remarkable for what he did not see,\nas for what he saw. I allude to Dr. Thomas Brown, whose theory of\nratiocination is peculiar. He saw the _petitio principii_ which is\ninherent in every syllogism, if we consider the major to be itself the\nevidence by which the conclusion is proved, instead of being, what in fact\nit is, an assertion of the existence of evidence sufficient to prove any\nconclusion of a given description. Seeing this, Dr. Brown not only failed\nto see the immense advantage, in point of security for correctness, which\nis gained by interposing this step between the real evidence and the\nconclusion; but he thought it incumbent on him to strike out the major\naltogether from the reasoning process, without substituting anything else,\nand maintained that our reasonings consist only of the minor premiss and\nthe conclusion, Socrates is a man, therefore Socrates is mortal: thus\nactually suppressing, as an unnecessary step in the argument, the appeal\nto former experience. The absurdity of this was disguised from him by the\nopinion he adopted, that reasoning is merely analysing our own general\nnotions, or abstract ideas; and that the proposition, Socrates is mortal,\nis evolved from the proposition, Socrates is a man, simply by recognising\nthe notion of mortality as already contained in the notion we form of a\nman.\n\nAfter the explanations so fully entered into on the subject of\npropositions, much further discussion cannot 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 distinctly asserted it. But if,\nas is in fact the case, the word man does not connote mortality, how does\nit appear that in the mind of every person who admits Socrates to be a\nman, the idea of man must include the idea of mortality? Dr. Brown could\nnot help seeing this difficulty, and in order to avoid it, was led,\ncontrary to his intention, to re-establish, under another name, that step\nin the argument which corresponds to the major, by affirming the necessity\nof _previously perceiving_ the relation between the idea of man and the\nidea of mortal. If the reasoner has not previously perceived this\nrelation, he will not, says Dr. Brown, infer because Socrates is a man,\nthat Socrates is mortal. But even this admission, though amounting to a\nsurrender of the doctrine that an argument consists of the minor and the\nconclusion alone, will not save the remainder of Dr. Brown\u2019s theory. The\nfailure of assent to the argument does not take place merely because the\nreasoner, for want of due analysis, does not perceive that his idea of man\nincludes the idea of mortality; it takes place, much more commonly,\nbecause in his mind that relation between the two ideas has never existed.\nAnd in truth it never does exist, except as the result of experience.\nConsenting, for the sake of the argument, to discuss the question on a\nsupposition of which we have recognised the radical incorrectness, namely,\nthat the meaning of a proposition relates to the ideas of the things\nspoken of, and not to the things themselves; I must yet observe, that the\nidea of man, as an universal idea, the common property of all rational\ncreatures, cannot involve anything but what is strictly implied in the\nname. If any one includes in his own private idea of man, as no doubt is\nalmost always the case, some other attributes, such for instance as\nmortality, he does so only as the consequence of experience, after having\nsatisfied himself that all men possess that attribute: so that whatever\nthe idea contains, in any person\u2019s mind, beyond what is included in the\nconventional signification of the word, has been added to it as the result\nof assent to a proposition; while Dr. Brown\u2019s theory requires us to\nsuppose, on the contrary, that assent to the proposition is produced by\nevolving, through an analytic process, this very element out of the idea.\nThis theory, therefore, may be considered as sufficiently refuted; and the\nminor premiss must be regarded as totally insufficient to prove the\nconclusion, except with the assistance of the major, or of that which the\nmajor represents, namely, the various singular propositions expressive of\nthe series of observations, of which the generalization called the major\npremiss is the result.\n\nIn the argument, then, which proves that Socrates is mortal, one\nindispensable part of the premisses 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 premiss, 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\nfrom this we conclude that he further resembles them in the attribute\nmortality.\n\n\u00a7 7. We have thus obtained what we were seeking, an 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 _bon\u00e2 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 recognise 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 conclusive 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\npremisses 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 anything is inferred respecting an unobserved case, as consisting of\nan Induction followed by a Deduction; because, although the process needs\nnot necessarily be carried on in this form, it is always susceptible of\nthe form, and must be thrown into it when assurance of scientific accuracy\nis needed and desired.\n\n\n\nNOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.\n\n\n    This theory of the syllogism, (which has received the important\n    adhesion of Dr. Whewell,(33)) has been controverted by a writer in\n    the \u201cBritish Quarterly Review.\u201d(34) The doctrine being new,\n    discussion respecting it is extremely desirable, to ensure that\n    nothing essential to the question escapes observation; and I\n    shall, therefore, reply to this writer\u2019s objections with somewhat\n    more minuteness than their strength may seem to require.\n\n\n    The reviewer denies that there is a _petitio principii_ in the\n    syllogism, or that the proposition, All men are mortal, asserts or\n    assumes that Socrates is mortal. In support of this denial, he\n    argues that we may, and in fact do, admit the general proposition\n    that all men are mortal, without having particularly examined the\n    case of Socrates, and even without knowing whether the individual\n    so named is a man or not. But this of course was never denied.\n    That we can and do draw conclusions concerning cases specifically\n    unknown to us, is the datum from which all who discuss this\n    subject must set out. The question is, in what terms the evidence,\n    or ground, on which we draw these conclusions, may best be\n    designated\u2014whether it is most correct to say, that the unknown\n    case is proved by known cases, or that it is proved by a general\n    proposition, including both sets of cases, the unknown and the\n    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,\n    is that all men are mortal. Turn it in what way we will, this\n    seems to me to be asserting that a thing is the proof of itself.\n    Whoever pronounces the words, All men are mortal, has affirmed\n    that Socrates is mortal, though he may never have heard of\n    Socrates; for since Socrates, whether known to be so or not,\n    really is a man, he is included in the words, All men, and in\n    every assertion of which they are the subject. If the reviewer\n    does not see that there is a difficulty here, I can only advise\n    him to reconsider the subject until he does: after which he will\n    be a more competent judge of the success or failure of an attempt\n    to remove the difficulty.(35) That he had reflected very little on\n    the point when he wrote his remarks, is shown by his oversight\n    respecting the _dictum de omni et nullo_. He acknowledges that\n    this maxim as commonly expressed,\u2014\u201cWhatever is true of a class, is\n    true of everything included in the class,\u201d is a mere identical\n    proposition, since the class _is_ nothing but the things included\n    in it. But he thinks this defect would be cured by wording the\n    maxim thus,\u2014\u201cWhatever is true of a class, is true of everything\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\n    a class means the sum of all the things included in the class, the\n    things which \u201ccan be shown\u201d to be included in it are a part of\n    these; it is the sum of them too, and the _dictum_ is as much an\n    identical proposition with respect to them as to the rest. One\n    would almost imagine that, in the reviewer\u2019s opinion, things are\n    not members of a class until they are called up publicly to take\n    their place in it\u2014that so long, in fact, as Socrates is not known\n    to be a man, he _is not_ a man, and any assertion which can be\n    made concerning men does not at all regard him, nor is affected as\n    to its truth or falsity by anything in which he is concerned.\n\n\n    The reviewer says that if the major premiss included the\n    conclusion, \u201cwe should be able to affirm the conclusion without\n    the intervention of the minor premiss; but every one sees that\n    that is impossible.\u201d It does not follow, because the major premiss\n    contains the conclusion, that the words themselves must show all\n    the conclusions which it contains, and which, or evidence of\n    which, it presupposes. The minor is equally required on both\n    theories. It is respecting the functions of the major premiss that\n    the theories differ; whether that premiss merely affirms the\n    existence of proof, or is itself part of the proof\u2014whether the\n    conclusion follows from the minor and major, or from the minor and\n    the particular instances which are the foundation of the major. On\n    either supposition, it is necessary that the new case should be\n    perceived to be one coming within the description of those to\n    which the previous experience is applicable; which is the purport\n    of the minor premiss. When we say that all men are mortal, we make\n    an assertion reaching beyond the sphere of our knowledge of\n    individual cases; and when a new individual, Socrates, is brought\n    within the field of our knowledge by means of the minor premiss,\n    we learn that we have already made an assertion respecting\n    Socrates without knowing it: our own general formula is, to that\n    extent, for the first time _interpreted_ to us. But according to\n    the reviewer\u2019s theory, it is our having _made_ the assertion which\n    proves the assertion: while I contend that the proof is not the\n    assertion, but the grounds (of experience) on which the assertion\n    was made, and by which it must be justified.\n\n\n    The reviewer comes much nearer to the gist of the question, when\n    he objects that the formula in which the major is left out\u2014\u201cA, B,\n    C, &c., were mortal, therefore the Duke of Wellington is mortal,\u201d\n    does not express all the steps of the mental process, but omits\n    one of the most essential, that which consists in recognising the\n    cases A, B, C, as _sufficient evidence_ of what is true of the\n    Duke of Wellington. This recognition of the sufficiency of the\n    induction he calls an \u201cinference,\u201d and says, that its result must\n    be interpolated between the cases A, B, C, and the case of the\n    Duke of Wellington; and that \u201cour final conclusion is from what is\n    thus interpolated, and not directly from the individual facts that\n    A, B, C, &c. were mortal.\u201d On this it may first be observed, that\n    the formula does express all that takes place in ordinary\n    unscientific reasoning. Mankind in general conclude at once from\n    experience of death in past cases, to the expectation of it in\n    future, without testing the experience by any principles of\n    induction, or passing through any general proposition. This is not\n    safe reasoning, but it is reasoning; and the syllogism, therefore,\n    is not the universal type of reasoning, but only a form in which\n    it is _desirable_ that we should reason. But, in the second place,\n    suppose that the enquirer does logically satisfy himself that the\n    conditions of legitimate induction are realized in the cases A, B,\n    C. It is still obvious, that if he knows the Duke of Wellington to\n    be a man, he is as much justified in concluding at once that the\n    Duke of Wellington is mortal, as in concluding that all men are\n    mortal. The general conclusion is not legitimate, unless the\n    particular one would be so too; and in no sense, intelligible to\n    me, can the particular conclusion be said to be drawn _from_ the\n    general one.(36) That the process of testing the sufficiency of an\n    inductive inference is an operation of a general character, I\n    readily concede to the reviewer; I had myself said as much, by\n    laying down as a fundamental law, that whenever there is ground\n    for drawing any conclusion at all from particular instances, there\n    is ground for a _general_ conclusion. But that this general\n    conclusion should be actually drawn, however useful, cannot be an\n    indispensable condition of the validity of the inference in the\n    particular case. A man gives away sixpence by the same power by\n    which he disposes of his whole fortune; but it is not necessary to\n    the lawfulness of his doing the one, that he should formally\n    assert, even to himself, his right to do the other.\n\n\n    The reviewer has recourse for an example, to syllogisms in the\n    second figure (though all are, by a mere verbal transformation,\n    reducible to the first), and asks, where is the _petitio\n    principii_ in this syllogism, \u201cEvery poet is a man of genius, A B\n    is not a man of genius, therefore A B is not a poet.\u201d It is true\n    that in a syllogism of this particular type, the _petitio\n    principii_ is disguised. A B is not included in the terms, every\n    poet. But the proposition, \u201cevery poet is a man of genius\u201d (a very\n    questionable proposition, by the way), cannot have been\n    inductively proved, unless the negative branch of the enquiry has\n    been attended to as well as the positive; unless it has been fully\n    considered whether among persons who are not \u201cmen of genius,\u201d\n    there are not some who ought to be termed poets, and unless this\n    has been determined in the negative. Therefore, the case of A B\n    has been decided by implication, as much as the case of Socrates\n    in the first example. The proposition, Every poet is a man of\n    genius, is confessedly \u00e6quipollent with \u201cNo one who is not a man\n    of genius is a poet,\u201d and in this the _petitio principii_, as\n    regards A B, is no longer implied, but express, as in an ordinary\n    syllogism of the first figure.\n\n\n    Another critic has endeavoured to get rid of the _petitio\n    principii_ in the syllogism by substituting for the common form of\n    expression, the following form\u2014All _known_ men were mortal,\n    Socrates is a man, therefore Socrates is mortal. To this, however,\n    there is the fatal objection, that the syllogism, thus\n    transformed, does not prove the conclusion; it wants not the form\n    only, but the substance of proof. It is not merely because a thing\n    is true in all _known_ instances that it can be inferred to be\n    true in any new instance: many things may be true of all known men\n    which would not be true of all men; while, on the other hand, a\n    thing may be superabundantly proved true of all men, without\n    having been ascertained by actual experience to be true of all\n    known men, or even of the hundredth part of them.\n\n\n\n\nCHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.\n\n\n\u00a7 1. In our analysis of the syllogism it appeared that the minor premiss\nalways affirms a resemblance between a new case, and some cases previously\nknown; while the major premiss 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 premiss, the examples\nwhich were exclusively employed in the preceding chapter; if the\nresemblance, which that premiss 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 cannot directly observe what is to be proved, but cannot directly\nobserve 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 premiss the establishment of which requires any\nanterior process of inquiry, is the major; and provided the induction of\nwhich that premiss 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:\u2014All 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:\u2014Whatever forms\na compound with hydrogen, which yields a black precipitate with nitrate of\nsilver, is arsenic; the substance before me conforms to this condition;\ntherefore it is arsenic. To establish, therefore, the ultimate conclusion,\nThe substance before me is poisonous, requires a process, which, in order\nto be syllogistically expressed, stands in need of two syllogisms; and we\nhave a Train of Reasoning.\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 the given\nprecipitate, and found that they possessed the properties connoted by the\nword arsenic; they were metallic, volatile, their vapour had a smell of\ngarlic, and so forth. Next, we, or others for us, have examined various\nspecimens which possessed this metallic and volatile character, whose\nvapour had this smell, &c., and have invariably found that they were\npoisonous. The first observation we judge that we may extend to all\nsubstances whatever which yield the precipitate: the second, to all\nmetallic and volatile substances resembling those we examined; and\nconsequently, not to those only which are seen to be such, but to those\nwhich are concluded to be such by the prior induction. The substance\nbefore us is only seen to come within one of these inductions; but by\nmeans of this one, it is brought within the other. We are still, as\nbefore, concluding from particulars to particulars; but we are now\nconcluding from particulars observed, to other particulars which are not,\nas in the simple case, _seen_ to resemble them in the material points, but\n_inferred_ to do so, because resembling them in something else, which we\nhave been led by quite a different set of instances to consider as a mark\nof 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:\u2014No 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 premiss in this argument we shall suppose not to be\nderived from considerations _\u00e0 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 likely to be overthrown, and it has been deemed that\nthose instances warranted an extension of the same predicate to any and\nevery government which resembles them in the attribute of desiring\nearnestly the good of its subjects. But _does_ the government in question\nthus resemble them? This may be debated _pro_ and _con_ by many arguments,\nand must, in any case, be proved by another induction; for we cannot\ndirectly observe the sentiments and desires of the persons who carry on\nthe government. To prove the minor, therefore, we require an argument in\nthis form: Every government which acts in a certain manner, desires the\ngood of its subjects; the supposed government acts in that particular\nmanner, therefore it desires the good of its subjects. But is it true that\nthe government acts in the manner supposed? This minor also may require\nproof; still another induction, as thus:\u2014What is asserted by intelligent\nand disinterested witnesses, may be believed to be true; that the\ngovernment acts in this manner, is asserted by such witnesses, therefore\nit may be believed to be true. The argument hence consists of three steps.\nHaving the 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 predicted 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 cannot, we determine once for all what are the\ndistinguishing marks by which such cases may be recognised. 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\npremisses 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\nrecognise at once, or by the aid of other marks, which by another previous\ninduction we collected to be marks of _them_. Even these marks of marks\nmay only be recognised 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 recognised 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\n_a b c_ a mark of _n_. Suppose, for example, the following combination of\ncircumstances: 1st, rays of light impinging on a reflecting surface; 2nd,\nthat surface parabolic; 3rd, 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\nan angle equal to the angle of incidence. The parabolic form of the\nsurface is a mark that, from any point of it, a line drawn to the focus\nand a line parallel to the axis will make equal angles with the surface.\nAnd finally, the parallelism of the rays to the axis is a mark that their\nangle of incidence coincides with one of these equal angles. The three\nmarks taken together are therefore a mark of all these three things\nunited. But the three united are evidently a mark that the angle of\nreflexion must coincide with the other of the two equal angles, that\nformed by a line drawn to the focus; and this again, by the fundamental\naxiom concerning straight lines, is a mark that the reflected rays pass\nthrough the focus. Most chains of physical deduction are of this more\ncomplicated type; and even in mathematics such are abundant, as in all\npropositions where the hypothesis includes numerous conditions: \u201c_If_ a\ncircle be taken, and _if_ within that circle a point be taken, not the\ncentre, and _if_ straight lines be drawn from that point to the\ncircumference, then,\u201d &c.\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 cannot 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 endeavour to prove in the next chapter, that\nthe first principles of geometry are results of induction. Our example\nshall be the fifth proposition of the first book of Euclid. The inquiry\nis, Are the angles at the base of an isosceles triangle equal or unequal?\nThe first thing to be considered is, what inductions we have, from which\nwe can infer equality or inequality. For inferring equality we have the\nfollowing formul\u00e6:\u2014Things 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 formul\u00e6 to\nprove equality. For inferring inequality we have the following:\u2014A whole\nand its parts are unequals. The sums of equal things and unequal things\nare unequals. The differences of equal things and unequal things are\nunequals. In all, eight formul\u00e6. The angles at the base of an isosceles\ntriangle do not obviously come within any of these. The formul\u00e6 specify\ncertain marks of equality and of inequality, but the angles cannot be\nperceived intuitively to have any of those marks. We can, however, examine\nwhether they have properties which, in any other formul\u00e6, are set down as\nmarks of those marks. On examination it appears that they have; and we\nultimately succeed in bringing them within this formula, \u201cThe differences\nof equal things are equal.\u201d Whence comes the difficulty in recognising\nthese angles as the differences of equal things? Because each of them is\nthe difference not of one pair only, but of innumerable pairs of angles;\nand out of these we had to imagine and select two, which could either be\nintuitively perceived to be equals, or possessed some of the marks of\nequality set down in the various formul\u00e6. By an exercise of ingenuity,\nwhich, on the part of the first inventor, deserves to be regarded as\nconsiderable, two pairs of angles were hit upon, which united these\nrequisites. First, it could be perceived intuitively that their\ndifferences were the angles at the base; and, secondly; they possessed one\nof the marks of equality, namely, coincidence when applied to one another.\nThis coincidence, however, was not perceived intuitively, but inferred, in\nconformity 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 premisses 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. _The sums of equals are equal._\n\nA D and A E are sums of equals by the supposition. Having that mark of\nequality, they are concluded by this formula to be equal.\n\nSECOND FORMULA. _Equal straight lines being applied to one another\ncoincide_.\n\nA C, A B, are within this formula by supposition; A D, A E, have been\nbrought within it by the preceding step. Both these pairs of straight\nlines have the property of equality; which, according to the second\nformula, is a mark that, if applied to each other, they will coincide.\nCoinciding altogether means coinciding in every part, and of course at\ntheir extremities, D, E, and B, C.\n\nTHIRD FORMULA. _Straight lines, having their extremities coincident,\ncoincide_.\n\nB E and C D have been brought within this formula by the preceding\ninduction; they will, therefore, coincide.\n\nFOURTH FORMULA. _Angles, having their sides coincident, coincide_.\n\nThe third induction having shown that B E and C D coincide, and the second\nthat A B, A C, coincide, the angles A B E and A C D are thereby brought\nwithin the fourth formula, and accordingly coincide.\n\nFIFTH FORMULA. _Things which coincide are equal_.\n\nThe angles A B E and A C D are brought within this formula by the\ninduction immediately preceding. This train of reasoning being also\napplicable, _mutatis mutandis_, to the angles E B C, D C B, these also are\nbrought within the fifth formula. And, finally,\n\nSIXTH FORMULA. _The differences of equals are equal_.\n\nThe angle A B C being the difference of A B E, C B E, and the angle A C B\nbeing the difference of A C D, D C B; which have been proved to be equals;\nA B C and A C B are brought within the last formula by the whole of the\nprevious process.\n\nThe difficulty here encountered is chiefly that of figuring to ourselves\nthe two angles at the base of the triangle A B C, 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 idea, it may be seen from an example so near the\nthreshold of mathematics, how much scope there may well be for scientific\ndexterity in the higher branches of that and other sciences, in order so\nto combine a few simple inductions, as to bring within each of them\ninnumerable cases which are not obviously included in it; and how long,\nand numerous, and complicated may be the processes necessary for bringing\nthe inductions together, even when each induction may itself be very easy\nand simple. All the inductions involved in all geometry are comprised in\nthose simple ones, the formul\u00e6 of which are the Axioms, and a few of the\nso-called Definitions. The remainder of the science is made up of the\nprocesses employed for bringing unforeseen cases within these inductions;\nor (in syllogistic language) for proving the minors necessary to complete\nthe syllogisms; the majors being the definitions and axioms. In those\ndefinitions and axioms are laid down the whole of the marks, by an artful\ncombination of which it has been found possible to discover and prove all\nthat is proved in geometry. The marks being so few, and the inductions\nwhich furnish them being so obvious and familiar; the connecting of\nseveral of them together, which constitutes Deductions, or Trains of\nReasoning, forms the whole difficulty of the science, and, with a trifling\nexception, its whole bulk; and hence Geometry is a Deductive Science.\n\n\u00a7 5. It will be seen hereafter that there are weighty scientific reasons\nfor giving to every science as much of the character of a Deductive\nScience as possible; for endeavouring to construct the science from the\nfewest and the simplest possible inductions, and to make these, by any\ncombinations however complicated, suffice for proving even such truths,\nrelating to complex cases, as could be proved, if we chose, by inductions\nfrom specific experience. Every branch of natural philosophy was\noriginally 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, and thermology, have\nsuccessively been rendered mathematical; and astronomy was brought by\nNewton within the laws of general mechanics. Why it is that the\nsubstitution of this circuitous mode of proceeding for a process\napparently much easier and more natural, is held, and justly, to be the\ngreatest triumph of the investigation of nature, we are not, in this stage\nof our inquiry, prepared to examine. But it is necessary to remark, that\nalthough, by this progressive transformation, all sciences tend to become\nmore and more Deductive, they are not therefore the less Inductive; every\nstep in the Deduction is still an Induction. The opposition is not between\nthe terms Deductive and Inductive, but between Deductive and Experimental.\nA science is experimental, in proportion as every new case, which presents\nany peculiar features, stands in need of a new set of observations and\nexperiments, a 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 cannot\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\n_c_ and _d_ marks of one another, without anything to connect _a_ or _b_\nwith _c_ or _d_; we have a science of detached and mutually independent\ngeneralizations, such as these, that acids redden vegetable blues, and\nthat alkalies colour 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_, &c. 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 be not perceptible in those objects, but\nonly inferrible. 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 connexion 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 colouring matters which are reddened by acids (as\nwell as, reciprocally, all red colouring matters which are rendered blue\nby alkalies) contain nitrogen: and it is quite possible that this\ncircumstance may one day furnish a bond of connexion between the two\npropositions in question, by showing that the antagonist action of acids\nand alkalies in producing or destroying the colour 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 coexistence\nwhich obtained between phenomena of the more known class, obtained also\nbetween the phenomena which corresponded to them in the other class. Every\nsound, being a mark of a particular oscillatory motion, became a mark of\neverything which, by the laws of dynamics, was known to be inferrible from\nthat motion; and everything 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 numbers, alone among all known\nphenomena, are, in the most rigorous sense, properties of all things\nwhatever. All things are not coloured, or ponderable, or even extended;\nbut all 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\nwhich are Qualities,) there corresponds a peculiar relation of quantity\nbetween either two or three rectilineal co-ordinates; insomuch that if the\nlaw were known according to which those co-ordinates vary relatively to\none another, 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 fulfil 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\ncannot directly ascertain (or not so conveniently) by experiment. We\ntravel from a given visible or tangible fact, through the truths of\nnumbers, to the fact sought. The given fact is a mark that a certain\nrelation subsists between the quantities of some of the elements\nconcerned; while the fact sought presupposes a certain relation between\nthe quantities of some other elements: now, if these last quantities are\ndependent in some known manner upon the former, or _vice versa_, we can\nargue from the numerical relation between the one set of quantities, to\ndetermine that which subsists between the other set; the theorems of the\ncalculus affording the intermediate links. And thus one of the two\nphysical facts becomes a mark of the other, by being a mark of a mark of a\nmark of it.\n\n\n\n\nCHAPTER V. OF 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 many) 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 descriptions, as far as they go, of the objects with\nwhich 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 false: there exist no real things exactly\nconformable to the definitions. There exist no points without magnitude;\nno lines without breadth, nor perfectly straight; no circles with all\ntheir radii exactly equal, nor squares with all their angles perfectly\nright. It will perhaps be said that the assumption does not extend to the\nactual, but only to the possible, existence of such things. I answer that,\naccording to any test we have of possibility, they are not even possible.\nTheir existence, so far as we can form any judgment, would seem to be\ninconsistent with the physical constitution of our planet at least, if not\nof the universe. To get rid of this difficulty, and at the same time to\nsave the credit of the supposed system of necessary truth, it is customary\nto say that the points, lines, circles, and squares which are the subject\nof geometry, exist in our conceptions merely, and are part of our minds;\nwhich minds, by working on their own materials, construct an _\u00e0 priori_\nscience, the evidence of which is purely mental, and has nothing whatever\nto do with outward experience. By howsoever high authorities this doctrine\nmay have been sanctioned, it appears to me psychologically incorrect. The\npoints, lines, circles, and squares, which any one has in his mind, are (I\napprehend) simply copies of the points, lines, circles, and squares which\nhe has known in his experience. Our idea of a point, I apprehend to be\nsimply our idea of the _minimum visibile_, the smallest portion of surface\nwhich we can see. A line, as defined by geometers, is wholly\ninconceivable. We can reason about a line as if it had no breadth; because\nwe have a power, which is the foundation of all the control we can\nexercise over the operations of our minds; the power, when a perception is\npresent to our senses, or a conception to our intellects, of _attending_\nto a part only of that perception or conception, instead of the whole. But\nwe cannot _conceive_ a line without breadth; we can form no mental picture\nof such a line: all the lines which we have in our minds are lines\npossessing breadth. If any one doubts this, we may refer him to his own\nexperience. I much question if any one who fancies that he can conceive\nwhat is called a mathematical line, thinks so from the evidence of his\nconsciousness: I suspect it is rather because he supposes that unless such\na conception were possible, mathematics could not exist as a science: a\nsupposition which there will be no difficulty in showing to be entirely\ngroundless.\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 cannot be supposed to be conversant about non-entities;\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 convenience,\nwe feign them to be divested of all properties, except those which are\nmaterial to our purpose, and in regard to which we design to consider\nthem.\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\nthey do 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.\n\nWhen, therefore, it is affirmed that the conclusions of geometry are\nnecessary truths, the necessity consists in reality only in this, that\nthey necessarily 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 necessarily 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 endeavoured to\nenforce, has been contested by Dr. Whewell, both in the dissertation\nappended to his excellent _Mechanical Euclid_, and in his more recent\nelaborate work on the _Philosophy of the Inductive Sciences_; in which\nlast he also replies to an article in the _Edinburgh Review_, (ascribed to\na writer of great scientific eminence,) in which Stewart\u2019s opinion was\ndefended against his former strictures. The supposed refutation of Stewart\nconsists in proving against him (as has also been done in this work) that\nthe premisses 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(37) And this is true; but this has never been\ncontradicted. Those who say that the premisses 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 non-entities,) it follows that any hypothesis we\nmake respecting an object, to facilitate our study of it, must not involve\nanything 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 suppressing some of those which it has, under the\nindispensable obligation of restoring them whenever, and in as far as,\ntheir presence or absence would make any material difference in the truth\nof our conclusions. Of this nature, accordingly, are the first principles\ninvolved in the definitions of geometry. In their positive part they are\nobserved facts; it is only in their negative part that they are\nhypothetical. That the hypotheses should be of this particular character,\nis however no further necessary, than inasmuch as no others could enable\nus to deduce conclusions which, with due corrections, would be true of\nreal objects: and in fact, when our aim is only to illustrate truths, and\nnot to 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 although 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\nanother\u2014If equals are added to equals the sums are equal\u2014If equals are\ntaken from equals 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 although these and several\nothers may be struck out of the list of first principles, because, though\nnot requiring demonstration, they are susceptible of it; there will be\nfound in the list of axioms two or three fundamental truths, not capable\nof being demonstrated: among which must be reckoned the proposition that\ntwo straight lines cannot inclose a space, (or its equivalent, Straight\nlines which coincide in two points coincide altogether,) and some property\nof parallel lines, other than that which constitutes their definition: the\nmost suitable, perhaps, being that selected by Professor Playfair: \u201cTwo\nstraight lines which intersect each other cannot both of them be parallel\nto a third straight line.\u201d(38)\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 cannot inclose a space\u2014or in other words, Two straight\nlines which have once met, do not meet again, but continue to diverge\u2014is\nan 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 one proposition enunciated in\nthis work for which a more unfavourable reception is to be expected. It\nis, however, no new opinion; and even if it were so, would be entitled to\nbe judged, not by its novelty, but by the strength of the arguments by\nwhich it can be supported. I consider it very fortunate that so eminent a\nchampion of the contrary opinion as Dr. Whewell, has recently found\noccasion for a most elaborate treatment of the whole theory of axioms, in\nattempting to construct the philosophy of the mathematical and physical\nsciences on the basis of the doctrine against which I now contend. Whoever\nis anxious that a discussion should go to the bottom of the subject, must\nrejoice to see the opposite side of the question worthily represented. If\nwhat is said by Dr. Whewell, in support of an opinion which he has made\nthe foundation of a systematic work, can be shown not to be conclusive,\nenough will have been done without going further to seek stronger\narguments and a more 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 cannot 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 _\u00e0 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 cannot, however, but allow that the truth of the axiom, Two straight\nlines cannot inclose a space, even if evident independently of experience,\nis also evident from experience. Whether the axiom _needs_ confirmation or\nnot, it _receives_ confirmation in almost every instant of our lives;\nsince we cannot look at any two straight lines which intersect one\nanother, without seeing that from that point they continue to diverge more\nand more. Experimental proof crowds in upon us in such endless profusion,\nand without one instance in which there can be even a suspicion of an\nexception to the rule, that we should soon have a 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 _\u00e0 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.\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,\ncannot 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 _\u00e0\npriori_ theory are obliged to have recourse to other arguments. These are\nreducible to two, which I shall endeavour 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 cannot 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 be\ntrue 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 recognise that two such lines cannot inclose a space. Intuition is\n\u201cimaginary looking;\u201d(39) 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 cannot 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 _cannot_\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 cannot 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 cannot 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, makes 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\npractised 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\ncannot 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 learnt 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 had never seen,\nfrom a picture made of it with a daguerreotype; but not until we had\nlearnt 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(40)\n\n\u00a7 6. The first of the two arguments in support of the theory that axioms\nare _\u00e0 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 cannot 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 cannot 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 cannot 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 cannot offer the smallest ground for the\nnecessity of a proposition. She can observe and record what has happened;\nbut she cannot 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\ncannot 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 cannot 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(41) 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(42)\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 cannot, even by an effort of\nimagination, or in a supposition, conceive the reverse of that which is\nasserted. That there are such truths cannot be doubted. We may take, for\nexample, all relations of number. Three and Two, added together, make\nFive. We cannot conceive it to be otherwise. We cannot, by any freak of\nthought, imagine Three and Two to make Seven.\u201d(43)\n\nAlthough Dr. Whewell has naturally and properly employed a variety of\nphrases to bring his meaning more forcibly home, he will, I presume, allow\nthat they are all equivalent; and that what he means by a necessary truth,\nwould be sufficiently defined, a proposition the negation of which is not\nonly 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 anything more.\n\nThis, therefore, is the principle asserted: that propositions, the\nnegation of which is inconceivable, or in other words, which we cannot\nfigure to ourselves as being false, must rest on evidence of a higher and\nmore cogent description than any which experience can afford. And we have\nnext to consider whether there is any ground for this assertion.\n\nNow I cannot 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\nanything 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 practised 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.(44)\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 everybody 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\nupwards instead of downwards. The Cartesians long rejected the Newtonian\ndoctrine of the gravitation of all bodies towards one another, on the\nfaith of a general proposition, the reverse of which seemed to them to be\ninconceivable\u2014the proposition that a body cannot 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.(45) And they no doubt found it as impossible\nto conceive that a body should act upon the earth, at the distance of the\nsun or moon, as we find it to conceive an end to space or time, or two\nstraight lines inclosing a space. Newton himself had not been able to\nrealize the conception, or we should not have had his hypothesis of a\nsubtle ether, the occult cause of gravitation; and his writings prove,\nthat although he deemed the particular nature of the intermediate agency a\nmatter of conjecture, the necessity of _some_ such agency appeared to him\nindubitable. It would seem that even now the majority of scientific men\nhave not completely got over this very difficulty; for though they have at\nlast learnt to conceive the sun _attracting_ the earth without any\nintervening fluid, they cannot yet conceive the sun _illuminating_ the\nearth without some such medium.\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 afterwards 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\nalthough 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 cannot help\nconceiving another instant after it. Nor is there any necessity to assume,\nas is done by a modern school of metaphysicians, a peculiar fundamental\nlaw of the mind to account for the feeling of infinity inherent in our\nconceptions of space and time; that apparent infinity is sufficiently\naccounted for by simpler and universally acknowledged laws.\n\nNow, in the case of a geometrical axiom, such, for example, as that two\nstraight lines cannot 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 cannot 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\nanything against the experimental origin of the conviction? Is it not\nclear that in whichever mode our belief in the proposition may have\noriginated, the impossibility of our conceiving the negative of it must,\non either hypothesis, be the same? As, then, Dr. Whewell exhorts those who\nhave any difficulty in recognising the distinction held by him between\nnecessary and contingent truths, to study geometry,\u2014a condition which I\ncan assure him I have conscientiously fulfilled,\u2014I, in return, with equal\nconfidence, exhort those who agree with him, to study the elementary laws\nof association; being convinced that nothing more is requisite than a\nmoderate familiarity with those laws, to dispel the illusion which\nascribes a peculiar necessity to our earliest inductions from experience,\nand measures the possibility of things in themselves, by the human\ncapacity of conceiving them.\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 recognised 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 coloured 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 cannot 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\nclearsighted; 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(46)\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\ncannot have been learnt 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 contrary of. He cannot intend to\njustify this mode of thought: he cannot mean to say, that we can be\n_right_ in 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(47)\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 for ever to move in the same\ndirection with undiminished velocity unless acted upon by some new force,\nwas a proposition which mankind found for a long time the greatest\ndifficulty in crediting. It stood opposed to apparent experience of the\nmost familiar kind, which taught that it was the nature of motion to abate\ngradually, and at last terminate of itself. Yet when once the contrary\ndoctrine was firmly established, mathematicians, as Dr. Whewell observes,\nspeedily began to believe that laws, thus contradictory to first\nappearances, and which, even after full proof had been obtained, it had\nrequired generations to render familiar to the minds of the scientific\nworld, were under \u201ca demonstrable necessity, compelling them to be such as\nthey are and no other;\u201d and he himself, though not venturing \u201cabsolutely\nto pronounce\u201d that _all_ these laws \u201ccan be rigorously traced to an\nabsolute necessity in the nature of things,\u201d(48) does actually think in\nthat manner of the law just mentioned; of which he says: \u201cThough the\ndiscovery of the first law of motion was made, historically speaking, by\nmeans of experiment, we have now attained a point of view in which we see\nthat it might have been certainly known to be true, independently of\nexperience.\u201d(49) Can there be a more striking exemplification than is here\nafforded, of the effect of association which we have described?\nPhilosophers, for generations, have the most extraordinary difficulty in\nputting certain ideas together; they at last succeed in doing so; and\nafter a sufficient repetition of the process, they first fancy a natural\nbond between the ideas, then experience a growing difficulty, which at\nlast, by the continuation of the same progress, becomes an impossibility,\nof severing them from one another. If such be the progress of an\nexperimental conviction of which the date is of yesterday, and which is in\nopposition to first appearances, how must it fare with those which are\nconformable to appearances familiar from the first dawn of intelligence,\nand of the conclusiveness of which, from the earliest records of human\nthought, no sceptic has suggested even a 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:(50) \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 cannot conceive a world\nin which this should not be the case_, it would appear that we cannot\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(51)\n\nThat a philosopher of Dr. Whewell\u2019s eminence should gravely assert that we\ncannot conceive a world in which the simple elements would 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.(52)\n\n\n\n\nCHAPTER VI. THE 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; of being certainly true if those\naxioms and definitions are so. But their claim to the character of\nnecessity in any sense beyond this, as implying an evidence independent of\nand superior to observation and experience, must depend on the previous\nestablishment of such a claim in favour of the definitions and axioms\nthemselves. With regard to axioms, we found that, considered as\nexperimental truths, they rest on superabundant and obvious evidence. We\ninquired, whether, since this is the case, it be necessary to suppose any\nother evidence of those truths than experimental evidence, any other\norigin for our belief of them than an experimental origin. We decided,\nthat the burden of proof lies with those who maintain the affirmative, and\nwe examined, at considerable length, such arguments as they have produced.\nThe examination having led to the rejection of those arguments, we have\nthought ourselves warranted in concluding that axioms are but a class, the\nhighest class, of inductions from experience; the simplest and easiest\ncases of generalization from the facts furnished to us by our senses or by\nour 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, although 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 formulas\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 _\u00e0 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 _\u00e0 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\nare 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,\n(as when we demonstrate a new geometrical theorem by algebra,) they have\nnot explained; 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 reconcileable 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\npremisses are translated from things into signs, and the end, when the\nconclusion is translated back from signs into things. Nothing, then, being\nin the reasoner\u2019s mind but the symbols, what can seem more inadmissible\nthan to contend that the reasoning process has to do with anything more?\nWe seem to have come to one of Bacon\u2019s Prerogative Instances; an\n_experimentum crucis_ 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 anything. 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 men,\nfour miles, or four pounds weight. We need only conceive a thing divided\ninto four equal parts, (and all things may be conceived as so divided,) to\nbe able to predicate of it every property of the number four, that is,\nevery arithmetical proposition in which the number four stands on one side\nof the equation. Algebra extends the generalization still farther: every\nnumber represents that particular number of all things without\ndistinction, but every algebraical symbol does more, it represents all\nnumbers without distinction. As soon as we conceive a thing divided into\nequal parts, without knowing into what number of parts, we may call it _a_\nor _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 coextensive with all nature. Since then algebraical truths are true\nof all things whatever, and not, like those of geometry, true of lines\nonly or angles only, it is no wonder that the symbols should not excite in\nour 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 of\nmere signs, is evident from the fact that our whole process of reasoning\nis carried on by predicating of them the properties of things. In\nresolving an algebraic equation, by what rules do we proceed? By applying\nat each step to _a_, _b_, and _x_ the proposition that equals added to\nequals make equals; that equals taken from equals leave equals; and other\npropositions founded on these two. These are not properties of language,\nor of signs as such, but of magnitudes, which is as much as to say, of all\nthings. The inferences, therefore, which are successively drawn, are\ninferences concerning things, not symbols; although as any Things whatever\nwill serve the turn, there is no necessity for keeping the idea of the\nThing at all distinct, and consequently the process of thought may, in\nthis case, be allowed without danger to do what all processes of thought,\nwhen they have been performed often, will do if permitted, namely, to\nbecome entirely mechanical. Hence the general language of algebra comes to\nbe used familiarly without exciting ideas, as all other general language\nis prone to do from mere habit, though in no other case than this can it\nbe done with complete safety. But when we look back to see from whence the\nprobative force of the process is derived, we find that at every single\nstep, unless we suppose ourselves to be thinking and talking of the\nthings, 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. This is, that when considered as\npropositions respecting Things, they all have the appearance of being\nidentical propositions. The assertion, Two and one are 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 are equal to three, as asserting\nmere identity 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, ten balls for\nexample, may by separation and re-arrangement exhibit to our senses all\nthe different sets of numbers the sum 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\nnecessarily follow from the hypothesis of the truth of premisses 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,\n&c., 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 already\nshown, results of induction; true of all objects whatever, and, as it may\nseem, 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 absolute certainty which is predicable of its demonstrations is\nindependent 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\nof the 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 a few such cases; as, for instance, an inquiry\ninto the amount of the population of any country. It is indifferent to\nthat inquiry whether they are grown people or children, strong or weak,\ntall or short; the only thing we want to ascertain is their number. But\nwhenever, from equality or inequality of number, equality or inequality in\nany other respect is to be inferred, arithmetic carried into such\ninquiries becomes as hypothetical a science as geometry. All units must be\nassumed to be equal in that other respect; and this is never practically\ntrue, for one actual pound weight is not exactly equal to another, nor one\nmile\u2019s length to another; a nicer balance, or more accurate measuring\ninstruments, would always detect some difference.\n\nWhat is commonly called mathematical certainty, therefore, which comprises\nthe twofold conception of unconditional truth and perfect accuracy, is not\nan attribute of all mathematical truths, but of those only which relate to\npure Number, as distinguished from Quantity in the more enlarged sense;\nand only so long as we abstain from supposing that the numbers are a\nprecise index to actual quantities. The certainty usually ascribed to the\nconclusions of geometry, and even to those of mechanics, is nothing\nwhatever but certainty of inference. We can have full assurance of\nparticular results under particular suppositions, but we cannot have the\nsame assurance that these suppositions are accurately true, nor that they\ninclude all the data which may exercise an influence over the result in\nany given instance.\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\nare to 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_\nwere a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a mark of\n_d_, which last conclusion was not thought of by those who laid down the\npremisses. 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 premisses,\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\npremisses 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 premisses, he is not involved in any\ndirect and express contradiction until he is compelled to deny some\npremiss; 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 anything, is a mark of\nwhatever 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\npremisses, fails to draw the conclusion, does not conform to the above\naxiom.\n\nWithout attaching exaggerated importance to the distinction now drawn, I\nthink it enables us to characterize in a more accurate manner than is\nusually done, the nature of demonstrative evidence and of logical\nnecessity. That is necessary, from which to withhold assent would be to\nviolate the above axiom. And since the axiom can only be violated by\nassenting to premisses and rejecting a legitimate conclusion from them,\nnothing is necessary, except the connexion between a conclusion and\npremisses; of which doctrine, the whole of this and the preceding chapter\nare submitted as the proof.\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\nWe here, therefore, close the Second Book. The theory of Induction, in the\nmost comprehensive sense of the term, will form the subject of the Third.\n\n\n\n\n\nBOOK III. OF 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. iv.\n    sect. 1.\n\n\n\n\nCHAPTER I. PRELIMINARY 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, cannot 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 another form of the\nvery same process: 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 endeavouring\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_\nof them; 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, cannot 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 we take in a new induction,\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.(53)\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\nCHAPTER II. OF 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 premisses\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\nanything be really concluded or not; and the induction is asserted to be\nnot perfect, unless every single individual of the class A is included in\nthe antecedent, or premiss: that is, unless what we affirm of the class\nhas already been ascertained to be true of every individual in it, so that\nthe nominal conclusion is not really a conclusion, but a mere reassertion\nof the premisses. If we were to say, All the planets shine by the sun\u2019s\nlight, from observation of each separate planet, or All the Apostles were\nJews, because this is true of Peter, Paul, John, and every other\napostle,\u2014these, and such as these, would, in the phraseology in question,\nbe called perfect, and the only perfect, Inductions. This, however, is a\ntotally different kind of induction from ours; it is no inference from\nfacts known to facts unknown, but a mere short-hand registration of facts\nknown. The two simulated arguments which we have quoted, are not\ngeneralizations; the propositions purporting to be conclusions from them,\nare not really general propositions. A general proposition is one in which\nthe predicate is affirmed or denied of an unlimited number of individuals;\nnamely, all, whether few or many, existing or capable of existing, which\npossess the properties connoted by the subject of the proposition. \u201cAll\nmen are mortal\u201d does not mean all now living, but all men past, present,\nand to come. When the signification of the term is limited so as to render\nit a name 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\n\u00a7 2. A second process which requires to be distinguished from Induction,\nis one to which mathematicians sometimes give that name: and which so far\nresembles Induction properly so called, that the propositions it leads to\nare really general propositions. For example, when we have proved with\nrespect to the circle, that a straight line cannot meet it in more than\ntwo points, and when the same thing has been successively proved of the\nellipse, the parabola, and the hyperbola, it may be laid down as an\nuniversal property of the sections of the cone. In this example there is\nno induction, because there is no inference: the conclusion is a mere\nsumming up of what was asserted in the various propositions from which it\nis drawn. A case somewhat, though not altogether, similar, is the proof of\na geometrical theorem by means of a diagram. Whether the diagram be on\npaper or only in the imagination, the demonstration (as formerly\nobserved(54)) does not prove directly the general theorem; it proves only\nthat the conclusion, which the theorem asserts generally, is true of the\nparticular triangle or circle exhibited in the diagram; but since we\nperceive that in the same way in which we have proved it of that circle,\nit might also be proved of any other circle, we gather up into one general\nexpression all the singular propositions susceptible of being thus proved,\nand embody them in an universal proposition. Having shown that the three\nangles of the triangle ABC are together equal to two right angles, we\nconclude that this is true of every other triangle, not because it is true\nof ABC, but for the same reason which proved it to be true of ABC. If this\nwere to be called Induction, an appropriate name for it would be,\ninduction by parity of reasoning. But the term cannot properly belong to\nit; the characteristic quality of Induction is wanting, since the truth\nobtained, though really general, is not believed on the evidence of\nparticular instances. We do not conclude that all triangles have the\nproperty because some triangles have, but from the ulterior demonstrative\nevidence which was the ground of our conviction in the particular\ninstances.\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 _\u00e0 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 _\u00e0 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, cannot\nbut perceive that in raising a binomial to a power, the coefficients must\ndepend on the laws of permutation and combination: and as soon as this is\nrecognised, the theorem is demonstrated. Indeed, when once it was seen\nthat the law prevailed in a few of the lower powers, its identity with the\nlaw of permutation would at once suggest the considerations which prove it\nto obtain universally. Even, therefore, such cases as these, are but\nexamples of what I have called induction by parity of reasoning, that is,\nnot 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 most elaborate treatise on the\ninductive philosophy which exists in our language. The error in question\nis that of confounding a mere description of a set of observed phenomena,\nwith 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 cannot 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 anything\nof the nature of an induction in this process? Did he infer anything that\nhad not been observed, from something else which had? Certainly not. He\nhad observed the whole of what the proposition asserts. That the land in\nquestion is an island, is not an inference from the partial facts which\nthe navigator saw in the course of his circumnavigation; it is the facts\nthemselves; it is a summary of those facts; the description of a complex\nfact, 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, (for it was of that body\nthat he first established two of the three great astronomical truths which\nbear his name.) To do this there was no other mode than that of direct\nobservation: and all which observation could do was to ascertain a great\nnumber of the successive places of the planet; or rather, of its apparent\nplaces. That the planet occupied successively all these positions, or at\nall events, positions which produced the same impressions on the eye, and\nthat it passed from one of these to another insensibly, and without any\napparent breach of continuity; thus much the senses, with the aid of the\nproper instruments, could ascertain. What Kepler did more than this, was\nto find what sort of a curve these different points would make, supposing\nthem to be all joined together. He expressed the whole series of the\nobserved places of Mars by what Dr. Whewell calls the general conception\nof an ellipse. This operation was far from being as easy as that of the\nnavigator who expressed the series of his observations on successive\npoints of the coast by the general conception of an island. But it is the\nvery same sort of operation; and if the one is not an induction but a\ndescription, this must also be true of the other.\n\nTo avoid misapprehension, we must remark that Kepler, in one respect,\nperformed a real act of induction; namely, in concluding that because the\nobserved places of Mars were correctly represented by points in an\nimaginary ellipse, therefore Mars would continue to revolve in that same\nellipse; and even in concluding that the position of the planet during the\ntime which intervened between two observations, must have coincided with\nthe intermediate points of the curve. But this really inductive operation\nrequires to be carefully distinguished from the mere act of bringing the\nfacts actually observed under a general description. So distinct are these\ntwo operations, that the one might have been performed without the other.\nMen might and did make correct inductions concerning the heavenly motions,\nbefore they had obtained correct general descriptions of them. It was\nknown that the planets always moved in the same paths, long before it had\nbeen ascertained that those paths were ellipses. Astronomers early\nremarked that the same set of apparent positions returned periodically.\nWhen they obtained a new description of the phenomenon, they did not\nnecessarily make any further induction, nor (which is the true test of a\nnew general truth) add anything to the power of prediction which they\nalready 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.(55) 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,(56) \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 connexion.\nThe pearls are there, but they will not hang together till some one\nprovides the string.\u201d\n\nThat a conception of the mind is introduced is indeed undeniable, and I\nwillingly concede, that to hit upon the right conception is often a far\nmore difficult and more meritorious achievement, than to prove its\napplicability when obtained. But a conception implies, and corresponds to,\nsomething conceived: and though the conception itself is not in the facts,\nbut in our mind, it must be a conception _of_ something which really is in\nthe facts, some property which they actually possess, and which they would\nmanifest to our senses, if our senses were able to take cognizance of\nthem. If, for instance, the planet left behind it in space a visible\ntrack, and if the observer were in a fixed position at such a distance\nabove the plane of the orbit as would enable him to see the whole of it at\nonce, he would see it to be an ellipse; and if gifted with appropriate\ninstruments, and powers of locomotion, he could prove it to be such by\nmeasuring its different dimensions. These things are indeed impossible to\nus, but not impossible in themselves; if they were so, Kepler\u2019s law could\nnot be true.\n\nSubject to the indispensable condition which has just been stated, I\ncannot perceive 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 anything 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 cannot 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 afterwards 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(57) 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 skilful 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, and facts were disclosed which were not reconcileable 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\nexcentrics 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 that\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 afterwards 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, precis\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(58)\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 one only 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 whenever one planet or\nsatellite is so situated as to cast its shadow upon another; the second,\nthat they will occur whenever some great calamity is impending over\nmankind. Do these two doctrines only differ in the degree of their truth,\nas expressing real facts with unequal degrees of accuracy? Assuredly the\none is true, and the other absolutely false.(59)\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, towards 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\nconnexion for those facts; a new principle for their classification.\n\nFurther, that general description, which is improperly confounded with\ninduction, is nevertheless a necessary preparation for induction; no less\nnecessary than correct observation of the facts themselves. Without the\nprevious colligation of detached observations by means of one general\nconception, we could never have obtained any basis for an induction,\nexcept in the case of phenomena of very limited compass. We should not be\nable to affirm any predicates at all, of a subject incapable of being\nobserved otherwise than piecemeal: much less could we extend those\npredicates by induction to other similar subjects. Induction, therefore,\nalways presupposes, not only that the necessary observations are made with\nthe necessary accuracy, but also that the results of these observations\nare, so far as practicable, connected together by general descriptions,\nenabling the mind to represent to itself as wholes whatever phenomena are\ncapable of being so represented.\n\n\u00a7 5. Dr. Whewell has replied at some length to the preceding observations,\nre-stating his opinions, but without (as far as I can perceive) adding\nanything to his former arguments. Since, however, mine have not had the\ngood fortune to make any impression upon him, I will subjoin a few\nremarks, tending to shew more clearly in what our difference of opinion\nconsists, as well as, in some measure, to account for it.\n\nAll the definitions of induction, by writers of authority, make it consist\nin drawing inferences from known cases to unknown; affirming of a class, a\npredicate which has been found true of some cases belonging to the class;\nconcluding, because some things have a certain property, that other things\nwhich resemble them have the same property\u2014or because a thing has\nmanifested a property at a certain time, that it has and will have that\nproperty 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. He left the subject\nas it was; the alteration he made was in the predicate. Instead of saying,\nthe successive places of Mars are so and so, he summed them up in the\nstatement, that the successive places of Mars are points in an ellipse. It\nis true, this statement, as Dr. Whewell says, was not the sum of the\nobservations _merely_; it was the sum of the observations _seen under a\nnew point of view_.(60) But it was not the sum of _more_ than the\nobservations, as a real induction is. It took in no cases but those which\nhad been actually observed, or which could have been inferred from the\nobservations before the new point of view presented itself. There was not\nthat transition from known cases to unknown, which constitutes Induction\nin the original and acknowledged meaning of the term.\n\nOld definitions, it is true, cannot prevail against new knowledge: and if\nthe Keplerian operation, as a logical process, were 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 join 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 but serve to\nconnect the observations, we have all we want. As the proposition in which\nit is embodied pretends to no other truth than what it may share with many\nother modes of representing the same facts, to be consistent with the\nfacts is all it requires: it neither needs nor admits of proof; though it\nmay serve to prove other things, inasmuch as, by placing the facts in\nmental connexion with other facts, not previously seen to resemble them,\nit assimilates the case to another class of phenomena, concerning which\nreal Inductions have already been made. Thus Kepler\u2019s so-called law\nbrought the orbit of Mars into the class ellipse, and by doing so, proved\nall the properties of an ellipse to be true of the orbit: but in this\nproof Kepler\u2019s law supplied the minor premiss, and not (as is the case\nwith real Inductions) the major.\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, provided it be\nclearly 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 the reader must refer for the removal of any\ndifficulty which the present discussion may have left.\n\n\n\n\nCHAPTER III. OF 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, we find, is so constituted,\nthat whatever is true in any one case, is true in all cases of a certain\ndescription; the only difficulty is, to find _what_ description.\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\nof our nature,\u2014they usually describe under some such name as \u201cour\nintuitive conviction that the future will resemble the past.\u201d Now it has\nbeen well pointed out, that (whether the tendency be or not an original\nand ultimate element of our nature), Time, in its modifications of past,\npresent, and future, has no concern either with the belief itself, or with\nthe grounds of it. We believe that fire will burn to-morrow, because it\nburned to-day and yesterday; but we believe, on precisely the same\ngrounds, that it burned before we were born, and that it burns this very\nday in Cochin-China. It is not from the past to the future, _as_ past and\nfuture, that we infer, but from the known to the unknown; from facts\nobserved to facts unobserved; from what we have perceived, or been\ndirectly conscious of, to what has not come within our experience. In this\nlast predicament is the whole region of the future; but also the vastly\ngreater 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\npremiss suppressed; or (as I prefer expressing it) every induction may be\nthrown into the form of a syllogism, by supplying a major premiss. 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\npremiss 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 cannot be\nfound a true major premiss.\n\nThe statement, that the uniformity of the course of nature is the ultimate\nmajor premiss in all cases of induction, may be thought to require some\nexplanation. The immediate major premiss 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, &c., are mortal, therefore\nall mankind are mortal,\u201d may, as he justly says, be thrown into a\nsyllogism by prefixing as a major premiss (what is at any rate a necessary\ncondition of the validity of the argument) namely, that what is true of\nJohn, Peter, &c, is true of all mankind. But how come we by this major\npremiss? 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, &c., 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 premiss the principle, or axiom, of the uniformity of\nthe course of nature.(61)\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.(62) 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\nbe explained, and a stricter than their ordinary signification given to\nthem, before 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, everybody\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 an 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 sure 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 cannot\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.(63) 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, cannot have been a good induction, since the conclusion has turned\nout erroneous. The experience, however, on which the conclusion rested was\ngenuine. From the earliest records, the testimony of the inhabitants of\nthe 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 colour, 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. When a chemist announces\nthe existence and properties of a newly-discovered substance, if we\nconfide in his accuracy, we feel assured that the conclusions he has\narrived at will hold universally, although the induction be founded but on\na single 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; an universal proposition from a\nsingular one. Now mark another case, and contrast it with this. Not all\nthe instances which have been observed since the beginning of the world,\nin support 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 grey.\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 towards\nestablishing an 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\nCHAPTER IV. OF 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 connexion between parts of the great whole which we term\nnature, a general tissue of connexion 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 pre-supposed, the others follow of course: the three first,\ntherefore, according to the stricter acceptation, are called laws of\nnature, the remainder not; because they are in truth mere _cases_ of the\nthree first; 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 a 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; although, 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\nwhen, in mathematics, we speak of the law of decrease of the successive\nterms of a converging series. But the expression, _law of nature_, has\ngenerally been employed with a sort of tacit reference to the original\nsense of the word _law_, namely, the expression of the will of a superior.\nWhen, therefore, it appeared that any of the uniformities which were\nobserved in nature, would result spontaneously from certain other\nuniformities, no separate act of creative will being supposed necessary\nfor the production of the derivative uniformities, these have not usually\nbeen spoken of as laws of nature. According to another mode of expression,\nthe question, What are the laws of nature? may be stated thus:\u2014What are\nthe fewest and simplest assumptions, which being granted, the whole\nexisting order of nature would result? Another mode of stating it would be\nthus: What are the fewest general propositions from which all the\nuniformities which exist in the universe might be deductively inferred?\n\nEvery great advance which marks an epoch in the progress of science, has\nconsisted in a step made towards 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\ntowards 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 laws into\nwhich 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\nanything but a mere verbal transformation of the problem; for the\nexpression, Laws of Nature, _means_ nothing but the uniformities which\nexist among natural phenomena (or, in other words, the results of\ninduction), when reduced to their simplest expression. It is, however,\nsomething, to have advanced so far, as to see that the study of nature is\nthe study of laws, not _a_ law; of uniformities, in the plural number:\nthat the different natural phenomena have their separate rules or modes of\ntaking place, which, though much intermixed and entangled with one\nanother, may, to a certain extent, be studied apart: that (to resume our\nformer metaphor) the regularity which exists in nature is a web composed\nof distinct threads, and only to be understood by tracing each of the\nthreads separately; for which purpose it is often necessary to unravel\nsome portion of the web, and exhibit the fibres apart. The rules of\nexperimental inquiry are the contrivances for unravelling 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 learnt, 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 connexion\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 afterwards 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 other 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 colours of\nanimals, than in the general structure of their internal anatomy. But how\ndo we know this? Doubtless, from experience. It appears, then, that we\nneed experience to inform us, in what degree, and in what cases, or sorts\nof cases, 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 touchstone to which we always\nendeavour 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 practised, 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 re-consideration 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:(64) and faith in such delusions seems quite capable of holding\nout against a great multitude of failures, provided it be nourished by a\nreasonable number of casual coincidences between the prediction and the\nevent. What has really put an end to these insufficient inductions, is\ntheir inconsistency with the stronger inductions subsequently obtained by\nscientific inquiry, respecting the causes on which terrestrial events\nreally depend; and where those scientific truths have not yet penetrated,\nthe 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 a ratiocination, are\nconfirmatory of one another: while any which lead deductively to\nconsequences that are incompatible, become mutually each other\u2019s test,\nshowing that one or other must be given up, or at least, more guardedly\nexpressed. In the case of inductions which confirm each other, the one\nwhich becomes a conclusion from ratiocination rises to at least the level\nof certainty of the weakest of those from which it is deduced; while in\ngeneral all are more or less increased in certainty. Thus the Torricellian\nexperiment, though a mere case of three more general laws, not only\nstrengthened greatly the evidence on which those laws rested, but\nconverted one of them (the weight of the atmosphere) from a doubtful\ngeneralization into one of the best-established doctrines in the range of\nphysical science.\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 as quite certain and quite\nuniversal; then by means of these uniformities, we may be able to raise\nmultitudes of other inductions to the same point in the scale. For if we\ncan show, with respect to any induction, that either it must be true, or\none of these certain and universal inductions must admit of an exception;\nthe former generalization will attain the same certainty, and\nindefeasibleness within the bounds assigned to it, which are the\nattributes of the latter. It will be proved to be a law; and if not a\nresult of other and simpler laws, 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\nCHAPTER V. OF 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 an uniform manner, to some phenomena that coexist with it, and\nto some that have preceded or 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, coexist; and the unvarying laws\nwhich are the subject of the science of geometry, are an expression of the\nmode of their coexistence.\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. If all the\nobjects in the universe were unchangeably fixed, and had remained in that\ncondition from eternity, the propositions of geometry would still be true\nof those objects. All things which possess extension, or in other words,\nwhich fill space, are subject to geometrical laws. Possessing extension,\nthey possess figure; possessing figure, they must possess some figure in\nparticular, and have all the properties which geometry assigns to that\nfigure. If one body be a sphere and another a cylinder, of equal height\nand diameter, the one will be exactly two-thirds of the other, let the\nnature and quality of the material be what it will. Again, each body, and\neach point of a body, must occupy some place or position among other\nbodies; and the position of two bodies relatively to each other, of\nwhatever nature the bodies be, may be unerringly inferred from the\nposition of each of them relatively to any third body.\n\nIn the laws of number, then, and in those of space, we recognise, 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 we are unable even to conceive any\nexception to them; and philosophers have been led, although (as I have\nendeavoured 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 degree of rigorous\ncertainty. But this we cannot do. From laws of space and number alone,\nnothing can be 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 premisses 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 towards it when taken by themselves. They can only be\nmade instrumental to that purpose when we combine with them additional\npremisses, expressive of uniformities of succession already known. By\ntaking, for instance, as premisses 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 of a\nparallelogram of the same base and altitude,) deduce another important\nuniformity of succession, viz. that a body moving round a centre of force\ndescribes areas proportional to the times. But unless there had been laws\nof succession in our premisses, there could have been no truths of\nsuccession in our conclusions. A similar remark might be extended to every\nother class of phenomena really peculiar; and, had it been attended to,\nwould have 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 phenomena, 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\nendeavour 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 recognise a law which\nis universal also in another sense; it is coextensive 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 coextensive 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 We must not, however, conclude that the generality of the\nprinciple is merely verbal; it will be found on inspection to be no vague\nor unmeaning assertion, 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 phenomena 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\nanything. 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\ncannot, or at least does not, exist between any physical fact and that\nother physical fact on which it is invariably consequent, and which is\npopularly termed its cause: and thence is deduced the supposed necessity\nof ascending higher, into the essences and inherent constitution of\nthings, to find the true cause, the cause which is not only followed by,\nbut actually _produces_, the effect. No such necessity exists for the\npurposes of the present inquiry, nor will any such doctrine be found in\nthe following pages. But neither will there be found anything incompatible\nwith it. We are in no way concerned in the question. The only notion of a\ncause, which the theory of induction requires, is such a notion as can be\ngained from experience. The Law of Causation, the recognition of which is\nthe main pillar of inductive science, is but the familiar truth, that\ninvariability of succession is found by observation to obtain between\nevery fact in nature and some other fact which has preceded it;\nindependently of all consideration respecting the ultimate mode of\nproduction of phenomena, and of every other question regarding the nature\nof \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 connexion 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 connexion\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 fulfilment 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. The production of the consequent required that they should\nall _exist_ immediately previous, though not that they should all _begin_\nto exist immediately previous. The statement of the cause is incomplete,\nunless in some shape or other we introduce all the conditions. A man takes\nmercury, goes out of doors, and catches cold. We say, perhaps, that the\ncause of his taking cold was exposure to the air. It is clear, however,\nthat his having taken mercury may have been a necessary condition of his\ncatching cold; and though it might consist with usage to say that the\ncause of his attack was exposure to the air, to be accurate we ought to\nsay 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 share of the responsibility, the\npart which any other person had in the transaction is not material.\n\nIn all these instances the fact which was dignified by the name of cause,\nwas the one condition which came last into existence. But it must not be\nsupposed that in the employment of the term this or any other rule is\nalways adhered to. Nothing can better shew the absence of any scientific\nground for the distinction between the cause of a phenomenon and its\nconditions, than the capricious manner in which we select from among the\nconditions that which we choose to denominate the cause. However numerous\nthe 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 analysing 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 schoolmen, by whom they were called the\n_material_ cause, _causa materialis_. The next condition is, there must be\nan earth: and accordingly it is often said, that the fall of a stone is\ncaused by the earth; or by a power or property of the earth, or a force\nexerted by the earth, all of which are merely roundabout ways of saying\nthat it is caused by the earth; or, lastly, the earth\u2019s attraction; which\nalso is only a technical mode of saying that the earth causes the motion,\nwith the additional particularity that the motion is _towards_ the earth,\nwhich is not a character of the cause, but of the effect. Let us now pass\nto another condition. It is not enough that the earth should exist; the\nbody must be within that distance from it, in which the earth\u2019s attraction\npreponderates over that of any other body. Accordingly we may say, and the\nexpression would be confessedly correct, that the cause of the stone\u2019s\nfalling is its being _within the sphere_ of the earth\u2019s attraction. We\nproceed to a further condition. The stone is immersed in water: it is\ntherefore a condition of its reaching the ground, that its specific\ngravity exceed that of the surrounding fluid, or in other words that it\nsurpass in weight an equal volume of water. Accordingly any one would be\nacknowledged to speak correctly who said, that the cause of the stone\u2019s\ngoing to the bottom is its exceeding in specific gravity the fluid in\nwhich 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 conspicuous\nor whose requisiteness to the production of the effect we happen to be\ninsisting on at the moment. So great is the force of this last\nconsideration, that it sometimes induces us to give the name of cause even\nto 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 preexisted 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 anything which had existed for an indeterminate length of\ntime 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.(65)\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,(66) enables us, by establishing\nthe general axiom that all causes are liable to be counteracted in their\neffects by one another, to dispense with the consideration of negative\nconditions entirely, and limit the notion of cause to the assemblage of\nthe positive conditions of the phenomenon: one negative condition\ninvariably understood, and the same in all instances (namely, the absence\nof all counteracting causes) being sufficient, along with the sum of the\npositive conditions, to make up the whole set of circumstances on which\nthe 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\nin which the effect takes place, is commonly included in the phrase by\nwhich the effect is spoken of, so that if it were also reckoned as part of\nthe cause, the seeming incongruity would arise of its being supposed to\ncause itself. In the instance which we have already had, of falling\nbodies, the question was thus put:\u2014What is the cause which makes a stone\nfall? and if the answer had been \u201cthe stone itself,\u201d the expression would\nhave been in apparent contradiction to the meaning of the word cause. The\nstone, therefore, is conceived as the patient, and the earth (or,\naccording to the common and most unphilosophical practice, some occult\nquality of the earth) is represented as the agent, or cause. But that\nthere is nothing fundamental in the distinction may be seen from this,\nthat it is quite possible to conceive the stone as causing its own fall,\nprovided the language employed be such as to save the mere verbal\nincongruity. We might say that the stone moves towards the earth by the\nproperties of the matter composing it; and according to this mode of\npresenting the phenomenon, the stone itself might without impropriety be\ncalled the agent; although, to save the established doctrine of the\ninactivity of matter, men usually prefer here also to ascribe the effect\nto an occult quality, and say that the cause is not the stone itself, but\nthe _weight_ or _gravitation_ of the 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 licence 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 statement of a scientific truth. Even those attributes of an object\nwhich might seem with greatest propriety to be called states of the object\nitself, its sensible qualities, its colour, hardness, shape, and the like,\nare, 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 those 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 upon 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 a complete one, none of them can with reason be excluded,\nexcept such as have already been implied in the words used for describing\nthe effect; nor by including even these would there be incurred any but a\nmerely verbal inconsistency.\n\n\u00a7 5. 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 anything (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 things\nendures, it always _will_ be so. And this would not be true of day and\nnight. We do not believe that night will be followed by day under all\nimaginable circumstances, but only that it will be so _provided_ the sun\nrises above the horizon. If the sun ceased to rise, which, for aught we\nknow, may be perfectly compatible with the general laws of matter, night\nwould be, or might be, eternal. On the other hand, if the sun is above the\nhorizon, his light not extinct, and no opaque body between us and him, we\nbelieve firmly that unless a change takes place in the properties of\nmatter, this combination of antecedents will be followed by the\nconsequent, 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(67) 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 have ever 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 the presence\nof a sufficiently luminous body, whether darkness had preceded or not.\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\nIt is evident, that from a limited number of unconditional sequences,\nthere will result a much greater number of conditional ones. Certain\ncauses being given, that is, certain antecedents which are unconditionally\nfollowed by certain consequents; the mere coexistence of these causes will\ngive rise to an unlimited number of additional uniformities. If two causes\nexist together, the effects of both will exist together; and if many\ncauses coexist, these causes (by what we shall term hereafter the\nintermixture of their laws) will give rise to new effects, accompanying or\nsucceeding one another in some particular order, which order will be\ninvariable while the causes continue to coexist, but no longer. The motion\nof the earth in a given orbit round the sun, is a series of changes which\nfollow one another as antecedents and consequents, and will continue to do\nso while the sun\u2019s attraction, and the force with which the earth tends to\nadvance in a direct line through space, continue to coexist in the same\nquantities as at present. But vary either of these causes, and the\nunvarying succession of motions would cease to take place. The series of\nthe earth\u2019s motions, therefore, though a case of sequence invariable\nwithin the limits of human experience, is not a case of causation. It is\nnot 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\ncoexistence, which, like the earth\u2019s motions, or the succession of day and\nnight, depend on the existence or on the coexistence of other antecedent\nfacts\u2014corresponds to the great division which Dr. Whewell and other\nwriters have made of the field of science, into the investigation of what\nthey 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.\nYet the distinction, however incorrectly expressed, is not only real, but\nis one of the fundamental distinctions in science; indeed it is on this\nalone, as we shall hereafter find, that the possibility rests of framing a\nrigorous Canon of Induction.\n\n\u00a7 6. 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 coexist; 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 force 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 a brain\nfever: will the fever go off as soon as he is moved out of the sunshine? A\nsword is run through his body: must the sword remain in his body in order\nthat he may continue dead? A ploughshare once made, remains a ploughshare,\nwithout any continuance of heating and hammering, and even after the man\nwho heated and hammered it has been gathered to his fathers. On the other\nhand, the pressure which forces up the mercury in an exhausted tube must\nbe continued in order to sustain it in the tube. This (it may be replied)\nis because another force is acting without intermission, the force of\ngravity, which would restore it to its level, unless counterpoised by a\nforce equally constant. But again; a tight bandage causes pain, which pain\nwill sometimes go off as soon as the bandage is removed. The illumination\nwhich the sun diffuses over the earth ceases 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; but more commonly its continuance requires\nno condition except negative ones. Most things, once produced, continue as\nthey are, until something changes or destroys them; but some require the\npermanent presence of the agencies which produced them at first. These\nmay, if we please, be considered as instantaneous phenomena, requiring to\nbe renewed at each instant by the cause by which they were at first\ngenerated. Accordingly, the illumination of any given point of space has\nalways been looked upon as an instantaneous fact, which perishes and is\nperpetually 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 these 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 a writer from whom I have quoted,(68)) I think the\ninquiry an unimportant one. There certainly are cases in which the effect\nfollows without any interval perceptible by our faculties; and when there\nis an interval, we cannot tell by how many intermediate links\nimperceptible to us that interval may really be filled up. But even\ngranting that an effect may commence simultaneously with its cause, the\nview I have taken of causation is in no way practically affected. Whether\nthe cause and its effect be necessarily successive or not, causation is\nstill the law of the succession of phenomena. Everything which begins to\nexist must have a cause; what does not begin to exist does not need a\ncause; what causation has to account for is the origin of phenomena, and\nall the successions of phenomena must be resolvable into causation. These\nare the axioms of our doctrine. If these be granted, we can afford, though\nI see no necessity for doing so, to drop the words antecedent and\nconsequent as applied to cause and effect. I have no objection to define a\ncause, the assemblage of phenomena, which occurring, some other phenomenon\ninvariably commences, or has its origin. Whether the effect coincides in\npoint of time with, or immediately follows, the hindmost of its\nconditions, is immaterial. At all events it does not precede it; and when\nwe are in doubt, between two coexistent phenomena, which is cause and\nwhich effect, we rightly deem the question solved if we can ascertain\nwhich of them preceded the other.\n\n\u00a7 7. 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 an immense magnet, causes\nthe phenomena of the magnetic needle. A crystal of galena causes the\nsensations of hardness, of weight, of cubical form, of grey colour, 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 colour, shape, weight, and hardness of a crystal. These\nare mere phrases, which explain nothing, and add nothing to our knowledge\nof the subject; but, considered as abstract names denoting the connexion\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 the\nother distinguishable substances, whether simple or compound, of which\nnature is made up, are such Permanent Causes. These have existed, and the\neffects or consequences which they were fitted to produce have taken\nplace, (as often as the other conditions of the production met,) from the\nvery beginning of our experience. But we can give no account of the origin\nof the Permanent Causes themselves. Why these particular natural agents\nexisted originally and no others, or why they are commingled in such and\nsuch proportions, and distributed in such and such a manner throughout\nspace, is a question we cannot answer. More than this: we can discover\nnothing regular in the distribution itself; we can reduce it to no\nuniformity, to no law. There are no means by which, from the distribution\nof these causes or agents in one part of space, we could conjecture\nwhether a similar distribution prevails in another. The coexistence,\ntherefore, of Primeval Causes, ranks, to us, among merely casual\nconcurrences: and all those sequences or coexistences among the effects of\nseveral such causes, which, though invariable while those causes coexist,\nwould, if the coexistence terminated, terminate along with it, we do not\nclass as cases of causation, or laws of nature: we can only calculate on\nfinding these sequences or coexistences where we know by direct evidence,\nthat the natural agents on the properties of which they ultimately depend,\nare distributed in the requisite manner. These Permanent Causes are not\nalways objects; they are sometimes events, that is to say, periodical\ncycles of events, that being the only mode in which events can possess the\nproperty of permanence. Not only, for instance, is the earth itself a\npermanent cause, or primitive natural agent, but the earth\u2019s rotation is\nso too: it is a cause which has produced, from the earliest period, (by\nthe aid of other necessary conditions,) the succession of day and night,\nthe ebb and flow of the sea, and many other effects, while, as we can\nassign no cause (except conjecturally) for the rotation itself, it is\nentitled to be ranked as a primeval cause. It is, however, only the\n_origin_ of the rotation which is mysterious to us: once begun, its\ncontinuance is accounted for by the first law of motion (that of the\npermanence of rectilinear motion once impressed) combined with the\ngravitation of the parts of the earth towards 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 an 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 coexist. 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 their properties, in other words the laws of their agency,\ncould predict the whole subsequent history of the universe, at least\nunless some new volition of a power capable of controlling the universe\nshould supervene.(69) And if any particular state of the entire universe\ncould ever recur a second time, all subsequent states would return too,\nand history would, like a circulating decimal of many figures,\nperiodically repeat itself:\u2014\n\nJam redit et virgo, redeunt Saturnia regna....\nAlter erit tum Tiphys, et altera qu\u00e6 vehat Argo\nDelectos heroas; erunt quoque altera bella,\nAtque iterum ad Troiam magnus mittetur Achilles.\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 _\u00e0 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\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 8. Since everything which occurs is determined by laws of causation and\ncollocations of the original causes, it follows that the coexistences\nwhich are observable among effects cannot be themselves the subject of any\nsimilar set of laws, distinct from laws of causation. Uniformities there\nare, as well of coexistence as of succession, among effects; but these\nmust in all cases be a mere result either of the identity or of the\ncoexistence of their causes: if the causes did not coexist, neither could\nthe effects. And these causes being also effects of prior causes, and\nthese 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 coexistences of phenomena can in no case be\nuniversal, unless the coexistences of the primeval causes to which the\neffects are ultimately traceable, can be reduced to an universal law: but\nwe have seen that they cannot. There are, accordingly, no original and\nindependent, in other words no unconditional, uniformities of coexistence\nbetween effects of different causes; if they coexist, it is only because\nthe causes have casually coexisted. The only independent and unconditional\ncoexistences which are sufficiently invariable to have any claim to the\ncharacter of laws, are between different and mutually independent effects\nof the same cause; in other words, between different properties of the\nsame natural agent. This portion of the Laws of Nature will be treated of\nin the latter part of the present Book, under the name of the Specific\nProperties of Kinds.\n\n\u00a7 9. It is proper in this place to advert to a doctrine at least as old as\nDr. Reid, though propounded by him not as certain but as probable; which\nhas been revived during the last few years in several quarters, and at\npresent gives more signs of life than any other theory of causation at\nvariance with that set forth in the preceding pages.\n\nAccording to the theory in question, Mind, or, to speak more 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 _\u00e0 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 cannot even conceive of change or phenomena\nwithout the energy of a mind.\u201d \u201cThe word _action_ itself,\u201d 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 connexion between them is a subject\nof experience. I cannot admit that our consciousness of the volition\ncontains in itself any _\u00e0 priori_ knowledge that the muscular motion will\nfollow. If our nerves of motion were paralyzed, or our muscles stiff and\ninflexible, and had been so all our lives, I do not see the slightest\nground for supposing that we should ever (unless by information from other\npeople) have known anything of volition as a physical power, or been\nconscious of any tendency in feelings of our mind to produce motions of\nour body, or of other bodies. I will not undertake to say whether we\nshould in that case have had the physical feeling which I suppose is meant\nwhen these writers speak of \u201cconsciousness of effort:\u201d I see no reason why\nwe should not; since that physical feeling is probably a state of nervous\nsensation beginning and ending in the brain, without involving the motory\napparatus; but we certainly should not have designated it by any term\nequivalent to effort, since effort implies consciously aiming at an end,\nwhich we should not only in that case have had no reason to do, but could\nnot even have had the idea of doing. If conscious at all of this peculiar\nsensation, we should have been conscious of it, I conceive, only as a kind\nof uneasiness, accompanying our feelings of desire.\n\nThose against whom I am contending have never produced, and do not pretend\nto produce, any positive evidence(70) 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\nsequences which come under our observation, and is familiar to every\nmoment\u2019s experience from our earliest infancy; more familiar than any\nsuccession of events exterior to our bodies, and especially more so than\nany other case of the apparent origination (as distinguished from the mere\ncommunication) of motion. Now, it is the natural tendency of the mind to\nbe always attempting 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 shew 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 cannot 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.\u201d\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 favour, 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(71)\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\nand its voluntary acts. As the notion of fixed laws of succession among\nexternal phenomena gradually establishes itself, the propensity to refer\nall phenomena to voluntary agency slowly gives way before it. The\nsuggestions, however, of daily life continuing to be more powerful than\nthose of scientific thought, the original instinctive philosophy maintains\nits ground in the mind, underneath the growths obtained by cultivation,\nand keeps up a constant resistance to their throwing their roots deep into\nthe soil. The theory against which I am contending derives its nourishment\nfrom that substratum. Its strength does not lie in argument, but in its\naffinity to an obstinate tendency of the 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\nthat the action of mind upon matter _was_. To some thinkers, and some\nschools of thinkers, both in ancient and in modern times, this last has\nappeared much more inconceivable than the former. Sequences entirely\nphysical and material, as soon as they had become sufficiently familiar to\nthe human mind, came to be thought perfectly natural, and were regarded\nnot only as needing no explanation themselves, but as being capable of\naffording it to others, and even of serving as the ultimate explanation of\nthings in general.\n\nOne of the most 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 connexion, where they meant\nby natural that which would _per se_ carry some presumption to their own\nmind.... 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(72) 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 eternal\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\nthat intelligible which was otherwise inconceivable, and gave the same\nfull satisfaction 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\nconnexion \u201cwhich would _per se_ carry some presumption to their own mind.\u201d\nAmong 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 connexion between physical antecedents and\ntheir consequents, he demanded some naturally and _per se_ efficient\nphysical antecedent as the bond of connexion between Volition itself and\nits effects. He distinctly refused to admit the will of a God as a\nsufficient explanation of anything except miracles; and insisted upon\nfinding something that would account _better_ for the phenomena of nature\nthan a mere reference to divine volition.(73)\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\nconnexion, no relation _\u00e0 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 afterwards extended to the action of Matter upon\nMatter, for, 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\u2014something \u1f04\u03bd\u03b5\u03c5 \u03bf\u1f55 \u03c4\u1f78 \u03b1\u1f34\u03c4\u03b9\u03bf\u03bd \u03bf\u1f50\u03ba \u1f02\u03bd \u03c0\u03bf\u03c4\u1fbd \u03b5\u1f34\u03b7\n\u03b1\u1f34\u03c4\u03b9\u03bf\u03bd. But we also see that this demand may be completely satisfied by an\nagency purely physical, provided it be much more familiar than that which\nit is invoked to explain. To Thales and Anaximenes, it appeared\ninconceivable that the antecedents which we see in nature, should produce\nthe consequents; but perfectly natural that water, or air, should produce\nthem. The writers whom I oppose declare this inconceivable, but can\nconceive that mind, or volition, is _per se_ an efficient cause: while the\nCartesians could not conceive even that, but peremptorily declared that no\nmode of production of any fact whatever was conceivable, except the direct\nagency of an omnipotent being. Thus giving additional proof of what finds\nnew confirmation in every stage of the history of science: that both what\npersons can, and what they cannot, conceive, is very much an affair of\naccident, and depends altogether on their experience, and their habits of\nthought; that by cultivating the requisite associations of ideas, people\nmay make themselves unable to conceive any given thing; and may make\nthemselves able to conceive most things, however inconceivable these may\nat first appear: and the same facts in each person\u2019s mental history which\ndetermine what is or is not conceivable to him, determine also which among\nthe various sequences in nature will appear to him so natural and\nplausible, as to need no other proof of their existence; to be evident by\ntheir own light, independent equally 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,\nB, appears to me more natural, conceivable, and credible _per se_ than the\nsuccession A, B; you are therefore mistaken in thinking that B depends\nupon A; I am certain, though I can give no other evidence of it, that C\ncomes in between A and B, and is the real and only cause of B. The other\nanswers\u2014the 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\nD, B, still more natural than C, B, or of nearer kin to the subject\nmatter, and prefers his D theory to the C theory. It is plain that there\nis no universal law operating here, except the law that each person\u2019s\nconceptions are governed and limited by his individual experience 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, and\nthe direct agent in producing even what is apparently produced by\nsomething else. Volitions are not known to produce anything 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? It is true\nthere are cases in which, with acknowledged propriety, we generalize from\na single instance to a multitude of instances. But they must be instances\nwhich resemble the one known instance, and not such as have no\ncircumstance in common with it except that of being instances. I have, for\nexample, no direct evidence that any creature is alive except myself: yet\nI attribute, with full assurance, life and sensation to other human beings\nand animals. But I do not conclude that all other things are alive merely\nbecause I am. I ascribe to certain other creatures a life like my own,\nbecause they manifest it by the same sort of indications by which mine is\nmanifested. I find that their phenomena and mine conform to the same laws,\nand it is for this reason that I believe both to arise from a similar\ncause. Accordingly I do not extend the conclusion beyond the grounds for\nit. Earth, fire, mountains, trees, are remarkable agencies, but their\nphenomena do not conform to the same laws as my actions do, and I\ntherefore do not believe earth or fire, mountains or trees, to possess\nanimal life. But the supporters of the Volition Theory ask us to infer\nthat volition causes everything, for no reason except that it causes one\nparticular thing; although that one phenomenon, far from being a type of\nall natural phenomena, is eminently peculiar; its laws bearing scarcely\nany resemblance to those of any other phenomenon, whether of inorganic or\nof organic nature.(74)\n\n\n\n\nCHAPTER VI. OF 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 effects of each cause when acting separately from\nthe other, we are often able to arrive deductively, or _\u00e0 priori_, at a\ncorrect prediction of what will arise from their conjunct agency. To\nenable us to do this, 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 realised 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 afterwards 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 entirely different from\nthose of either of the two substances separately, or 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 colour of green vitriol a mixture of the\ncolours 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 all 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 observed when separate: whatever would have\nhappened in consequence of each cause taken by itself, happens when they\nare together, and we have only to cast up the results. Not so in the\nphenomena which are the peculiar subject of the science of chemistry.\nThere, most of the uniformities to which the causes conformed when\nseparate, cease altogether when they are conjoined; and we are not, at\nleast in the present state of our knowledge, able to foresee what result\nwill follow from any new combination, until we have tried the specific\nexperiment.\n\nIf this be true of chemical combinations, it is still more true of those\nfar more complex combinations of elements which constitute organised\nbodies; and in which those extraordinary new uniformities arise, which are\ncalled the laws of life. All organised 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, fibrin, 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 fibrin could themselves\ntaste; for no elementary fact can be in the conclusion, which was not\nfirst in the premisses.\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\ntowards 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,(75) and the stream had flowed in for as long afterwards. Each agent\nproduced 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 operation 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, its 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 a solid mass, instead of merely a\nlarger amount of liquid.\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; between laws which work together without\nalteration, and laws which, when called upon to work together, cease and\ngive place to others; is one of the fundamental distinctions in nature.\nThe former case, that of the Composition of Causes, is the general one;\nthe other is always special and exceptional. There are no objects which do\nnot, as to some of their phenomena, obey the principle of the Composition\nof Causes; none that have not some laws which are rigidly fulfilled in\nevery combination into which the objects enter. The weight of a body, for\ninstance, is a property which it retains in all the combinations in which\nit is placed. The weight of a chemical compound, or of an organized body,\nis equal to the sum of the weights of the elements which compose it. The\nweight either of the elements or of the compound will vary, if they be\ncarried farther from their centre of attraction, or brought nearer to it;\nbut whatever affects the one affects the other. They always remain\nprecisely equal. So again, the component parts of a vegetable or animal\nsubstance do not lose their mechanical and chemical properties as separate\nagents, when, by a peculiar mode of juxta-position, they, as an aggregate\nwhole, acquire physiological or vital properties in addition. Those bodies\ncontinue, as before, to obey mechanical and chemical laws, in so far as\nthe operation of those laws is not counteracted by the new laws which\ngovern them as organised beings. When, in short, a concurrence of causes\ntakes place which calls into action new laws bearing no analogy to any\nthat we can trace in the separate operation of the causes, the new laws,\nwhile they supersede one portion of the previous laws, may co-exist with\nanother portion, and may even compound the effect of those previous laws\nwith their own.\n\nAgain, laws which were themselves generated in the second mode, may\ngenerate others in the first. Though there be 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 result 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 analysed 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. Thus it appears that even heteropathic laws, such laws of\ncombined 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 premisses 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 incumbered 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 cannot of course be applicable\nto cases in which the augmentation of the cause alters the _kind_ of\neffect; that is, in which the surplus quantity super-added to the cause\ndoes not become compounded with it, but the two together generate an\naltogether new phenomenon. Suppose that the application of a certain\nquantity of heat to a body merely increases its bulk, that a double\nquantity melts it, and a triple quantity decomposes it: these three\neffects being heterogeneous, no ratio, whether corresponding or not to\nthat of the quantities of heat applied, can be established between them.\nThus the supposed axiom of the proportionality of effects to their causes\nfails at the precise point where the principle of the Composition of\nCauses also fails; viz. where the concurrence of causes is such as to\ndetermine a change in the properties of the body generally, and render it\nsubject to new laws, more or less dissimilar to those to which it\nconformed in its previous state. The recognition, therefore, of any such\nlaw of proportionality, is superseded by the more comprehensive principle,\nin which as much of it as is true is implicitly asserted.\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 coexistence, are either, as we have seen, themselves\nlaws of causation, or consequences resulting from, and corollaries capable\nof being deduced from, such laws. If we could determine what causes are\ncorrectly assigned to what effects, and what effects to what causes, we\nshould be virtually acquainted with the whole course of nature. All those\nuniformities which are mere results of causation, might then be explained\nand accounted for; and every individual fact or event might be predicted,\nprovided we had the requisite data, that is, the requisite knowledge of\nthe circumstances which, in the particular instance, preceded it.\n\nTo ascertain, therefore, what are the laws of causation which exist in\nnature; to determine the effects of every cause, and the causes of all\neffects,\u2014is the main business of Induction; and to point out how this is\ndone is the chief object of Inductive Logic.\n\n\n\n\nCHAPTER VII. OF 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 somewhere among the facts which immediately preceded the occurrence,\nmay be taken for certain. The whole of the present facts are the\ninfallible result of all past facts, and more immediately of all the facts\nwhich existed at the moment previous. Here, then, is a great sequence,\nwhich we know to be uniform. If the whole prior state of the entire\nuniverse could again recur, it would again be followed by the present\nstate. The question is, how to resolve this complex uniformity into the\nsimpler uniformities which compose it, and assign to each portion of the\nvast antecedent the portion of the consequent which is attendant on it.\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 endeavour 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 farther 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 hardly ever occurred that what was called by one abstract name\nmight, in reality, be several phenomena, or that there was a possibility\nof decomposing the facts of the universe into any elements but those which\nordinary language already recognised.\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 (_\u00e0 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 recognised: 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\nwhich is 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 everything 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 voltaic battery, and\nthe Leyden jar, 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. Instead of being able to choose what\nthe concomitant circumstances shall be, we now have to discover what they\nare; which, when we go beyond the simplest and most accessible cases, it\nis next to impossible to do, with any precision and completeness. Let us\ntake, as an exemplification of a phenomenon which we have no means of\nfabricating artificially, a human mind. Nature produces many; but the\nconsequence of our not being able to produce it by art is, that in every\ninstance in which we see a human mind developing itself, or acting upon\nother things, we see it surrounded and obscured by an indefinite multitude\nof unascertainable circumstances, rendering the use of the common\nexperimental methods almost delusive. We may conceive to what extent this\nis true, if we consider, among other things, that whenever nature produces\na human mind, she produces, in close connexion with it, also a body; that\nis, a vast complication of physical facts, in no two cases perhaps exactly\nsimilar, and most of which (except the mere structure, which we can\nexamine in a sort of coarse way after it has ceased to act), are radically\nout of the reach of our means of exploration. If, instead of a human mind,\nwe suppose the subject of investigation to be a human society or State,\nall the same difficulties recur 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 physiology, mental philosophy, and the\nsocial science,) induction from direct experience is practised at a\ndisadvantage generally equivalent to impracticability: from which it\nfollows that the methods of those sciences, in order to accomplish\nanything worthy of attainment, must be to a great extent, if not\nprincipally, deductive. This is already known to be the case with the\nfirst of the sciences we have mentioned, astronomy; that it is not\ngenerally recognised as true of the others, is probably one of the reasons\nwhy they are still in their infancy.\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 cannot 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 substance 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 cannot, 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 study\nit where it offers itself spontaneously. If nature happens to present us\nwith instances sufficiently varied in their circumstances, and if we are\nable to discover, either among the proximate antecedents or among some\nother order of antecedents, something which is always found when the\neffect is found, however various the circumstances, and never found when\nit is not; we may discover, by mere observation without experiment, a real\nuniformity in nature.\n\nBut though this is certainly the most favourable 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.(76) But we have then added the\nevidence of experiment to that of simple observation. Until we had done\nso, we had only proved _invariable_ antecedence, but not _unconditional_\nantecedence, or causation. Until it had been shown by the actual\nproduction of the antecedent under known circumstances, and the occurrence\nthereupon of the consequent, that the antecedent was really the condition\non which it depended; the uniformity of succession which was proved to\nexist between them might, for aught we knew, be (like the succession of\nday and night) no case of causation at all; both antecedent and consequent\nmight be successive stages of the effect of an ulterior cause.\nObservation, in short, without experiment (supposing no aid from\ndeduction) can ascertain sequences and coexistences, but cannot prove\ncausation.\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 coexistence, 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 cannot 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, the name of experimentation would here be\ncompletely misapplied. Such are the facts: and what is the result? That on\nthis vast subject, which affords so much and such varied scope for\nobservation, we have not, properly speaking, ascertained a single cause, a\nsingle unconditional uniformity. We know not, in the case of most of the\nphenomena that we find conjoined, which is the condition of the other;\nwhich is cause, and which effect, or whether either of them is so, or they\nare not rather conjunct effects of causes yet to be discovered, complex\nresults of laws hitherto unknown.\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\nCHAPTER VIII. OF 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\ntwo-fold 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_\n_b_ _c_; and suppose that A is next tried with D and E, but without B and\nC, and that the effect is _a_ _d_ _e_. Then we may reason thus: _b_ and\n_c_ are not 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_ cannot 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\ncircumstance, 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 cannot take a phenomenon of\nwhich 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_\n_c_, and _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, cannot 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 farther, 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 cannot 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 analyse 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 circumstance 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 principle the following\ncanon:\u2014\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 endeavoured 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\ngun-shot which killed him: for he was in the fulness 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 cannot 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:\u2014\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 cause, or a necessary\npart 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\neliminated, _is_ 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 coexistent\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\nlimiting the identity which is required between the two instances, A B C\nand B C, to such circumstances as are not already known to be indifferent;\nit is very seldom that nature affords two instances, of which we can be\nassured that 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. Comte observes,) the very nature\nof an experiment, to introduce into the pre-existing state of\ncircumstances a change perfectly definite. We choose a previous state of\nthings with which we are well acquainted, so that no unforeseen alteration\nin that state is likely to pass unobserved; and into this we introduce, as\nrapidly as possible, the phenomenon which we wish to study; so that in\ngeneral we are entitled to feel complete assurance, that the pre-existing\nstate, and the state which we have produced, differ in nothing except the\npresence or absence of that phenomenon. If a bird is taken from a cage,\nand instantly plunged into carbonic acid gas, the experimentalist may be\nfully assured (at all events after one or two repetitions) that no\ncircumstance capable of causing suffocation had supervened in the interim,\nexcept the change from immersion in the atmosphere to immersion in\ncarbonic acid gas. There is one doubt, indeed, which may remain in some\ncases of this description; the effect may have been produced not by the\nchange, but by the means employed to produce the change. The possibility,\nhowever, of this last supposition generally admits of being conclusively\ntested by other experiments. It thus appears that in the study of the\nvarious kinds of phenomena which we can, by our voluntary agency, modify\nor control, we can in general satisfy the requisitions of the Method of\nDifference; but that by the spontaneous operations of nature those\nrequisitions are seldom fulfilled.\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\nanything, 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_,\nthen _a_ is an invariable consequent of A. If _a_ _b_ _c_, _a_ _d_ _e_,\n_a_ _f_ _g_, all number A among their antecedents, then A is connected as\nan antecedent, by some invariable law, with _a_. But to determine whether\nthis invariable antecedent is a cause, or this invariable consequent an\neffect, we must be able, in addition, to produce the one by means of the\nother; or, at least, to obtain that which alone constitutes our assurance\nof having produced anything, namely, an instance in which the effect, _a_,\nhas come into existence, with no other change in the pre-existing\ncircumstances than the addition of A. And this, if we can do it, is an\napplication of the Method of 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\ncannot be made available at all, or not without a previous employment of\nthe Method of Agreement. This occurs when the agency by which we can\nproduce the phenomenon is not that of one single antecedent, but of a\ncombination of antecedents, which we have no power of separating from each\nother and exhibiting apart. For instance, suppose the subject of inquiry\nto be the cause of the double refraction of light. We can produce this\nphenomenon at pleasure, by employing any one of the many substances which\nare known to refract light in that peculiar manner. But if, taking one of\nthose substances, as Iceland spar for example, we wish to determine on\nwhich of the properties of Iceland spar this remarkable phenomenon\ndepends, we can make no use, for that purpose, of the Method of\nDifference; for we cannot find another substance precisely resembling\nIceland spar except in some one property. The only mode, therefore, of\nprosecuting this inquiry is that afforded by the Method of Agreement; by\nwhich, in fact, through a comparison of all the known substances which\nhave the property of doubly refracting light, it was ascertained that they\nagree in the circumstance of being crystalline substances; and though the\nconverse does not hold, though all crystalline substances have not the\nproperty of double refraction, it was concluded, with reason, that there\nis a real connexion between these two properties; that either crystalline\nstructure, or the cause which gives rise to that structure, is one of the\nconditions of double 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\nconnexion between A and _a_. In order to convert this evidence of\nconnexion 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, to\nleave 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\nconnexion 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 when\nA 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:\u2014\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 cause, or a necessary part of the cause, of the phenomenon._\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 cannot 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 the 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 by\nthis means apprised that the effect of A is _a_, and that the effect of B\nis _b_. Subtracting the sum of these effects from the total phenomenon,\nthere remains _c_, which now, without any fresh experiment, we may know to\nbe the 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\nin the case A B C where they act together.\n\nOf the two instances, therefore, which the Method of Difference\nrequires,\u2014the one positive, the other negative,\u2014the negative one, or that\nin which the given phenomenon is absent, is not the direct result of\nobservation and experiment, but has been arrived at by deduction. As one\nof the forms of the Method of Difference, the Method of Residues partakes\nof its rigorous certainty, provided the previous inductions, those which\ngave the effects of A and B, were obtained by the same infallible method,\nand provided we are certain that C is the _only_ antecedent to which the\nresidual phenomenon _c_ can be referred; the only agent of which we had\nnot already calculated and subducted the effect. But as we can never be\nquite certain of this, the evidence derived from the Method of Residues is\nnot complete unless we can obtain C artificially and try it separately, or\nunless its agency, when once suggested, can be accounted for, and proved\ndeductively, from known laws.\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:\u2014\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 cannot be prevented from coexisting. In respect,\nindeed, to most of the permanent causes, no such difficulty exists; since\nthough we cannot eliminate them as coexisting facts, we can eliminate them\nas influencing agents, by simply trying our experiment in a local\nsituation beyond the limits of their influence. The pendulum, for example,\nhas its oscillations disturbed by the vicinity of a mountain: we remove\nthe 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 everything 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 cannot be removed from the influence of the earth: we cannot 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\ncoexistent 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\na body. Being unable, then, to separate Body and Heat, we cannot effect\nsuch a variation of circumstances as the foregoing three methods require;\nwe cannot ascertain, by those methods, what portion of the phenomena\nexhibited by any body are 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\nproperties; for as we have never been able to observe any bodies without a\nportion of heat in them, the effects due to that heat might form a part of\nthe very results, which we were affecting to subtract in order that the\neffect of heat 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 cannot 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, _vice vers\u00e2_, 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 cannot 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 other\nwords, 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 relations to other things, of which\nrelations the principal is its position in space. In the previous example,\nthe modification which was produced in the antecedent was an alteration in\nits quantity. Let us now suppose the question to be, what influence the\nmoon exerts on the surface of the earth. We cannot try an experiment in\nthe absence of the moon, so as to observe what terrestrial phenomena her\nannihilation would put an end to; but when we find that all the variations\nin the _position_ of the moon are followed by corresponding variations in\nthe time and place of high water, the place being always either the part\nof the earth which is nearest to, or that which is most remote from, the\nmoon, we have ample evidence that the moon is, wholly or partially, the\ncause which determines the tides. It very commonly happens, as it does in\nthis instance, that the variations of an effect are correspondent, or\nanalogous, to those of its cause; as the moon moves further towards the\neast, the high water point does the same: but this is not an indispensable\ncondition; as may be seen in the same example, for along with that high\nwater point, there is at the same instant another high water point\ndiametrically opposite to it, and which, therefore, of necessity, moves\ntowards the west as the moon followed by the nearer of the tide waves\nadvances towards the east: and yet both these motions are equally effects\nof 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 towards 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:\u2014\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 endeavouring 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 cannot ourselves\nproduce the variations, we must endeavour, though it is an attempt which\nis seldom successful, to find them produced by nature in some case in\nwhich the pre-existing 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 endeavour 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 _towards_ 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 ratio to the sun\u2019s distance from the\nearth, that is, according to another relation of the sun. Thus we see that\nthere is not only an invariable connexion between the sun and the earth\u2019s\ngravitation, but that two of the relations of the sun, its position with\nrespect to the earth and its distance from the earth, are invariably\nconnected as antecedents with the quantity and direction of the earth\u2019s\ngravitation. The cause of the earth\u2019s gravitating at all, is simply the\nsun; but the cause of its gravitating with a given intensity and in a\ngiven direction, is the existence of the sun in a given direction and at a\ngiven distance. It is not strange that a modified cause, which is in truth\na 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 anything 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 instance\nif _a_ were proportional to the square of A. If, on the other hand, _a_ is\nnot wholly the effect of A, but yet varies when A varies, it is probably a\nmathematical function not of A alone but of A and something else: its\nchanges, for example, may be such as would occur if part of it remained\nconstant, or varied on some other principle, and the remainder varied in\nsome numerical relation to the variations of A. In that case, when A\ndiminishes, _a_ will seem to approach not towards zero, but towards some\nother limit: and when the series of variations is such as to indicate what\nthat limit is, if constant, or the law of its variation if variable, the\nlimit will exactly measure how much of _a_ is the effect of some other and\nindependent cause, and the remainder will be the effect of A (or of the\ncause 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 cannot, 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 cannot 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 accordingly\nthe ancients, with their _inductio per enumerationem simplicem_, imagined\nto be the law. Every moving body, however, encounters various obstacles,\nas friction, the resistance of the atmosphere, &c., which we know by daily\nexperience to be causes capable of destroying motion. It was suggested\nthat the whole of the retardation might be owing to these causes. How was\nthis inquired into? If the obstacles could have been entirely removed, the\ncase would have been amenable to the Method of Difference. They could not\nbe removed, they could only be diminished, and the case, therefore,\nadmitted only of the Method of Concomitant Variations. This accordingly\nbeing employed, it was found that every diminution of the obstacles\ndiminished the retardation of the motion: and inasmuch as in this case\n(unlike the case of heat) the total quantities both of the antecedent and\nof the consequent were known; it was practicable to estimate, with an\napproach to accuracy, both the amount of the retardation and the amount of\nthe retarding causes, or resistances, and to judge how near they both were\nto being exhausted; and it appeared that the effect dwindled as rapidly,\nand at each step was as far on the road towards annihilation, as the cause\nwas. The simple oscillation of a weight suspended from a fixed point, and\nmoved a little out of the perpendicular, which in ordinary circumstances\nlasts but a few minutes, was prolonged in Borda\u2019s experiments to more than\nthirty hours, by diminishing as much as possible the friction at the point\nof suspension, and by making the body oscillate in a space exhausted as\nnearly as possible of its air. There could therefore be no hesitation in\nassigning the whole of the retardation of motion to the influence of the\nobstacles: and since, after subducting this retardation from the total\nphenomenon, the remainder was an uniform velocity, the result was the\nproposition known as 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\nin comparison with the total quantities, there is much danger lest we\nshould mistake the numerical law, and be led to miscalculate the\nvariations which would take place beyond the limits; a miscalculation\nwhich would vitiate any conclusion respecting the dependence of the effect\nupon the cause, that could be founded on those variations. Examples are\nnot wanting of such mistakes. \u201cThe formul\u00e6,\u201d says Sir John Herschel,(77)\n\u201cwhich have been empirically deduced for the elasticity of steam, (till\nvery recently,) and those for the resistance of fluids, and other similar\nsubjects,\u201d when relied on beyond the limits of the observations from which\nthey were deduced, \u201chave almost invariably failed to support the\ntheoretical structures 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\nconnexion 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, cannot 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\nconnexion 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, of direct induction _\u00e0\nposteriori_, as distinguished from deduction: at least, I know not, nor am\nable to imagine, any others. And even of these, the Method of Residues, as\nwe have seen, 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\nCHAPTER IX. MISCELLANEOUS 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, Professor Liebig. The object\nin view, is to ascertain the immediate cause of the death produced by\nmetallic poisons.\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 afterwards 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 afterwards 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 _\u00e0 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 cannot 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, cannot act at all on animal tissues. So,\nagain, sugar is a well-known antidote to poisoning by salts of copper; and\nsugar reduces those salts either into metallic copper, or into the red\nsuboxide, neither of which enters into combination with animal matter. The\ndisease called painter\u2019s colic, so common in manufactories of white lead,\nis unknown where the workmen are accustomed to take, as a preservative,\nsulphuric-acid-lemonade (a solution of sugar rendered acid by sulphuric\nacid). Now diluted sulphuric acid has the property of decomposing all\ncompounds of lead with organic matter, or of preventing them from being\nformed.\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 neighbouring 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, through 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;\nalthough 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 rigour of that method requires, ought to differ only in the presence\nor absence of one single circumstance. Now, in the preceding argument,\nthey differ in the presence or absence not of a single _circumstance_, but\nof a single _substance_: and as every substance has innumerable\nproperties, there is no knowing what number of real differences are\ninvolved in what is nominally and apparently only one difference. It is\nconceivable that the antidote, the peroxide of iron for example, may\ncounteract the poison through some other of its properties than that of\nforming an insoluble compound with it; and if so, the theory would fall to\nthe ground, so far as it is supported by that instance. This source of\nuncertainty, which is a serious hindrance to all extensive generalizations\nin chemistry, is however reduced in the present case to almost the lowest\ndegree possible, when we find that not only one substance, but many\nsubstances, possess the capacity of acting as antidotes to metallic\npoisons, and that all these agree in the property of forming insoluble\ncompounds with the poisons, while they cannot be ascertained to agree in\nany other property whatsoever. We have thus, in favour of the theory, all\nthe evidence which can be obtained by what we termed the Indirect Method\nof Difference, or the Joint Method of Agreement and Difference; the\nevidence of which, though it never can amount to that of the Method of\nDifference properly so called, may approach indefinitely near to it.\n\n\u00a7 2. Let the object be(78) 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 electrical 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 neighbourhood 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 is it\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 cannot 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 cannot 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 neighbouring\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 cannot 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 neighbouring 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 neighbouring 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\nneighbouring 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 neighbouring 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 neighbouring 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.(79)\n\n\u00a7 3. Our third example shall be extracted from Sir John Herschel\u2019s\n_Discourse on the Study of Natural Philosophy_, a work replete with\nhappily-selected exemplifications of inductive processes from almost every\ndepartment of physical science, and in which alone, of all books which I\nhave met with, the four methods of induction are distinctly recognised,\nthough not so clearly characterized and defined, nor their correlation so\nfully shown, as has appeared to me desirable. The present example is\ndescribed by Sir John Herschel as \u201cone of the most beautiful specimens\u201d\nwhich can be cited \u201cof inductive experimental inquiry lying within a\nmoderate compass;\u201d the theory of dew, first promulgated by the late Dr.\nWells, and now universally adopted by scientific authorities. The passages\nin inverted commas are extracted verbatim from the \u201cDiscourse.\u201d(80)\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\ndew from rain, and the moisture of fogs, and limit the application of the\nterm to what is really meant, which is, the spontaneous appearance of\nmoisture on substances exposed in the open air when no rain or _visible_\nwet is falling.\u201d This answers to a preliminary operation which will be\ncharacterized in the ensuing book, treating of operations subsidiary to\ninduction.(81) The state of the question being fixed, we come to the\nsolution.\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 on.\u201d\nComparing these cases, we find that they all contain the phenomenon which\nwas proposed as the subject of investigation. Now \u201call these instances\nagree in one point, the coldness of the object dewed, in comparison with\nthe air in contact with it.\u201d But there still remains the most important\ncase of all, that of nocturnal dew: does the same circumstance exist in\nthis case? \u201cIs it a fact that the object dewed _is_ colder than the air?\nCertainly not, one would at first be inclined to say; for what is to\n_make_ it so? But ... the experiment is easy: we have only to lay a\nthermometer in contact with the dewed substance, and hang one at a little\ndistance above it, out of reach of its influence. The experiment has been\ntherefore made; the question has been asked, and the answer has been\ninvariably in the affirmative. Whenever an object contracts dew, it _is_\ncolder than the air.\u201d\n\nHere then is a complete application of the Method of Agreement,\nestablishing the fact of an invariable connexion between the deposition of\ndew 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 for a comparison between instances of\ndew and instances of no dew, is the condition necessary to bring the\nMethod of 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 upwards, and\nin some cases the under side of a horizontal plate of glass is also\ndewed.\u201d Here is an instance in which the effect is produced, and another\ninstance in which it is not produced; but we cannot yet pronounce, as the\ncanon of the Method of Difference requires, that the latter instance\nagrees with the former in all its circumstances except one; for the\ndifferences between glass and polished metals are manifold, and the only\nthing we can as yet be sure of is, that the cause of dew will be found\namong the circumstances by which the former substance is distinguished\nfrom the latter. But if we could be sure that glass, and the various other\nsubstances on which dew is deposited, have only _one_ quality in common,\nand that 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\nrecognise, 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 well,\nresist dew most effectually.\u201d The complication increases; here is the\nMethod of Concomitant Variations called to our assistance; and no other\nmethod was practicable on this occasion; for the quality of conducting\nheat could not be excluded, since all substances conduct heat in some\ndegree. The conclusion obtained is, that _c\u00e6teris paribus_ the deposition\nof dew is in some proportion to the power which the body possesses of\nresisting the passage of heat; and that this, therefore, (or something\nconnected with this,) must be at least one of the causes which assist in\nproducing 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,\n&c., as unfavourable, but those of a loose one, as cloth, velvet, wool,\neiderdown, cotton, &c., as eminently favourable 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 cause\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 (so 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\nhave been realized the requisitions of what we have termed the Indirect\nMethod of 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 coexistence between the two properties; so that the property of\nbeing 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 must be one which, by its own\nproperties or laws, would, if exposed in the night, become colder than the\nsurrounding air. The coldness therefore, being accounted for independently\nof the dew, while it is proved that there is a connexion between the two,\nit must 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 vapour 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 vapour 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 vapour\nsuspended as the air will contain at its existing temperature, any\nlowering of that temperature will cause a portion of the vapour to be\ncondensed, and become water. But, again, we know deductively, from the\nlaws of heat, that the contact of the air with a body colder than itself,\nwill necessarily lower the temperature of the stratum of air immediately\napplied to its surface; and will therefore cause it to part with a portion\nof its water, which accordingly will, by the ordinary laws of gravitation\nor cohesion, attach itself to the surface of the body, thereby\nconstituting dew. This deductive proof, it will have been seen, has the\nadvantage of proving at once, causation as well as coexistence; 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\nvapour, comparatively to its temperature, that even when somewhat cooled\nby the contact of the colder body, it can still continue to hold in\nsuspension all the vapour which was previously suspended in it: thus in a\nvery dry summer there are no dews, in a very dry winter no hoar frost.\nHere, therefore, is an additional condition of the production of dew,\nwhich the methods we previously made use of failed to detect, and which\nmight have remained still undetected, if recourse had not been had to the\nplan of deducing the effect from the ascertained properties of the agents\nknown to be 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.(82)\n\nThe accumulated proof of which the Theory of Dew has been found\nsusceptible, is a striking instance of the fulness 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 last example will have conveyed to any one by whom it has been\nduly followed, so clear a conception of the use and practical management\nof three of the four methods of experimental inquiry, as to supersede the\nnecessity of any further exemplification of them. The remaining method,\nthat of Residues, not having found any place either in this or in the two\npreceding investigations, I shall extract 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 Encke, a\ngreat many times in succession, and the general good agreement of its\ncalculated with its observed place during any one of its periods of\nvisibility, would lead us to say that its gravitation towards the sun and\nplanets is the sole and sufficient cause of all the phenomena of its\norbitual motion: but when the effect of this cause is strictly calculated\nand subducted from the observed motion, there is found to remain behind a\n_residual phenomenon_, which would never have been otherwise ascertained\nto exist, which is a small anticipation of the time of its reappearance,\nor a diminution of its periodic time, which cannot be accounted for by\ngravity, and whose cause is therefore to be inquired into. Such an\nanticipation would be caused by the resistance of a medium disseminated\nthrough the celestial regions; and as there are other good reasons for\nbelieving this to be a _vera causa_,\u201d (an actually existing antecedent,)\n\u201cit has therefore been ascribed to such a resistance.\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_ (antecedents known to\nexist) \u201cwhy it _should_ come at length to rest, viz. the resistance of the\nair, which opposes, and at length destroys, all motions performed in it;\nand 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.\" 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 _\u00e0 priori_, from the laws obtained\nby separate and foregone experiments.\u201d\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 a 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\nanalysed. It is on this principle, too, that the small concentrated\nresidues of great operations in the arts are almost sure to be the lurking\nplaces of new chemical ingredients: witness iodine, brome, selenium, and\nthe new metals accompanying platina in the experiments of Wollaston and\nTennant. It was a happy thought of Glauber to examine what everybody else\nthrew away.\u201d(83)\n\n\u201cAlmost all the greatest discoveries in Astronomy,\u201d says the same\nauthor,(84) \u201chave resulted from the consideration of residual phenomena of\na quantitative or numerical kind.... It was thus that the grand discovery\nof the precession of the equinoxes resulted as a residual phenomenon, from\nthe imperfect explanation of the return of the seasons by the return of\nthe sun to the same apparent place among the fixed stars. Thus, also,\naberration and nutation resulted as residual phenomena from that portion\nof the changes of the apparent places of the fixed stars which was left\nunaccounted for by precession. And thus again the apparent proper motions\nof the stars are the observed residues of their apparent movements\noutstanding and unaccounted for by strict calculation of the effects of\nprecession, nutation, and aberration. The nearest approach which human\ntheories can make to perfection is to diminish this residue, this _caput\nmortuum_ of observation, as it may be considered, as much as practicable,\nand, if possible, to reduce it to nothing, either by showing that\nsomething 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\ntowards 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 ever shewn 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\nassertors 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 been\nso aptly exemplified in the inductive processes which produced the Theory\nof Dew, we may here close our exposition of the four methods, considered\nas employed in the investigation of the simpler and more elementary order\nof the combinations of phenomena.(85)\n\n\n\n\nCHAPTER X. OF 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 coexistent\nphenomena the particular effect due to a given cause, or the particular\ncause which gave birth to a given effect; it has been necessary to\nsuppose, in the first instance, for the sake of simplification, that this\nanalytical operation is encumbered by no other difficulties than what are\nessentially 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 coexistent effect. We have regarded _a b c d e_,\nthe aggregate of the phenomena existing at any moment, as consisting of\ndissimilar facts, _a_, _b_, _c_, _d_, and _e_, for each of which one, and\nonly 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.\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 motion: many causes may produce some kinds of sensation: many\ncauses may produce death. A given effect may really be produced by a\ncertain cause, and yet be perfectly capable of being produced 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 be concluded that A is an invariable antecedent of _a_, and even\nthat it is the unconditional invariable antecedent, or cause, if we could\nbe sure that there is no other antecedent common to the two cases. That\nthis difficulty may not stand in the way, let us suppose the two cases\npositively ascertained to have no antecedent in common except A. The\nmoment, however, that we let in the possibility of a plurality of causes,\nthe conclusion fails. For it involves a tacit supposition, that _a_ must\nhave been produced in both instances by the same cause. If there can\npossibly have been two causes, those two may, for example, be C and E: the\none may have been the cause of _a_ in the former of the instances, the\nother in the latter, A having no influence in either case.\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 innumerable; 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, although 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 favour 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 towards a solution of this doubt. For\nif we try A F G, A H K, &c., all unlike one another except in containing\nthe circumstance A, and if we find the effect _a_ entering into the result\nin all 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 favour 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 the effect of\nA divested of the characteristic imperfection and reduced to a virtual\ncertainty? This is a question which we cannot be exempted from answering;\nbut the consideration of it belongs to what is called the Theory of\nProbability, which will form the subject of a chapter hereafter. It is\nseen, however, at once, that the conclusion does amount to a practical\ncertainty after a sufficient number of instances, and that the method,\ntherefore, is not radically vitiated by the characteristic imperfection.\nThe result of these considerations is only, in the first place, to point\nout a new source of inferiority in the Method of Agreement as compared\nwith other modes of investigation, and new reasons for never resting\ncontented with the results obtained by it, without attempting to confirm\nthem either by the Method of Difference, or by connecting them deductively\nwith some law or laws already ascertained by that superior method. And, in\nthe second place, we learn from this the true theory of the value of mere\n_number_ of instances in inductive inquiry. The Plurality of Causes is the\nonly reason why mere number is of any importance. The tendency of\nunscientific inquirers is to rely too much on number, without analysing\nthe instances; without looking closely enough into their nature, to\nascertain what circumstances are or are not eliminated by means of them.\nMost people hold their conclusions with a degree of assurance proportioned\nto the mere _mass_ of the experience on which they appear to rest; not\nconsidering that by the addition of instances to instances, all of the\nsame kind, that is, differing from one another only in points already\nrecognised as immaterial, nothing whatever is added to the evidence of the\nconclusion. A single instance eliminating some antecedent which existed in\nall the other cases, is of more value than the greatest multitude of\ninstances which are reckoned by their number alone. It is necessary, no\ndoubt, to assure ourselves, by a repetition of the observation or\nexperiment, that no error has been committed concerning the individual\nfacts observed; and until we have assured ourselves of this, instead of\nvarying the circumstances, we cannot too scrupulously repeat the same\nexperiment or observation without any change. But when once this assurance\nhas been obtained, the multiplication of instances which do not exclude\nany more circumstances would be entirely useless, were it not for the\nPlurality 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 premisses, (if\nthey may be so called,) the negative premiss. The Method of Agreement,\nwhen applied to negative instances, or those in which a phenomenon does\n_not_ take place, is certainly free from the characteristic imperfection\nwhich affects it in the affirmative case. The negative premiss, it might\ntherefore be supposed, could be worked as a simple case of the Method of\nAgreement, without requiring an affirmative premiss to be joined with it.\nBut although 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\nin which 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 might, and perhaps\nwill, be discovered, that in the production of heat by friction,\npercussion, chemical action, &c., the ultimate source is one and the same.\nBut if (as continually happens) we cannot take this ulterior step, the\ndifferent antecedents must be set down provisionally as distinct causes,\neach sufficient of itself to produce 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\npremisses 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\nways. In 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; the conditions on which it depends, the facts which make up\nits cause.\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. Further, even if we could have\nascertained, by the Method of Agreement, that oxygen and hydrogen were\nboth present when water is produced, no experimentation on oxygen and\nhydrogen separately, no knowledge of their laws, could have enabled us\ndeductively to infer that they would produce water. We require a specific\nexperiment 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 towards 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\nreappear 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 what\nwas then called red precipitate, while the air, on being examined after\nthe experiment, proved to have lost weight, and to have become incapable\nof supporting life or combustion. When red precipitate was exposed to a\nstill greater heat, it became mercury again, and gave off a gas which did\nsupport life and flame. Thus the agents which by their combination\nproduced red precipitate, namely the mercury and the gas, reappear as\neffects resulting from that precipitate when acted upon by heat. So, if we\ndecompose water by means of iron filings, we produce two effects, rust and\nhydrogen: now rust is already known by experiments upon the component\nsubstances, to be an effect of the union of iron and oxygen: the iron we\nourselves supplied, but the oxygen must have been produced from the water.\nThe result therefore is that water has disappeared, and hydrogen and\noxygen have appeared in its stead: or in other words, the original laws of\nthese gaseous agents, which had been suspended by the superinduction of\nthe new laws called the properties of water, have again started into\nexistence, and the causes of water are found among its effects.\n\nWhere two phenomena, between the laws or properties of which considered in\nthemselves no connexion can be traced, are thus reciprocally cause and\neffect, 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 fact 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, then, when the heteropathic effect (as we called it in a\nformer chapter)(86) is but a transformation of its cause, or in other\nwords, when 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 cannot be reproduced from the product: just as a youth can\ngrow into an old man, but an old man cannot grow into a youth. We cannot\nascertain from what simple feelings any of our complex states of mind are\ngenerated, 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\nfrom deduction 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 recognising 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_, - _a_, 1/2 _b_, - _b_, 2 _b_, &c., some of\nwhich cancel one another, while many others do not appear distinguishably,\nbut merge 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\nalthough 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 it in a given time a certain distance to the west, the\nother if acting alone would carry it exactly as far towards the east; and\nthe result is the same as if it had been first carried to the west as far\nas the one force would carry it, and then back towards the east as far as\nthe other would carry it, that 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,\nyet the sum of the effects of two causes of motion may be rest. Again, a\nbody solicited by two forces in directions making an angle with one\nanother, moves in the diagonal; and it seems a paradox to say that motion\nin the diagonal is the sum of two motions in two other lines. Motion,\nhowever, is but change of place, and at every instant the body is in the\nexact place it would have been in if the forces had acted during alternate\ninstants instead of acting in the same instant; (saving that if we suppose\ntwo forces 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 coexisted 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 are, from the very\nfirst, retarded by the action of gravity and other resisting forces, and\nat last stopped altogether; it is clear that the general proposition,\nthough it would be true under a certain hypothesis, would not express the\nfacts as they actually occur. To accommodate the expression of the law to\nthe real phenomena, we must say, not that the object moves, but that it\n_tends_ to move, in the direction and with the velocity specified. We\nmight, indeed, guard our expression in a different mode, by saying that\nthe body moves in that manner unless prevented, or except in so far as\nprevented, by some counteracting cause. But the body does not only move in\nthat manner unless counteracted; it _tends_ to move in that manner even\nwhen counteracted; it still exerts, in the original direction, the same\nenergy of movement as if its first impulse had been undisturbed, and\nproduces, by that energy, an exactly equivalent quantity of effect. This\nis true even when the force leaves the body as it found it, in a state of\nabsolute rest; as when we attempt to raise a body of three tons weight\nwith a force equal to one ton. For if, while we are applying this force,\nwind or water or any other agent supplies an additional force just\nexceeding two tons, the body will be raised; thus proving that the force\nwe applied exerted its full effect, by neutralizing an equivalent portion\nof the weight which it was insufficient altogether to overcome. And if,\nwhile we are exerting this force of one ton upon the object in a direction\ncontrary to that of gravity, it be put into a scale and weighed, it will\nbe found to have lost a ton of its weight, or in other words, to press\ndownwards with a force only equal to the 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 not.\n\u201cWhat is thought to be an exception to a principle,\u201d (to quote words used\non a different occasion,) \u201cis always some other and distinct principle\ncutting into the former; some other force which impinges(87) against the\nfirst force, and deflects it from its direction. There are not a law and\nan exception to that law, the law acting in ninety-nine cases and the\nexception in one. There are two laws, each possibly acting in the whole\nhundred 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\ntowards the earth, with a force exactly equal to that with which the earth\ntends towards 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(88)\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, the\ncircumstances in which it maybe expected again to occur. The conditions of\na 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 is\ntherefore in itself capable of being deduced from these laws. This is\ncalled the method _\u00e0 priori_. The other, or _\u00e0 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 that cause in\nthe ordinary 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 favourite 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 that 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 to restore health. The\nexperimental method would simply administer mercury in as many cases as\npossible, noting the age, sex, temperament, and other peculiarities of\nbodily constitution, the particular form or variety of the disease, the\nparticular stage of its progress, &c., remarking in which of these cases\nit produced a salutary effect, and with what circumstances it was on those\noccasions combined. The method of simple observation would compare\ninstances of recovery, to find whether they agreed in having been preceded\nby the administration of mercury; or would compare instances of recovery\nwith instances of failure, to find cases which, agreeing in all other\nrespects, differed only in the fact that mercury had been administered, or\nthat 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 so often spoken of as\nconstituting the characteristic imperfection of the Method of Agreement;\nPlurality of Causes. Supposing even that mercury does tend to cure the\ndisease, so many other causes, both natural and artificial, also tend to\ncure it, that there are sure to be abundant instances of recovery, in\nwhich mercury has not been administered: unless, indeed, the practice be\nto administer it in all cases; on which supposition it will equally be\nfound in the cases of failure.\n\nWhen an effect results from the union of many causes, the share which each\nhas in the determination of the effect cannot in general be great: and the\neffect is not likely, even in its presence or absence, still less in its\nvariations, to follow, even approximatively, 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 favourable 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.\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\nrecognised; we shall next inquire whether any greater benefit can be\nexpected from the other branch of the _\u00e0 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 everything which partakes\nof the nature not of an experimental but of a deductive operation. If for\ninstance we try experiments with mercury upon a person in health, in order\nto ascertain the general laws of its action upon the human body, and then\nreason from these laws to determine how it will act upon persons affected\nwith a particular disease, this may be a really effectual method, but this\nis deduction. The experimental method does not derive the law of a complex\ncase from the simpler laws which conspire to produce it, but makes its\nexperiments directly upon the complex case. We must make entire\nabstraction of all knowledge of the simpler tendencies, the _modi\noperandi_ of mercury in detail. Our experimentation must aim at obtaining\na direct answer to the specific question, Does or does not mercury tend to\ncure 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\n(though I should think never in physiology) concurrences of many causes,\nin which we yet know accurately what the causes are. But when we have got\nclear of this obstacle we encounter another still more serious. In other\ncases, when we intend to try an experiment, we do not reckon it enough\nthat 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 do\nknow, shall have effects susceptible of being confounded with those of the\nagent 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 no. 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\ncannot tell that those other circumstances may not have produced the whole\nof the effect, independently or even in spite of the mercury. The Method\nof Difference, in the ordinary mode of its use, namely by comparing the\nstate of things following the experiment with the state which preceded it,\nis thus, in the case of intermixture of effects, entirely unavailing;\nbecause other causes than that whose effect we are seeking to determine,\nhave been operating during the transition. As for the other mode of\nemploying the Method of Difference, namely by comparing, not the same case\nat two different periods, but different cases, this in the present\ninstance is quite chimerical. In phenomena so complicated it is\nquestionable if two cases similar in all respects but one ever occurred;\nand were they to occur, we could not possibly know that they were so\nexactly similar.\n\nAnything like a scientific use of the method of experiment, in these\ncomplicated cases, is therefore out of the question. We can in the most\nfavourable cases only discover, by a succession of trials, that a certain\ncause is _very often_ followed by a certain effect. For, in one of these\nconjunct effects, the portion which is determined by any one of the\ninfluencing agents, is generally, as we before remarked, but small; and it\nmust be a more potent cause than most, if even the tendency which it\nreally exerts is not thwarted by other tendencies in nearly as many cases\nas it is fulfilled.\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,\nmore complicated than even those of physiology, the phenomena of politics\nand history. There, Plurality of Causes exists in almost boundless excess,\nand the effects are, for the most part, inextricably interwoven with one\nanother. To add to the embarrassment, most of the inquiries in political\nscience relate to the production of effects of a most comprehensive\ndescription, such as the public wealth, public security, public morality,\nand the like: results liable to be affected directly or indirectly either\nin _plus_ or in _minus_ by nearly every fact which exists, or event which\noccurs, in human society. The vulgar notion, that the safe methods on\npolitical subjects are those of Baconian induction, that the true guide is\nnot general reasoning, but specific experience, will one day be quoted as\namong the most unequivocal marks of a low state of the speculative\nfaculties in any age in which it is accredited. Nothing can be more\nludicrous than the sort of parodies on experimental reasoning which one is\naccustomed to meet with, not in popular discussion only, but in grave\ntreatises, when the affairs of nations are the theme. \u201cHow,\u201d it is asked,\n\u201ccan an institution be bad, when the country has prospered under it?\u201d \u201cHow\ncan such or such causes have contributed to the prosperity of one country,\nwhen another has prospered without them?\u201d Whoever makes use of an argument\nof this kind, not intending to deceive, should be sent back to learn the\nelements of some one of the more easy physical sciences. Such reasoners\nignore the fact of Plurality of Causes in the very case which affords the\nmost signal example of it. So little could be concluded, in such a case,\nfrom any possible collation of individual instances, that even the\nimpossibility, in social phenomena, of making artificial experiments, a\ncircumstance otherwise so prejudicial to directly inductive inquiry,\nhardly affords, in this case, additional reason of regret. For even if we\ncould try experiments upon a nation or upon the human race, with as little\nscruple as M. Majendie tries them upon dogs or rabbits, we should never\nsucceed in making two instances identical in every respect except the\npresence or absence of some one indefinite circumstance. The nearest\napproach to an experiment in the philosophical sense, which takes place in\npolitics, is the introduction of a new operative element into national\naffairs by some special and assignable measure of government, such as the\nenactment or repeal of a particular law. But where there are so many\ninfluences at work, it requires some time for the influence of any new\ncause upon national phenomena to become apparent; and as the causes\noperating in so extensive a sphere are not only infinitely numerous, but\nin a state of perpetual alteration, it is always certain that before the\neffect of the new cause becomes conspicuous enough to be a subject of\ninduction, so many of the other influencing circumstances will have\nchanged as to vitiate the experiment.\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 computes the effect from the\nbalance of the different tendencies which produce it: in short, the\ndeductive, or _\u00e0 priori_ method. The more particular consideration of this\nintellectual process requires a chapter to itself.\n\n\n\n\nCHAPTER XI. OF 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; and 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; although in many\nparticular investigations the place of the induction may be supplied by a\nprior deduction; but the premisses 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 premisses on\nobservation or experiment. Thus, if the subject be social or historical\nphenomena, the premisses 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\nstudy, may or may not be difficult. In the case last mentioned, this first\ncondition is of easy fulfilment. 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 organised 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 cannot 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 unfavourable\nposition for tracing, by means of such cases, the law of the tendency\nitself. It would have been difficult to discover the law that every body\nin motion tends to continue moving in a straight line, by an induction\nfrom instances 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 impossible to separate the different agencies which\ncollectively compose an organised body, without destroying the very\nphenomena which it is our object to investigate:\n\n    following life, in creatures we dissect,\nWe lose it, in the moment we detect.\n\nAnd for this reason I am inclined to the opinion, that physiology is\nembarrassed by greater natural difficulties, and is probably susceptible\nof a less degree of ultimate perfection, than even the social science;\ninasmuch as it is possible to study the laws and operations of one human\nmind apart from other minds, much less imperfectly than we can study the\nlaws of one organ or tissue of the human body apart from the other organs\nor 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 available 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. As this experimentation is not intended to\nobtain a direct solution of any practical question, but to discover\ngeneral laws, from which afterwards the conditions of any particular\neffect may be obtained by deduction; the best cases to select are those of\nwhich the circumstances can be best ascertained: and such are generally\nnot those in which there is any practical object in view. The experiments\nare best tried, not in a state of disease, which is essentially a\nchangeable state, but in the condition of health, comparatively a fixed\nstate. In the one, unusual agencies are at work, the results of which we\nhave no means of predicting; in the other, the course of the accustomed\nphysiological phenomena would, it may generally be presumed, remain\nundisturbed, were it not for the disturbing cause which we introduce.\n\nSuch, with the occasional aid of the method of Concomitant Variations,\n(the latter 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 cannot yet decide\nwhether they are cases of causation or mere results of it. Not only has\nthe order in which the facts of organization and life successively\nmanifest themselves, from the first germ of existence to death, been found\nto be uniform, and very accurately ascertainable; but, by a great\napplication of the Method of Concomitant Variations to the entire facts of\ncomparative anatomy and physiology, the conditions of organic structure\ncorresponding to each class of functions have been determined with\nconsiderable precision. Whether these organic conditions are the whole of\nthe conditions, and indeed whether they are conditions at all, or mere\ncollateral effects of some common cause, we are quite ignorant: nor are we\never likely to know, unless we could construct an organized body, and try\nwhether 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 simple\ninstances are meant, of course, those in which the action of each cause\nwas not intermixed or interfered with, or not to any great extent, by\nother causes whose laws were unknown. And only when the induction which\nfurnished the premisses 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 premisses the\ntheorems of the science of number, in the whole immense extent of that\nscience. Not only are the highest truths of mathematics often required to\nenable us to compute an effect, the numerical law of which we already\nknow; but, even by the aid of those highest truths, we can go but a little\nway. In so simple a case as the common problem of three bodies gravitating\ntowards one another, with a force directly as their mass and inversely as\nthe square of the distance, all the resources of the calculus have not\nhitherto sufficed to obtain any general solution but an approximate one.\nIn a case a little more complex, but still one of the simplest which arise\nin practice, that of the motion of a projectile, the causes which affect\nthe velocity and range (for example) of a cannon-ball may be all known and\nestimated; the force of the gunpowder, the angle of elevation, the density\nof the air, the strength and direction of the wind; but it is one of the\nmost difficult of mathematical problems to combine all these, so as to\ndetermine the effect resulting from their collective action.\n\nBesides the theorems of number, those of geometry also come in as\npremisses, 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,\nto say 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; and 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\nfulfil 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 _\u00e0 priori_ have\ntaken 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 pretence 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\nfulfilled, to make the calculation transcends, in any but very simple\ncases, the utmost power of mathematical science with 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 forms,\nunder the name of Verification, the third essential component part of the\nDeductive Method; without which all the results it can give have little\nother value than that of guess-work. To warrant reliance on the general\nconclusions arrived at by deduction, these conclusions must be found, on\ncareful comparison, to accord with the results of direct observation\nwherever it can be had. If, when we have experience to compare with them,\nthis experience confirms them, we may safely trust to them in other cases\nof which our specific experience is yet to come. But if our deductions\nhave led to the conclusion that from a particular combination of causes a\ngiven effect would result, then in all known cases where that combination\ncan be shown to have existed, and where the effect has not followed, we\nmust be able to show (or at least to make a probable surmise) what\nfrustrated it: if we cannot, the theory is imperfect, and not yet to be\nrelied upon. Nor is the verification complete, unless some of the cases in\nwhich 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\nIt needs scarcely be observed, that,\u2014if direct observation and collation\nof instances have furnished us with any empirical laws of the effect,\nwhether true in all observed cases or only true for the most part,\u2014the\nmost effectual verification of which the theory could be susceptible would\nbe, that it led deductively to those empirical laws; that the\nuniformities, whether complete or incomplete, which were observed to exist\namong the phenomena, were _accounted for_ by the laws of the causes\u2014were\nsuch as could not _but_ exist if those be really the causes by which the\nphenomena are produced. Thus it was very reasonably deemed an essential\nrequisite of any true theory of the causes of the celestial motions, that\nit should lead by deduction to Kepler\u2019s laws: which, accordingly, the\nNewtonian 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 analyse\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 connexion\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 characterised 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, making\nwith the reaction of the body itself, and the tangential force (as I see\nno objection to calling the force generated by the body\u2019s own motion, and\nacting in the direction of the tangent(89)) only four different agents on\nthe concurrence of which the motions of that body depend; a much smaller\nnumber, no doubt, than that by which any other of the great phenomena of\nnature is determined or modified. Yet how could we ever have ascertained\nthe combination of forces on which the motions of the earth and planets\nare dependent, by merely comparing the orbits, or velocities, of different\nplanets, or the different velocities or positions of the same planet?\nNotwithstanding the regularity which manifests itself in those motions, in\na degree so rare among the effects of a concurrence of causes; although\nthe periodical recurrence of exactly the same effect, affords positive\nproof that all the combinations of causes which occur at all, recur\nperiodically; we should not have known what the causes were, if the\nexistence 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\nanalyse, 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\nCHAPTER XII. OF 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, of which the concurrence 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 and\nholds 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 effects 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 tangential force, which tends to produce an uniform motion in the\ntangent, and the law of the centripetal force, which tends to produce an\naccelerating motion towards 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 language 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 a\nlength as dispenses with the necessity of further insisting on it here.\nThe first mode, then, of the explanation of Laws of Causation, is when the\nlaw of an effect is resolved into the various tendencies of which it is\nthe result, and into 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 immediate link;\na fact caused by the antecedent, and in its turn causing the consequent;\nso that the cause at first assigned is but the remote cause, operating\nthrough the intermediate phenomenon. A seemed the cause of C, but it\nsubsequently appeared that A was only the cause of B, and that it is B\nwhich was the cause of C. For example: mankind were aware that the act of\ntouching an outward object caused a sensation. It was, however, at last\ndiscovered, that after we have touched the object, and before we\nexperience the sensation, some change takes place in a kind of thread\ncalled a nerve, which extends from our outward organs to the brain.\nTouching the object, therefore, is only the remote cause of our sensation;\nthat is, not the cause, properly speaking, but the cause of the cause;\u2014the\nreal cause of the sensation is the change in the state of the nerve.\nFuture experience may not only give us more knowledge than we now have of\nthe particular nature of this change, but may also interpolate another\nlink: between the contact (for example) of the object with our outward\norgans, and the production of the change of state in the nerve, there may\ntake place some electric phenomenon; or some phenomenon of a nature not\nresembling the effects of any known agency. Hitherto, however, no such\nintermediate link has been discovered; and the touch of the object must be\nconsidered, provisionally at least, as the proximate cause of the\naffection of the nerve. The sequence, therefore, of a sensation of touch\non contact with an object, is ascertained not to be an ultimate law; it is\nresolved, as the phrase is, into two other laws,\u2014the law, that contact\nwith an object produces an affection of the nerve; and the law, that an\naffection of the nerve produces 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 colouring 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 colouring 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-fulfilment 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 anything 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 often 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 affect 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 causes 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. It is also manifest that the complex law is liable to\nbe oftener unfulfilled than any one of the simpler laws of which it is the\nresult, since every contingency which defeats any of the laws prevents so\nmuch of the effect as depends on it, and thereby defeats the complex law.\nThe mere rusting, for example, of some small part of a great machine,\noften suffices entirely to prevent the effect which ought to result from\nthe joint action of all the parts. The law of the effect of a combination\nof causes 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 a still stronger 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 demonstrable that the motion produced\nwould be in a circle, or a parabola, or an hyperbola: and it has been\nsurmised that in the case of some comets one of these is really the fact.\nYet the law of the parabolic motion would be resolvable into the very same\nsimple laws into which that of the elliptical motion is revolved, namely,\nthe law of the permanence of rectilineal motion, and the law of\ngravitation. If, therefore, in the course of ages, some circumstance were\nto manifest itself which, without defeating the law of either of those\nforces, should merely alter their proportion to one another, (such as the\nshock of a comet, 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\nheavenly 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 towards 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 towards the earth being ascertained to\nvary as the inverse square of the distance, it was deduced from this, by\ndirect calculation, that if the moon were as near to the earth as\nterrestrial objects are, and the tangential force were suspended, the moon\nwould fall towards the earth through exactly as many feet in a second as\nthose objects do by virtue of their weight. Hence the inference was\nirresistible, that the moon also tends to the earth by virtue of its\nweight: and that the two phenomena, the tendency of the moon to the earth\nand the tendency of terrestrial objects to the earth, being not only\nsimilar in quality, but, when in the same circumstances, identical in\nquantity, are cases of one and the same law of causation. But the tendency\nof the moon to the earth and the tendency of the earth and planets to the\nsun, were already known to be cases of the same law of causation: and thus\nthe law of all these tendencies, and the law of terrestrial gravity, were\nrecognized as identical, or in other words, were subsumed under one\ngeneral law, that of gravitation.\n\nIn a similar manner, the laws of magnetic phenomena have recently been\nsubsumed under known laws of electricity. It is thus that the most general\nlaws of nature are usually arrived at: we mount to them by successive\nsteps. For, to arrive by correct induction at laws which hold under such\nan immense variety of circumstances, laws so general as to be independent\nof any varieties of space or time which we are able to observe, requires\nfor the most part many distinct sets of experiments or observations,\nconducted at different times and by different people. One part of the law\nis first ascertained, afterwards another part: one set of observations\nteaches us that the law holds good under some conditions, another that it\nholds good under other conditions, by combining which observations we find\nthat it holds good under conditions much more general, or even\nuniversally. The general law, in this case, is literally the sum of all\nthe partial ones; it is the recognition of the same sequence in different\nsets of instances; and may, in fact, be regarded as merely one step in the\nprocess of elimination. That tendency of bodies towards one another, which\nwe now call gravity, had at first been observed only on the earth\u2019s\nsurface, where it manifested itself only as a tendency of all bodies\ntowards 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 unfavourable 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 performed\nfrom which it appeared that their laws and those of terrestrial gravity\ncorresponded, those celestial observations became a set of instances which\nexactly eliminated the circumstance of proximity to the earth; and proved\nthat in the original case, that of terrestrial objects, it was not the\nearth, as such, that caused the motion or the pressure, but the\ncircumstance common to that case with the celestial instances, namely, the\npresence 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\ncomparison of 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 extend to, and others besides. In the first two modes they are\nalso 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 is resolved into a tendency of\nall particles of matter towards one another. It must be kept constantly in\nview, 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\ntowards 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 anything more than\nwhat 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\nCHAPTER XIII. MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.\n\n\n\u00a7 1. Some of the most remarkable instances which have occurred since the\ngreat Newtonian generalization, of the explanation of laws of causation\nsubsisting among complex phenomena, by resolving them into simpler and\nmore general laws, are to be found among the speculations of Liebig in\norganic chemistry. These speculations, though they have not yet been\nsufficiently long before the world to entitle us positively to assume that\nno well-grounded objection can be made to any part of them, afford,\nhowever, so admirable an example of the spirit of the Deductive Method,\nthat I may be permitted to present some specimens of them here.\n\nIt had been observed in certain cases, that chemical action is, as it\nwere, contagious; that is to say, a substance which would not of itself\nyield to a particular chemical attraction, (the force of the attraction\nnot being sufficient to overcome cohesion, or to destroy some chemical\ncombination in which the substance was already held), will nevertheless do\nso if placed in contact with some other body which is in the act of\nyielding to the same force. Nitric acid, for example, does not dissolve\npure platinum, which may \u201cbe boiled with this acid without being oxidized\nby it, even when in a state of such fine division that it no longer\nreflects light.\u201d But the same acid easily dissolves silver. Now if an\nalloy of silver and platinum be treated with nitric acid, the acid does\nnot, as might naturally be expected, separate the two metals, dissolving\nthe silver, and leaving the platinum; it dissolves both: the platinum as\nwell as the silver becomes oxidized, and in that state combines with the\nundecomposed portion of the acid. In like manner, \u201ccopper does not\ndecompose water, even when boiled in dilute sulphuric acid; but an alloy\nof copper, zinc, and nickel, dissolves easily in this acid with evolution\nof hydrogen gas.\u201d These phenomena cannot be explained by the laws of what\nis termed chemical affinity. They point to a peculiar law, by which the\noxidation which one body suffers, causes another, in contact with it, to\nsubmit to the same change. And not only chemical composition, but chemical\ndecomposition, is capable of being similarly propagated. The peroxide of\nhydrogen, a compound formed by hydrogen with a greater amount of oxygen\nthan the quantity necessary to form water, is held together by a chemical\nattraction of so weak a nature, that the slightest circumstance is\nsufficient to decompose it; and it even, though very slowly, gives off\noxygen and is reduced to water spontaneously (being, I presume, decomposed\nby the tendency of its oxygen to absorb heat and assume the gaseous\nstate). Now it has been observed, that if this decomposition of the\nperoxide of hydrogen takes place in contact with some metallic oxides, as\nthose of silver, and the peroxides of lead and manganese, it superinduces\na corresponding chemical action upon those substances; they also give\nforth the whole or a portion of their oxygen, and are reduced to the metal\nor to the protoxide; although they do not undergo this change\nspontaneously, and there is no chemical affinity at work to make them do\nso. Other similar phenomena are mentioned by Liebig. \u201cNow no other\nexplanation,\u201d he observes, \u201cof these phenomena can be given, than that a\nbody in the act of combination or decomposition enables another body, with\nwhich it is in contact, to enter into the same state.\u201d\n\nHere, therefore, is a law of nature of great simplicity, but which, owing\nto the extremely special and limited character of the phenomena in which\nalone it can be detected experimentally, (because in them alone its\nresults are not intermixed and blended with those of other laws,) had been\nvery little recognised by chemists, and no one could have ventured, on\nexperimental evidence, to affirm it as a law common to all chemical\naction; owing to the impossibility of a rigorous employment of the Method\nof Difference where the properties of different kinds of substance are\ninvolved, an impossibility which we noticed and characterized in a\nprevious chapter.(90) Now this extremely special and apparently precarious\ngeneralization has, in the hands of Liebig, been converted, by a masterly\nemployment of the Deductive Method, into a law pervading all nature, in\nthe same way as gravitation assumed that character in the hands of Newton;\nand has been found to explain, in the most unexpected manner, numerous\ndetached generalizations of a more limited kind, reducing the phenomena\nconcerned in those generalizations into mere cases of itself.\n\nThe contagious influence of chemical action is not a powerful force, and\nis only capable of overcoming weak affinities: we, may, therefore, expect\nto find it principally exemplified in the decomposition of substances\nwhich are held together by weak chemical forces. Now the force which holds\na compound substance together is generally weaker, the more compound the\nsubstance is; and organic products are the most compound substances known,\nthose which have the most complex atomic constitution. It is, therefore,\nupon such substances that the self-propagating power of chemical action is\nlikely to exert itself in the most marked manner. Accordingly, first, it\nexplains the remarkable laws of fermentation, and some of those of\nputrefaction. \u201cA little leaven,\u201d that is, dough in a certain state of\nchemical action, impresses a similar chemical action upon \u201cthe whole\nlump.\u201d The contact of any decaying substance, occasions the decay of\nmatter previously sound. Again, yeast is a substance actually in a process\nof decomposition from the action of air and water, evolving carbonic acid\ngas. Sugar is a substance which, from the complexity of its composition,\nhas no great energy of coherence in its existing form, and is capable of\nbeing easily converted (by combination with the elements of water) into\ncarbonic acid and alcohol. Now the mere presence of yeast, the mere\nproximity of a substance of which the elements are separating from each\nother, and combining with the elements of water, causes sugar to undergo\nthe same change, giving out carbonic acid gas, and becoming alcohol. It is\nnot the elements contained in the yeast which do this. \u201cAn aqueous\ninfusion of yeast may be mixed with a solution of sugar, and preserved in\nvessels from which the air is excluded, without either experiencing the\nslightest change.\u201d Neither does the insoluble residue of the yeast, after\nbeing treated with water, possess the power of exciting fermentation.\n(Here we have the method of Difference). It is not the yeast itself,\ntherefore; it is the yeast in a state of decomposition. The sugar, which\nwould not decompose and oxidize by the mere presence of oxygen and water,\nis induced to do so when another oxidation is at work in the midst of it.\n\nBy the same principle Liebig is enabled to explain many cases of malaria;\nthe pernicious influence of putrid substances; a variety of poisons;\ncontagious diseases; and other phenomena. Of all substances, those\ncomposing the animal body are the most complex in their composition, and\nare in the least stable condition of union. The blood, in particular, is\nthe most unstable compound known. It is, therefore, not surprising that\ngaseous or other substances, in the act of undergoing the chemical changes\nwhich constitute, for instance, putrefaction, should, when brought into\ncontact with the tissues by respiration or otherwise, and still more when\nintroduced by inoculation into the blood itself, impress upon some of the\nparticles a chemical action similar to its own; which is propagated in\nlike manner to other particles, until the whole system is placed in a\nstate of chemical action more or less inconsistent with the chemical\nconditions of vitality.\n\nOf the three modes in which we observed in the last chapter that the\nresolution of a special law into more general ones may take place, this\nspeculation exemplifies the second. The laws explained are such as this,\nthat yeast puts sugar into a state of fermentation. Between the remote\ncause, the presence of yeast, and the consequent fermentation of the\nsugar, there has been interpolated a proximate cause, the chemical action\nbetween the particles of the yeast and the elements of air and water. The\nspecial law is thus resolved into two others, more general than itself:\nthe first, that yeast is decomposed by the presence of air and water; the\nsecond, that matter undergoing chemical action has a tendency to produce\nsimilar chemical action in other matter in contact with it. But while the\ninvestigation thus aptly exhibits the second mode of the resolution of a\ncomplex law, it no less happily exemplifies the third; the subsumption of\nspecial laws under a more general law, by gathering them up into one more\ncomprehensive expression which includes them all. For the curious fact of\nthe contagious nature of chemical action is only raised into a law of\n_all_ chemical action by these very investigations; just as the Newtonian\nattraction was only recognised as a law of all matter when it was found to\nexplain the phenomena of terrestrial gravity. Previously to Liebig\u2019s\ninvestigations, the property in question had only been observed in a few\nspecial cases of chemical action; but when his deductive reasonings have\nestablished that innumerable effects produced upon weak compounds, by\nsubstances none of whose known peculiarities would account for their\nhaving such a power, might be explained by considering the supposed\nspecial property to exist in all those cases, these numerous\ngeneralizations on separate substances are brought together into one law\nof chemical action in general: the peculiarities of the various substances\nbeing, in fact, eliminated, just as the Newtonian deduction eliminated\nfrom the instances of terrestrial gravity the circumstance of proximity to\nthe earth.\n\n\u00a7 2. Another speculation of the same chemist, which, if it should\nultimately be found to agree with all the facts of the extremely\ncomplicated phenomenon to which it relates, will constitute one of the\nfinest examples of the Deductive Method on record, is his theory of\nrespiration.\n\nThe facts of respiration, or in other words the special laws which it is\nattempted to explain from, and resolve into, more general ones, are, that\nthe blood in passing through the lungs absorbs oxygen and gives out\ncarbonic acid gas, changing thereby its colour from a blackish purple to a\nbrilliant red. The absorption and exhalation are evidently chemical\nphenomena; and the carbon of the carbonic acid must have been derived from\nthe body, that is, must have been absorbed by the blood from the\nsubstances with which it came into contact in its passage through the\norganism. Required to find the intermediate links\u2014the precise nature of\nthe two chemical actions which take place; first, the absorption of the\ncarbon or of the carbonic acid by the blood, in its circulation through\nthe body; next, the excretion of the carbon, or the exchange of the\ncarbonic acid for oxygen, in its passage through the lungs.\n\nDr. Liebig believes himself to have found the solution of this _vexata\nqu\u00e6stio_ in a class of chemical actions in which scarcely any less acute\nand penetrating inquirer would have thought of looking for it.\n\nBlood is composed of two parts, the serum and the globules. The serum\nabsorbs and holds in solution carbonic acid in great quantity, but has no\ntendency either to part with it or to absorb oxygen. The globules,\ntherefore, are concluded to be the portion of the blood which is operative\nin respiration. These globules contain a certain quantity of iron, which\nfrom chemical tests is inferred to be in the state of oxide.\n\nDr. Liebig recognised, in the known chemical properties of the oxides of\niron, laws which, if followed out deductively, would lead to the\nprediction of the precise series of phenomena which respiration exhibits.\n\nThere are two oxides of iron, a protoxide and a peroxide. In the arterial\nblood the iron is in the form of peroxide: in the venous blood we have no\ndirect evidence which of the oxides is present, but the considerations to\nbe presently stated lead to the conclusion that it is the protoxide. As\narterial and venous blood are in a perpetual state of alternate conversion\ninto one another, the question arises, in what circumstances the protoxide\nof iron is capable of being converted into the peroxide, and _vice vers\u00e2_.\nNow the protoxide readily combines with oxygen in the presence of water,\nforming the hydrated peroxide: these conditions it finds in passing\nthrough the lungs; it derives oxygen from the air, and finds water in the\nblood itself. This would already explain one portion of the phenomena of\nrespiration. But the arterial blood, in quitting the lungs, is charged\nwith hydrated peroxide: in what manner is the peroxide brought back to its\nformer state?\n\nThe chemical conditions for the reduction of the hydrated peroxide into\nthe state of protoxide, are precisely those which the blood meets with in\ncirculating through the body; namely, contact with organic compounds.\n\nHydrated peroxide of iron, when treated with organic compounds (where no\nsulphur is present) gives forth oxygen and water, which oxygen, attracting\nthe carbon from the organic substance, becomes carbonic acid; while the\nperoxide, being reduced to the state of protoxide, combines with the\ncarbonic acid, and becomes a carbonate. Now this carbonate needs only come\nagain into contact with oxygen and water to be decomposed; the carbonic\nacid being given off, and the protoxide, by the absorption of oxygen and\nwater, becoming again the hydrated peroxide.\n\nThe mysterious chemical phenomena connected with respiration can now, by a\nbeautiful deductive process, be completely explained. The arterial blood,\ncontaining iron in the form of hydrated peroxide, passes into the\ncapillaries, where it meets with the decaying tissues, receiving also in\nits course certain non-azotised but highly carbonised animal products, in\nparticular the bile. In these it finds the precise conditions required for\ndecomposing the peroxide into oxygen and the protoxide. The oxygen\ncombines with the carbon of the decaying tissues, and forms carbonic acid,\nwhich, though insufficient in amount to neutralize the whole of the\nprotoxide, combines with a portion (one-fourth) of it, and returns in the\nform of a carbonate, along with the other three-fourths of the protoxide,\nthrough the venous system into the lungs. There it again meets with oxygen\nand water: the free protoxide becomes hydrated peroxide: the carbonate of\nprotoxide parts with its carbonic acid, and by absorbing oxygen and water,\nenters also into the state of hydrated peroxide. The heat evolved in the\ntransition from protoxide to peroxide, as well as in the previous\noxidation of the carbon contained in the tissues, is considered by Liebig\nas the cause which sustains the temperature of the body. But into this\nportion of the speculation we need not enter.(91)\n\nThis example displays the second mode of resolving complex laws, by the\ninterpolation of intermediate links in the chain of causation; and some of\nthe steps of the deduction exhibit cases of the first mode, that which\ninfers the joint effect of two or more causes from their separate effects;\nbut to trace out in detail these exemplifications may be left to the\nintelligence of the reader. The third mode is not employed in this\nexample, since the simpler laws into which those of respiration are\nresolved (the laws of the chemical action of the oxides of iron) were laws\nalready known, and do not acquire any additional generality from their\nemployment in the present case.\n\n\u00a7 3. The property which salt possesses of preserving animal substances\nfrom putrefaction is resolved by Liebig into two more general laws, the\nstrong attraction of salt for water, and the necessity of the presence of\nwater as 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 azotised 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 azotised substances, compared with\nthe gradual decay of non-azotised 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\nThe purgative effect of salts with alkaline bases, when administered in\nconcentrated solutions, is explained from the two following principles:\nAnimal tissues (such as the stomach) do _not_ absorb concentrated\nsolutions of alkaline salts; and such solutions _do_ dissolve the solids\ncontained in the intestines. The simpler laws into which the complex law\nis here resolved, are the second of the two foregoing principles combined\nwith a third, namely that the peristaltic contraction acts easily upon\nsubstances in a state of solution. The negative general proposition, that\nanimal substances do not absorb these salts, contributes to the\nexplanation by accounting for the absence of a counteracting cause,\nnamely, absorption by the stomach, which in the case of other substances\npossessed of the requisite chemical properties, interferes to prevent them\nfrom reaching the substances which they are destined to dissolve.\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 with\nelectricity 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 waterfalls will naturally\nbecome electric.\n\nFor a second example; it has recently been found, chiefly by the\nresearches of Professor Graham, that gases have a strong tendency to\npermeate animal membranes, and diffuse themselves through the spaces which\nsuch membranes inclose, notwithstanding the presence of other gases in\nthose spaces. Proceeding from this general law, and reviewing a variety of\ncases in which gases lie contiguous to membranes, we are enabled to\ndemonstrate or to explain the following more special laws: 1st. The human\nor animal body, when surrounded with any gas not already contained within\nthe body, absorbs it rapidly; such, for instance, as the gases of\nputrefying matters: which helps to explain malaria. 2nd. The carbonic acid\ngas of effervescing drinks, evolved in the stomach, permeates its\nmembranes, and rapidly spreads through the system, where, as suggested in\na former note, it probably combines with the iron contained in the blood.\n3rd. Alcohol taken into the stomach passes into vapour and spreads through\nthe system with great rapidity; (which, combined with the high\ncombustibility of alcohol, or in other words its ready combination with\noxygen, may perhaps help to explain the bodily warmth immediately\nconsequent on drinking spirituous liquors.) 4th. In any state of the body\nin which peculiar gases are formed within it, these will rapidly exhale\nthrough all parts of the body; and hence the rapidity with which, in\ncertain states of disease, the surrounding atmosphere becomes tainted.\n5th. The putrefaction of the interior parts of a carcase will proceed as\nrapidly as that of the exterior, from the ready passage outwards of the\ngaseous products. 6th. The exchange of oxygen and carbonic acid in the\nlungs is not prevented, but rather promoted, by the intervention of the\nmembrane of the lungs and the coats of the blood vessels between the blood\nand the air. It is necessary, however, that there should be a substance in\nthe blood with which the oxygen of the air may immediately combine;\notherwise instead of passing into the blood, it would permeate the whole\norganism: and it is necessary that the carbonic acid, as it is formed in\nthe capillaries, should also find a substance in the blood with which it\ncan combine; otherwise it would leave the body at all points, instead of\nbeing discharged through the lungs.\n\n\u00a7 5. The following is a deduction which confirms, by explaining, the old\nbut not undisputed empirical generalization, that soda powders weaken the\nhuman system. These powders, consisting of a mixture of tartaric acid with\nbicarbonate of soda, from which the carbonic acid is set free, must pass\ninto the stomach as tartrate of soda. Now, neutral tartrates, citrates,\nand acetates of the alkalis are found, in their passage through the\nsystem, to be changed into carbonates; and to convert a tartrate into a\ncarbonate requires an additional quantity of oxygen, the abstraction of\nwhich must lessen the oxygen destined for assimilation with the blood, on\nthe quantity of which the vigorous action of the human system partly\ndepends.\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 and\nLiebig. The processes of the medical art are even now mostly empirical:\ntheir efficacy is concluded, in each instance, from a special and most\nprecarious experimental generalization: but as science advances in\ndiscovering the simple laws of chemistry and physiology, progress is made\nin ascertaining the intermediate links in the series of phenomena, and the\nmore general laws on which they depend; and thus, while the old processes\nare either exploded, or their efficacy, in so far as real, explained,\nbetter processes, founded on the knowledge of proximate causes, are\ncontinually suggested and brought into use.(92) Many even of the truths of\ngeometry were generalizations from experience before they were deduced\nfrom first principles. The quadrature of the cycloid is said to have been\nfirst effected by measurement, or rather by weighing a cycloidal card, and\ncomparing its weight with that of a piece of similar card of known\ndimensions.\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:\u2014the 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, that the same elementary law of our mental constitution,\nsuitably followed out, would explain a variety of mental phenomena\nhitherto 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 endeavoured, on another occasion, to pursue farther, and to examine\nhow far it will avail towards explaining the peculiarities of the poetical\ntemperament. It is at least an example which may serve, instead of many\nothers, 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 I have exemplified the discovery and\nexplanation of special laws of phenomena by deduction from simpler and\nmore general ones, 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 premisses 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 recognised 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 as the law of gravitation appeared to the cotemporaries of\nNewton; possibly even more so, since Newton\u2019s law, after all, was but an\nextension of the law of weight\u2014that is, of a generalization familiar from\nof old, and which already comprehended a not inconsiderable body of\nnatural phenomena. The general laws, of a similarly commanding character,\nwhich we still look forward to the discovery of, may not always find so\nmuch 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 premisses for the purpose of deducing from\nthem the known laws of concrete phenomena. But this, though their initial,\ncannot 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, premisses 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\nEND OF VOL. I.\n\n\n\n\n\nBOOKS PUBLISHED BY\n\nJohn W. Parker, West Strand, London.\n\nMr. J. S. Mill\u2019s Principles of Political Economy. Second Edition. 2 vols.\nOctavo. 30_s._\n\nMr. J. S. Mill\u2019s Essays on some Unsettled Questions of Political Economy.\nOctavo. 6_s._ 6_d._\n\nArchbishop Whately\u2019s Introductory Lectures on Political Economy. Third\nEdition. Octavo, 8_s._\n\nMr. Cornewall Lewis on the Influence of Authority in Matters of Opinion.\nOctavo, 10_s._ 6_d._\n\nMr. E. G. Wakefield\u2019s View of the Art of Colonization. Octavo, 12_s._\n\nThe Evils of England, Social and Economical. 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If I have imputed\n      that opinion to him erroneously, I am glad to find myself mistaken;\n      but he has not altered the passages in which the opinion appeared to\n      me to be conveyed, and which I still think inconsistent with the\n      belief that Induction can be reduced to strict rules.\n\n    2 Archbishop Whately.\n\n    3 This important theory has recently 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_.) It may be necessary to add, that some other\n      processes of comparison than those described in the text (but\n      equally the result of experience), appear occasionally to enter into\n      our judgment of distances by the eye.\n\n_    4 Computation or Logic_, chap. ii.\n\n    5 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    6 It would, perhaps, be more correct to say that inflected cases are\n      names and something more; and that this addition prevents them from\n      being used as the subjects of propositions. But the purposes of our\n      inquiry do not demand that we should enter with scrupulous accuracy\n      into similar minuti\u00e6.\n\n_    7 Notare_ to mark; _con_notare, to mark _along with_; to mark one\n      thing _with_ or _in addition to_ another.\n\n    8 Archbishop Whately, who in the more recent editions of his _Elements\n      of Logic_ has aided in reviving the important distinction treated of\n      in the text, proposes the term \u201cAttributive\u201d as a substitute for\n      \u201cConnotative,\u201d (p. 122, 9th ed.) The expression is, in itself,\n      appropriate; but, as it has not the advantage of being connected\n      with any verb, of so markedly distinctive a character as \u201cto\n      connote,\u201d it is not, I think, fitted to supply the place of the word\n      Connotative in scientific use.\n\n    9 It would be well if this degeneracy of language took place only in\n      the hands of the untaught vulgar; but some of the most remarkable\n      instances are to be found in terms of art, and among technically\n      educated persons, such as English lawyers. _Felony_, for example, is\n      a law term, with the sound of which all are familiar; but there is\n      no lawyer who would undertake to tell what a felony is, otherwise\n      than by enumerating the various offences which are so called.\n      Originally the word felony had a meaning; it denoted all offences,\n      the penalty of which included forfeiture of lands or goods; but\n      subsequent acts of parliament have declared various offences to be\n      felonies without enjoining that penalty, and have taken away the\n      penalty from others which continue nevertheless to be called\n      felonies, insomuch that the acts so called have now no property\n      whatever in common, save that of being unlawful and punishable.\n\n   10 Before quitting the subject of connotative names, it is proper to\n      observe, that the first writer who, in our own times, has adopted\n      from the schoolmen the word _to connote_, Mr. Mill, in his _Analysis\n      of the Phenomena of the Human Mind_, employs it in a signification\n      different from that in which it is here used. He uses the word in a\n      sense coextensive with its etymology, applying it to every case in\n      which a name, while pointing directly to one thing, (which is\n      consequently termed its signification,) includes also a tacit\n      reference to some other thing. In the case considered in the text,\n      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_.\n      And the schoolmen, to whom we are indebted for the greater part of\n      our logical language, gave us this also, and in this very sense. For\n      although some of their general expressions countenance the use of\n      the 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 fulfil 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, &c. 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   11 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_   12 Philosophy of the Inductive Sciences_, vol. i. p. 40.\n\n   13 This doctrine is laid down in the clearest and strongest terms by M.\n      Cousin, whose observations on the subject are the more worthy of\n      attention, as, in consequence of the ultra-German and ontological\n      character of his philosophy considered generally, they may be\n      regarded as the admissions of an opponent.\n\n      \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 quelles 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 resembleraient \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 la 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 independamment\n      d\u2019un sujet quelconque, et que quand on demande si les propri\u00e9t\u00e9s de\n      la mati\u00e8re 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   14 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 cannot possibly be copies of any impression upon the senses;\n      and they ask, from what sensations our notions of extension and\n      figure have been derived? The gauntlet thrown down by Reid was taken\n      up by Brown, who, applying greater powers of analysis than had\n      previously been applied to the notions of extension and figure,\n      showed clearly what are the sensations from which those notions are\n      derived, viz. 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. Whoever wishes to be\n      more particularly acquainted with this excellent specimen of\n      metaphysical analysis, may consult the first volume of Brown\u2019s\n      _Lectures_, or Mill\u2019s _Analysis of the Mind_.\n\n      On this subject also, M. Cousin may be quoted in favour of\n      conclusions rejected by some of the most eminent thinkers of the\n      school to which he belongs. M. Cousin recognises, in opposition to\n      Reid, the essential _subjectivity_ of our conceptions of the primary\n      qualities of matter, as extension, solidity, &c., equally with those\n      of colour, heat, and the remainder of what are called secondary\n      qualities.\u2014_Cours_, ut supra, 9me le\u00e7on.\n\n_   15 Analysis of the Human Mind_, i. 126 et seqq.\n\n   16 Dr. Whewell (_Of Induction_, p. 10) questions this statement, and\n      asks, \u201cAre we to say that a mole cannot dig the ground, except he\n      has an idea of the ground, and of the snout and paws with which he\n      digs it?\u201d I thought it had been evident that I was here speaking of\n      rational digging, and not of digging by instinct.\n\n   17 \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_, ch. iii. sect. 8.\n\n   18 \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 uses 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_, ch. v., sect. 1.\n\n   19 Ch. iii. sect. 3.\n\n   20 Book iv. ch. vii.\n\n   21 \u039a\u03b1\u03b8\u03cc\u03bb\u03bf\u03c5 \u03bc\u1f72\u03bd \u03bf\u1f56\u03bd \u03c0\u1fb1\u03c3\u03b1 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u1f70 \u03c0\u03c1\u03bf\u03b3\u03b9\u03bd\u03bf\u03bc\u03ad\u03bd\u03b7 \u03c4\u03b9\u03bd\u1f76 \u1f11\u03c4\u03b5\u03c1\u03bf\u1fd6\u03bf\u03bd \u03c0\u03bf\u03b9\u03b5\u1fd6; \u1f00\u03bb\u03bb\u1fbd\n      \u03b1\u1f31 \u03bc\u1f72\u03bd \u03ba\u03bf\u03b9\u03bd\u1ff6\u03c2 \u03c4\u03b5 \u03ba\u03b1\u1f76 \u1f30\u03b4\u03af\u03c9\u03c2 (differences in the accidental\n      properties) \u1f00\u03bb\u03bb\u03bf\u1fd6\u03bf\u03bd \u03c0\u03bf\u03b9\u03bf\u1fe6\u03c3\u03b9\u03bd; \u03b1\u1f31 \u03b4\u1f72 \u1f30\u03b4\u03b9\u03b1\u03af\u03c4\u03b1\u03c4\u03b1 (differences in the\n      essential properties) \u1f04\u03bb\u03bb\u03bf\u2014_Isag._ cap. iii.\n\n   22 Few among the great names in mental science have met with a harder\n      measure of justice from the present generation than Locke; the\n      unquestioned founder of the analytic philosophy of mind, but whose\n      doctrines were first caricatured, then, when the reaction arrived,\n      cast off by the prevailing school even with contumely, and who is\n      now regarded by one of the conflicting parties in philosophy as an\n      apostle of heresy and sophistry, while among those who still adhere\n      to the standard which he raised, there has been a disposition in\n      later times to sacrifice his reputation in favour of Hobbes; a great\n      writer, and a great thinker for his time, but inferior to Locke not\n      only in sober judgment but even in profundity and original genius.\n      Locke, the most candid of philosophers, and one whose speculations\n      bear on every subject the strongest marks of having been wrought out\n      from the materials of his own mind, has been mistaken for an\n      unworthy plagiarist, while Hobbes has been extolled as having\n      anticipated many of his leading doctrines. He did anticipate many of\n      them, and the present is an instance in what manner it was generally\n      done. They both rejected the scholastic doctrine of essences; but\n      Locke understood and explained what these supposed essences really\n      were; Hobbes, instead of explaining the distinction between\n      essential and accidental properties, and between essential and\n      accidental propositions, jumped over it, and gave a definition which\n      suits at most only essential propositions, and scarcely those, as\n      the definition of Proposition in general.\n\n   23 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 only\n      one which, as it appears to me, precisely 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   24 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   25 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 anything _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 everything which can\n      be deduced by reasoning from the attributes connoted). Even this, as\n      he adds, is usually called, not a Definition, but a Description; and\n      (as it seems to me) rightly so called. A Description, I conceive,\n      can only be ranked among Definitions, when taken (as in the case of\n      the zoological definition of man) to fulfil the true office of a\n      Definition, by declaring the connotation given to a word in some\n      special use, as a term of science or art; which special connotation\n      of course would _not_ be expressed by the proper definition of the\n      word in its ordinary 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 spirting 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   26 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      premisses, 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 premiss.\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 cannot 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 premisses 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      premiss 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 premiss (A dragon is a\n      serpent) is false. This is exactly what I have myself said of the\n      premiss, considered as a statement of fact: but it is not false as\n      part of the definition of a dragon; and since the premisses, or one\n      of them, _must_ be false, (the conclusion being so,) the real\n      premiss cannot be the definition, which is true, but the statement\n      of fact, which is false.\n\n   27 \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 connexion, upon which, though perhaps unable to\n      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 vain-glory\n      of the mere logician, who, hobbling after him, evinces his own\n      superior wisdom by pausing on its brink, and giving up as desperate\n      his proper business of bridging it over.\u201d\n\n   28 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; No A is B\n      Some A is B; and Some A is not B\n\n   29 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._\n\n      Mr. De Morgan\u2019s \u201cFormal Logic, or the Calculus of Inference,\n      Necessary and Probable,\u201d (a work published since the statement in\n      the text was made,) far exceeds in elaborate minuteness Lambert\u2019s\n      treatise on the syllogism. Mr. De Morgan\u2019s principal object is to\n      bring within strict technical rules the cases in which a conclusion\n      can be drawn from premisses of a form usually classed as particular.\n      He observes, very justly, that from the premisses Most Bs are Cs,\n      most Bs are As, it may be concluded with certainty that some As are\n      Cs, since two portions of the class B, each of them comprising more\n      than half, must necessarily in part consist of the same individuals.\n      Following out this line of thought, it is equally evident that if we\n      knew exactly what proportion the \u201cmost\u201d in each of the premisses\n      bear to the entire class B, we could increase in a corresponding\n      degree the definiteness of the conclusion. Thus if 60 per cent of B\n      are included in C, and 70 per cent in A, 30 per cent at least must\n      be common to both; in other words, the number of As which are Cs,\n      and 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\n      one 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 premisses of this description, Mr. De Morgan establishes\n      universal formul\u00e6 for such inferences; creating for that purpose not\n      only a new technical language, but a formidable array of symbols\n      analogous 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 formulae 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. The \u201cquantification of the predicate,\u201d\n      an invention to which Sir William Hamilton attaches so much\n      importance as to have raised an angry dispute with Mr. De Morgan\n      respecting its authorship, appears to me, I confess, as an accession\n      to the art of Logic, of singularly small value. It is of course\n      true, that \u201cAll men are mortal\u201d is equivalent to \u201cEvery man is\n      _some_ mortal.\u201d But as mankind certainly will not be persuaded to\n      \u201cquantify\u201d their predicates in common discourse, they want a logic\n      which will teach them to reason correctly with propositions in the\n      usual form, by furnishing them with a type of ratiocination to which\n      propositions can be referred, retaining that form. Not to mention\n      that the quantification of the predicate, instead of being a means\n      of bringing out more clearly the meaning of the proposition,\n      actually leads the mind out of the proposition, into another order\n      of ideas. For when we say, All men are mortal, we simply mean to\n      affirm the attribute mortality of all men; without thinking at all\n      of the _class_ mortal in the concrete, or troubling ourselves about\n      whether it contains any other beings or not. It is only for some\n      artificial purpose that we ever look at the proposition in the\n      aspect in which the predicate also is thought of as a class-name,\n      either including the subject only, or the subject and something\n      more.\n\n   30 Supr\u00e0, p. 129.\n\n   31 Logic, p. 239 (9th ed.)\n\n   32 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_   33 Of Induction_, p. 85.\n\n   34 For August 1846.\n\n   35 There is a striking passage in the Metaphysics of Aristotle\n      (commencement of chap. iii.) on the necessity of beginning the study\n      of a subject by a clear perception of its difficulties. \u0395\u03c3\u03c4\u03af \u03c4\u03bf\u1fd6\u03c2\n      \u03b5\u1f50\u03c0\u03bf\u03c1\u1fc6\u03c3\u03b1\u03b9 \u03b2\u03bf\u03c5\u03bb\u03bf\u03bc\u03ad\u03bd\u03bf\u03b9\u03c2 \u03c0\u03c1\u03bf\u1fe6\u03c1\u03b3\u03bf\u03c5 \u03c4\u1f78 \u03b4\u03b9\u03b1\u03c0\u03bf\u03c1\u1fc6\u03c3\u03b1\u03b9 \u03ba\u03b1\u03bb\u1ff6\u03c2. \u1f21 \u03b3\u1f70\u03c1 \u1f55\u03c3\u03c4\u03b5\u03c1\u03bf\u03bd\n      \u03b5\u1f50\u03c0\u03bf\u03c1\u03af\u03b1 \u03bb\u03cd\u03c3\u03b9\u03c2 \u03c4\u03c9\u03bd \u03c0\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03bd \u1f00\u03c0\u03bf\u03c1\u03bf\u03c5\u03bc\u03ad\u03bd\u03c9\u03bd \u1f10\u03c3\u03c4\u03af. \u03bb\u03cd\u03b5\u03b9\u03bd \u03b4\u1fbd \u03bf\u1f50\u03ba \u1f14\u03c3\u03c4\u03b9\u03bd\n      \u1f00\u03b3\u03bd\u03bf\u03bf\u1fe6\u03bd\u03c4\u03b1 \u03c4\u1f78\u03bd \u03b4\u03b5\u03c3\u03bc\u03cc\u03bd: \u1f00\u03bb\u03bb\u1fbd \u1f21 \u03c4\u03b7\u03c2 \u03b4\u03b9\u03b1\u03bd\u03bf\u03af\u03b1\u03c2 \u1f00\u03c0\u03bf\u03c1\u03af\u03b1 \u03b4\u03b7\u03bb\u03bf\u1fd6 \u03c4\u03bf\u1fe6\u03c4\u03bf \u03c0\u03b5\u03c1\u1f76\n      \u03c4\u03bf\u1fe6 \u03c0\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03bf\u03c2 ... \u03b4\u03b9\u1f78 \u03b4\u03b5\u1fd6 \u03c4\u1f70\u03c2 \u03b4\u03c5\u03c3\u03c7\u03b5\u03c1\u03b5\u03af\u03b1\u03c2 \u03c4\u03b5\u03bb\u03b5\u03c9\u03c1\u03b7\u03ba\u03ad\u03bd\u03b1\u03b9 \u03c0\u03ac\u03c3\u03b1\u03c2\n      \u03c0\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf\u03bd, \u03c4\u03bf\u03cd\u03c4\u03c9\u03bd \u03c4\u03b5 \u03c7\u03ac\u03c1\u03b9\u03bd \u03ba\u03b1\u1f76 \u03b4\u03b9\u1f70 \u03c4\u1f78 \u03c4\u03bf\u1f7a\u03c2 \u03b6\u03b7\u03c4\u03bf\u1fe6\u03bd\u03c4\u03b1\u03c2 \u1f04\u03bd\u03b5\u03c5 \u03c4\u03bf\u1fe6\n      \u03b4\u03b9\u03b1\u03c0\u03bf\u03c1\u1fc6\u03c3\u03b1\u03b9 \u03c0\u03c1\u1ff6\u03c4\u03bf\u03bd, \u1f41\u03bc\u03bf\u03af\u03bf\u03c5\u03c2 \u03b5\u1f30\u03bd\u03b1\u1f76 \u03c4\u03bf\u1fd6\u03c2 \u03c0\u03bf\u1fd6 \u03b4\u03b5\u03b9 \u03b2\u03b1\u03b4\u03af\u03b6\u03b5\u03b9\u03bd \u1f00\u03b3\u03bd\u03bf\u03bf\u1fe6\u03c3\u03b9: \u03ba\u03b1\u1f76\n      \u03c0\u03c1\u1f78\u03c2 \u03c4\u03bf\u03cd\u03c4\u03bf\u03b9\u03c2, \u03bf\u1f50\u03b4\u1fbd \u1f10\u03af \u03c0\u03bf\u03c4\u03b5 \u03c4\u1f78 \u03b6\u03b7\u03c4\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf\u03bd \u03b5\u1f55\u03c1\u03b7\u03ba\u03b5\u03bd \u1f23 \u03bc\u1f74, \u03b3\u03b5\u03bd\u03ce\u03c3\u03ba\u03b5\u03b9\u03bd. \u03c4\u1f78\n      \u03b3\u1f70\u03c1 \u03c4\u03ad\u03bb\u03bf\u03c2 \u03c4\u03bf\u03cd\u03c4\u1ff3 \u03bc\u1f72\u03bd \u03bf\u1f50 \u03b4\u1fc6\u03bb\u03bf\u03bd, \u03c4\u1ff3 \u03b4\u1f72 \u03ba\u03b1\u03bb\u1ff6\u03c2 \u03c0\u03c1\u03bf\u03b7\u03c0\u03bf\u03c1\u03ba\u03cc\u03c4\u03b9 \u03b4\u1fc6\u03bb\u03bf\u03bd.\n\n   36 The reviewer misunderstands me when he supposes me to say that \u201cthe\n      conclusion must be admitted _before_ we can admit the major\n      premiss.\u201d What I say is, that there must be ground for admitting it\n      _simultaneously_, or else the major premise is not proved.\n\n_   37 Mechanical Euclid_, pp. 149 _et seqq._\n\n   38 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\n      any straight line which intersects one of them shall, if prolonged,\n      meet 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 other\n      than those which are parallel according to the definition, had the\n      property of never meeting although indefinitely produced, the\n      demonstrations of the subsequent portions of the theory of parallels\n      could not be maintained.\n\n   39 Whewell\u2019s _Philosophy of the Inductive Sciences_, i. 130.\n\n   40 Dr. Whewell (_Of Induction_ p. 84) thinks it unreasonable to contend\n      that we know by experience, that our idea of a line exactly\n      resembles a real line. \u201cIt does not appear,\u201d he says, \u201chow we can\n      compare our ideas with the realities, since we know the realities\n      only by our ideas.\u201d We know the realities (I conceive) by our eyes.\n      Dr. Whewell surely does not hold the \u201cdoctrine of perception by\n      means of ideas,\u201d which Reid gave himself so much trouble to refute.\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 colour or an odour with the\n      same distinctness and accuracy with which almost every one can\n      mentally reproduce an image of a straight line or a triangle. To the\n      extent, however, of their capabilities of accuracy, our\n      recollections of colours or of odours may serve as subjects of\n      experimentation, as well as those of lines and spaces, and may yield\n      conclusions which will be true of their external prototypes. A\n      person in whom, either from natural gift or from cultivation, the\n      impressions of colour were peculiarly vivid and distinct, if asked\n      which of two blue flowers was of the darkest tinge, though he might\n      never have compared the two, or even looked at them together, might\n      be able to give a confident answer on the faith of his distinct\n      recollection of the colours; that is, he might examine his mental\n      pictures, and find there a property of the outward objects. But in\n      hardly any case except that of simple geometrical forms, could this\n      be done by mankind generally, with a degree of assurance equal to\n      that which is given by a contemplation of the objects themselves.\n      Persons differ most widely in the precision of their recollection,\n      even of forms: one person, when he has looked any one in the face\n      for half a minute, can draw an accurate likeness of him from memory;\n      another may have seen him every day for six months, and hardly know\n      whether his nose is long or short. But everybody has a perfectly\n      distinct mental image of a straight line, a circle, or a rectangle.\n      And every one concludes confidently from these mental images to the\n      corresponding outward things.\n\n_   41 Phil. Ind. Sc._ i. 59-61.\n\n   42 Ibid. 57.\n\n   43 Ibid. 54, 55.\n\n   44 \u201cIf all mankind had spoken one language, we cannot doubt that there\n      would have been a powerful, perhaps a universal, school of\n      philosophers, who would have believed in the inherent connexion\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, &c.\u201d De Morgan, _Formal\n      Logic_, p. 246.\n\n   45 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:\u2014\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 Dieu 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 quil m\u00eet un ange \u00e0 ses trousses, ou enfin il faudrait\n      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_   46 Phil. Ind. Sc._ ii. 174.\n\n_   47 Phil. Ind. Sc._ i., 238.\n\n_   48 Phil. Ind. Sc._ i. 237.\n\n_   49 Ibid._ 213.\n\n_   50 Ibid._ 384, 385.\n\n   51 In his recent pamphlet (p. 81), Dr. Whewell greatly attenuates the\n      opinion here quoted, reducing it to a surmise \u201cthat if we could\n      conceive the composition of bodies distinctly, we might be able to\n      see that it is necessary that the modes of their composition should\n      be definite.\u201d The passage in the text asserts that we already see,\n      or may and ought to see, this necessity; giving as the reason, that\n      no other mode of combination is conceivable. That Dr. Whewell should\n      ever have made this statement, is enough for the purposes of my\n      illustration. To what he now says I have nothing to object.\n      Undoubtedly, if we understood the ultimate molecular composition of\n      bodies, we might find that their combining with one another in\n      definite proportions is, in the present order of nature, a\n      _necessary consequence_ of that molecular composition; and has thus\n      the only kind of necessity of which, in my view of the subject, any\n      law of nature is susceptible. But in that case, the doctrine would\n      be taken out of the class of axioms altogether. It would be no\n      longer an ultimate principle, but a mere derivative law; regarded as\n      necessary, not because self-evident, but because demonstrable.\n\n   52 The _Quarterly Review_ for June 1841, contains an article of great\n      ability on Dr. Whewell\u2019s two great works, the writer of which\n      maintains, on the subject of axioms, the doctrine advanced in the\n      text, that they are generalizations from experience, and supports\n      that opinion by a line of argument strikingly coinciding with mine.\n      When I state that the whole of the present chapter was written\n      before I had seen the article, (the greater part, indeed, before it\n      was published,) it is not my object to occupy the reader\u2019s attention\n      with a matter so unimportant as the degree of originality which may\n      or may not belong to any portion of my own speculations, but to\n      obtain for an opinion which is opposed to reigning doctrines, the\n      recommendation derived from a striking concurrence of sentiment\n      between two inquirers entirely independent of one another. I embrace\n      the opportunity of citing from a writer of the extensive\n      acquirements in physical and metaphysical knowledge and the capacity\n      of systematic thought which the article evinces, passages so\n      remarkably in unison with my own views as the following:\u2014\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 cannot\n      inclose a space, and that two straight lines which cut one another\n      cannot 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 cannot 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 cannot 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 cannot 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:\u2014\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 _\u00e0 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, coextensive at least with all human experience. That\n      they pervade all the objects of experience, must ensure their\n      continual suggestion _by_ experience; that they are true, must\n      ensure 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 cannot, therefore, but be present to our minds whenever\n      that object is contemplated, and must therefore make a part of the\n      mental picture or idea of that object which we may on any occasion\n      summon before our imagination.... All propositions, therefore,\n      become not only untrue but inconceivable_, if ... axioms be violated\n      in their enunciation.\u201d\n\n      Another high authority (if indeed it be another authority) may be\n      cited in favour of the doctrine that axioms rest on the evidence of\n      induction. \u201cThe axioms of geometry themselves may be regarded as in\n      some sort an appeal to experience, not corporeal, but mental. When\n      we say, the whole is greater than its part, we announce a general\n      fact, which rests, it is true, on our ideas of whole and part; but,\n      in abstracting these notions, we begin by considering them as\n      subsisting in space, and time, and body, and again, in linear, and\n      superficial, and solid space. Again, when we say, the equals of\n      equals are equal, we mentally make comparisons, in equal spaces,\n      equal times, &c., so that these axioms, however self-evident, are\n      still general propositions so far of the inductive kind, that,\n      independently of experience, they would not present themselves to\n      the mind. The only difference between these and axioms obtained from\n      extensive induction is this, that, in raising the axioms of\n      geometry, the instances offer themselves spontaneously, and without\n      the trouble of search, and are few and simple; in raising those of\n      nature, they are infinitely numerous, complicated, and remote, so\n      that the most diligent research and the utmost acuteness are\n      required to unravel their web and place their meaning in\n      evidence.\u201d\u2014SIR J. HERSCHEL\u2019s _Discourse on the Study of Natural\n      Philosophy_, pp. 95, 96.\n\n   53 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 (in p. 15 of his pamphlet) \u201cis not the same thing\n      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. 8) 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 endeavoured to shew 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   54 Supr\u00e0, p. 214.\n\n_   55 Phil. Ind. Sc._ ii. 213, 214.\n\n_   56 Ibid._\n\n_   57 Phil. Ind. Sc._ ii. p. 173.\n\n_   58 Cours de Philosophie Positive_, vol. ii, p. 202.\n\n   59 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 (p. 25):\n      \u201cUndoubtedly all these explanations may be true and consistent with\n      each other, and would be so if each had been followed out so as to\n      shew in what manner it could be made consistent with the facts. And\n      this was, in reality, in a great measure done. The doctrine that the\n      heavenly bodies were moved by vortices was successively modified, so\n      that it came to coincide in its results with the doctrine of an\n      inverse-quadratic centripetal force.... When this point was reached,\n      the vortex was merely a machinery, well or ill devised, for\n      producing such a centripetal force, and therefore did not contradict\n      the doctrine of a centripetal force. Newton himself does not appear\n      to have been averse to explaining gravity by impulse. So little is\n      it true that if one theory be true the other must be false. The\n      attempt to explain gravity by the impulse of streams of particles\n      flowing through the universe in all directions, which I have\n      mentioned in the _Philosophy_, is so far from being inconsistent\n      with the Newtonian theory, that it is founded entirely upon it. And\n      even with regard to the doctrine, that the heavenly bodies move by\n      an inherent virtue; if this doctrine had been maintained in any such\n      way that it was brought to agree with the facts, the inherent virtue\n      must have had its laws determined; and then it would have been found\n      that the virtue had a reference to the central body; and so, the\n      \u2018inherent virtue\u2019 must have coincided in its effect with the\n      Newtonian force; and then, the two explanations would agree, except\n      so far as the word \u2018inherent\u2019 was concerned. And if such a part of\n      an earlier theory as this word _inherent_ indicates, is found to be\n      untenable, it is of course rejected in the transition to later and\n      more exact theories, in Inductions of this kind, as well as in what\n      Mr. Mill 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 reconcileable 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\u2019 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; a kind of\n      motion which the vortices did not, and as it was rectilineal, could\n      not, explain. The one explanation, therefore, absolutely excludes\n      the other. Either the planets are not moved by vortices, or they do\n      not move by the law by which heavy bodies fall. It is impossible\n      that both opinions can be true. As well might it be said that there\n      is no contradiction between the assertions, that a man died because\n      somebody killed him, and that he 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 by \u201ca\n      virtue,\u201d _i.e._ by a power of some sort.\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      reconcileable; 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 cannot both be true,\n      still less, surely, can different predictions. Dr. Whewell quarrels\n      (on what ground it is not necessary to consider) with the example I\n      had chosen on this point, and thinks an objection to an illustration\n      a sufficient answer to a theory. Examples not liable to his\n      objection are easily found, if the proposition that conflicting\n      predictions cannot both be true, can be made clearer by any\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_   60 Of Induction_, p. 33.\n\n   61 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 said to be\n      known that _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   62 Infra, chap. xxi.\n\n   63 Infra, chap. xxi, xxii.\n\n   64 Dr. Whewell (_Of Induction_, p. 16) will not allow these and similar\n      erroneous opinions to be called inductions; inasmuch as such\n      superstitious fancies \u201cwere not collected from the facts by seeking\n      a law of their occurrence, but were suggested by an imagination of\n      the anger of superior powers, shown by such deviations from the\n      ordinary course of nature.\u201d I conceive the question to be, not in\n      what manner these notions were at first suggested, but by what\n      evidence they have, from time to time, been supposed to be\n      substantiated. If the believers in these erroneous opinions had been\n      put on their defence, they would have referred to experience; to the\n      comet which preceded the assassination of Julius C\u00e6sar, or to\n      oracles and other prophecies known to have been fulfilled. It is by\n      such appeals to facts that all analogous superstitions, even in our\n      day, attempt to justify themselves; the supposed evidence of\n      experience is what really gives them their hold on the mind. I quite\n      admit that the influence of such coincidences would not be what it\n      is, if strength were not lent to it by an antecedent presumption;\n      but this is not peculiar to such cases; preconceived notions of\n      probability form part of the explanation of many other cases of\n      belief on insufficient evidence. The _\u00e0 priori_ prejudice does not\n      prevent the erroneous opinion from being sincerely regarded as a\n      legitimate conclusion from experience; but is, on the contrary, the\n      very thing which predisposes the mind to that interpretation of\n      experience.\n\n      Thus much in defence 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   65 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, (_Prospective Review_ for February 1850,) who\n      maintains that \u201cwe always apply the word cause rather to that\n      element in the antecedents which exercises _force_, and which would\n      _tend_ at all times to produce the same or a similar effect to that\n      which, under certain conditions, it would actually produce.\u201d And he\n      says, that \u201cevery one would feel\u201d the expression, that the cause of\n      a surprise was the sentinel\u2019s being off his post, to be incorrect;\n      but that \u201cthe allurement or force which _drew_ him off his post,\n      might be so called, because in doing so it removed a resisting power\n      which would have prevented the surprise.\u201d I cannot think that it\n      would be wrong to say, that the event took place because the\n      sentinel was absent, and yet right to say that it took place because\n      he was bribed to be absent. Since the only direct effect of the\n      bribe was his absence, the bribe could be called the remote cause of\n      the surprise, only on the supposition that the absence was the\n      proximate cause; nor does it seem to me that any one, who had not a\n      theory to support, would use the one expression and reject the\n      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\n      weight\u2014for his weight, and not the motion of his foot, was the\n      active force which determined his fall. If a person walking out in a\n      frosty day, stumbled and fell, it might be said that he stumbled\n      because the ground was slippery, or because he was not sufficiently\n      careful; but few people, I suppose, would say that he stumbled\n      because he walked. Yet the only active force concerned was that\n      which he exerted in walking: the others were mere negative\n      conditions; but they happened to be the only ones which there could\n      be any necessity to state; for he walked, most likely, in exactly\n      his usual manner, and the negative conditions made all the\n      difference. Again, if a person were asked why the army of Xerxes\n      defeated that of Leonidas, he would probably say, because they were\n      a thousand times the number; but I do not think he would say, it was\n      because they fought; although that was the element of active force.\n      The reviewer adds, \u201cthere are some conditions absolutely passive,\n      and yet absolutely necessary to physical phenomena, viz., the\n      relations of space and time; and to these no one ever applies the\n      word cause without being immediately arrested by those who hear\n      him.\u201d Even from this statement I am compelled to dissent. Few\n      persons would feel it incongruous to say (for example) that a secret\n      became known because it was spoken of when A. B. was within hearing;\n      which is a condition of space; or that the cause why one of two\n      particular trees is taller than the other, is that it has been\n      longer planted; which is a condition of time.\n\n   66 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, since we should still have to enumerate specially the\n      negative conditions of each phenomenon, instead of regarding them as\n      implicitly contained in the positive laws of the various other\n      agencies in nature.\n\n   67 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   68 The reviewer of Dr. Whewell in the _Quarterly Review_.\n\n   69 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. ch. 2).\n      In the meantime I may remark that these metaphysicians, who, it must\n      be observed, ground the main part of their objection on the supposed\n      repugnance of the doctrine in question to our consciousness, seem to\n      me to mistake the fact which consciousness testifies against. What\n      is really in contradiction to consciousness, they would, I think, on\n      strict self-examination, find to be, the application to human\n      actions and volitions of the ideas involved in the common use of the\n      term Necessity; which I agree with them in objecting to. But if they\n      would consider that by saying that a person\u2019s actions _necessarily_\n      follow from his character, all that is really meant (for no more is\n      meant in any case whatever of causation) is that he invariably\n      _does_ act in conformity to his character, and that any one who\n      thoroughly knew his character could certainly predict how he would\n      act in any supposable case; they probably would not find this\n      doctrine either contrary to their experience or revolting to their\n      feelings. And no more than this is contended for by any one but an\n      Asiatic fatalist.\n\n   70 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 _\u00e0 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 cannot _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 anything _more_ than\n      antecedence and consequence.\n\n   71 Reid\u2019s _Essays on the Active Powers_, Essay iv. ch. 3.\n\n_   72 Prospective Review_ for February 1850.\n\n_   73 Vide supra_, p. 267, note.\n\n   74 In combating the theory, that Volition is the universal cause, I\n      have purposely abstained from one of the strongest positive\n      arguments against it\u2014that volitions themselves obey causes, and even\n      external causes, namely, the inducements, or motives, which\n      determine the will to act; because an objector might say that to\n      employ this argument would be begging the question against the\n      freedom of the will. Though it is not begging the question to affirm\n      a doctrine, referring elsewhere for the proof of it, I am unwilling\n      without necessity to build any part of my reasoning on a proposition\n      which I am aware that those opposed to me in the present discussion\n      do not admit.\n\n   75 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.\n\n   76 Unless, indeed, the consequent was generated not by the antecedent,\n      but by the means we 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_   77 Discourse on the Study of Natural Philosophy_, p. 179.\n\n   78 For this speculation I am indebted to Mr. Alexander Bain.\n\n   79 This view of the necessary coexistence 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   80 Pp. 159-162.\n\n   81 Infra, book iv., chap. ii. On Abstraction.\n\n   82 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 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 analyse, and can form\n      therefore no sufficient judgment what portion of the effects may be\n      due, not to the supposed cause, but to some unknown agency of the\n      means by which that cause was produced. In the natural experiment\n      which we are speaking of, the means used was the clearing off a\n      canopy of clouds; and we certainly do not know sufficiently in what\n      this process consists, or on what it depends, to be certain _\u00e0\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 favourable 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   83 Discourse, pp. 156-8, and 171.\n\n_   84 Outlines of Astronomy_, p. 584.\n\n   85 Dr. Whewell, in his reply, expresses a very unfavourable opinion of\n      the utility of the Four Methods, as well as of the aptness of the\n      examples by which I have attempted to illustrate them. His words are\n      these (pp. 44-6):\n\n      \u201cUpon these methods, the obvious thing to remark is, that they take\n      for granted the very thing which is most difficult to discover, the\n      reduction of the phenomena to formul\u00e6 such as are here presented to\n      us. When we have any set of complex facts offered to us; for\n      instance, those which were offered in the cases of discovery which I\n      have mentioned,\u2014the facts of the planetary paths, of falling bodies,\n      of refracted rays, of cosmical motions, of chemical analysis; and\n      when, in any of these cases, we would discover the law of nature\n      which governs them, or, if any one chooses so to term it, the\n      feature in which all the cases agree, where are we to look for our\n      A, B, C, and _a, b, c_? Nature does not present to us the cases in\n      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\n      _a b d_, then we may draw our inference. Granted; but when and where\n      are we to find such combinations? Even now that the discoveries are\n      made, who will point out to us what are the A, B, C, and _a, b, c_\n      elements of the cases which have just been enumerated? Who will tell\n      us which of the methods of inquiry those historically real and\n      successful inquiries exemplify? Who will carry these formul\u00e6 through\n      the history of the sciences, as they have really grown up; and shew\n      us that these four methods have been operative in their formation;\n      or that any light is thrown upon the steps of their progress by\n      reference to these formul\u00e6?\u201d\n\n      He adds that, in this work, the methods have not been applied \u201cto a\n      large body of conspicuous and undoubted examples of discovery,\n      extending along the whole history of science,\u201d which ought to have\n      been done in order that the methods might be shown to possess the\n      \u201cadvantage\u201d (which he claims as belonging to his own) of being those\n      \u201cby which all great discoveries in science have really been\n      made.\u201d\u2014(p. 66.)\n\n      There is a striking similarity between the objections here made\n      against Canons of Induction, and what was alleged, in the last\n      century, by as able men as Dr. Whewell, against the acknowledged\n      Canon of Ratiocination. Those who protested against the Aristotelian\n      Logic said of the Syllogism, what Dr. Whewell says of the Inductive\n      Methods, that it \u201ctakes for granted the very thing which is most\n      difficult to discover, the reduction of the argument to formul\u00e6 such\n      as are here presented to us.\u201d The grand difficulty, they said, is to\n      obtain your syllogism, not to judge of its correctness when\n      obtained. On the matter of fact, both they and Dr. Whewell are\n      right. The greatest difficulty in both cases is first that of\n      obtaining the evidence, and next, of reducing it to the form which\n      tests its conclusiveness. But if we try so to reduce it without\n      knowing _to what_, we are not likely to make much progress. It is a\n      more difficult thing to solve a geometrical problem, than to judge\n      whether a proposed solution is correct: but if people were not able\n      to judge of the solution when found, they would have little chance\n      of finding it. And it cannot be pretended that to judge of an\n      induction when found, is perfectly easy, is a thing for which aids\n      and instruments are superfluous; for erroneous inductions, false\n      inferences from experience, are quite as common, on some subjects\n      much commoner, than true ones. The business of Inductive Logic is to\n      provide rules and models (such as the Syllogism and its rules are\n      for ratiocination) to which if inductive arguments conform, those\n      arguments are conclusive, and not otherwise. This is what the Four\n      Methods profess to be, and what I believe they are universally\n      considered to be by experimental philosophers, who had practised all\n      of them long before any one sought to reduce the practice to theory.\n\n      The assailants of the Syllogism had also anticipated Dr. Whewell in\n      the other branch of his argument. They said that no discoveries were\n      ever made by syllogism; and Dr. Whewell says, or seems to say, that\n      none were ever made by the four Methods of Induction. To the former\n      objectors, Archbishop Whately very pertinently answered, that their\n      argument, if good at all, was good against the reasoning process\n      altogether; for whatever cannot be reduced to syllogism, is not\n      reasoning. And Dr. Whewell\u2019s argument, if good at all, is good\n      against all inferences from experience. In saying that no\n      discoveries were ever made by the four Methods, he affirms that none\n      were ever made by observation and experiment; for assuredly if any\n      were, it was by one or other of those methods.\n\n      This difference between us accounts for the dissatisfaction which my\n      examples give him; for I did not select them with a view to satisfy\n      any one who required to be convinced that observation and experiment\n      are modes of acquiring knowledge: I confess that in the choice of\n      them I thought only of illustration, and of facilitating the\n      _conception_ of the Methods by concrete instances. If it had been my\n      object to justify the processes themselves as means of\n      investigation, there would have been no need to look far off, or\n      make use of recondite or complicated instances. As a specimen of a\n      truth ascertained by the Method of Agreement, I might have chosen\n      the proposition, \u201cDogs bark.\u201d This dog, and that dog, and the other\n      dog, answer to A B C, A D E, A F G. The circumstance of being a dog,\n      answers to A. Barking answers to _a_. As a truth made known by the\n      Method of Difference, \u201cFire burns\u201d might have sufficed. Before I\n      touch the fire I am not burnt; this is B C; I touch it, and am\n      burnt; this is A B C, _a_ B C.\n\n      Such familiar experimental processes are not regarded as inductions\n      by Dr. Whewell; but they are perfectly homogeneous with those by\n      which, even on his own shewing, the pyramid of science is supplied\n      with its base. In vain he attempts to escape from this truth by\n      laying the most arbitrary restrictions on the choice of examples\n      admissible as instances of Induction: they must neither be such as\n      are still matter of discussion (p. 47), nor must any of them be\n      drawn from mental and social subjects (p. 53), nor from ordinary\n      observation and practical life (pp. 11-15). They must be taken\n      exclusively from the generalizations by which scientific thinkers\n      have ascended to great and comprehensive laws of natural phenomena.\n      Now it is seldom possible, in these complicated inquiries, to go\n      much beyond the initial steps, without calling in the instrument of\n      Deduction, and the temporary aid of hypotheses; as I myself, in\n      common with Dr. Whewell, have maintained against the purely\n      empirical school. Since therefore such cases could not conveniently\n      be selected to illustrate the principles of mere observation and\n      experiment, Dr. Whewell takes advantage of their absence to\n      represent the Experimental Methods as serving no purpose in\n      scientific investigation; forgetting that if those methods had not\n      supplied the first generalizations, there would have been no\n      materials for his own conception of Induction to work upon.\n\n      His challenge, however, to point out which of the four methods are\n      exemplified in certain important cases of scientific inquiry, is\n      easily answered. \u201cThe planetary paths,\u201d as far as they are a case of\n      induction at all, (see, on this point, the second chapter of the\n      present Book) fall under the Method of Agreement. The law of\n      \u201cfalling bodies,\u201d namely that they describe spaces proportional to\n      the squares of the times, was historically a deduction from the\n      first law of motion; but the experiments by which it was verified,\n      and by which it might have been discovered, were examples of the\n      Method of Agreement; and the apparent variation from the true law,\n      caused by the resistance of the air, was cleared up by experiments\n      _in vacuo_, constituting an application of the Method of Difference.\n      The law of \u201crefracted rays,\u201d (the constancy of the ratio between the\n      sines of incidence and of refraction for each refracting substance)\n      was ascertained by direct measurement, and therefore by the Method\n      of Agreement. The \u201ccosmical motions\u201d were determined by highly\n      complex processes of thought, in which Deduction was predominant,\n      but the Methods of Agreement and of Concomitant Variations had a\n      large part in establishing the empirical laws. Every case without\n      exception of \u201cchemical analysis\u201d constitutes a well marked example\n      of the Method of Difference. To any one acquainted with the\n      subjects\u2014to Dr. Whewell himself, there would not be the smallest\n      difficulty in setting out \u201cthe A B C and _a b c_ elements\u201d of these\n      cases.\n\n      If discoveries are ever made by observation and experiment without\n      Deduction, the four methods are methods of discovery: but even if\n      they were not methods of discovery, it would not be the less true\n      that they are the sole methods of Proof; and in that character, even\n      the results of Deduction are amenable to them. The great\n      generalizations which begin as Hypotheses must end by being proved,\n      and are in reality (as will be shown hereafter) proved by the Four\n      Methods. Now it is with Proof, as such, that Logic is principally\n      concerned. This distinction has indeed no chance of finding favour\n      with Dr. Whewell; for it is the peculiarity of his system not to\n      recognise, in cases of Induction, any necessity for proof. If, after\n      assuming an hypothesis and carefully collating it with facts,\n      nothing is brought to light inconsistent with it, that is, if\n      experience does not _dis_prove it, he is content: at least until a\n      simpler hypothesis, equally consistent with experience, presents\n      itself. If this be Induction, doubtless there is no necessity for\n      the four methods. But to suppose that it is so, appears to me a\n      radical misconception of the nature of the evidence of physical\n      truths.\n\n_   86 Ante_, p. 378.\n\n   87 It seems hardly necessary to say that the word _impinges_, as a\n      general term to express collision of forces, was here used by a\n      figure of speech, and not as expressive of any theory respecting the\n      nature of force.\n\n_   88 Essays on some Unsettled Questions of Political Economy_, Essay V.\n\n   89 There is no danger of confounding this acceptation of the term with\n      the peculiar employment of the phrase \u201ctangential force\u201d in the\n      theory of the planetary perturbations.\n\n   90 Supr\u00e0, p. 420.\n\n   91 As corroborating the opinion that the protoxide of iron in the\n      venous blood is only partially carbonated, the fact has been\n      suggested, that the system shows great readiness to absorb an extra\n      quantity of carbonic acid, as furnished in effervescing drinks. In\n      such cases the acid must combine with something, and that something\n      is not improbably the free protoxide. It would be worth ascertaining\n      whether the protoxide itself or its carbonate has the greatest\n      facility in absorbing oxygen and turning itself into hydrated\n      peroxide in the lungs. If the carbonate, then the beneficial effect,\n      on the animal economy, of drinks which give an artificial supply of\n      carbonic acid to the system, would be, to that extent, deductively\n      established.\n\n   92 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 tumours 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 tumour, from being nourished; in the case\n      of inflammation, it removes the stimulus, which the organ is unfit\n      to receive: in the case of tumours, by keeping back the nutritive\n      fluid it causes the absorption of matter to exceed the supply, and\n      the diseased mass is gradually absorbed and disappears.","title":"A System of Logic, Ratiocinative and Inductive (Vol. 1 of 2)","tradition":"philosophy-ethics","translated_text":null,"word_count":182819}