{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_35420/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_35420","id":"gutenberg_35420","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/35420","summary":null,"tags":["Category: Language & Communication","Category: Philosophy & Ethics","Knowledge, Theory of","Logic","Philosophy","Science -- Methodology"],"text":"\n\n\n\nProduced by David Clarke, Stephen H. Sentoff and the Online\nDistributed Proofreading Team at https://www.pgdp.net (This\nfile was produced from images generously made available\nby The Internet Archive/Canadian Libraries)\n\n\n\n\n\n\n\nA\nSYSTEM OF LOGIC\n\nRATIOCINATIVE AND INDUCTIVE\n\nVOL. I.\n\n\n\n\nA\nSYSTEM OF LOGIC\n\nRATIOCINATIVE AND INDUCTIVE\n\nBEING A CONNECTED VIEW OF THE\nPRINCIPLES OF EVIDENCE\nAND THE\nMETHODS OF SCIENTIFIC INVESTIGATION\n\nBY\n\nJOHN STUART MILL\n\n\nIN TWO VOLUMES\n\nVOL. I.\n\nSEVENTH EDITION\n\n\nLONDON:\nLONGMANS, GREEN, READER, AND DYER\n\nMDCCCLXVIII\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\nembody and systematize, the best ideas which have been either\npromulgated on its subject by speculative writers, or conformed to by\naccurate thinkers in their scientific inquiries.\n\nTo cement together the detached fragments of a subject, never yet\ntreated as a whole; to harmonize the true portions of discordant\ntheories, by supplying the links of thought necessary to connect them,\nand by disentangling them from the errors with which they are always\nmore or less interwoven; must necessarily require a considerable amount\nof original speculation. To other originality than this, the present\nwork lays no claim. In the existing state of the cultivation of the\nsciences, there would be a very strong presumption against any one who\nshould imagine that he had effected a revolution in the theory of the\ninvestigation of truth, or added any fundamentally new process to the\npractice of it. The improvement which remains to be effected in the\nmethods of philosophizing (and the author believes that they have much\nneed of improvement) can only consist in performing, more systematically\nand accurately, operations with which, at least in their elementary\nform, the human intellect in some one or other of its employments is\nalready 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\nno means participates; though the scientific theory on which its defence\nis usually 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\nas is well grounded in the doctrines and objections of its assailants.\n\nThe same abstinence from details could not be observed in the First\nBook, on Names and Propositions; because many useful principles and\ndistinctions which were contained in the old Logic, have been gradually\nomitted from the writings of its later teachers; and it appeared\ndesirable both to revive these, and to reform and rationalize the\nphilosophical foundation on which they stood. The earlier chapters of\nthis preliminary Book will consequently appear, to some readers,\nneedlessly elementary and scholastic. But those who know in what\ndarkness the nature of our knowledge, and of the processes by which it\nis obtained, is often involved by a confused apprehension of the import\nof the different classes of Words and Assertions, will not regard these\ndiscussions as either frivolous, or irrelevant to the topics considered\nin 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,\nby which so many important and recondite laws of nature have, in the\nvarious sciences, been aggregated to the stock of human knowledge. That\nthis is not a task free from difficulty may be presumed from the fact,\nthat even at a very recent period, eminent writers (among whom it is\nsufficient to name Archbishop Whately, and the author of a celebrated\narticle on Bacon in the _Edinburgh Review_) have not scrupled to\npronounce it impossible.[1] The author has endeavoured to combat their\ntheory in the manner in which Diogenes confuted the sceptical reasonings\nagainst the possibility of motion; remembering that Diogenes' argument\nwould have been equally conclusive, though his individual perambulations\nmight not have extended beyond the circuit of his own tub.\n\nWhatever may be the value of what the author has succeeded in effecting\non this branch of his subject, it is a duty to acknowledge that for much\nof it he has been indebted to several important treatises, partly\nhistorical and partly philosophical, on the generalities and processes\nof physical science, which have been published within the last few\nyears. To these treatises, and to their authors, he has endeavoured to\ndo justice in the body of the work. But as with one of these writers,\nDr. Whewell, he has occasion frequently to express differences of\nopinion, it is more particularly incumbent on him in this place to\ndeclare, that without the aid derived from the facts and ideas contained\nin that gentleman's _History of the Inductive Sciences_, the\ncorresponding portion of this work would probably not have been written.\n\nThe concluding Book is an attempt to contribute towards the solution of\na question, which the decay of old opinions, and the agitation that\ndisturbs European society to its inmost depths, render as important in\nthe present day to the practical interests of human life, as it must at\nall times be to the completeness of our speculative knowledge: viz.\nWhether moral and social phenomena are really exceptions to the general\ncertainty and uniformity of the course of nature; and how far the\nmethods, by which so many of the laws of the physical world have been\nnumbered among truths irrevocably acquired and universally assented to,\ncan be made instrumental to the formation of a similar body of received\ndoctrine in moral and political science.\n\n\n\n\nPREFACE TO THE THIRD AND FOURTH EDITIONS.\n\n\nSeveral criticisms, of a more or less controversial character, on this\nwork, have appeared since the publication of the second edition; and Dr.\nWhewell has lately published a reply to those parts of it in which some\nof his opinions were controverted.[2]\n\nI have carefully reconsidered all the points on which my conclusions\nhave been assailed. But I have not to announce a change of opinion on\nany matter of importance. Such minor oversights as have been detected,\neither by myself or by my critics, I have, in general silently,\ncorrected: but it is not to be inferred that I agree with the objections\nwhich have been made to a passage, in every instance in which I have\naltered or cancelled it. I have often done so, merely that it might not\nremain a stumbling-block, when the amount of discussion necessary to\nplace the matter in its true light would have exceeded what was suitable\nto the occasion.\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\nopinions can make a plausible show of evidence while each has the\nstatement of its own case; and it is only possible to ascertain which of\nthem is in the right, after hearing and comparing what each can say\nagainst the other, and 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 argument strengthened. And I should have been well\npleased if the book had undergone a much greater amount of attack; as in\nthat case I should probably have been enabled to improve it still more\nthan I believe I have now done.\n\n * * * * *\n\nIn the subsequent editions, the attempt to improve the work by additions\nand corrections, suggested by criticism or by thought, has been\ncontinued. In the present (seventh) edition, a few further corrections\nhave been made, but no material additions.\n\nFOOTNOTES:\n\n[1] In the later editions of Archbishop Whately's _Logic_, he states his\nmeaning to be, not that \"rules\" for the ascertainment of truths by\ninductive investigation cannot be laid down, or that they may not be \"of\neminent service,\" but that they \"must always be comparatively vague and\ngeneral, and incapable of being built up into a regular demonstrative\ntheory like that of the Syllogism.\" (Book IV. ch. iv. \u00a7 3.) And he\nobserves, that to devise a system for this purpose, capable of being\n\"brought into a scientific form,\" would be an achievement which \"he must\nbe more sanguine than scientific who expects.\" (Book IV. ch. ii. \u00a7 4.)\nTo effect this, however, being the express object of the portion of the\npresent work which treats of Induction, the words in the text are no\noverstatement of the difference of opinion between Archbishop Whately\nand me on the subject.\n\n[2] Now forming a chapter in his volume on _The Philosophy of\nDiscovery_.\n\n\n\n\nCONTENTS\nOF\nTHE FIRST VOLUME.\n\n\n INTRODUCTION.\n\n\n \u00a7 1. A definition at the commencement of a subject must be\n provisional 1\n\n 2. Is logic the art and science of reasoning? 2\n\n 3. Or the art and science of the pursuit of truth? 3\n\n 4. Logic is concerned with inferences, not with intuitive truths 5\n\n 5. Relation of logic to the other sciences 8\n\n 6. Its utility, how shown 10\n\n 7. Definition of logic stated and illustrated 11\n\n\n BOOK I.\n\n OF NAMES AND PROPOSITIONS.\n\n\n CHAPTER I. _Of the Necessity of commencing with an\n Analysis of Language._\n\n \u00a7 1. Theory of names, why a necessary part of logic 17\n\n 2. First step in the analysis of Propositions 18\n\n 3. Names must be studied before Things 21\n\n\n CHAPTER II. _Of Names._\n\n \u00a7 1. Names are names of things, not of our ideas 23\n\n 2. Words which are not names, but parts of names 24\n\n 3. General and Singular names 26\n\n 4. Concrete and Abstract 29\n\n 5. Connotative and Non-connotative 31\n\n 6. Positive and Negative 42\n\n 7. Relative and Absolute 44\n\n 8. Univocal and \u00c6quivocal 47\n\n\n CHAPTER III. _Of the Things denoted by Names._\n\n \u00a7 1. Necessity of an enumeration of Nameable Things. The\n Categories of Aristotle 49\n\n 2. Ambiguity of the most general names 51\n\n 3. Feelings, or states of consciousness 54\n\n 4. Feelings must be distinguished from their physical\n antecedents. Perceptions, what 56\n\n 5. Volitions, and Actions, what 58\n\n 6. Substance and Attribute 59\n\n 7. Body 61\n\n 8. Mind 67\n\n 9. Qualities 69\n\n 10. Relations 72\n\n 11. Resemblance 74\n\n 12. Quantity 78\n\n 13. All attributes of bodies are grounded on states of\n consciousness 79\n\n 14. So also all attributes of mind 80\n\n 15. Recapitulation 81\n\n\n CHAPTER IV. _Of Propositions._\n\n \u00a7 1. Nature and office of the copula 85\n\n 2. Affirmative and Negative propositions 87\n\n 3. Simple and Complex 89\n\n 4. Universal, Particular, and Singular 93\n\n\n CHAPTER V. _Of the Import of Propositions._\n\n \u00a7 1. Doctrine that a proposition is the expression of a relation\n between two ideas 96\n\n 2. Doctrine that it is the expression of a relation between the\n meanings of two names 99\n\n 3. Doctrine that it consists in referring something to, or\n excluding something from, a class 103\n\n 4. What it really is 107\n\n 5. It asserts (or denies) a sequence, a coexistence, a simple\n existence, a causation 110\n\n 6. --or a resemblance 112\n\n 7. Propositions of which the terms are abstract 115\n\n\n CHAPTER VI. _Of Propositions merely Verbal._\n\n \u00a7 1. Essential and Accidental propositions 119\n\n 2. All essential propositions are identical propositions 120\n\n 3. Individuals have no essences 124\n\n 4. Real propositions, how distinguished from verbal 126\n\n 5. Two modes of representing the import of a Real proposition 127\n\n\n CHAPTER VII. _Of the Nature of Classification, and\n the Five Predicables._\n\n \u00a7 1. Classification, how connected with Naming 129\n\n 2. The Predicables, what 131\n\n 3. Genus and Species 131\n\n 4. Kinds have a real existence in nature 134\n\n 5. Differentia 139\n\n 6. Differenti\u00e6 for general purposes, and differenti\u00e6 for\n special or technical purposes 141\n\n 7. Proprium 144\n\n 8. Accidens 146\n\n\n CHAPTER VIII. _Of Definition._\n\n \u00a7 1. A definition, what 148\n\n 2. Every name can be defined, whose meaning is susceptible\n of analysis 150\n\n 3. Complete, how distinguished from incomplete definitions 152\n\n 4. --and from descriptions 154\n\n 5. What are called definitions of Things, are definitions of\n Names with an implied assumption of the existence of\n Things corresponding to them 157\n\n 6. --even when such things do not in reality exist 165\n\n 7. Definitions, though of names only, must be grounded on\n knowledge of the corresponding Things 167\n\n\n BOOK II.\n\n OF REASONING.\n\n\n CHAPTER I. _Of Inference, or Reasoning, in general._\n\n \u00a7 1. Retrospect of the preceding book 175\n\n 2. Inferences improperly so called 177\n\n 3. Inferences proper, distinguished into inductions and\n ratiocinations 181\n\n\n CHAPTER II. _Of Ratiocination, or Syllogism._\n\n \u00a7 1. Analysis of the Syllogism 184\n\n 2. The _dictum de omni_ not the foundation of reasoning,\n but a mere identical proposition 191\n\n 3. What is the really fundamental axiom of Ratiocination 196\n\n 4. The other form of the axiom 199\n\n\n CHAPTER III. _Of the Functions, and Logical Value, of the\n Syllogism._\n\n \u00a7 1. Is the syllogism a _petitio principii_? 202\n\n 2. Insufficiency of the common theory 203\n\n 3. All inference is from particulars to particulars 205\n\n 4. General propositions are a record of such inferences, and\n the rules of the syllogism are rules for the interpretation\n of the record 214\n\n 5. The syllogism not the type of reasoning, but a test of it 218\n\n 6. The true type, what 222\n\n 7. Relation between Induction and Deduction 226\n\n 8. Objections answered 227\n\n 9. Of Formal Logic, and its relation to the Logic of Truth 231\n\n\n CHAPTER IV. _Of Trains of Reasoning, and Deductive\n Sciences._\n\n \u00a7 1. For what purpose trains of reasoning exist 234\n\n 2. A train of reasoning is a series of inductive inferences 234\n\n 3. --from particulars to particulars through marks of marks 237\n\n 4. Why there are deductive sciences 240\n\n 5. Why other sciences still remain experimental 244\n\n 6. Experimental sciences may become deductive by the progress\n of experiment 246\n\n 7. In what manner this usually takes place 247\n\n\n CHAPTER V. _Of Demonstration, and Necessary Truths._\n\n \u00a7 1. The Theorems of geometry are necessary truths only in\n the sense of necessarily following from hypotheses 251\n\n 2. Those hypotheses are real facts with some of their\n circumstances exaggerated or omitted 255\n\n 3. Some of the first principles of geometry are axioms, and\n these are not hypothetical 256\n\n 4. --but are experimental truths 258\n\n 5. An objection answered 261\n\n 6. Dr. Whewell's opinions on axioms examined 264\n\n\n CHAPTER VI. _The same Subject continued._\n\n \u00a7 1. All deductive sciences are inductive 281\n\n 2. The propositions of the science of number are not verbal,\n but generalizations from experience 284\n\n 3. In what sense hypothetical 289\n\n 4. The characteristic property of demonstrative science is to\n be hypothetical 290\n\n 5. Definition of demonstrative evidence 292\n\n\n CHAPTER VII. _Examination of some Opinions opposed to\n the preceding doctrines._\n\n \u00a7 1. Doctrine of the Universal Postulate 294\n\n 2. The test of inconceivability does not represent the\n aggregate of past experience 296\n\n 3. --nor is implied in every process of thought 299\n\n 4. Sir W. Hamilton's opinion on the Principles of\n Contradiction and Excluded Middle 306\n\n\n BOOK III.\n\n OF INDUCTION.\n\n\n CHAPTER I. _Preliminary Observations on Induction in general._\n\n \u00a7 1. Importance of an Inductive Logic 313\n\n 2. The logic of science is also that of business and life 314\n\n\n CHAPTER II. _Of Inductions improperly so called._\n\n \u00a7 1. Inductions distinguished from verbal transformations 319\n\n 2. --from inductions, falsely so called, in mathematics 321\n\n 3. --and from descriptions 323\n\n 4. Examination of Dr. Whewell's theory of Induction 326\n\n 5. Further illustration of the preceding remarks 336\n\n\n CHAPTER III. _On the Ground of Induction._\n\n \u00a7 1. Axiom of the uniformity of the course of nature 341\n\n 2. Not true in every sense. Induction _per enumerationem\n simplicem_ 346\n\n 3. The question of Inductive Logic stated 348\n\n\n CHAPTER IV. _Of Laws of Nature._\n\n \u00a7 1. The general regularity in nature is a tissue of partial\n regularities, called laws 351\n\n 2. Scientific induction must be grounded on previous\n spontaneous inductions 355\n\n 3. Are there any inductions fitted to be a test of all others? 357\n\n\n CHAPTER V. _Of the Law of Universal Causation._\n\n \u00a7 1. The universal law of successive phenomena is the Law of\n Causation 360\n\n 2. --_i.e._ the law that every consequent has an invariable\n antecedent 363\n\n 3. The cause of a phenomenon is the assemblage of its\n conditions 365\n\n 4. The distinction of agent and patient illusory 373\n\n 5. The cause is not the invariable antecedent, but the\n _unconditional_ invariable antecedent 375\n\n 6. Can a cause be simultaneous with its effect? 380\n\n 7. Idea of a Permanent Cause, or original natural agent 383\n\n 8. Uniformities of coexistence between effects of different\n permanent causes, are not laws 386\n\n 9. Doctrine that volition is an efficient cause, examined 387\n\n\n CHAPTER VI. _Of the Composition of Causes._\n\n \u00a7 1. Two modes of the conjunct action of causes, the mechanical\n and the chemical 405\n\n 2. The composition of causes the general rule; the other case\n exceptional 408\n\n 3. Are effects proportional to their causes? 412\n\n\n CHAPTER VII. _Of Observation and Experiment._\n\n \u00a7 1. The first step of inductive inquiry is a mental analysis of\n complex phenomena into their elements 414\n\n 2. The next is an actual separation of those elements 416\n\n 3. Advantages of experiment over observation 417\n\n 4. Advantages of observation over experiment 420\n\n\n CHAPTER VIII. _Of the Four Methods of Experimental\n Inquiry._\n\n \u00a7 1. Method of Agreement 425\n\n 2. Method of Difference 428\n\n 3. Mutual relation of these two methods 429\n\n 4. Joint Method of Agreement and Difference 433\n\n 5. Method of Residues 436\n\n 6. Method of Concomitant Variations 437\n\n 7. Limitations of this last method 443\n\n\n CHAPTER IX. _Miscellaneous Examples of the Four Methods._\n\n \u00a7 1. Liebig's theory of metallic poisons 449\n\n 2. Theory of induced electricity 453\n\n 3. Dr. Wells' theory of dew 457\n\n 4. Dr. Brown-S\u00e9quard's theory of cadaveric rigidity 465\n\n 5. Examples of the Method of Residues 471\n\n 6. Dr. Whewell's objections to the Four Methods 475\n\n\n CHAPTER X. _Of Plurality of Causes; and of the Intermixture\n of Effects._\n\n \u00a7 1. One effect may have several causes 482\n\n 2. --which is the source of a characteristic imperfection of\n the Method of Agreement 483\n\n 3. Plurality of Causes, how ascertained 487\n\n 4. Concurrence of Causes which do not compound their effects 489\n\n 5. Difficulties of the investigation, when causes compound\n their effects 494\n\n 6. Three modes of investigating the laws of complex effects 499\n\n 7. The method of simple observation inapplicable 500\n\n 8. The purely experimental method inapplicable 501\n\n\n CHAPTER XI. _Of the Deductive Method._\n\n \u00a7 1. First stage; ascertainment of the laws of the separate\n causes by direct induction 507\n\n 2. Second stage; ratiocination from the simple laws of the\n complex cases 512\n\n 3. Third stage; verification by specific experience 514\n\n\n CHAPTER XII. _Of the Explanation of Laws of Nature._\n\n \u00a7 1. Explanation defined 518\n\n 2. First mode of explanation, by resolving the law of a complex\n effect into the laws of the concurrent causes and\n the fact of their coexistence 518\n\n 3. Second mode; by the detection of an intermediate link in\n the sequence 519\n\n 4. Laws are always resolved into laws more general than\n themselves 520\n\n 5. Third mode; the subsumption of less general laws under\n a more general one 524\n\n 6. What the explanation of a law of nature amounts to 526\n\n\n CHAPTER XIII. _Miscellaneous Examples of the Explanation of\n Laws of Nature._\n\n \u00a7 1. The general theories of the sciences 529\n\n 2. Examples from chemical speculations 531\n\n 3. Example from Dr. Brown-S\u00e9quard's researches on the\n nervous system 533\n\n 4. Examples of following newly-discovered laws into their\n complex manifestations 534\n\n 5. Examples of empirical generalizations, afterwards confirmed\n and explained deductively 536\n\n 6. Example from mental science 538\n\n 7. Tendency of all the sciences to become deductive 539\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\ndifferent view of some of the particulars which these branches of\nknowledge are usually understood to include; each has so framed his\ndefinition as to indicate beforehand his own peculiar tenets, and\nsometimes to beg the question 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 anything, until there is agreement about the\nthing itself. To define, is to select from among all the properties of a\nthing, those which shall be understood to be designated and declared by\nits name; and the properties must be well known to us before we can be\ncompetent to determine which of them are fittest to be chosen for this\npurpose. Accordingly, in the case of so complex an aggregation of\nparticulars as are comprehended in anything which can be called a\nscience, the definition we set out with is seldom that which a more\nextensive knowledge of the subject shows to be the most appropriate.\nUntil we know the particulars themselves, we cannot fix upon the most\ncorrect and compact mode of circumscribing them by a general\ndescription. It was not until after an extensive and accurate\nacquaintance with the details of chemical phenomena, that it was found\npossible to frame a rational definition of chemistry; and the definition\nof the science of life and organization is still a matter of dispute. So\nlong as the sciences are imperfect, the definitions must partake of\ntheir imperfection; and if the former are progressive, the latter ought\nto be so too. As much, therefore, as is to be expected from a definition\nplaced at the commencement of a subject, is that it should define the\nscope of our inquiries: and the definition which I am about to offer of\nthe science of logic, pretends to nothing more, than to be a statement\nof the question which I have put to myself, and which this book is an\nattempt to resolve. The reader is at liberty to object to it as a\ndefinition of logic; but it is at all events a correct definition of the\nsubject of these volumes.\n\n\n\u00a7 2. Logic has often been called the Art of Reasoning. A writer[1] who\nhas done more than any other person to restore this study to the rank\nfrom which it had fallen in the estimation of the cultivated class in\nour own country, has adopted the above definition with an amendment; he\nhas defined Logic to be the Science, as well as the Art, of reasoning;\nmeaning by the former term, the analysis of the mental process which\ntakes place whenever we reason, and by the latter, the rules, grounded\non that analysis, for conducting the process correctly. There can be no\ndoubt as to the propriety of the emendation. A right understanding of\nthe mental process itself, of the conditions it depends on, and the\nsteps of which it consists, is the only basis on which a system of\nrules, fitted for the direction of the process, can possibly be founded.\nArt necessarily presupposes knowledge; art, in any but its infant state,\npresupposes scientific knowledge: and if every art does not bear the\nname of a science, it is only because several sciences are often\nnecessary to form the groundwork of a single art. So complicated are the\nconditions which govern our practical agency, that to enable one thing\nto be _done_, it is often requisite to _know_ the nature and properties\nof 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\nbe called (with sufficient accuracy for the present purpose) concluding\nfrom generals to particulars. In another of its senses, to reason is\nsimply to infer any assertion, from assertions already admitted: and in\nthis sense induction is as much entitled to be called reasoning as the\ndemonstrations of 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\nmean to use it. I do this by virtue of the right I claim for every\nauthor, to give whatever provisional definition he pleases of his own\nsubject. But sufficient reasons will, I believe, unfold themselves as we\nadvance, why this should be not only the provisional but the final\ndefinition. It involves, at all events, no arbitrary change in the\nmeaning of the word; for, with the general usage of the English\nlanguage, the wider signification, I believe, accords better than the\nmore restricted one.\n\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\nare commonly termed, the scholastic, logicians. Yet even with them, in\ntheir systematic treatises, argumentation was the subject only of the\nthird part: the two former treated of Terms, and of Propositions; under\none or other of which heads were also included Definition and Division.\nBy some, indeed, these previous topics were professedly introduced only\non account of their connexion with reasoning, and as a preparation for\nthe doctrine and rules of the syllogism. Yet they were treated with\ngreater minuteness, and dwelt on at greater length, than was required\nfor that purpose alone. More recent writers on logic have generally\nunderstood the term as it was employed by the able author of the Port\nRoyal Logic; viz. as equivalent to the Art of Thinking. Nor is this\nacceptation confined to books, and scientific inquiries. Even in\nordinary conversation, the ideas connected with the word Logic include\nat least precision of language, and accuracy of classification: and we\nperhaps oftener hear persons speak of a logical arrangement, or of\nexpressions logically defined, than of conclusions logically deduced\nfrom premises. Again, a man is often called a great logician, or a man\nof powerful logic, not for the accuracy of his deductions, but for the\nextent of his command over premises; because the general propositions\nrequired for explaining a difficulty or refuting a sophism, copiously\nand promptly occur to him: because, in short, his knowledge, besides\nbeing ample, is well under his command for argumentative use. Whether,\ntherefore, we conform to the practice of those who have made the subject\ntheir particular study, or to that of popular writers and common\ndiscourse, the province of logic will include several operations of the\nintellect not usually considered to fall within the meaning of the terms\nReasoning 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\nthis ultimate end, naming, classification, definition, and all other\noperations over which logic has ever claimed jurisdiction, are\nessentially subsidiary. They may all be regarded as contrivances for\nenabling a person to know the truths which are needful to him, and to\nknow them at the precise moment at which they are needful. Other\npurposes, indeed, are also served by these operations; for instance,\nthat of imparting our knowledge to others. But, viewed with regard to\nthis purpose, they have never been considered as within the province of\nthe logician. The sole object of Logic is the guidance of one's own\nthoughts: the communication of those thoughts to others falls under the\nconsideration of Rhetoric, in the large sense in which that art was\nconceived by the ancients; or of the still more extensive art of\nEducation. Logic takes cognizance of our intellectual operations, only\nas they conduce to our own knowledge, and to our command over that\nknowledge for our own uses. If there were but one rational being in the\nuniverse, that being might be a perfect logician; and the science and\nart of logic would be the same for that one person as for the whole\nhuman race.\n\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;[2] the latter, of Inference. The\ntruths known by intuition are the original premises from which all\nothers are inferred. Our assent to the conclusion being grounded on the\ntruth of the premises, we never could arrive at any knowledge by\nreasoning, unless something could be known antecedently to all\nreasoning.\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\noccurrences which took place while we were absent, the events recorded\nin history, or the theorems of mathematics. The two former we infer from\nthe testimony adduced, or from the traces of those past occurrences\nwhich still exist; the latter, from the premises laid down in books of\ngeometry, under the title of definitions and axioms. Whatever we are\ncapable of knowing must belong to the one class or to the other; must\nbe in the number of the primitive data, or of the conclusions which can\nbe drawn from these.\n\nWith the original data, or ultimate premises of our knowledge; with\ntheir number or nature, the mode in which they are obtained, or the\ntests by which they may be distinguished; logic, in a direct way at\nleast, has, in the sense in which I conceive the science, nothing to do.\nThese questions are partly not a subject of science at all, partly that\nof a very different 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\npurpose of establishing such truths; no rules of art can render our\nknowledge of them more certain than it is in itself. There is no logic\nfor this portion of our knowledge.\n\nBut we may fancy that we see or feel what we in reality infer. A truth,\nor supposed truth, which is really the result of a very rapid inference,\nmay seem to be apprehended intuitively. It has long been agreed by\nthinkers of the most opposite schools, that this mistake is actually\nmade 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\nascertained, that what is perceived by the eye, is at most nothing more\nthan a variously coloured surface; that when we fancy we see distance,\nall we really see is certain variations of apparent size, and degrees of\nfaintness of colour; that our estimate of the object's distance from us\nis the result partly of a rapid inference from the muscular sensations\naccompanying the adjustment of the focal distance of the eye to objects\nunequally remote from us, and partly of a comparison (made with so much\nrapidity that we are unconscious of making it) between the size and\ncolour of the object as they appear at the time, and the size and colour\nof the same or of similar objects as they appeared when close at hand,\nor when their degree of remoteness was known by other evidence. The\nperception of distance by the eye, which seems so like intuition, is\nthus, in reality, an inference grounded on experience; an inference,\ntoo, which we learn to make; and which we make with more and more\ncorrectness as our experience increases; though in familiar cases it\ntakes place so rapidly as to appear exactly on a par with those\nperceptions of sight which are really intuitive, our perceptions of\ncolour.[3]\n\nOf the science, therefore, which expounds the operations of the human\nunderstanding in the pursuit of truth, one essential part is the\ninquiry: What are the facts which are the objects of intuition or\nconsciousness, and what are those which we merely infer? But this\ninquiry has never been considered a portion of logic. Its place is in\nanother and a perfectly distinct department of science, to which the\nname metaphysics more particularly belongs: that portion of mental\nphilosophy which attempts to determine what part of the furniture of the\nmind belongs to it originally, and what part is constructed out of\nmaterials furnished to it from without. To this science appertain the\ngreat and much debated questions of the existence of matter; the\nexistence of spirit, and of a distinction between it and matter; the\nreality of time and space, as things without the mind, and\ndistinguishable from the objects which are said to exist in them. For in\nthe present state of the discussion on these topics, it is almost\nuniversally allowed that the existence of matter or of spirit, of space\nor of time, is in its nature unsusceptible of being proved; and that if\nanything is known of them, it must be by immediate intuition. To the\nsame science belong the inquiries into the nature of Conception,\nPerception, Memory, and Belief; all of which are operations of the\nunderstanding in the pursuit of truth; but with which, as phenomena of\nthe mind, or with the possibility which may or may not exist of\nanalysing any of them into simpler phenomena, the logician as such has\nno concern. To this science must also be referred the following, and all\nanalogous questions: To what extent our intellectual faculties and our\nemotions are innate--to what extent the result of association: Whether\nGod, and duty, are realities, the existence of which is manifest to us\n_\u00e0 priori_ by the constitution of our rational faculty; or whether our\nideas of them are acquired notions, the origin of which we are able to\ntrace and explain; and the reality of the objects themselves a question\nnot of consciousness or intuition, but of evidence and reasoning.\n\nThe province of logic must be restricted to that portion of our\nknowledge which consists of inferences from truths previously known;\nwhether those antecedent data be general propositions, or particular\nobservations and perceptions. Logic is not the science of Belief, but\nthe science of Proof, or Evidence. In so far as belief professes to be\nfounded on proof, the office of logic is to supply a test for\nascertaining whether or not the belief is well grounded. With the claims\nwhich any proposition has to belief on the evidence of consciousness,\nthat is, without evidence in the proper sense of the word, logic has\nnothing to do.\n\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,\nnearly the whole, not only of science, but of human conduct, is amenable\nto the authority of logic. To draw inferences has been said to be the\ngreat business of life. Every one has daily, hourly, and momentary need\nof ascertaining facts which he has not directly observed; not from any\ngeneral purpose of adding to his stock of knowledge, but because the\nfacts themselves are of importance to his interests or to his\noccupations. The business of the magistrate, of the military commander,\nof the navigator, of the physician, of the agriculturist, is merely to\njudge of evidence, and to act accordingly. They all have to ascertain\ncertain facts, in order that they may afterwards apply certain rules,\neither devised by themselves, or prescribed for their guidance by\nothers; and as they do this well or ill, so they discharge well or ill\nthe duties of their several callings. It is the only occupation in\nwhich the mind never ceases to be engaged; and is the subject, not of\nlogic, but of knowledge in general.\n\nLogic, however, is not the same thing with knowledge, though the field\nof logic is coextensive with the field of knowledge. Logic is the common\njudge and arbiter of all particular investigations. It does not\nundertake to find evidence, but to determine whether it has been found.\nLogic neither observes, nor invents, nor discovers; but judges. It is no\npart of the business of logic to inform the surgeon what appearances are\nfound to accompany a violent death. This he must learn from his own\nexperience and observation, or from that of others, his predecessors in\nhis peculiar pursuit. But logic sits in judgment on the sufficiency of\nthat observation and experience to justify his rules, and on the\nsufficiency of his rules to justify his conduct. It does not give him\nproofs, but teaches him what makes them proofs, and how he is to judge\nof them. It does not teach that any particular fact proves any other,\nbut points out to what conditions all facts must conform, in order that\nthey may prove other facts. To decide whether any given fact fulfils\nthese conditions, or whether facts can be found which fulfil them in a\ngiven case, belongs exclusively to the particular art or science, or to\nour 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\ndata and conclusions from those data, of proofs and what they prove: now\nlogic points out what relations must subsist between data and whatever\ncan be concluded from them, between proof and everything which it can\nprove. If there be any such indispensable relations, and if these can be\nprecisely determined, every particular branch of science, as well as\nevery individual in the guidance of his conduct, is bound to conform to\nthose relations, under the penalty of making false inferences, of\ndrawing conclusions which are not grounded in the realities of things.\nWhatever has at any time been concluded justly, whatever knowledge has\nbeen acquired otherwise than by immediate intuition, depended on the\nobservance of the laws which it is the province of logic to investigate.\nIf the conclusions are just, and the knowledge real, those laws, whether\nknown or not, have been observed.\n\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\nscience of logic exists, or is capable of existing, it must be useful.\nIf there be rules to which every mind consciously or unconsciously\nconforms in every instance in which it infers rightly, there seems\nlittle necessity for discussing whether a person is more likely to\nobserve those rules, when he knows the rules, than when he is\nunacquainted 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,\nacquire empirically in the course of their studies. Mankind judged of\nevidence, and often correctly, before logic was a science, or they never\ncould have made it one. And they executed great mechanical works before\nthey understood the laws of mechanics. But there are limits both to what\nmechanicians can do without principles of mechanics, and to what\nthinkers can do without principles of logic. A few individuals, by\nextraordinary genius, or by the accidental acquisition of a good set of\nintellectual habits, may work without principles in the same way, or\nnearly the same way, in which they would have worked if they had been in\npossession of principles. But the bulk of mankind require either to\nunderstand the theory of what they are doing, or to have rules laid down\nfor them by those who have understood the theory. In the progress of\nscience from its easiest to its more difficult problems, each great step\nin advance has usually had either as its precursor, or as its\naccompaniment and necessary condition, a corresponding improvement in\nthe notions and principles of logic received among the most advanced\nthinkers. And if several of the more difficult sciences are still in so\ndefective a state; if not only so little is proved, but disputation has\nnot terminated even about the little which seemed to be so; the reason\nperhaps is, that men's logical notions have not yet acquired the degree\nof extension, or of accuracy, requisite for the estimation of the\nevidence proper to those particular departments of knowledge.\n\n\n\u00a7 7. Logic, then, is the science of the operations of the understanding\nwhich are subservient to the estimation of evidence: both the process\nitself of advancing from known truths to unknown, and all other\nintellectual operations in so far as auxiliary to this. It includes,\ntherefore, the operation of Naming; for language is an instrument of\nthought, as well as a means of communicating our thoughts. It includes,\nalso, Definition, and Classification. For, the use of these operations\n(putting all other minds than one's own out of consideration) is to\nserve not only for keeping our evidences and the conclusions from them\npermanent and readily accessible in the memory, but for so marshalling\nthe facts which we may at any time be engaged in investigating, as to\nenable us to perceive more clearly what evidence there is, and to judge\nwith fewer chances of error whether it be sufficient. These, therefore,\nare operations specially instrumental to the estimation of evidence,\nand, as such, are within the province of Logic. There are other more\nelementary processes, concerned in all thinking, such as Conception,\nMemory, and the like; but of these it is not necessary that Logic should\ntake any peculiar cognizance, since they have no special connexion with\nthe problem of Evidence, further than that, like all other problems\naddressed to the understanding, it presupposes them.\n\nOur object, then, will be, to attempt a correct analysis of the\nintellectual process called Reasoning or Inference, and of such other\nmental operations as are intended to facilitate this; as well as, on the\nfoundation of this analysis, and _pari passu_ with it, to bring together\nor frame a set of rules or canons for testing the sufficiency of any\ngiven 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\nelements. It is enough if the analysis as far as it goes is correct,\nand if it goes far enough for the practical purposes of logic considered\nas an art. The separation of a complicated phenomenon into its component\nparts is not like a connected and interdependent chain of proof. If one\nlink of an argument breaks, the whole drops to the ground; but one step\ntowards an analysis holds good and has an independent value, though we\nshould never be able to make a second. The results which have been\nobtained by analytical chemistry are not the less valuable, though it\nshould be discovered that all which we now call simple substances are\nreally compounds. All other things are at any rate compounded of those\nelements: whether the elements themselves admit of decomposition, is an\nimportant inquiry, but does not affect the certainty of the science up\nto that point.\n\nI shall, accordingly, attempt to analyse the process of inference, and\nthe processes subordinate to inference, so far only as may be requisite\nfor ascertaining the difference between a correct and an incorrect\nperformance of those processes. The reason for thus limiting our design,\nis evident. It has been said by objectors to logic, that we do not learn\nto use our muscles by studying their anatomy. The fact is not quite\nfairly stated; for if the action of any of our muscles were vitiated by\nlocal weakness, or other physical defect, a knowledge of their anatomy\nmight be very necessary for effecting a cure. But we should be justly\nliable to the criticism involved in this objection, were we, in a\ntreatise on logic, to carry the analysis of the reasoning process beyond\nthe point at which any inaccuracy which may have crept into it must\nbecome visible. In learning bodily exercises (to carry on the same\nillustration) we do, and must, analyse the bodily motions so far as is\nnecessary for distinguishing those which ought to be performed from\nthose which ought not. To a similar extent, and no further, it is\nnecessary that the logician should analyse the mental processes with\nwhich Logic is concerned. Logic has no interest in carrying the analysis\nbeyond the point at which it becomes apparent whether the operations\nhave in any individual case been rightly or wrongly performed: in the\nsame manner as the science of music teaches us to discriminate between\nmusical notes, and to know the combinations of which they are\nsusceptible, but not what number of vibrations in a second correspond to\neach; which, though useful to be known, is useful for totally different\npurposes. The extension of Logic as a Science is determined by its\nnecessities as an Art: whatever it does not need for its practical ends,\nit leaves to the larger science which may be said to correspond, not to\nany particular art, but to art in general; the science which deals with\nthe constitution of the human faculties; and to which, in the part of\nour mental nature which concerns Logic, as well as in all other parts,\nit belongs to decide what are ultimate facts, and what are resolvable\ninto other facts. And I believe it will be found that most of the\nconclusions arrived at in this work have no necessary connexion with any\nparticular views respecting the ulterior analysis. Logic is common\nground on which the partisans of Hartley and of Reid, of Locke and of\nKant, may meet and join hands. Particular and detached opinions of all\nthese thinkers will no doubt occasionally be controverted, since all of\nthem were logicians as well as metaphysicians; but the field on which\ntheir principal battles have been fought, lies beyond the boundaries of\nour science.\n\nIt cannot, indeed, be pretended that logical principles can be\naltogether irrelevant to those more abstruse discussions; nor is it\npossible but that the view we are led to take of the problem which logic\nproposes, must have a tendency favourable to the adoption of some one\nopinion, on these controverted subjects, rather than another. For\nmetaphysics, in endeavouring to solve its own peculiar problem, must\nemploy means, the validity of which falls under the cognizance of logic.\nIt proceeds, no doubt, as far as possible, merely by a closer and more\nattentive interrogation of our consciousness, or more properly speaking,\nof our memory; and so far is not amenable to logic. But wherever this\nmethod is insufficient to attain the end of its inquiries, it must\nproceed, like other sciences, by means of evidence. Now, the moment this\nscience begins to draw inferences from evidence, logic becomes the\nsovereign judge whether its inferences are well grounded, or what other\ninferences would be so.\n\nThis, however, constitutes no nearer or other relation between logic\nand metaphysics, than that which exists between logic and every other\nscience. 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.[4]\n\nFOOTNOTES:\n\n[1] Archbishop Whately.\n\n[2] I use these terms indiscriminately, because, for the purpose in\nview, there is no need for making any distinction between them. But\nmetaphysicians usually restrict the name Intuition to the direct\nknowledge we are supposed to have of things external to our minds, and\nConsciousness to our knowledge of our own mental phenomena.\n\n[3] This important theory has of late been called in question by a\nwriter of deserved reputation, Mr. Samuel Bailey; but I do not conceive\nthat the grounds on which it has been admitted as an established\ndoctrine for a century past, have been at all shaken by that gentleman's\nobjections. I have elsewhere said what appeared to me necessary in reply\nto his arguments. (_Westminster Review_ for October 1842; reprinted in\n_Dissertations and Discussions_, vol. ii.)\n\n[4] The view taken in the text, of the definition and purpose of Logic,\nstands in marked opposition to that of the school of philosophy which,\nin this country, is represented by the writings of Sir William Hamilton\nand of his numerous pupils. Logic, as this school conceives it, is \"the\nScience of the Formal Laws of Thought;\" a definition framed for the\nexpress purpose of excluding, as irrelevant to Logic, whatever relates\nto Belief and Disbelief, or to the pursuit of truth as such, and\nrestricting the science to that very limited portion of its total\nprovince, which has reference to the conditions, not of Truth, but of\nConsistency. What I have thought it useful to say in opposition to this\nlimitation of the field of Logic, has been said at some length in a\nseparate work, first published in 1865, and entitled _An Examination of\nSir William Hamilton's Philosophy, and of the Principal Philosophical\nQuestions discussed in his Writings_. For the purposes of the present\nTreatise, I am content that the justification of the larger extension\nwhich I give to the domain of the science, should rest on the sequel of\nthe Treatise itself. Some remarks on the relation which the Logic of\nConsistency bears to the Logic of Truth, and on the place which that\nparticular part occupies in the whole to which it belongs, will be found\nin the present volume (Book II. chap. iii. \u00a7 9).\n\n\n\n\nBOOK I.\n\nOF NAMES AND PROPOSITIONS.\n\n\n'La scolastique, qui produisit dans la logique, comme dans la morale,\net dans une partie de la m\u00e9taphysique, une subtilit\u00e9, une pr\u00e9cision\nd'id\u00e9es, dont l'habitude inconnue aux anciens, a contribu\u00e9 plus qu'on ne\ncroit au progr\u00e8s de la bonne philosophie.'--CONDORCET, _Vie de Turgot_.\n\n'To the schoolmen the vulgar languages are principally indebted for what\nprecision and analytic subtlety they possess.'--SIR W. HAMILTON,\n_Discussions in Philosophy_.\n\n\n\n\nCHAPTER I.\n\nOF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE.\n\n\n\u00a7 1. It is so much the established practice of writers on logic to\ncommence their treatises by a few general observations (in most cases,\nit is 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\nto require a formal justification. Logic is a portion of the Art of\nThinking: Language is evidently, and by the admission of all\nphilosophers, one of the principal instruments or helps of thought; and\nany imperfection in the instrument, or in the mode of employing it, is\nconfessedly liable, still more than in almost any other art, to confuse\nand impede the process, and destroy all ground of confidence in the\nresult. For a mind not previously versed in the meaning and right use of\nthe various kinds of words, to attempt the study of methods of\nphilosophizing, would be as if some one should attempt to become an\nastronomical observer, having never learned to adjust the focal distance\nof his optical instruments so as to see distinctly.\n\nSince Reasoning, or Inference, the principal subject of logic, is an\noperation which usually takes place by means of words, and in\ncomplicated cases can take place in no other way; those who have not a\nthorough insight into the signification and purposes of words, will be\nunder chances, amounting almost to certainty, of reasoning or inferring\nincorrectly. And logicians have generally felt that unless, in the very\nfirst stage, they removed this source of error; unless they taught their\npupil to put away the glasses which distort the object, and to use\nthose which are adapted to his purpose in such a manner as to assist,\nnot perplex, 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's\nconsideration: because without it he cannot examine into the import of\nPropositions. Now this is a subject which stands on the very threshold\nof the 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\ngreatest portion) which is not intuitive: and by what criterion we can,\nin matters not self-evident, distinguish between things proved and\nthings not proved, between what is worthy and what is unworthy of\nbelief. Of the various questions which present themselves to our\ninquiring faculties, some receive an answer from direct consciousness,\nothers, if resolved at all, can only be resolved by means of evidence.\nLogic is concerned with these last. But before inquiring into the mode\nof resolving questions, it is necessary to inquire what are those which\noffer themselves; what questions are conceivable; what inquiries are\nthere, to which mankind have either obtained, or been able to imagine it\npossible that they should obtain, an answer. This point is best\nascertained by a survey and analysis of Propositions.\n\n\n\u00a7 2. The answer to every question which it is possible to frame, must be\ncontained in a Proposition, or Assertion. Whatever can be an object of\nbelief, or even of disbelief, must, when put into words, assume the form\nof a proposition. All truth and all error lie in propositions. What, by\na convenient misapplication of an abstract term, we call a Truth, means\nsimply a True Proposition; and errors are false propositions. To know\nthe import of all possible propositions, would be to know all questions\nwhich can be raised, all matters which are susceptible of being either\nbelieved or disbelieved. How many kinds of inquiries can be propounded;\nhow many kinds of judgments can be made; and how many kinds of\npropositions it is possible to frame with a meaning; are but different\nforms of one and the same question. Since, then, the objects of all\nBelief and of all Inquiry express themselves in propositions; a\nsufficient scrutiny of Propositions and of their varieties will apprize\nus what questions mankind have actually asked of themselves, and what,\nin the nature of answers to those questions, they have actually thought\nthey 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,\nand the Copula. The predicate is the name denoting that which is\naffirmed or denied. The subject is the name denoting the person or thing\nwhich something is affirmed or denied of. The copula is the sign\ndenoting that there is an affirmation or denial; and thereby enabling\nthe hearer or reader to distinguish a proposition from any other kind of\ndiscourse. Thus, in the proposition, The earth is round, the Predicate\nis the word _round_, which denotes the quality affirmed, or (as the\nphrase is) predicated: _the earth_, words denoting the object which that\nquality is affirmed of, compose the Subject; the word _is_, which serves\nas the connecting mark between the subject and predicate, to show that\none of them 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;\nbrings together two names, in a particular manner. This is already a\nfirst step towards what we are in quest of. It appears from this, that\nfor an act of belief, _one_ object is not sufficient; the simplest act\nof belief supposes, and has something to do with, _two_ objects: two\nnames, to say the least; and (since the names must be names of\nsomething) two _nameable things_. A large class of thinkers would cut\nthe matter short by saying, two _ideas_. They would say, that the\nsubject and predicate are both of them names of ideas; the idea of gold,\nfor instance, and the idea of yellow; and that what takes place (or part\nof what takes place) in the act of belief, consists in bringing (as it\nis often expressed) one of these ideas under the other. But this we are\nnot yet in a condition to say: whether such be the correct mode of\ndescribing the phenomenon, is an after consideration. The result with\nwhich for the present we must be contented, is, that in every act of\nbelief _two_ objects are in some manner taken cognizance of; that there\ncan be no belief claimed, or question propounded, which does not embrace\ntwo distinct (either material or intellectual) subjects of thought; each\nof them capable, or not, of being conceived by itself, but incapable of\nbeing believed by itself.\n\nI may say, for instance, \"the sun.\" The word has a meaning, and suggests\nthat meaning to the mind of any one who is listening to me. But suppose\nI ask 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, \"the sun exists.\" 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\nit not be said that this second conception, existence, is involved in\nthe first; for the sun may be conceived as no longer existing. \"The sun\"\ndoes not convey all the meaning that is conveyed by \"the sun exists:\"\n\"my father\" does not include all the meaning of \"my father exists,\" for\nhe may be dead; \"a round square\" does not include the meaning of \"a\nround square exists,\" for it does not and cannot exist. When I say \"the\nsun,\" \"my father,\" or a \"round square,\" I do not call upon the hearer\nfor any belief or disbelief, nor can either the one or the other be\nafforded me; but if I say, \"the sun exists,\" \"my father exists,\" or \"a\nround square exists,\" I call for belief; and should, in the first of the\nthree instances, meet with it; in the second, with belief or disbelief,\nas the case might be; in the third, with disbelief.\n\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\nof language. If we attempt to proceed further in the same path, that is,\nto analyse any further the import of Propositions; we find forced upon\nus, as a subject of previous consideration, the import of Names. For\nevery proposition consists of two names; and every proposition affirms\nor denies one of these names, of the other. Now what we do, what passes\nin our mind, when we affirm or deny two names of one another, must\ndepend on what they are names of; since it is with reference to that,\nand not to the mere names themselves, that we make the affirmation or\ndenial. Here, therefore, we find a new reason why the signification of\nnames, and the relation generally between names and the things signified\nby them, must occupy the preliminary stage of the inquiry we are engaged\nin.\n\nIt may be objected that the meaning of names can guide us at most only\nto the opinions, possibly the foolish and groundless opinions, which\nmankind have formed concerning things, and that as the object of\nphilosophy is truth, not opinion, the philosopher should dismiss words\nand look into things themselves, to ascertain what questions can be\nasked and answered in regard to them. This advice (which no one has it\nin his power to follow) is in reality an exhortation to discard the\nwhole fruits of the labours of his predecessors, and conduct himself as\nif he were the first person who had ever turned an inquiring eye upon\nnature. What does any one's personal knowledge of Things amount to,\nafter subtracting all which he has acquired by means of the words of\nother people? Even after he has learned as much as people usually do\nlearn from others, will the notions of things contained in his\nindividual mind afford as sufficient a basis for a _catalogue raisonn\u00e9_\nas the notions which are in the minds of all mankind?\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\nremain to be established, by a subsequent examination of names, that the\nenumeration has omitted nothing which ought to have been included. But\nif we begin with names, and use them as our clue to the things, we bring\nat once before us all the distinctions which have been recognised, not\nby a single inquirer, but by all inquirers taken together. It doubtless\nmay, and I believe it will, be found, that mankind have multiplied the\nvarieties unnecessarily, and have imagined distinctions among things,\nwhere there were only distinctions in the manner of naming them. But we\nare not entitled to assume this in the commencement. We must begin by\nrecognising the distinctions made by ordinary language. If some of these\nappear, on a close examination, not to be fundamental, the enumeration\nof the different kinds of realities may be abridged accordingly. But to\nimpose upon the facts in the first instance the yoke of a theory, while\nthe grounds of the theory are reserved for discussion in a subsequent\nstage, is not a course which a logician can reasonably adopt.\n\n\n\n\nCHAPTER II.\n\nOF NAMES.\n\n\n\u00a7 1. \"A name,\" says Hobbes,[1] \"is a word taken at pleasure to serve for\na mark 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[2] before in his mind.\" 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\nthought, and a sign to make it known to others, appears unexceptionable.\nNames, indeed, do much more than this; but whatever else they do, grows\nout of, and 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\nof things? The first is the expression in common use; the last is that\nof some 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. \"But seeing,\" he\ncontinues, \"names 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\ncollects that he that pronounces it thinks of a stone.\"\n\nIf it be merely meant that the conception alone, and not the thing\nitself, is recalled by the name, or imparted to the hearer, this of\ncourse cannot be denied. Nevertheless, there seems good reason for\nadhering to the common usage, and calling the word _sun_ the name of\nthe sun, and not the name of our idea of the sun. For names are not\nintended only to make the hearer conceive what we conceive, but also to\ninform him what we believe. Now, when I use a name for the purpose of\nexpressing a belief, it is a belief concerning the thing itself, not\nconcerning my idea of it. When I say, \"the sun is the cause of day,\" I\ndo not mean that my idea of the sun causes or excites in me the idea of\nday; or in other words, that thinking of the sun makes me think of day.\nI mean, that a certain physical fact, which is called the sun's presence\n(and which, in the ultimate analysis, resolves itself into sensations,\nnot ideas) causes another physical fact, which is called day. It seems\nproper to consider a word as the _name_ of that which we intend to be\nunderstood by it when we use it; of that which any fact that we assert\nof it is to be understood of; that, in short, concerning which, when we\nemploy the word, we intend to give information. Names, therefore, shall\nalways be spoken of in this work as the names of things themselves, and\nnot 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\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's_; and even\nadjectives, as _large_, _heavy_. These words do not express things of\nwhich anything can be affirmed or denied. We cannot say, Heavy fell, or\nA heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the\nroom. Unless, indeed, we are speaking of the mere words themselves, as\nwhen we say, Truly is an English word, or, Heavy is an adjective. In\nthat case they are complete names, viz. names of those particular\nsounds, or of those particular collections of written characters. This\nemployment of a word to denote the mere letters and syllables of which\nit is composed, was termed by the schoolmen the _suppositio materialis_\nof the word. In any other sense we cannot introduce one of these words\ninto the subject of a proposition, unless in combination with other\nwords; as, A heavy _body_ fell, A truly _important fact_ was asserted, A\n_member_ of _parliament_ was 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\nas the subject, for we may say, White is an agreeable colour. The\nadjective is often said to be so used by a grammatical ellipsis: Snow is\nwhite, instead of Snow is a white object; White is an agreeable colour,\ninstead of, A white colour, or, The colour white, is agreeable. The\nGreeks and Romans were allowed, by the rules of their language, to\nemploy this ellipsis universally in the subject as well as in the\npredicate of a proposition. In English this cannot, generally speaking,\nbe done. We may say, The earth is round; but we cannot say, Round is\neasily moved; we must say, A round object. This distinction, however, is\nrather grammatical than logical. Since there is no difference of meaning\nbetween _round_, and _a round object_, it is only custom which\nprescribes that on any given occasion one shall be used, and not the\nother. We shall, therefore, without scruple, speak of adjectives as\nnames, whether in their own right, or as representative of the more\ncircuitous forms of expression above exemplified. The other classes of\nsubsidiary words have no title whatever to be considered as names. An\nadverb, or an accusative case, cannot under any circumstances (except\nwhen their mere letters and syllables are spoken of) figure as one of\nthe 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[Greek: syn], with, and [Greek: kat\u00eagore\u00f4], to predicate, because it was\nonly _with_ some other word that they could be predicated. A word which\ncould be used either as the subject or predicate of a proposition\nwithout being accompanied by any other word, was termed by the same\nauthorities a Categorematic term. A combination of one or more\nCategorematic, and one or more Syncategorematic words, as A heavy body,\nor A court of justice, they sometimes called a _mixed_ term; but this\nseems a needless multiplication of technical expressions. A mixed term\nis, in the only useful sense of the word, Categorematic. It belongs to\nthe class of what have been called many-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\"the place which the wisdom or policy of antiquity had destined for the\nresidence of the Abyssinian princes,\" 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,\nwho was the mayor of the town, died yesterday--by this predication we\nmake but one assertion; whence it appears that \"John Nokes, who was the\nmayor of the town,\" is no more than one name. It is true that in this\nproposition, besides the assertion that John Nokes died yesterday, there\nis included another assertion, namely, that John Nokes was mayor of the\ntown. But this last assertion was already made: we did not make it by\nadding the predicate, \"died yesterday.\" Suppose, however, that the words\nhad been, John Nokes _and_ the mayor of the town, they would have formed\ntwo names instead of one. For when we say, John Nokes and the mayor of\nthe town died yesterday, we make two assertions; one, that John Nokes\ndied yesterday; the 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\nof, but according to their signification.\n\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\nnames; there is a name for every person, and for every remarkable place.\nOther objects, of which we have not occasion to speak so frequently, we\ndo not designate by a name of their own; but when the necessity arises\nfor naming them, we do so by putting together several words, each of\nwhich, by itself, might be and is used for an indefinite number of other\nobjects; as when I say, _this stone_: \"this\" and \"stone\" being, each of\nthem, names that may be used of many other objects besides the\nparticular one meant, though the only object of which they can both be\nused at the given moment, consistently with their signification, may be\nthe one of which I wish to speak.\n\nWere this the sole purpose for which names, that are common to more\nthings than one, could be employed; if they only served, by mutually\nlimiting each other, to afford a designation for such individual objects\nas have no names of their own; they could only be ranked among\ncontrivances for economizing the use of language. But it is evident that\nthis is not their sole function. It is by their means that we are\nenabled to assert _general_ propositions; to affirm or deny any\npredicate of an indefinite number of things at once. The distinction,\ntherefore, between _general_ names, and _individual_ or _singular_\nnames, is fundamental; and may be considered as the first grand division\nof 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\nof being truly affirmed, in the same sense, of one thing.\n\nThus, _man_ is capable of being truly affirmed of John, George, Mary,\nand other persons without assignable limit; and it is affirmed of all of\nthem in the same sense; for the word man expresses certain qualities,\nand when we predicate it of those persons, we assert that they all\npossess those qualities. But _John_ is only capable of being truly\naffirmed of one single person, at least in the same sense. For though\nthere are many persons who bear that name, it is not conferred upon\nthem to indicate any qualities, or anything which belongs to them in\ncommon; and cannot be said to be affirmed of them in any _sense_ at all,\nconsequently not in the same sense. \"The king who succeeded William the\nConqueror,\" is also an individual name. For, that there cannot be more\nthan one person of whom it can be truly affirmed, is implied in the\nmeaning of the words. Even \"_the_ king,\" when the occasion or the\ncontext defines the individual of whom it is to be understood, may\njustly be regarded as an individual name.\n\nIt is not unusual, by way of explaining what is meant by a general name,\nto say that it is the name of a _class_. But this, though a convenient\nmode of expression for some purposes, is objectionable as a definition,\nsince it explains the clearer of two things by the more obscure. It\nwould be more logical to reverse the proposition, and turn it into a\ndefinition of the word _class_: \"A class is the indefinite multitude of\nindividuals denoted by a general name.\"\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,\nbut only of all taken together. \"The 76th regiment of foot in the\nBritish army,\" which is a collective name, is not a general but an\nindividual name; for though it can be predicated of a multitude of\nindividual soldiers taken jointly, it cannot be predicated of them\nseverally. We may say, Jones is a soldier, and Thompson is a soldier,\nand Smith is a soldier, but we cannot say, Jones is the 76th regiment,\nand Thompson is the 76th regiment, and Smith is the 76th regiment. We\ncan only say, Jones, and Thompson, and Smith, and Brown, and so forth\n(enumerating all the soldiers), are the 76th regiment.\n\n\"The 76th regiment\" is a collective name, but not a general one: \"a\nregiment\" is both a collective and a general name. General with respect\nto all individual regiments, of each of which separately it can be\naffirmed; collective with respect to the individual soldiers of whom any\nregiment is composed.\n\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\na name of a thing, or rather of things. Whiteness, again, is the name of\na quality 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,\nand whose definitions, in logic at least, though they never went more\nthan a little way into the subject, have seldom, I think, been altered\nbut to be spoiled. A practice, however, has grown up in more modern\ntimes, which, if not introduced by Locke, has gained currency chiefly\nfrom his example, of applying the expression \"abstract name\" to all\nnames which are the result of abstraction or generalization, and\nconsequently to all general names, instead of confining it to the names\nof attributes. The metaphysicians of the Condillac school,--whose\nadmiration of Locke, passing over the profoundest speculations of that\ntruly original genius, usually fastens with peculiar eagerness upon his\nweakest points,--have gone on imitating him in this abuse of language,\nuntil there is now some difficulty in restoring the word to its original\nsignification. A more wanton alteration in the meaning of a word is\nrarely to be met with; for the expression _general name_, the exact\nequivalent of which exists in all languages I am acquainted with, was\nalready available for the purpose to which _abstract_ has been\nmisappropriated, while the misappropriation leaves that important class\nof words, the names of attributes, without any compact distinctive\nappellation. The old acceptation, however, has not gone so completely\nout of use, as to deprive those who still adhere to it of all chance of\nbeing understood. By _abstract_, then, I shall always, in Logic, mean\nthe opposite of _concrete_: by an abstract name, the name of an\nattribute; by a concrete name, the name of an object.\n\nDo abstract names belong to the class of general, or to that of singular\nnames? Some of them are certainly general. I mean those which are names\nnot of one single and definite attribute, but of a class of attributes.\nSuch is the word _colour_, which is a name common to whiteness, redness,\n&c. Such is even the word whiteness, in respect of the different shades\nof whiteness to which it is applied in common; the word magnitude, in\nrespect of the various degrees of magnitude and the various dimensions\nof space; the word weight, in respect of the various degrees of weight.\nSuch also is the word _attribute_ itself, the common name of all\nparticular attributes. But when only one attribute, neither variable in\ndegree nor in kind, is designated by the name; as visibleness;\ntangibleness; equality; squareness; milkwhiteness; then the name can\nhardly be considered general; for though it denotes an attribute of many\ndifferent objects, the attribute itself is always conceived as one, not\nmany.[3] To avoid needless logomachies, the best course would probably\nbe to consider these names as neither general nor individual, and to\nplace them in 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,\nthat is, when we employ it in predication. When we say snow is white,\nmilk is white, linen is white, we do not mean it to be understood that\nsnow, or linen, or milk, is a colour. We mean that they are things\nhaving the colour. The reverse is the case with the word whiteness; what\nwe affirm to _be_ whiteness is not snow, but the colour of snow.\nWhiteness, therefore, is the name of the colour exclusively: white is a\nname of all things whatever having the colour; a name, not of the\nquality whiteness, but of every white object. It is true, this name was\ngiven to all those various objects on account of the quality; and we may\ntherefore say, without impropriety, that the quality forms part of its\nsignification; but a name can only be said to stand for, or to be a name\nof, the things of which it can be predicated. We shall presently see\nthat all names which can be said to have any signification, all names by\napplying which to an individual we give any information respecting that\nindividual, may be said to _imply_ an attribute of some sort; but they\nare not names of the attribute; it has its own proper abstract name.\n\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\npossesses attributes. Thus John, or London, or England, are names which\nsignify a subject only. Whiteness, length, virtue, signify an attribute\nonly. None of these names, therefore, are connotative. But _white_,\n_long_, _virtuous_, are connotative. The word white, denotes all white\nthings, as snow, paper, the foam of the sea, &c., and implies, or as it\nwas termed by the schoolmen, _connotes_[4], the attribute _whiteness_.\nThe word white is not predicated of the attribute, but of the subjects,\nsnow, &c.; but when we predicate it of them, we imply, or connote, that\nthe attribute whiteness belongs to them. The same may be said of the\nother words above cited. Virtuous, for example, is the name of a class,\nwhich includes Socrates, Howard, the Man of Ross, and an undefinable\nnumber of other individuals, past, present, and to come. These\nindividuals, collectively and severally, can alone be said with\npropriety to be denoted by the word: of them alone can it properly be\nsaid to be a name. But it is a name applied to all of them in\nconsequence of an attribute which they are supposed to possess in\ncommon, the attribute which has received the name of virtue. It is\napplied to all beings that are considered to possess this attribute; and\nto 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\nindividuals, of whom, taken as a class, it is the name. But it is\napplied to them, because they possess, and to signify that they possess,\ncertain attributes. These seem to be, corporeity, animal life,\nrationality, and a certain external form, which for distinction we call\nthe human. Every existing thing, which possessed all these attributes,\nwould be called a man; and anything which possessed none of them, or\nonly one, or two, or even three of them without the fourth, would not be\nso called. For example, if in the interior of Africa there were to be\ndiscovered a race of animals possessing reason equal to that of human\nbeings, but with the form of an elephant, they would not be called men.\nSwift's Houyhnhnms would not be so called. Or if such newly-discovered\nbeings possessed the form of man without any vestige of reason, it is\nprobable that some other name than that of man would be found for them.\nHow it happens that there can be any doubt about the matter, will appear\nhereafter. The word _man_, therefore, signifies all these attributes,\nand all subjects which possess these attributes. But it can be\npredicated only of the subjects. What we call men, are the subjects, the\nindividual Stiles and Nokes; not the qualities by which their humanity\nis constituted. The name, therefore, is said to signify the subjects\n_directly_, the attributes _indirectly_; it _denotes_ the subjects, and\nimplies, or involves, or indicates, or as we shall say henceforth\n_connotes_, the attributes. It is a connotative name.\n\nConnotative names have hence been also called _denominative_, because\nthe subject which they denote is denominated by, or receives a name\nfrom, the attribute which they connote. Snow, and other objects, receive\nthe name white, because they possess the attribute which is called\nwhiteness; Peter, James, and others receive the name man, because they\npossess the attributes which are considered to constitute humanity. The\nattribute, or attributes, may therefore be said to denominate those\nobjects, or to give them a common name.[5]\n\nIt has been seen that all concrete general names are connotative. Even\nabstract names, though the names only of attributes, may in some\ninstances be justly considered as connotative; for attributes themselves\nmay have attributes ascribed to them; and a word which denotes\nattributes may connote an attribute of those attributes. Of this\ndescription, for example, is such a word as _fault_; equivalent to _bad_\nor _hurtful quality_. This word is a name common to many attributes, and\nconnotes hurtfulness, an attribute of those various attributes. When,\nfor example, we say that slowness, in a horse, is a fault, we do not\nmean that the slow movement, the actual change of place of the slow\nhorse, is a bad thing, but that the property or peculiarity of the\nhorse, from which it derives that name, the quality of being a slow\nmover, is an undesirable peculiarity.\n\nIn regard to those concrete names which are not general but individual,\na distinction 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,\nor a dog by the name C\u00e6sar, these names are simply marks used to enable\nthose individuals to be made subjects of discourse. It may be said,\nindeed, that we must have had some reason for giving them those names\nrather than any others; and this is true; but the name, once given, is\nindependent of the reason. A man may have been named John, because that\nwas the name of his father; a town may have been named Dartmouth,\nbecause it is situated at the mouth of the Dart. But it is no part of\nthe signification of the word John, that the father of the person so\ncalled bore the same name; nor even of the word Dartmouth, to be\nsituated at the mouth of the Dart. If sand should choke up the mouth of\nthe river, or an earthquake change its course, and remove it to a\ndistance from the town, the name of the town would not necessarily be\nchanged. That fact, therefore, can form no part of the signification of\nthe word; for otherwise, when the fact confessedly ceased to be true, no\none would any longer think of applying the name. Proper names are\nattached to the objects themselves, and are not dependent on the\ncontinuance 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, though we may give to an individual a name utterly unmeaning, which\nwe call a proper name,--a 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. \"The sun\" is a name of this\ndescription; \"God,\" when used by a monotheist, is another. These,\nhowever, are scarcely examples of what we are now attempting to\nillustrate, being, in strictness of language, general, not individual\nnames: for, however they may be _in fact_ predicable only of one object,\nthere is nothing in the meaning of the words themselves which implies\nthis: and, accordingly, when we are imagining and not affirming, we may\nspeak of many suns; and the majority of mankind have believed, and still\nbelieve, that there are many gods. But it is easy to produce words which\nare real instances of connotative individual names. It may be part of\nthe meaning of the connotative name itself, that there can exist but\none individual possessing the attribute which it connotes: as, for\ninstance, \"the _only_ son of John Stiles;\" \"the _first_ emperor of\nRome.\" Or the attribute connoted may be a connexion with some\ndeterminate event, and the connexion may be of such a kind as only one\nindividual could have; or may at least be such as only one individual\nactually had; and this may be implied in the form of the expression.\n\"The father of Socrates\" is an example of the one kind (since Socrates\ncould not have had two fathers); \"the author of the Iliad,\" \"the\nmurderer of Henri Quatre,\" of the second. For, though it is conceivable\nthat more persons than one might have participated in the authorship of\nthe Iliad, or in the murder of Henri Quatre, the employment of the\narticle _the_ implies that, in fact, this was not the case. What is here\ndone by the word _the_, is done in other cases by the context: thus,\n\"C\u00e6sar's army\" is an individual name, if it appears from the context\nthat the army meant is that which C\u00e6sar commanded in a particular\nbattle. The still more general expressions, \"the Roman army,\" or \"the\nChristian army,\" may be individualized in a similar manner. Another case\nof frequent occurrence has already been noticed; it is the following.\nThe name, being a many-worded one, may consist, in the first place, of a\n_general_ name, capable therefore in itself of being affirmed of more\nthings than one, but which is, in the second place, so limited by other\nwords joined with it, that the entire expression can only be predicated\nof one object, consistently with the meaning of the general term. This\nis exemplified in such an instance as the following: \"the present prime\nminister of England.\" Prime Minister of England is a general name; the\nattributes which it connotes may be possessed by an indefinite number of\npersons: in succession however, not simultaneously; since the meaning of\nthe name itself imports (among other things) that there can be only one\nsuch person at a time. This being the case, and the application of the\nname being afterwards limited by the article and the word _present_, to\nsuch individuals as possess the attributes at one indivisible point of\ntime, it becomes applicable only to one individual. And as this appears\nfrom the meaning of the name, without any extrinsic proof, it is\nstrictly an individual name.\n\nFrom the preceding observations it will easily be collected, that\nwhenever the names given to objects convey any information, that is,\nwhenever they have properly any meaning, the meaning resides not in what\nthey _denote_, but in what they _connote_. The only names of objects\nwhich connote nothing are _proper_ names; and these have, strictly\nspeaking, no signification.[6]\n\nIf, like the robber in the Arabian Nights, we make a mark with chalk on\na house to enable us to know it again, the mark has a purpose, but it\nhas not properly any meaning. The chalk does not declare anything about\nthe house; it does not mean, This is such a person's house, or This is a\nhouse which contains booty. The object of making the mark is merely\ndistinction. I say to myself, All these houses are so nearly alike that\nif I lose sight of them I shall not again be able to distinguish that\nwhich I am now looking at, from any of the others; I must therefore\ncontrive to make the appearance of this one house unlike that of the\nothers, that I may hereafter know, when I see the mark--not indeed any\nattribute of the house--but simply that it is the same house which I am\nnow looking at. Morgiana chalked all the other houses in a similar\nmanner, and defeated the scheme: how? simply by obliterating the\ndifference of appearance between that house and the others. The chalk\nwas still there, but it no longer served the purpose of a distinctive\nmark.\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\nin our minds with the idea of the object, in order that whenever the\nmark meets our eyes or occurs to our thoughts, we may think of that\nindividual object. Not being attached to the thing itself, it does not,\nlike the chalk, enable us to distinguish the object when we see it; but\nit enables us to distinguish it when it is spoken of, either in the\nrecords of our own experience, or in the discourse of others; to know\nthat what we find asserted in any proposition of which it is the\nsubject, is asserted of the individual thing with which we were\npreviously acquainted.\n\nWhen we predicate of anything its proper name; when we say, pointing to\na man, this is Brown or Smith, or pointing to a city, that it is York,\nwe do not, merely by so doing, convey to the hearer any information\nabout them, except that those are their names. By enabling him to\nidentify the individuals, we may connect them with information\npreviously possessed by him; by saying, This is York, we may tell him\nthat it contains the Minster. But this is in virtue of what he has\npreviously heard concerning York; not by anything implied in the name.\nIt is otherwise when objects are spoken of by connotative names. When we\nsay, The town is built of marble, we give the hearer what may be\nentirely new information, and this merely by the signification of the\nmany-worded connotative name, \"built of marble.\" Such names are not\nsigns of the mere objects, invented because we have occasion to think\nand speak of those objects individually; but signs which accompany an\nattribute: a kind of livery in which the attribute clothes all objects\nwhich are recognised as possessing it. They are not mere marks, but\nmore, that is to say, significant marks; and the connotation is what\nconstitutes their significance.\n\nAs a proper name is said to be the name of the one individual which it\nis predicated of, so (as well from the importance of adhering to\nanalogy, as for the other reasons formerly assigned) a connotative name\nought to be considered a name of all the various individuals which it is\npredicable of, or in other words _denotes_, and not of what it connotes.\nBut by learning what things it is a name of, we do not learn the meaning\nof the name: for to the same thing we may, with equal propriety, apply\nmany names, not equivalent in meaning. Thus, I call a certain man by the\nname Sophroniscus: I call him by another name, The father of Socrates.\nBoth these are names of the same individual, but their meaning is\naltogether different; they are applied to that individual for two\ndifferent purposes; the one, merely to distinguish him from other\npersons who are spoken of; the other to indicate a fact relating to him,\nthe fact that Socrates was his son. I further apply to him these other\nexpressions: a man, a Greek, an Athenian, a sculptor, an old man, an\nhonest man, a brave man. All these are, or may be, names of\nSophroniscus, not indeed of him alone, but of him and each of an\nindefinite 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\nmeaning. It is even possible that I might know every single individual\nof whom a given name could be with truth affirmed, and yet could not be\nsaid to know the meaning of the name. A child knows who are its brothers\nand sisters, long before it has any definite conception of the nature of\nthe facts which 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\noccasion a difference in the name. Thus, it is clear that the word man,\nbesides animal life and rationality, connotes also a certain external\nform; but it would be impossible to say precisely what form; that is, to\ndecide how great a deviation from the form ordinarily found in the\nbeings whom we are accustomed to call men, would suffice in a\nnewly-discovered race to make us refuse them the name of man.\nRationality, also, being a quality which admits of degrees, it has never\nbeen settled what is the lowest degree of that quality which would\nentitle any creature to be considered a human being. In all such cases,\nthe meaning of the general name is so far unsettled and vague; mankind\nhave not come to any positive agreement about the matter. When we come\nto treat of Classification, we shall have occasion to show under what\nconditions this vagueness may exist without practical inconvenience; and\ncases will appear in which the ends of language are better promoted by\nit than by complete precision; in order that, in natural history for\ninstance, individuals or species of no very marked character may be\nranged with those more strongly characterized individuals or species to\nwhich, in all their properties taken together, they bear the nearest\nresemblance.\n\nBut this partial uncertainty in the connotation of names can only be\nfree from 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\nfrom observing what objects they are used to denote. It is in this\nmanner that we all acquire, and inevitably so, our first knowledge of\nour vernacular language. A child learns the meaning of the words _man_,\nor _white_, by hearing them applied to a variety of individual objects,\nand finding out, by a process of generalization and analysis which he\ncould not himself describe, what those different objects have in common.\nIn the case of these two words the process is so easy as to require no\nassistance from culture; the objects called human beings, and the\nobjects called white, differing from all others by qualities of a\npeculiarly definite and obvious character. But in many other cases,\nobjects bear a general resemblance to one another, which leads to their\nbeing familiarly classed together under a common name, while, without\nmore analytic habits than the generality of mankind possess, it is not\nimmediately apparent what are the particular attributes, upon the\npossession of which in common by them all, their general resemblance\ndepends. When this is the case, people use the name without any\nrecognised connotation, that is, without any precise meaning; they talk,\nand consequently think, vaguely, and remain contented to attach only the\nsame degree of significance to their own words, which a child three\nyears old attaches to the words brother and sister. The child at least\nis seldom puzzled by the starting up of new individuals, on whom he is\nignorant whether or not to confer the title; because there is usually an\nauthority close at hand competent to solve all doubts. But a similar\nresource does not exist in the generality of cases; and new objects are\ncontinually presenting themselves to men, women, and children, which\nthey are called upon to class _proprio motu_. They, accordingly, do this\non 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\nthem most to resemble: as an unknown substance found in the ground will\nbe called, according to its texture, earth, sand, or a stone. In this\nmanner, names creep on from subject to subject, until all traces of a\ncommon meaning sometimes disappear, and the word comes to denote a\nnumber of things not only independently of any common attribute, but\nwhich have actually no attribute in common; or none but what is shared\nby other things to which the name is capriciously refused. Even\nscientific writers have aided in this perversion of general language\nfrom its purpose; sometimes because, like the vulgar, they knew no\nbetter; and sometimes in deference to that aversion to admit new words,\nwhich induces mankind, on all subjects not considered technical, to\nattempt to make the original stock of names serve with but little\naugmentation to express a constantly increasing number of objects and\ndistinctions, and, consequently, to express them in a manner\nprogressively more and more imperfect.\n\nTo what a degree this loose mode of classing and denominating objects\nhas rendered the vocabulary of mental and moral philosophy unfit for the\npurposes of accurate thinking, is best known to whoever has most\nmeditated on the present condition of those branches of knowledge.\nSince, however, the introduction of a new technical language as the\nvehicle of speculations on subjects belonging to the domain of daily\ndiscussion, is extremely difficult to effect, and would not be free from\ninconvenience even if effected, the problem for the philosopher, and one\nof the most difficult which he has to resolve, is, in retaining the\nexisting phraseology, how best to alleviate its imperfections. This can\nonly be accomplished by giving to every general concrete name which\nthere is frequent occasion to predicate, a definite and fixed\nconnotation; in order that it may be known what attributes, when we call\nan object by that name, we really mean to predicate of the object. And\nthe question of most nicety is, how to give this fixed connotation to a\nname, with the least possible change in the objects which the name is\nhabitually employed to denote; with the least possible disarrangement,\neither by adding or subtraction, of the group of objects which, in\nhowever imperfect a manner, it serves to circumscribe and hold together;\nand with the least vitiation of the truth of any propositions which are\ncommonly received as true.\n\nThis desirable purpose, of giving a fixed connotation where it is\nwanting, is the end aimed at whenever any one attempts to give a\ndefinition of a general name already in use; every definition of a\nconnotative name being an attempt either merely to declare, or to\ndeclare and analyse, the connotation of the name. And the fact, that no\nquestions which have arisen in the moral sciences have been subjects of\nkeener controversy than the definitions of almost all the leading\nexpressions, is a proof how great an extent the evil to which we have\nadverted 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\nones; as the word _post_, for example, or the word _box_, the various\nsenses of which it would be endless to enumerate. And the paucity of\nexisting names, in comparison with the demand for them, may often render\nit advisable and even necessary to retain a name in this multiplicity\nof acceptations, distinguishing these so clearly as to prevent their\nbeing confounded with one another. Such a word may be considered as two\nor more names, accidentally written and spoken alike.[7]\n\n\n\u00a7 6. The fourth principal division of names, is into _positive_ and\n_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,\n_not-tree_, _not-good_. To every positive concrete name, a corresponding\nnegative one might be framed. After giving a name to any one thing, or\nto any plurality of things, we might create a second name which should\nbe a name of all things whatever, except that particular thing or\nthings. These negative names are employed whenever we have occasion to\nspeak collectively of all things other than some thing or class of\nthings. When the positive name is connotative, the corresponding\nnegative name is connotative likewise; but in a peculiar way, connoting\nnot the presence but the absence of an attribute. Thus, _not-white_\ndenotes all things whatever except white things; and connotes the\nattribute of not possessing whiteness. For the non-possession of any\ngiven attribute is also an attribute, and may receive a name as such;\nand thus negative concrete names may obtain negative abstract names to\ncorrespond to them.\n\nNames which are positive in form are often negative in reality, and\nothers are 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\nof discomfort or annoyance. So the word _unpleasant_, notwithstanding\nits negative form, does not connote the mere absence of pleasantness,\nbut a less degree of what is signified by the word _painful_, which, it\nis hardly necessary to say, is positive. _Idle_, on the other hand, is a\nword which, 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\ndrunken_.\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\nto _not seeing_, or to _not capable of seeing_, for it would not, except\nby a poetical or rhetorical figure, be applied to stocks and stones. A\nthing is not usually said to be blind, unless the class to which it is\nmost familiarly referred, or to which it is referred on the particular\noccasion, be chiefly composed of things which can see, as in the case of\na blind man, or a blind horse; or unless it is supposed for any reason\nthat it ought to see; as in saying of a man, that he rushed blindly into\nan abyss, or of philosophers or the clergy that the greater part of them\nare blind guides. The names called privative, therefore, connote two\nthings: the absence of certain attributes, and the presence of others,\nfrom which the presence also of the former might naturally have been\nexpected.\n\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\nthe word _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),\nof which 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\nanother distance which is shorter. When we say of any object that it is\nlike, we mean that it is like some other object, which is also said to\nbe like the first. In this last case both objects receive the same name;\nthe relative term 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\nconcrete _like_ has its abstract _likeness_; the concretes, father and\nson, have, or might have, the abstracts, paternity, and filiety, or\nsonship. The concrete name connotes an attribute, and the abstract name\nwhich answers to it denotes that attribute. But of what nature is the\nattribute? Wherein consists the peculiarity in the connotation of a\nrelative 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\ninsight may best be obtained into the nature of all attributes: of all\nthat is meant by an attribute.\n\nIt is obvious, in fact, that if we take any two correlative names,\n_father_ and _son_ for instance, though the objects _de_noted by the\nnames are different, they both, in a certain sense, connote the same\nthing. They cannot, indeed, be said to connote the same _attribute_: to\nbe a father, is not the same thing as to be a son. But when we call one\nman a father, another a son, what we mean to affirm is a set of facts,\nwhich are exactly the same in both cases. To predicate of A that he is\nthe father of B, and of B that he is the son of A, is to assert one and\nthe same fact in different words. The two propositions are exactly\nequivalent: neither of them asserts more or asserts less than the\nother. The paternity of A and the filiety of B are not two facts, but\ntwo modes of expressing the same fact. That fact, when analysed,\nconsists of a series of physical events or phenomena, in which both A\nand B are parties concerned, and from which they both derive names. What\nthose names really connote, is this series of events: that is the\nmeaning, and the whole meaning, which either of them is intended to\nconvey. The series of events may be said to _constitute_ the relation;\nthe schoolmen called it the foundation of the relation, _fundamentum\nrelationis_.\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\nthem, may be either considered as constituting an attribute of the one,\nor an attribute of the other. According as we consider it in the former,\nor in the latter aspect, it is connoted by the one or the other of the\ntwo correlative names. _Father_ connotes the fact, regarded as\nconstituting an attribute of A: _son_ connotes the same fact, as\nconstituting an attribute of B. It may evidently be regarded with equal\npropriety in either light. And all that appears necessary to account for\nthe existence of relative names, is, that whenever there is a fact in\nwhich two individuals are concerned, an attribute grounded on that fact\nmay be ascribed to either of these individuals.\n\nA name, therefore, is said to be relative, when, over and above the\nobject which it denotes, it implies in its signification the existence\nof another object, also deriving a denomination from the same fact which\nis the ground of the first name. Or (to express the same meaning in\nother words) a name is relative, when, being the name of one thing, its\nsignification cannot be explained but by mentioning another. Or we may\nstate it thus--when the name cannot be employed in discourse so as to\nhave a meaning, unless the name of some other thing than what it is\nitself the name of, be either expressed or understood. These definitions\nare all, at bottom, equivalent, being modes of variously expressing this\none distinctive circumstance--that every other attribute of an object\nmight, without any contradiction, be conceived still to exist if no\nobject besides that one had ever existed;[8] but those of its\nattributes which are expressed by relative names, would on that\nsupposition be swept away.\n\n\n\u00a7 8. Names have been further distinguished into _univocal_ and\n_\u00e6quivocal_: these, however, are not two kinds of names, but two\ndifferent modes of employing names. A name is univocal, or applied\nunivocally, with respect to all things of which it can be predicated _in\nthe same sense_: it is \u00e6quivocal, or applied \u00e6quivocally, as respects\nthose things of which it is predicated in different senses. It is\nscarcely necessary to give instances of a fact so familiar as the double\nmeaning of a word. In reality, as has been already observed, an\n\u00e6quivocal or ambiguous word is not one name, but two names, accidentally\ncoinciding in sound. _File_ meaning a steel instrument, and _file_\nmeaning a line of soldiers, have no more title to be considered one\nword, because written alike, than _grease_ and _Greece_ have, because\nthey are pronounced alike. They are one sound, appropriated to form two\ndifferent 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\nthem may be considered the primary, and the other a secondary\nsignification. As when we speak of a brilliant light and a brilliant\nachievement. The word is not applied in the same sense to the light and\nto the achievement; but having been applied to the light in its original\nsense, that of brightness to the eye, it is transferred to the\nachievement in a derivative signification, supposed to be somewhat like\nthe primitive one. The word, however, is just as properly two names\ninstead of one, in this case, as in that of the most perfect ambiguity.\nAnd one of the commonest forms of fallacious reasoning arising from\nambiguity, is that of arguing from a metaphorical expression as if it\nwere literal; that is, as if a word, when applied metaphorically, were\nthe same name as when taken in its original sense: which will be seen\nmore particularly in its place.\n\n\n\n\nCHAPTER III.\n\nOF THE THINGS DENOTED BY NAMES.\n\n\n\u00a7 1. Looking back now to the commencement of our inquiry, let us attempt\nto measure how far it has advanced. Logic, we found, is the Theory of\nProof. But proof supposes something provable, which must be a\nProposition or Assertion; since nothing but a Proposition can be an\nobject of belief, or therefore of proof. A Proposition is, discourse\nwhich affirms or denies something of some other thing. This is one step:\nthere must, it seems, be two things concerned in every act of belief.\nBut what are these Things? They can be no other than those signified by\nthe two names, which being joined together by a copula constitute the\nProposition. If, therefore, we knew what all names signify, we should\nknow everything which in the existing state of human knowledge, is\ncapable either of being made a subject of affirmation or denial, or of\nbeing itself affirmed or denied of a subject. We have accordingly, in\nthe preceding chapter, reviewed the various kinds of Names, in order to\nascertain what is signified by each of them. And we have now carried\nthis survey far enough to be able to take an account of its results, and\nto exhibit an enumeration of all 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,\ndid not escape the attention of the schoolmen, and of their master\nAristotle, the most comprehensive, if not also the most sagacious, of\nthe ancient philosophers. The Categories, or Predicaments--the former a\nGreek word, the latter its literal translation in the Latin\nlanguage--were intended by him and his followers as an enumeration of\nall things capable of being named; an enumeration by the _summa\ngenera_, _i.e._ the most extensive classes into which things could be\ndistributed; which, therefore, were so many highest Predicates, one or\nother of which was supposed capable of being affirmed with truth of\nevery nameable thing whatsoever. The following are the classes into\nwhich, according to this school of philosophy, Things in general might\nbe reduced:--\n\n [Greek: Ousia], Substantia.\n [Greek: Poson], Quantitas.\n [Greek: Poion], Qualitas.\n [Greek: Pros ti], Relatio.\n [Greek: Poiein], Actio.\n [Greek: Paschein], Passio.\n [Greek: Pou], Ubi.\n [Greek: Pote], Quando.\n [Greek: Keisthai], Situs.\n [Greek: Echein], 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\nomitted, and others repeated several times under different heads. It is\nlike a division of animals into men, quadrupeds, horses, asses, and\nponies. That, for instance, could not be a very comprehensive view of\nthe nature of Relation which could exclude action, passivity, and local\nsituation from that category. The same observation applies to the\ncategories Quando (or position in time), and Ubi (or position in space);\nwhile the distinction between the latter and Situs is merely verbal. The\nincongruity of erecting into a _summum genus_ the class which forms the\ntenth category is manifest. On the other hand, the enumeration takes no\nnotice of anything besides substances and attributes. In what category\nare we to place sensations, or any other feelings and states of mind; as\nhope, joy, fear; sound, smell, taste; pain, pleasure; thought, judgment,\nconception, and the like? Probably all these would have been placed by\nthe Aristotelian school in the categories of _actio_ and _passio_; and\nthe relation of such of them as are active, to their objects, and of\nsuch of them as are passive, to their causes, would rightly be so\nplaced; but the things themselves, the feelings or states of mind,\nwrongly. Feelings, or states of consciousness, are assuredly to be\ncounted among realities, but they cannot be reckoned either among\nsubstances or attributes.\n\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\nonly substances. But substances are not all that exists; attributes, if\nsuch things are to be spoken of, must be said to exist; feelings\ncertainly exist. Yet when we speak of an _object_, or of a _thing_, we\nare almost always supposed to mean a substance. There seems a kind of\ncontradiction in using such an expression as that one _thing_ is merely\nan attribute of another thing. And the announcement of a Classification\nof Things would, I believe, prepare most readers for an enumeration like\nthose in natural history, beginning with the great divisions of animal,\nvegetable, and mineral, and subdividing them into classes and orders.\nIf, rejecting the word Thing, we endeavour to find another of a more\ngeneral import, or at least more exclusively confined to that general\nimport, a word denoting all that exists, and connoting only simple\nexistence; no word might be presumed fitter for such a purpose than\n_being_: originally the present participle of a verb which in one of its\nmeanings is exactly equivalent to the verb _exists_; and therefore\nsuitable, even by its grammatical formation, to be the concrete of the\nabstract _existence_. But this word, strange as the fact may appear, is\nstill more completely spoiled for the purpose which it seemed expressly\nmade for, than the word Thing. _Being_ is, by custom, exactly synonymous\nwith substance; except that it is free from a slight taint of a second\nambiguity; being applied impartially to matter and to mind, while\nsubstance, though originally and in strictness applicable to both, is\napt to suggest in preference the idea of matter. Attributes are never\ncalled Beings; nor are feelings. A Being is that which excites feelings,\nand which possesses attributes. The soul is called a Being; God and\nangels are called Beings; but if we were to say, extension, colour,\nwisdom, virtue, are beings, we should perhaps be suspected of thinking\nwith some of the ancients, that the cardinal virtues are animals; or, at\nthe least, of holding with the Platonic school the doctrine of\nself-existent Ideas, or with the followers of Epicurus that of Sensible\nForms, which detach themselves in every direction from bodies, and by\ncoming in contact with our organs, cause our perceptions. We should be\nsupposed, in short, to believe that Attributes are Substances.\n\nIn consequence of this perversion of the word Being, philosophers\nlooking about for something to supply its place, laid their hands upon\nthe word Entity, a piece of barbarous Latin, invented by the schoolmen\nto be used as an abstract name, in which class its grammatical form\nwould seem to place it; but being seized by logicians in distress to\nstop a leak in their terminology, it has ever since been used as a\nconcrete name. The kindred word _essence_, born at the same time and of\nthe same parents, scarcely underwent a more complete transformation\nwhen, from being the abstract of the verb _to be_, it came to denote\nsomething sufficiently concrete to be enclosed in a glass bottle. The\nword Entity, since it settled down into a concrete name, has retained\nits universality of signification somewhat less impaired than any of the\nnames before mentioned. Yet the same gradual decay to which, after a\ncertain age, all the language of psychology seems liable, has been at\nwork even here. If you call virtue an _entity_, you are indeed somewhat\nless strongly suspected of believing it to be a substance than if you\ncalled it a _being_; but you are by no means free from the suspicion.\nEvery word which was originally intended to connote mere existence,\nseems, after a long time, to enlarge its connotation to _separate_\nexistence, or existence freed from the condition of belonging to a\nsubstance; which condition being precisely what constitutes an\nattribute, attributes are gradually shut out; and along with them\nfeelings, which in ninety-nine cases out of a hundred have no other name\nthan that of the attribute which is grounded on them. Strange that when\nthe greatest embarrassment felt by all who have any considerable number\nof thoughts to express, is to find a sufficient variety of precise words\nfitted to express them, there should be no practice to which even\nscientific thinkers are more addicted than that of taking valuable words\nto express ideas which are sufficiently expressed by other words already\nappropriated to them.\n\nWhen it is impossible to obtain good tools, the next best thing is to\nunderstand thoroughly the defects of those we have. I have therefore\nwarned the reader of the ambiguity of the names which, for want of\nbetter, I am necessitated to employ. It must now be the writer's\nendeavour so to employ them as in no case to leave the meaning doubtful\nor obscure. No one of the above terms being altogether unambiguous, I\nshall not confine myself to any one, but shall employ on each occasion\nthe word which seems least likely in the particular case to lead to\nmisunderstanding; nor do I pretend to use either these or any other\nwords with a rigorous adherence to one single sense. To do so would\noften leave us without a word to express what is signified by a known\nword in some one or other of its senses: unless authors had an unlimited\nlicence to coin new words, together with (what it would be more\ndifficult to assume) unlimited power of making readers understand them.\nNor would it be wise in a writer, on a subject involving so much of\nabstraction, to deny himself the advantage derived from even an improper\nuse of a term, when, by means of it, some familiar association is called\nup which brings the meaning home to the mind, as it were by a flash.\n\nThe difficulty both to the writer and reader, of the attempt which must\nbe made to use vague words so as to convey a precise meaning, is not\nwholly a matter of regret. It is not unfitting that logical treatises\nshould afford an example of that, to facilitate which is among the most\nimportant uses of logic. Philosophical language will for a long time,\nand popular language still longer, retain so much of vagueness and\nambiguity, that logic would be of little value if it did not, among its\nother advantages, exercise the understanding in doing its work neatly\nand correctly with these 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\nI. FEELINGS, OR STATES OF CONSCIOUSNESS.\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,\nwhich forms a part of its own sentient existence. In popular language\nFeeling is not always synonymous with State of Consciousness; being\noften taken more peculiarly for those states which are conceived as\nbelonging to the sensitive, or to the emotional, phasis of our nature,\nand sometimes, with a still narrower restriction, to the emotional\nalone, as distinguished from what are conceived as belonging to the\npercipient or to the intellectual phasis. But this is an admitted\ndeparture from correctness of language; just as, by a popular perversion\nthe exact converse of this, the word Mind is withdrawn from its rightful\ngenerality of signification, and restricted to the intellect. The still\ngreater perversion by which Feeling is sometimes confined not only to\nbodily sensations, but to the sensations of a single sense, that of\ntouch, needs not be more particularly adverted to.\n\nFeeling, in the proper sense of the term, is a genus, of which\nSensation, Emotion, and Thought, are subordinate species. Under the word\nThought is here to be included whatever we are internally conscious of\nwhen we are said to think; from the consciousness we have when we think\nof a red colour without having it before our eyes, to the most recondite\nthoughts of a philosopher or poet. Be it remembered, however, that by a\nthought is to be understood what passes in the mind itself, and not any\nobject external to the mind, which the person is commonly said to be\nthinking of. He may be thinking of the sun, or of God, but the sun and\nGod are not thoughts; his mental image, however, of the sun, and his\nidea of God, are thoughts; states of his mind, not of the objects\nthemselves; and so also is his belief of the existence of the sun, or of\nGod; or his disbelief, if the case be so. Even imaginary objects (which\nare said to exist only in our ideas) are to be distinguished from our\nideas of them. I may think of a hobgoblin, as I may think of the loaf\nwhich was eaten yesterday, or of the flower which will bloom to-morrow.\nBut the hobgoblin which never existed is not the same thing with my idea\nof a hobgoblin, any more than the loaf which once existed is the same\nthing with my idea of a loaf, or the flower which does not yet exist,\nbut which will exist, is the same with my idea of a flower. They are\nall, not thoughts, but objects of thought; though at the present time\nall the objects are alike non-existent.\n\nIn like manner, a Sensation is to be carefully distinguished from the\nobject which causes the sensation; our sensation of white from a white\nobject: nor is it less to be distinguished from the attribute whiteness,\nwhich we ascribe to the object in consequence of its exciting the\nsensation. Unfortunately for clearness and due discrimination in\nconsidering these subjects, our sensations seldom receive separate\nnames. We have a name for the objects which produce in us a certain\nsensation: the word _white_. We have a name for the quality in those\nobjects, to which we ascribe the sensation: the name _whiteness_. But\nwhen we speak of the sensation itself (as we have not occasion to do\nthis often except in our scientific speculations), language, which\nadapts itself for the most part only to the common uses of life, has\nprovided us with no single-worded or immediate designation; we must\nemploy a circumlocution, and say, The sensation of white, or The\nsensation of whiteness; we must denominate the sensation either from the\nobject, or from the attribute, by which it is excited. Yet the\nsensation, though it never _does_, might very well be _conceived_ to\nexist, without anything whatever to excite it. We can conceive it as\narising spontaneously in the mind. But if it so arose, we should have no\nname to denote it which would not be a misnomer. In the case of our\nsensations of hearing we are better provided; we have the word Sound,\nand a whole vocabulary of words to denote the various kinds of sounds.\nFor as we are often conscious of these sensations in the absence of any\nperceptible object, we can more easily conceive having them in the\nabsence of any object whatever. We need only shut our eyes and listen to\nmusic, to have a conception of 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.\nThus, _colour_ stands for the sensations of white, red, &c., but also\nfor the quality in the coloured object. We talk of the colours of things\nas among their _properties_.\n\n\n\u00a7 4. In the case of sensations, another distinction has also to be kept\nin view, 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\nthe sentient mind, not states of the body, as distinguished from it.\nWhat I am conscious of when I see the colour blue, is a feeling of blue\ncolour, which is one thing; the picture on my retina, or the phenomenon\nof hitherto mysterious nature which takes place in my optic nerve or in\nmy brain, is another thing, of which I am not at all conscious, and\nwhich scientific investigation alone could have apprised me of. These\nare states of my body; but the sensation of blue, which is the\nconsequence of these states of body, is not a state of body: that which\nperceives and is conscious is called Mind. When sensations are called\nbodily feelings, it is only as being the class of feelings which are\nimmediately occasioned by bodily states; whereas the other kinds of\nfeelings, thoughts, for instance, or emotions, are immediately excited\nnot by anything acting upon the bodily organs, but by sensations, or by\nprevious thoughts. This, however, is a distinction not in our feelings,\nbut in the agency which produces our feelings: all of them when actually\nproduced are states of mind.\n\nBesides the affection of our bodily organs from without, and the\nsensation thereby produced in our minds, many writers admit a third link\nin the chain of phenomena, which they call a Perception, and which\nconsists in the recognition of an external object as the exciting cause\nof the sensation. This perception, they say, is an _act_ of the mind,\nproceeding from its own spontaneous activity; while in a sensation the\nmind is passive, being merely acted upon by the outward object. And\naccording to some metaphysicians, it is by an act of the mind, similar\nto perception, except in not being preceded by any sensation, that the\nexistence of God, the soul, and other hyper-physical objects is\nrecognised.\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[9]) to indicate that as they\nare \"_merely_ states of mind,\" it is superfluous to inquire into their\ndistinguishing peculiarities. I abstain from the inquiry as irrelevant\nto the science of logic. In these so-called perceptions, or direct\nrecognitions by the mind, of objects, whether physical or spiritual,\nwhich are external to itself, I can see only cases of belief; but of\nbelief which claims to be intuitive, or independent of external\nevidence. When a stone lies before me, I am conscious of certain\nsensations which I receive from it; but if I say that these sensations\ncome to me from an external object which I _perceive_, the meaning of\nthese words is, that receiving the sensations, I intuitively _believe_\nthat an external cause of those sensations exists. The laws of intuitive\nbelief, and the conditions under which it is legitimate, are a subject\nwhich, as we have already so often remarked, belongs not to logic, but\nto the science of the ultimate laws of the human mind.\n\nTo the same region of speculation belongs all that can be said\nrespecting the distinction which the German metaphysicians and their\nFrench and English followers so elaborately draw between the _acts_ of\nthe mind and its merely passive _states_; between what it receives from,\nand what it gives to, the crude materials of its experience. I am aware\nthat with reference to the view which those writers take of the primary\nelements of thought and knowledge, this distinction is fundamental. But\nfor the present purpose, which is to examine, not the original\ngroundwork of our knowledge, but how we come by that portion of it which\nis not original; the difference between active and passive states of\nmind is of secondary importance. For us, they all are states of mind,\nthey all are feelings; by which, let it be said once more, I mean to\nimply nothing of passivity, but simply that they are psychological\nfacts, facts which take place in the mind, and are to be carefully\ndistinguished from the external or physical facts with which they may be\nconnected either as effects or as causes.\n\n\n\u00a7 5. Among active states of mind, there is, however, one species which\nmerits particular attention, because it forms a principal part of the\nconnotation of some important classes of names. I mean _volitions_, or\nacts of the will. When we speak of sentient beings by relative names, a\nlarge portion of the connotation of the name usually consists of the\nactions of those beings; actions past, present, and possible or probable\nfuture. Take, for instance, the words Sovereign and Subject. What\nmeaning do these words convey, but that of innumerable actions, done or\nto be done by the sovereign and the subjects, to or in regard to one\nanother reciprocally? So with the words physician and patient, leader\nand follower, tutor and pupil. In many cases the words also connote\nactions which would be done under certain contingencies by persons other\nthan those denoted: as the words mortgagor and mortgagee, obligor and\nobligee, and many other words expressive of legal relation, which\nconnote what a court of justice would do to enforce the legal obligation\nif not fulfilled. There are also words which connote actions previously\ndone by persons other than those denoted either by the name itself or by\nits correlative; as the word brother. From these instances, it may be\nseen how large a portion of the connotation of names consists of\nactions. Now what is an action? Not one thing, but a series of two\nthings: the state of mind called a volition, followed by an effect. The\nvolition or intention to produce the effect, is one thing; the effect\nproduced in consequence of the intention, is another thing; the two\ntogether constitute the action. I form the purpose of instantly moving\nmy arm; that is a state of my mind: my arm (not being tied or paralytic)\nmoves in obedience to my purpose; that is a physical fact, consequent on\na state of mind. The intention, followed by the fact, or (if we prefer\nthe expression) the fact when preceded and caused by the intention, is\ncalled the action of moving my arm.\n\n\n\u00a7 6. Of the first leading division of nameable things, viz. Feelings or\nStates of Consciousness, we began by recognising three subdivisions;\nSensations, Thoughts, and Emotions. The first two of these we have\nillustrated at considerable length; the third, Emotions, not being\nperplexed by similar ambiguities, does not require similar\nexemplification. And, finally, we have found it necessary to add to\nthese three a fourth species, commonly known by the name Volitions.\nWithout seeking to prejudge the metaphysical question whether any mental\nstate or phenomenon can be found which is not included in one or other\nof these four species, it appears to me that the amount of illustration\nbestowed upon these may, so far as we are concerned, suffice for the\nwhole genus. We shall, therefore, proceed to the two remaining classes\nof nameable things; all things which are external to the mind being\nconsidered as belonging either to the class of Substances or to that of\nAttributes.\n\nII. SUBSTANCES.\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\nmake in the grammatical structure of the sentence, according as we are\nspeaking of substances or of attributes. Such definitions are rather\nlessons of English, or of Greek, Latin, or German, than of mental\nphilosophy. An attribute, say the school logicians, must be the\nattribute _of_ something; colour, for example, must be the colour _of_\nsomething; goodness must be the goodness _of_ something: and if this\nsomething should cease to exist, or should cease to be connected with\nthe attribute, the existence of the attribute would be at an end. A\nsubstance, on the contrary, is self-existent; in speaking about it, we\nneed not put _of_ after its name. A stone is not the stone _of_\nanything; the moon is not the moon _of_ anything, but simply the moon.\nUnless, indeed, the name which we choose to give to the substance be a\nrelative name; if so, it must be followed either by _of_, or by some\nother particle, implying, as that preposition does, a reference to\nsomething else: but then the other characteristic peculiarity of an\nattribute would fail; the _something_ might be destroyed, and the\nsubstance might still subsist. Thus, a father must be the father _of_\nsomething, and so far resembles an attribute, in being referred to\nsomething besides himself: if there were no child, there would be no\nfather: but this, when we look into the matter, only means that we\nshould not call him father. The man called father might still exist\nthough there were no child, as he existed before there was a child: and\nthere would be no contradiction in supposing him to exist, though the\nwhole universe except himself were destroyed. But destroy all white\nsubstances, and where would be the attribute whiteness? Whiteness,\nwithout any white thing, is a contradiction in terms.\n\nThis is the nearest approach to a solution of the difficulty, that will\nbe found in the common treatises on logic. It will scarcely be thought\nto be a satisfactory one. If an attribute is distinguished from a\nsubstance by being the attribute _of_ something, it seems highly\nnecessary to understand what is meant by _of_; a particle which needs\nexplanation too much itself, to be placed in front of the explanation of\nanything else. And as for the self-existence of substance, it is very\ntrue that a substance may be conceived to exist without any other\nsubstance, but so also may an attribute without any other attribute: and\nwe can no more imagine a substance without attributes than we can\nimagine attributes without a substance.\n\nMetaphysicians, however, have probed the question deeper, and given an\naccount of Substance considerably more satisfactory than this.\nSubstances are usually distinguished as Bodies or Minds. Of each of\nthese, philosophers have at length provided us with a definition which\nseems unexceptionable.\n\n\n\u00a7 7. A Body, according to the received doctrine of modern\nmetaphysicians, may be defined, the external cause to which we ascribe\nour sensations. When I see and touch a piece of gold, I am conscious of\na sensation of yellow colour, and sensations of hardness and weight; and\nby varying the mode of handling, I may add to these sensations many\nothers completely distinct from them. The sensations are all of which I\nam directly conscious; but I consider them as produced by something not\nonly existing independently of my will, but external to my bodily organs\nand to my mind. This external something I call a body.\n\nIt may be asked, how come we to ascribe our sensations to any external\ncause? And is there sufficient ground for so ascribing them? It is\nknown, that there are metaphysicians who have raised a controversy on\nthe point; maintaining that we are not warranted in referring our\nsensations to a cause such as we understand by the word Body, or to any\nexternal cause whatever. Though we have no concern here with this\ncontroversy, nor with the metaphysical niceties on which it turns, one\nof the best ways of showing what is meant by Substance is, to consider\nwhat position it is necessary to take up, in order to maintain its\nexistence against 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\nbeings, habitually occurring simultaneously. My conception of the table\nat which I am writing is compounded of its visible form and size, which\nare complex sensations of sight; its tangible form and size, which are\ncomplex sensations of our organs of touch and of our muscles; its\nweight, which is also a sensation of touch and of the muscles; its\ncolour, which is a sensation of sight; its hardness, which is a\nsensation of the muscles; its composition, which is another word for all\nthe varieties of sensation which we receive under various circumstances\nfrom the wood of which it is made, and so forth. All or most of these\nvarious sensations frequently are, and, as we learn by experience,\nalways might be, experienced simultaneously, or in many different orders\nof succession, at our own choice: and hence the thought of any one of\nthem makes us think of the others, and the whole becomes mentally\namalgamated into one mixed state of consciousness, which, in the\nlanguage of the school of Locke and Hartley, is termed a Complex Idea.\n\nNow, there are philosophers who have argued as follows. If we conceive\nan orange to be divested of its natural colour without acquiring any new\none; to lose its softness without becoming hard, its roundness without\nbecoming square or pentagonal, or of any other regular or irregular\nfigure whatever; to be deprived of size, of weight, of taste, of smell;\nto lose all its mechanical and all its chemical properties, and acquire\nno new ones; to become, in short, invisible, intangible, imperceptible\nnot only by all our senses, but by the senses of all other sentient\nbeings, real or possible; nothing, say these thinkers, would remain.\nFor of what nature, they ask, could be the residuum? and by what token\ncould it manifest its presence? To the unreflecting its existence seems\nto rest on the evidence of the senses. But to the senses nothing is\napparent except the sensations. We know, indeed, that these sensations\nare bound together by some law; they do not come together at random, but\naccording to a systematic order, which is part of the order established\nin the 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\noccur together, does not, say these philosophers, necessarily require\nwhat is called a substratum to support them. The conception of a\nsubstratum is but one of many possible forms in which that connexion\npresents itself to our imagination; a mode of, as it were, realizing the\nidea. If there be such a substratum, suppose it this instant\nmiraculously annihilated, and let the sensations continue to occur in\nthe same order, and how would the substratum be missed? By what signs\nshould we be able to discover that its existence had terminated? Should\nwe not have as much reason to believe that it still existed as we now\nhave? And if we should not then be warranted in believing it, how can we\nbe so now? A body, therefore, according to these metaphysicians, is not\nanything intrinsically different from the sensations which the body is\nsaid to produce in us; it is, in short, a set of sensations, or rather,\nof possibilities of sensation, 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\ncertain uniform manner, imply not only a law or laws of connexion, but a\ncause external to our mind, which cause, by its own laws, determines the\nlaws according to which the sensations are connected and experienced.\nThe schoolmen used to call this external cause by the name we have\nalready employed, 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 cannot 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\nan external 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\nof something external to them: this knowledge, therefore, it is\naffirmed, is as evidently intuitive as our knowledge of our sensations\nthemselves is intuitive. And here the question merges in the fundamental\nproblem of metaphysics 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\nknow_ of objects is the sensations which they give us, and the order of\nthe occurrence of those sensations. Kant himself, on this point, is as\nexplicit as Berkeley or Locke. However firmly convinced that there\nexists an universe of \"Things in themselves,\" totally distinct from the\nuniverse of phenomena, or of things as they appear to our senses; and\neven when bringing into use a technical expression (_Noumenon_) to\ndenote what the thing is in itself, as contrasted with the\n_representation_ of it in our minds; he allows that this representation\n(the matter of which, he says, consists of our sensations, though the\nform is given by the laws of the mind itself) is all we know of the\nobject: and that the real nature of the Thing is, and by the\nconstitution of our faculties ever must remain, at least in the present\nstate of existence, an impenetrable mystery to us. \"Of things absolutely\nor in themselves,\" says Sir William Hamilton,[10] \"be they external, be\nthey internal, we know nothing, or know them only as incognisable; and\nbecome aware of their incomprehensible existence, only as this is\nindirectly and accidentally revealed to us, through certain qualities\nrelated to our faculties of knowledge, and which qualities, again, we\ncannot think as unconditioned, irrelative, existent in and of\nthemselves. All that we know is therefore ph\u00e6nomenal,--ph\u00e6nomenal of the\nunknown.\"[11] The same doctrine is laid down in the clearest and\nstrongest terms by M. Cousin, whose observations on the subject are the\nmore worthy of attention, as, in consequence of the ultra-German and\nontological character of his philosophy in other respects, they may be\nregarded as the admissions of an opponent.[12]\n\nThere is not the slightest reason for believing that what we call the\nsensible 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\nsuch, resemble its effects; an east wind is not like the feeling of\ncold, nor heat like the steam of boiling water. Why then should matter\nresemble our sensations? Why should the inmost nature of fire or water\nresemble the impressions made by those objects upon our senses?[13] Or\non what principle are we authorized to deduce from the effects, anything\nconcerning the cause, except that it is a cause adequate to produce\nthose effects? It may, therefore, safely be laid down as a truth both\nobvious in itself, and admitted by all whom it is at present necessary\nto take into consideration, that, of the outward world, we know and can\nknow absolutely nothing, except the sensations which we experience from\nit.[14]\n\n\n\u00a7 8. Body having now been defined the external cause, and (according to\nthe more reasonable opinion) the unknown external cause, to which we\nrefer our sensations; it remains to frame a definition of Mind. Nor,\nafter the preceding observations, will this be difficult. For, as our\nconception of a body is that of an unknown exciting cause of sensations,\nso our conception of a mind is that of an unknown recipient, or\npercipient, of them; and not of them alone, but of all our other\nfeelings. As body is understood to be the mysterious something which\nexcites the mind to feel, so mind is the mysterious something which\nfeels and thinks. It is unnecessary to give in the case of mind, as we\ngave in the case of matter, a particular statement of the sceptical\nsystem by which its existence as a Thing in itself, distinct from the\nseries of what are denominated its states, is called in question. But it\nis necessary to remark, that on the inmost nature (whatever be meant by\ninmost nature) of the thinking principle, as well as on the inmost\nnature of matter, we are, and with our faculties must always remain,\nentirely in the dark. All which we are aware of, even in our own minds,\nis (in the words of Mr. James Mill) a certain \"thread of consciousness;\"\na series of feelings, that is, of sensations, thoughts, emotions, and\nvolitions, more or less numerous and complicated. There is a something I\ncall Myself, or, by another form of expression, my mind, which I\nconsider as distinct from these sensations, thoughts, &c.; a something\nwhich I conceive to be not the thoughts, but the being that has the\nthoughts, and which I can conceive as existing for ever in a state of\nquiescence, without any thoughts at all. But what this being is, though\nit is myself, I have no knowledge, other than the series of its states\nof consciousness. As bodies manifest themselves to me only through the\nsensations of which I regard them as the causes, so the thinking\nprinciple, or mind, in my own nature, makes itself known to me only by\nthe feelings of which it is conscious. I know nothing about myself, save\nmy capacities of feeling or being conscious (including, of course,\nthinking and willing): and were I to learn anything new concerning my\nown 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 scholastic sense of the\nterm) of all feelings; that which has or feels them. But of the nature\nof either body or mind, further than the feelings which the former\nexcites, and which the latter experiences, we do not, according to the\nbest existing doctrine, know anything; and if anything, logic has\nnothing to do with it, or with the manner in which the knowledge is\nacquired. With this result we may conclude this portion of our subject,\nand pass to the third and only remaining class or division of Nameable\nThings.\n\n\nIII. ATTRIBUTES: AND, FIRST, QUALITIES.\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 in\nothers, those sensations must be all that we can, at bottom, mean by\ntheir attributes; and the distinction which we verbally make between the\nproperties of things and the sensations we receive from them, must\noriginate in the convenience of discourse rather than in the nature of\nwhat is signified by the terms.\n\nAttributes are usually distributed under the three heads of Quality,\nQuantity, and Relation. We shall come to the two latter presently: in\nthe first 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\nsnow has the quality whiteness, what do we really assert? Simply, that\nwhen snow is present to our organs, we have a particular sensation,\nwhich we are accustomed to call the sensation of white. But how do I\nknow that snow is present? Obviously by the sensations which I derive\nfrom it, and not otherwise. I infer that the object is present, because\nit gives me a certain assemblage or series of sensations. And when I\nascribe to it the attribute whiteness, my meaning is only, that, of the\nsensations composing this group or series, that which I call the\nsensation of white colour is one.\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;\nthat the fact of our receiving from snow the particular sensation which\nis called a sensation of white, is the _ground_ on which we ascribe to\nthat substance the quality whiteness; the sole proof of its possessing\nthat quality. But because one thing may be the sole evidence of the\nexistence of another thing, it does not follow that the two are one and\nthe same. The attribute whiteness (it may be said) is not the fact of\nreceiving the sensation, but something in the object itself; a _power_\ninherent in it; something _in virtue_ of which the object produces the\nsensation. And when we affirm that snow possesses the attribute\nwhiteness, we do not merely assert that the presence of snow produces in\nus that sensation, but that it does so through, and by reason of, that\npower or quality.\n\nFor the purposes of logic it is not of material importance which of\nthese opinions we adopt. The full discussion of the subject belongs to\nthe other department of scientific inquiry, so often alluded to under\nthe name of metaphysics; but it may be said here, that for the doctrine\nof the existence of a peculiar species of entities called qualities, I\ncan see no foundation except in a tendency of the human mind which is\nthe cause of many delusions. I mean, the disposition, wherever we meet\nwith two names which are not precisely synonymous, to suppose that they\nmust be the names of two different things; whereas in reality they may\nbe names of the same thing viewed in two different lights, or under\ndifferent suppositions as to surrounding circumstances. Because\n_quality_ and _sensation_ cannot be put indiscriminately one for the\nother, it is supposed that they cannot both signify the same thing,\nnamely, the impression or feeling with which we are affected through our\nsenses by the presence of an object; though there is at least no\nabsurdity in supposing that this identical impression or feeling may be\ncalled a sensation when considered merely in itself, and a quality when\nlooked at in relation to any one of the numerous objects, the presence\nof which to our organs excites in our minds that among various other\nsensations or feelings. And if this be admissible as a supposition, it\nrests with those who contend for an entity _per se_ called a quality, to\nshow that their opinion is preferable, or is anything in fact but a\nlingering remnant of the scholastic doctrine of occult causes; the very\nabsurdity which Moli\u00e8re so happily ridiculed when he made one of his\npedantic physicians account for the fact that \"l'opium endormit,\" by the\nmaxim \"parcequ'il a une vertu soporifique.\"\n\nIt is evident that when the physician stated that opium had \"une vertu\nsoporifique,\" he did not account for, but merely asserted over again,\nthe fact that it _endormit_. In like manner, when we say that snow is\nwhite because it has the quality of whiteness, we are only re-asserting\nin more technical language the fact that it excites in us the sensation\nof white. If it be said that the sensation must have some cause, I\nanswer, its cause is the presence of the assemblage of phenomena which\nis termed the object. When we have asserted that as often as the object\nis present, and our organs in their normal state, the sensation takes\nplace, we have stated all that we know about the matter. There is no\nneed, after assigning a certain and intelligible cause, to suppose an\noccult cause besides, for the purpose of enabling the real cause to\nproduce its effect. If I am asked, why does the presence of the object\ncause this sensation in me, I cannot tell: I can only say that such is\nmy nature, and the nature of the object; that the fact forms a part of\nthe constitution of things. And to this we must at last come, even after\ninterpolating the imaginary entity. Whatever number of links the chain\nof causes and effects may consist of, how any one link produces the one\nwhich is next to it, remains equally inexplicable to us. It is as easy\nto comprehend that the object should produce the sensation directly and\nat once, as that it should produce the same sensation by the aid of\nsomething else called the _power_ of producing 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\nthe nature of qualities. I shall say,--what at least admits of no\ndispute,--that the quality of whiteness ascribed to the object snow, is\n_grounded_ on its exciting in us the sensation of white; and adopting\nthe language already used by the school logicians in the case of the\nkind of attributes called Relations, I shall term the sensation of\nwhite the foundation of the quality whiteness. For logical purposes the\nsensation is the only essential part of what is meant by the word; the\nonly part which we ever can be concerned in proving. When that is\nproved, the quality is proved; if an object excites a sensation, it has,\nof course, the power of exciting it.\n\n\nIV. RELATIONS.\n\n\u00a7 10. The _qualities_ of a body, we have said, are the attributes\ngrounded on the sensations which the presence of that particular body to\nour organs excites in our minds. But when we ascribe to any object the\nkind of attribute called a Relation, the foundation of the attribute\nmust be something in which other objects are concerned besides itself\nand the percipient.\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;\none thing _greater_, _equal_, _less_, than another; one thing the\n_cause_ of another, the _effect_ of another; one person the _master_,\n_servant_, _child_, _parent_, _debtor_, _creditor_, _sovereign_,\n_subject_, _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\ncommon to all these cases, and only one; that in each of them there\nexists or occurs, or has existed or occurred, or may be expected to\nexist or occur, some fact or phenomenon, into which the two things which\nare said to be related to each other, both enter as parties concerned.\nThis fact, or phenomenon, is what the Aristotelian logicians called the\n_fundamentum relationis_. Thus in the relation of greater and less\nbetween two magnitudes, the _fundamentum relationis_ is the fact that\none of the two magnitudes could, under certain conditions, be included\nin, without entirely filling, the space occupied by the other magnitude.\nIn the relation of master and servant, the _fundamentum relationis_ is\nthe fact that the one has undertaken, or is compelled, to perform\ncertain services for the benefit and at the bidding of the other.\nExamples might be indefinitely multiplied; but it is already obvious\nthat whenever two things are said to be related, there is some fact, or\nseries of facts, into which they both enter; and that whenever any two\nthings are involved in some one fact, or series of facts, we may ascribe\nto those two things a mutual relation grounded on the fact. Even if they\nhave nothing in common but what is common to all things, that they are\nmembers of the universe, we call that a relation, and denominate them\nfellow-creatures, fellow-beings, or fellow-denizens of the universe. But\nin proportion as the fact into which the two objects enter as parts is\nof a more special and peculiar, or of a more complicated nature, so also\nis the relation grounded upon it. And there are as many conceivable\nrelations as there are conceivable kinds of fact in which two things can\nbe 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\nthe object, so an attribute grounded on some fact into which the object\nenters jointly with another object, is a relation between it and that\nother object. But the fact in the latter case consists of the very same\nkind of elements as the fact in the former; namely, states of\nconsciousness. In the case, for example, of any legal relation, as\ndebtor and creditor, principal and agent, guardian and ward, the\n_fundamentum relationis_ consists entirely of thoughts, feelings, and\nvolitions (actual or contingent), either of the persons themselves or of\nother persons concerned in the same series of transactions; as, for\ninstance, the intentions which would be formed by a judge, in case a\ncomplaint were made to his tribunal of the infringement of any of the\nlegal obligations imposed by the relation; and the acts which the judge\nwould perform in consequence; acts being (as we have already seen)\nanother word for intentions followed by an effect, and that effect being\nbut another word for sensations, or some other feelings, occasioned\neither to the agent himself or to somebody else. There is no part of\nwhat the names expressive of the relation imply, that is not resolvable\ninto states of consciousness; outward objects being, no doubt, supposed\nthroughout as the causes by which some of those states of consciousness\nare excited, and minds as the subjects by which all of them are\nexperienced, but neither the external objects nor the minds making their\nexistence known otherwise than by the states of consciousness.\n\nCases of relation are not always so complicated as those to which we\nlast alluded. The simplest of all cases of relation are those expressed\nby the words antecedent and consequent, and by the word simultaneous. If\nwe say, for instance, that dawn preceded sunrise, the fact in which the\ntwo things, dawn and sunrise, were jointly concerned, consisted only of\nthe two things themselves; no third thing entered into the fact or\nphenomenon at all. Unless, indeed, we choose to call the succession of\nthe two objects a third thing; but their succession is not something\nadded to the things themselves; it is something involved in them. Dawn\nand sunrise announce themselves to our consciousness by two successive\nsensations. Our consciousness of the succession of these sensations is\nnot a third sensation or feeling added to them; we have not first the\ntwo feelings, and then a feeling of their succession. To have two\nfeelings at all, implies having them either successively, or else\nsimultaneously. Sensations, or other feelings, being given, succession\nand simultaneousness are the two conditions, to the alternative of which\nthey are subjected by the nature of our faculties; and no one has been\nable, or needs expect, to analyse the matter any farther.\n\n\n\u00a7 11. In a somewhat similar position are two other sorts of relations,\nLikeness and Unlikeness. I have two sensations; we will suppose them to\nbe simple 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_\nof this relation? The two sensations first, and then what we call a\nfeeling of resemblance, or of want of resemblance. Let us confine\nourselves to the former case. Resemblance is evidently a feeling; a\nstate of the consciousness of the observer. Whether the feeling of the\nresemblance of the two colours be a third state of consciousness, which\nI have _after_ having the two sensations of colour, or whether (like the\nfeeling of their succession) it is involved in the sensations\nthemselves, may be a matter of discussion. But in either case, these\nfeelings of resemblance, and of its opposite dissimilarity, are parts of\nour nature; and parts so far from being capable of analysis, that they\nare presupposed in every attempt to analyse any of our other feelings.\nLikeness and unlikeness, therefore, as well as antecedence, sequence,\nand simultaneousness, must stand apart among relations, as things _sui\ngeneris_. They are attributes grounded on facts, that is, on states of\nconsciousness, but on states which are peculiar, unresolvable, and\ninexplicable.\n\nBut, though likeness or unlikeness cannot be resolved into anything\nelse, complex cases of likeness or unlikeness can be resolved into\nsimpler ones. When we say of two things which consist of parts, that\nthey are like one another, the likeness of the wholes does admit of\nanalysis; it is compounded of likenesses between the various parts\nrespectively, and of likeness in their arrangement. Of how vast a\nvariety 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\nthe accents and intonations of the voice; likeness in the choice of\nwords, and in the thoughts or sentiments expressed, whether by word,\ncountenance, or gesture.\n\nAll likeness and unlikeness of which we have any cognizance, resolve\nthemselves into likeness and unlikeness between states of our own, or\nsome other, mind. When we say that one body is like another, (since we\nknow nothing of bodies but the sensations which they excite,) we mean\nreally that there is a resemblance between the sensations excited by the\ntwo bodies, or between some portions at least of those sensations. If we\nsay that 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\nthat they are called the same relation. The relation in which Cromwell\nstood to England resembles the relation in which Napoleon stood to\nFrance, though not so closely as to be called the same relation. The\nmeaning in both these instances must be, that a resemblance existed\nbetween the facts which 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\nexists a 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\nbeing said that the two relations resemble; provided, of course, the\npoints of resemblance are found in those portions of the two phenomena\nrespectively which 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\ntwo similar things are said to be the same. I say often, not always; for\nwe do not say that two visible objects, two persons for instance, are\nthe same, because they are so much alike that one might be mistaken for\nthe other: but we constantly use this mode of expression when speaking\nof feelings; as when I say that the sight of any object gives me the\n_same_ sensation or emotion to-day that it did yesterday, or the _same_\nwhich it gives to some other person. This is evidently an incorrect\napplication of the word _same_; for the feeling which I had yesterday is\ngone, never to return; what I have to-day is another feeling, exactly\nlike the former perhaps, but distinct from it; and it is evident that\ntwo different persons cannot be experiencing the same feeling, in the\nsense in which we say that they are both sitting at the same table. By a\nsimilar ambiguity we say, that two persons are ill of the _same_\ndisease; that two persons hold the _same_ office; not in the sense in\nwhich we say that they are engaged in the same adventure, or sailing in\nthe same ship, but in the sense that they fill offices exactly similar,\nthough, perhaps, in distant places. Great confusion of ideas is often\nproduced, and many fallacies engendered, in otherwise enlightened\nunderstandings, by not being sufficiently alive to the fact (in itself\nnot always to be avoided), that they use the same name to express ideas\nso different as those of identity and undistinguishable resemblance.\nAmong modern writers, Archbishop Whately stands almost alone in having\ndrawn attention to this distinction, and to the ambiguity connected with\nit.\n\nSeveral relations, generally called by other names, are really cases of\nresemblance. As, for example, equality; which is but another word for\nthe exact 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\nwhich, as already remarked, Attributes are commonly arranged.\n\n\nV. QUANTITY.\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,\nlike any other external object, makes its presence known to us by a set\nof sensations which it excites. Ten gallons of water are also an\nexternal object, making its presence known to us in a similar manner;\nand as we do not mistake ten gallons of water for a gallon of water, it\nis plain that the set of sensations is more or less different in the two\ncases. In like manner, a gallon of water, and a gallon of wine, are two\nexternal objects, making their presence known by two sets of sensations,\nwhich sensations are different from each other. In the first case,\nhowever, we say that the difference is in quantity; in the last there is\na difference in quality, while the quantity of the water and of the wine\nis the same. What is the real distinction between the two cases? It is\nnot the province of Logic to analyse it; nor to decide whether it is\nsusceptible of analysis or not. For us the following considerations are\nsufficient. It is evident that the sensations I receive from the gallon\nof water, and those I receive from the gallon of wine, are not the same,\nthat is, not precisely alike; neither are they altogether unlike: they\nare partly similar, partly dissimilar; and that in which they resemble\nis precisely that in which alone the gallon of water and the ten gallons\ndo not resemble. That in which the gallon of water and the gallon of\nwine are like each other, and in which the gallon and the ten gallons of\nwater are unlike each other, is called their quantity. This likeness\nand unlikeness I do not pretend to explain, no more than any other kind\nof likeness or unlikeness. But my object is to show, that when we say of\ntwo things that they differ in quantity, just as when we say that they\ndiffer in quality, the assertion is always grounded on a difference in\nthe sensations which they excite. Nobody, I presume, will say, that to\nsee, or to lift, or to drink, ten gallons of water, does not include in\nitself a different set of sensations from those of seeing, lifting, or\ndrinking one gallon; or that to see or handle a foot-rule, and to see or\nhandle a yard-measure made exactly like it, are the same sensations. I\ndo not undertake to say what the difference in the sensations is.\nEverybody knows, and nobody can tell; no more than any one could tell\nwhat white is to a person who had never had the sensation. But the\ndifference, so far as cognizable by our faculties, lies in the\nsensations. Whatever difference we say there is in the things\nthemselves, is, in this as in all other cases, grounded, and grounded\nexclusively, on a difference in the sensations excited by them.\n\n\nVI. ATTRIBUTES CONCLUDED.\n\n\u00a7 13. Thus, then, all the attributes of bodies which are classed under\nQuality or Quantity, are grounded on the sensations which we receive\nfrom those bodies, and may be defined, the powers which the bodies have\nof exciting those sensations. And the same general explanation has been\nfound to apply to most of the attributes usually classed under the head\nof Relation. They, too, are grounded on some fact or phenomenon into\nwhich the related objects enter as parts; that fact or phenomenon having\nno meaning and no existence to us, except the series of sensations or\nother states of consciousness by which it makes itself known; and the\nrelation being simply the power or capacity which the object possesses\nof taking part along with the correlated object in the production of\nthat series of sensations or states of consciousness. We have been\nobliged, indeed, to recognise a somewhat different character in certain\npeculiar relations, those of succession and simultaneity, of likeness\nand unlikeness. These, not being grounded on any fact or phenomenon\ndistinct from the related objects themselves, do not admit of the same\nkind of analysis. But these relations, though not, like other relations,\ngrounded on states of consciousness, are themselves states of\nconsciousness: resemblance is nothing but our feeling of resemblance;\nsuccession is nothing but our feeling of succession. Or, if this be\ndisputed (and we cannot, without transgressing the bounds of our\nscience, discuss it here), at least our knowledge of these relations,\nand even our possibility of knowledge, is confined to those which\nsubsist between sensations, or other states of consciousness; for,\nthough we ascribe resemblance, or succession, or simultaneity, to\nobjects and to attributes, it is always in virtue of resemblance or\nsuccession or simultaneity in the sensations or states of consciousness\nwhich those objects excite, and on which those attributes are grounded.\n\n\n\u00a7 14. In the preceding investigation we have, for the sake of\nsimplicity, considered bodies only, and omitted minds. But what we have\nsaid, is applicable, _mutatis mutandis_, to the latter. The attributes\nof minds, as well as those of bodies, are grounded on states of feeling\nor consciousness. 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\nattribute of a mind consists either in being itself affected in a\ncertain way, or affecting other minds in a certain way. Considered in\nitself, we can predicate nothing of it but the series of its own\nfeelings. When we say of any mind, that it is devout, or superstitious,\nor meditative, or cheerful, we mean that the ideas, emotions, or\nvolitions implied in those words, form a frequently recurring part of\nthe series of feelings, or states of consciousness, which fill up the\nsentient existence of that mind.\n\nIn addition, however, to those attributes of a mind which are grounded\non its own states of feeling, attributes may also be ascribed to it, in\nthe same manner as to a body, grounded on the feelings which it excites\nin other minds. A mind does not, indeed, like a body, excite\nsensations, but it may excite thoughts or emotions. The most important\nexample of attributes ascribed on this ground, is the employment of\nterms expressive of approbation or blame. When, for example, we say of\nany character, or (in other words) of any mind, that it is admirable, we\nmean that the contemplation of it excites the sentiment of admiration;\nand indeed somewhat more, for the word implies that we not only feel\nadmiration, but approve that sentiment in ourselves. In some cases,\nunder the semblance of a single attribute, two are really predicated:\none of them, a state of the mind itself; the other, a state with which\nother minds are affected by thinking of it. As when we say of any one\nthat he is generous. The word generosity expresses a certain state of\nmind, but being a term of praise, it also expresses that this state of\nmind excites in us another mental state, called approbation. The\nassertion made, therefore, is twofold, and of the following purport:\nCertain feelings form habitually a part of this person's sentient\nexistence; and the idea of those feelings of his, excites the sentiment\nof 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\nthis attribute is grounded on the peculiar feeling of pleasure which the\nstatue produces in our minds; which is not a sensation, but an emotion.\n\n\nVII. GENERAL RESULTS.\n\n\u00a7 15. Our survey of the varieties of Things which have been, or which\nare capable of being, named--which have been, or are capable of being,\neither predicated of other Things, or themselves made the subject of\npredications--is 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\nfour sorts: Sensations, Thoughts, Emotions, and Volitions. What are\ncalled Perceptions are merely a particular case of Belief, and belief is\na kind of thought. Actions are merely volitions followed by an effect.\nIf there be any other kind of mental state not included under these\nsubdivisions, we did not think it necessary or proper in this place to\ndiscuss its existence, 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\nwhich have been raised concerning the existence of Matter and Mind as\nobjective realities, we stated as sufficient for us the conclusion in\nwhich the best thinkers are now for the most part agreed, that all we\ncan know of Matter is the sensations which it gives us, and the order of\noccurrence of those sensations; and that while the substance Body is the\nunknown cause of our sensations, the substance Mind is the unknown\nrecipient.\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\nunlikeness, succession and simultaneity, are similarly grounded on some\nfact or phenomenon, 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.\nAll attributes, therefore, are to us nothing but either our sensations\nand other states of feeling, or something inextricably involved\ntherein; and to this even the peculiar and simple relations just\nadverted to are not exceptions. Those peculiar relations, however, are\nso important, and, even if they might in strictness be classed among\nstates of consciousness, are so fundamentally distinct from any other of\nthose states, that it would be a vain subtlety to bring them under that\ncommon description, and it is necessary that they should be classed\napart.\n\nAs the result, therefore, of our analysis, we obtain the following as an\nenumeration and classification of all Nameable Things:--\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\nthem; these last being included rather in compliance with common\nopinion, and because their existence is taken for granted in the common\nlanguage from which I cannot prudently deviate, than because the\nrecognition of such powers or properties as real existences appears to\nbe warranted by a sound philosophy.\n\n4th, and last. The Successions and Co-existences, the Likenesses and\nUnlikenesses, between feelings or states of consciousness. Those\nrelations, when considered as subsisting between other things, exist in\nreality only between the states of consciousness which those things, if\nbodies, excite, if minds, either excite or experience.\n\nThis, until a better can be suggested, may serve as a substitute for the\nabortive Classification of Existences, termed the Categories of\nAristotle. The practical application of it will appear when we commence\nthe inquiry into the Import of Propositions; in other words, when we\ninquire what it is which the mind actually believes, when it gives what\nis called its assent 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's sake, every fact which is solely composed of feelings\nor states 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,\nthen, that every objective fact is grounded on a corresponding\nsubjective one; and has no meaning to us, (apart from the subjective\nfact which corresponds to it,) except as a name for the unknown and\ninscrutable process by which that subjective or psychological fact is\nbrought to pass.\n\n\n\n\nCHAPTER IV.\n\nOF PROPOSITIONS.\n\n\n\u00a7 1. In treating of Propositions, as already in treating of Names, some\nconsiderations of a comparatively elementary nature respecting their\nform and varieties must be premised, before entering upon that analysis\nof the import conveyed by them, which is the real subject and purpose of\nthis preliminary 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\na predicate and a subject, that is, that one of them is intended to be\naffirmed or denied of the other, it is necessary that there should be\nsome mode 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;\nor by some other part of the verb _to be_. The word which thus serves\nthe purpose of a sign of predication is called, as we formerly observed,\nthe _copula_. It is important that there should be no indistinctness in\nour conception of the nature and office of the copula; for confused\nnotions respecting it are among the causes which have spread mysticism\nover the field of logic, and perverted its speculations into\nlogomachies.\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\nthe quality _just_ can be affirmed of Socrates, but moreover that\nSocrates _is_, that is to say, exists. This, however, only shows that\nthere is an ambiguity in the word _is_; a word which not only performs\nthe function of the copula in affirmations, but has also a meaning of\nits own, in virtue of which it may itself be made the predicate of a\nproposition. That the employment of it as a copula does not necessarily\ninclude the affirmation of existence, appears from such a proposition as\nthis, A centaur is a fiction of the poets; where it cannot possibly be\nimplied that a centaur exists, since the proposition itself expressly\nasserts that the thing has no real existence.\n\nMany volumes might be filled with the frivolous speculations concerning\nthe nature of Being, ([Greek: to on, ousia], Ens, Entitas, Essentia, and\nthe like) which have arisen from overlooking this double meaning of the\nword _to be_; from supposing that when it signifies _to exist_, and when\nit signifies to _be_ some specified thing, as to _be_ a man, to _be_\nSocrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a\nnonentity, it must still, at bottom, answer to the same idea; and that a\nmeaning must be found for it which shall suit all these cases. The fog\nwhich rose from this narrow spot diffused itself at an early period over\nthe whole surface of metaphysics. Yet it becomes us not to triumph over\nthe great intellects of Plato and Aristotle because we are now able to\npreserve ourselves from many errors into which they, perhaps inevitably,\nfell. The fire-teazer of a modern steam-engine produces by his exertions\nfar greater effects than Milo of Crotona could, but he is not therefore\na stronger 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\nlanguages which eminent thinkers have used as the vehicle of their\nthoughts, is the practical lesson we learn respecting the ambiguities of\nwords, by finding that the same word in one language corresponds, on\ndifferent occasions, to different words in another. When not thus\nexercised, even the strongest understandings find it difficult to\nbelieve that things which have a common name, have not in some respect\nor other a common nature; and often expend much labour very unprofitably\n(as was frequently done by the two philosophers just mentioned) in vain\nattempts to discover in what this common nature consists. But, the habit\nonce formed, intellects much inferior are capable of detecting even\nambiguities which are common to many languages: and it is surprising\nthat the one now under consideration, though it exists in the modern\nlanguages as well as in the ancient, should have been overlooked by\nalmost all authors. The quantity of futile speculation which had been\ncaused by a misapprehension of the nature of the copula, was hinted at\nby Hobbes; but Mr. James Mill[15] was, I believe, the first who\ndistinctly characterized the ambiguity, and pointed out how many errors\nin the received systems of philosophy it has had to answer for. It has\nindeed misled the moderns scarcely less than the ancients, though their\nmistakes, because our understandings are not yet so completely\nemancipated from their influence, do not appear equally irrational.\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\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\nwhich the predicate is _affirmed_ of the subject; as, C\u00e6sar is dead. A\nnegative proposition is that in which the predicate is _denied_ of the\nsubject; as, C\u00e6sar is not dead. The copula, in this last species of\nproposition, consists of the words _is not_, which are the sign of\nnegation; _is_ being the sign of affirmation.\n\nSome logicians, among whom may be mentioned Hobbes, state this\ndistinction differently; they recognise only one form of copula, _is_,\nand attach the negative sign to the predicate. \"C\u00e6sar is dead,\" and\n\"C\u00e6sar is not dead,\" according to these writers, are propositions\nagreeing not in the subject and predicate, but in the subject only. They\ndo not consider \"dead,\" but \"not dead,\" to be the predicate of the\nsecond proposition, and they accordingly define a negative proposition\nto be one in which the predicate is a negative name. The point, though\nnot of much practical moment, deserves notice as an example (not\nunfrequent in logic) where by means of an apparent simplification, but\nwhich is merely verbal, matters are made more complex than before. The\nnotion of these writers was, that they could get rid of the distinction\nbetween affirming and denying, by treating every case of denying as the\naffirming of a negative name. But what is meant by a negative name? A\nname expressive of the _absence_ of an attribute. So that when we affirm\na negative name, what we are really predicating is absence and not\npresence; we are asserting not that anything is, but that something is\nnot; to express which operation no word seems so proper as the word\ndenying. The fundamental distinction is between a fact and the\nnon-existence of that fact; between seeing something and not seeing it,\nbetween C\u00e6sar's being dead and his not being dead; and if this were a\nmerely verbal distinction, the generalization which brings both within\nthe same form of assertion would be a real simplification: the\ndistinction, however, being real, and in the facts, it is the\ngeneralization confounding the distinction that is merely verbal; and\ntends to obscure the subject, by treating the difference between two\nkinds of truths as if it were only a difference between two kinds of\nwords. To put things together, and to put them or keep them asunder,\nwill remain different operations, whatever tricks we may play with\nlanguage.\n\nA remark of a similar nature may be applied to most of those\ndistinctions among propositions which are said to have reference to\ntheir _modality_; as, difference of tense or time; the sun _did_ rise,\nthe sun _is_ rising, the sun _will_ rise. These differences, like that\nbetween affirmation and negation, might be glossed over by considering\nthe incident of time as a mere modification of the predicate: thus, The\nsun is _an object having risen_, The sun is _an object now rising_, The\nsun is _an object to rise hereafter_. But the simplification would be\nmerely verbal. Past, present, and future, do not constitute so many\ndifferent kinds of rising; they are designations belonging to the event\nasserted, to the _sun's_ rising to-day. They affect, not the predicate,\nbut the applicability of the predicate to the particular subject. That\nwhich we affirm to be past, present, or future, is not what the subject\nsignifies, nor what the predicate signifies, but specifically and\nexpressly what the predication signifies; what is expressed only by the\nproposition as such, and not by either or both of the terms. Therefore\nthe circumstance of time is properly considered as attaching to the\ncopula, which is the sign of predication, and not to the predicate. If\nthe same cannot be said of such modifications as these, C\u00e6sar _may_ be\ndead; C\u00e6sar is _perhaps_ dead; it is _possible_ that C\u00e6sar is dead; it\nis only because these fall altogether under another head, being properly\nassertions not of anything relating to the fact itself, but of the state\nof our own mind in regard to it; namely, our absence of disbelief of it.\nThus \"C\u00e6sar may be dead\" means \"I am not sure that C\u00e6sar is alive.\"\n\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\nof one subject. A complex proposition is that in which there is more\nthan one predicate, 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\ndivide horses into single horses and teams of horses. And it is true\nthat what is called a complex proposition is often not a proposition at\nall, but several propositions, held together by a conjunction. Such, for\nexample, is this: C\u00e6sar is dead, and Brutus is alive: or even this,\nC\u00e6sar is dead, _but_ Brutus is alive. There are here two distinct\nassertions; and we might as well call a street a complex house, as\nthese two propositions a complex proposition. It is true that the\nsyncategorematic words _and_ and _but_ have a meaning; but that meaning\nis so far from making the two propositions one, that it adds a third\nproposition to them. All particles are abbreviations, and generally\nabbreviations of propositions; a kind of short-hand, whereby something\nwhich, to be expressed fully, would have required a proposition or a\nseries of propositions, is suggested to the mind at once. Thus the\nwords, C\u00e6sar is dead and Brutus is alive, are equivalent to these: C\u00e6sar\nis dead; Brutus is alive; it is desired that the two preceding\npropositions should be thought of together. If the words were, C\u00e6sar is\ndead _but_ Brutus is alive, the sense would be equivalent to the same\nthree propositions together with a fourth; \"between the two preceding\npropositions there exists a contrast:\" 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, \"Peter and James\npreached at Jerusalem and in Galilee,\" which contains four propositions:\nPeter preached at Jerusalem, Peter preached in Galilee, James preached\nat Jerusalem, 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\na plurality of subjects and of predicates, and may be said in one sense\nof the word to consist of several propositions, contains but one\nassertion; and its truth does not at all imply that of the simple\npropositions which compose it. An example of this is, when the simple\npropositions are connected by the particle _or_; as, Either A is B or C\nis D; or by the particle _if_; as, A is B if C is D. In the former case,\nthe proposition is called _disjunctive_, in the latter, _conditional_:\nthe name _hypothetical_ was originally common to both. As has been well\nremarked by Archbishop Whately and others, the disjunctive form is\nresolvable into the conditional; every disjunctive proposition being\nequivalent to two or more conditional ones. \"Either A is B or C is D,\"\nmeans, \"if A is not B, C is D; and if C is not D, A is B.\" All\nhypothetical propositions, therefore, though disjunctive in form, are\nconditional in meaning; and the words hypothetical and conditional may\nbe, as indeed they generally are, used synonymously. Propositions in\nwhich the assertion is not dependent on a condition, are said, in the\nlanguage of logicians, to be _categorical_.\n\nAn hypothetical proposition is not, like the pretended complex\npropositions which we previously considered, a mere aggregation of\nsimple propositions. The simple propositions which form part of the\nwords in which it is couched, form no part of the assertion which it\nconveys. When we say, If the Koran comes from God, Mahomet is the\nprophet of God, we do not intend to affirm either that the Koran does\ncome from God, or that Mahomet is really his prophet. Neither of these\nsimple propositions may be true, and yet the truth of the hypothetical\nproposition may be indisputable. What is asserted is not the truth of\neither of the propositions, but the inferribility of the one from the\nother. What, then, is the subject, and what the predicate of the\nhypothetical proposition? \"The Koran\" is not the subject of it, nor is\n\"Mahomet:\" for nothing is affirmed or denied either of the Koran or of\nMahomet. The real subject of the predication is the entire proposition,\n\"Mahomet is the prophet of God;\" and the affirmation is, that this is a\nlegitimate inference from the proposition, \"The Koran comes from God.\"\nThe subject and predicate, therefore, of an hypothetical proposition are\nnames of propositions. The subject is some one proposition. The\npredicate is a general relative name applicable to propositions; of this\nform--\"an inference from so and so.\" A fresh instance is here afforded\nof the remark, that particles are abbreviations; since \"_If_ A is B, C\nis D,\" is found to be an abbreviation of the following: \"The proposition\nC is D, is a legitimate inference from the proposition A is B.\"\n\nThe distinction, therefore, between hypothetical and categorical\npropositions, is not so great as it at first appears. In the\nconditional, as well as in the categorical form, one predicate is\naffirmed of one subject, and no more: but a conditional proposition is a\nproposition concerning a proposition; the subject of the assertion is\nitself an assertion. Nor is this a property peculiar to hypothetical\npropositions. There are other classes of assertions concerning\npropositions. Like other things, a proposition has attributes which may\nbe predicated of it. The attribute predicated of it in an hypothetical\nproposition, is that of being an inference from a certain other\nproposition. But this is only one of many attributes that might be\npredicated. We may say, That the whole is greater than its part, is an\naxiom in mathematics: That the Holy Ghost proceeds from the Father\nalone, is a tenet of the Greek Church: The doctrine of the divine right\nof kings was renounced by Parliament at the Revolution: The\ninfallibility of the Pope has no countenance from Scripture. In all\nthese cases the subject of the predication is an entire proposition.\nThat which these different predicates are affirmed of, is _the\nproposition_, \"the whole is greater than its part;\" _the proposition_,\n\"the Holy Ghost proceeds from the Father alone;\" _the proposition_,\n\"kings have a divine right;\" _the proposition_, \"the Pope is\ninfallible.\"\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\nwhich they have been selected to fill in treatises on logic, if we did\nnot remember that what they predicate of a proposition, namely, its\nbeing an inference from something else, is precisely that one of its\nattributes with which most of all a logician is concerned.\n\n\n\u00a7 4. The next of the common divisions of Propositions is into\nUniversal, Particular, Indefinite, and Singular: a distinction founded\non the degree of generality in which the name, which is the subject of\nthe proposition, is to be understood. The following are examples:\n\n _All men_ are mortal-- Universal.\n _Some men_ are mortal-- Particular.\n _Man_ is mortal-- Indefinite.\n _Julius C\u00e6sar_ is mortal-- Singular.\n\nThe proposition is Singular, when the subject is an individual name. The\nindividual name needs not be a proper name. \"The Founder of Christianity\nwas crucified,\" is as much a singular proposition as \"Christ was\ncrucified.\"\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\naffirmed or denied of all and each of the things denoted by the subject,\nthe proposition is universal; when of some undefined portion of them\nonly, it is particular. Thus, All men are mortal; Every man is mortal;\nare universal 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\nexactly equivalent to the following, Every man is not-immortal. But\n\"some men are wise,\" \"some men are not wise,\" are particular\npropositions; the predicate _wise_ being in the one case affirmed and in\nthe other denied not of each and every individual denoted by the term\nman, but only of each and every one of some portion of those\nindividuals, without specifying what portion; for if this were\nspecified, the proposition would be changed either into a singular\nproposition, or into an universal proposition with a different subject;\nas, for instance, \"all _properly instructed_ men are wise.\" There are\nother forms of particular propositions; as, \"_Most_ men are imperfectly\neducated:\" it being immaterial how large a portion of the subject the\npredicate is asserted of, as long as it is left uncertain how that\nportion is to be distinguished from the rest.\n\nWhen the form of the expression does not clearly show whether the\ngeneral name which is the subject of the proposition is meant to stand\nfor all the individuals denoted by it, or only for some of them, the\nproposition is, by some logicians, called Indefinite; but this, as\nArchbishop Whately observes, is a solecism, of the same nature as that\ncommitted by some grammarians when in their list of genders they\nenumerate the _doubtful_ gender. The speaker must mean to assert the\nproposition either as an universal or as a particular proposition,\nthough he has failed to declare which: and it often happens that though\nthe words do not show which of the two he intends, the context, or the\ncustom of speech, supplies the deficiency. Thus, when it is affirmed\nthat \"Man is mortal,\" nobody doubts that the assertion is intended of\nall human beings; and the word indicative of universality is commonly\nomitted, only because the meaning is evident without it. In the\nproposition, \"Wine is good,\" it is understood with equal readiness,\nthough for somewhat different reasons, that the assertion is not\nintended to be universal, but particular.[16]\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\ndistributed, because the only mortals who are spoken of in the\nproposition are those who happen to be men; while the word may, for\naught that appears, and in fact does, comprehend within it an indefinite\nnumber of objects besides men. In the proposition, Some men are mortal,\nboth the predicate and the subject are undistributed. In the following,\nNo men have wings, both the predicate and the subject are distributed.\nNot only is the attribute of having wings denied of the entire class\nMan, but that class is severed and cast out from the whole of the class\nWinged, and not merely from some part of that class.\n\nThis phraseology, which is of great service in stating and\ndemonstrating the rules of the syllogism, enables us to express very\nconcisely the definitions of an universal and a particular proposition.\nAn universal proposition is that of which the subject is distributed; a\nparticular proposition 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\nexplaining and illustrating these, more suitable opportunities will\noccur in the sequel.\n\n\n\n\nCHAPTER V.\n\nOF THE IMPORT OF PROPOSITIONS.\n\n\n\u00a7 1. An inquiry into the nature of propositions must have one of two\nobjects: to analyse the state of mind called Belief, or to analyse what\nis believed. All language recognises a difference between a doctrine or\nopinion, and the fact of entertaining the opinion; between assent, and\nwhat is assented to.\n\nLogic, according to the conception here formed of it, has no concern\nwith the nature of the act of judging or believing; the consideration of\nthat act, 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;\nand would have treated with great disrespect any attempt to analyse the\nimport of Propositions, unless founded on an analysis of the act of\nJudgment. A proposition, they would have said, is but the expression in\nwords of a Judgment. The thing expressed, not the mere verbal\nexpression, is the important matter. When the mind assents to a\nproposition, it judges. Let us find out what the mind does when it\njudges, and we shall know what propositions 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\ntheory of Propositions, from one end to the other, a theory of\nJudgments. They considered a Proposition, or a Judgment, for they used\nthe two words indiscriminately, to consist in affirming or denying one\n_idea_ of another. To judge, was to put two ideas together, or to bring\none idea under another, or to compare two ideas, or to perceive the\nagreement or disagreement between two ideas: and the whole doctrine of\nPropositions, together with the theory of Reasoning, (always necessarily\nfounded on the theory of Propositions,) was stated as if Ideas, or\nConceptions, or whatever other term the writer preferred as a name for\nmental representations generally, constituted essentially the subject\nmatter and substance of those operations.\n\nIt is, of course, true, that in any case of judgment, as for instance\nwhen we judge that gold is yellow, a process takes place in our minds,\nof which some one or other of these theories is a partially correct\naccount. We must have the idea of gold and the idea of yellow, and these\ntwo ideas must be brought together in our mind. But in the first place,\nit is evident that this is only a part of what takes place; for we may\nput two ideas together without any act of belief; as when we merely\nimagine something, such as a golden mountain; or when we actually\ndisbelieve: for in order even to disbelieve that Mahomet was an apostle\nof God, we must put the idea of Mahomet and that of an apostle of God\ntogether. To determine what it is that happens in the case of assent or\ndissent besides putting two ideas together, is one of the most intricate\nof metaphysical problems. But whatever the solution may be, we may\nventure to assert that it can have nothing whatever to do with the\nimport of propositions; for this reason, that propositions (except\nsometimes when the mind itself is the subject treated of) are not\nassertions respecting our ideas of things, but assertions respecting the\nthings themselves. In order to believe that gold is yellow, I must,\nindeed, have the idea of gold, and the idea of yellow, and something\nhaving reference to those ideas must take place in my mind; but my\nbelief has not reference to the ideas, it has reference to the things.\nWhat I believe, is a fact relating to the outward thing, gold, and to\nthe 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\nmental history, not a fact of external nature. It is true, that in order\nto believe this fact in external nature, another fact must take place in\nmy mind, a process must be performed upon my ideas; but so it must in\neverything else that I do. I cannot dig the ground unless I have the\nidea of the ground, and of a spade, and of all the other things I am\noperating upon, and unless I put those ideas together.[17] But it would\nbe a very ridiculous description of digging the ground to say that it is\nputting one idea into another. Digging is an operation which is\nperformed upon the things themselves, though it cannot be performed\nunless I have in my mind the ideas of them. And in like manner,\nbelieving is an act which has for its subject the facts themselves,\nthough a previous mental conception of the facts is an indispensable\ncondition. When I say that fire causes heat, do I mean that my idea of\nfire causes my idea of heat? No: I mean that the natural phenomenon,\nfire, causes the natural phenomenon, heat. When I mean to assert\nanything respecting the ideas, I give them their proper name, I call\nthem ideas: as when I say, that a child's idea of a battle is unlike the\nreality, or that the ideas entertained of the Deity have a great effect\non 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\nthe subject and predicate, (instead of the relation between the two\n_phenomena_ which they respectively express,) seems to me one of the\nmost fatal errors ever introduced into the philosophy of Logic; and the\nprincipal cause why the theory of the science has made such\ninconsiderable progress during the last two centuries. The treatises on\nLogic, and on the branches of Mental Philosophy connected with Logic,\nwhich have been produced since the intrusion of this cardinal error,\nthough sometimes written by men of extraordinary abilities and\nattainments, almost always tacitly imply a theory that the investigation\nof truth consists in contemplating and handling our ideas, or\nconceptions of things, instead of the things themselves: a doctrine\ntantamount to the assertion, that the only mode of acquiring knowledge\nof nature is to study it at second hand, as represented in our own\nminds. Meanwhile, inquiries into every kind of natural phenomena were\nincessantly establishing great and fruitful truths on most important\nsubjects, by processes upon which these views of the nature of Judgment\nand Reasoning threw no light, and in which they afforded no assistance\nwhatever. No wonder that those who knew by practical experience how\ntruths are arrived at, should deem a science futile, which consisted\nchiefly of such speculations. What has been done for the advancement of\nLogic since these doctrines came into vogue, has been done not by\nprofessed logicians, but by discoverers in the other sciences; in whose\nmethods 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\nknown of the art of philosophizing by the old logicians, because their\nmodern interpreters have written to so little purpose respecting it.\n\nWe have to inquire, then, on the present occasion, not into Judgment,\nbut judgments; not into the act of believing, but into the thing\nbelieved. What is the immediate object of belief in a Proposition? What\nis the matter of fact signified by it? What is it to which, when I\nassert the proposition, I give my assent, and call upon others to give\ntheirs? What is that which is expressed by the form of discourse called\na Proposition, and the conformity of which to fact constitutes the truth\nof the proposition?\n\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,\nthe belief of the speaker that the predicate is a name of the same thing\nof which the subject is a name; and if it really is so, the proposition\nis true. Thus the proposition, All men are living beings (he would say)\nis true, because _living being_ is a name of everything of which _man_\nis a name. All men are six feet high, is not true, because _six feet\nhigh_ is not a name of everything (though it is of some things) of which\n_man_ is a name.\n\nWhat is stated in this theory as the definition of a true proposition,\nmust be allowed to be a property which all true propositions possess.\nThe subject and predicate being both of them names of things, if they\nwere names of quite different things the one name could not,\nconsistently with its signification, be predicated of the other. If it\nbe true that some men are copper-coloured, it must be true--and the\nproposition does really assert--that among the individuals denoted by\nthe name man, there are some who are also among those denoted by the\nname copper-coloured. If it be true that all oxen ruminate, it must be\ntrue that all the individuals denoted by the name ox are also among\nthose denoted by the name ruminating; and whoever asserts that all oxen\nruminate, undoubtedly does assert that this relation subsists between\nthe two names.\n\nThe assertion, therefore, which, according to Hobbes, is the only one\nmade in any proposition, really is made in every proposition: and his\nanalysis has consequently one of the requisites for being the true one.\nWe may go a step farther; it is the only analysis that is rigorously\ntrue of all propositions without exception. What he gives as the meaning\nof propositions, is part of the meaning of all propositions, and the\nwhole meaning of some. This, however, only shows what an extremely\nminute fragment of meaning it is quite possible to include within the\nlogical formula of a proposition. It does not show that no proposition\nmeans more. To warrant us in putting together two words with a copula\nbetween them, it is really enough that the thing or things denoted by\none of the names should be capable, without violation of usage, of being\ncalled by the other name also. If, then, this be all the meaning\nnecessarily implied in the form of discourse called a Proposition, why\ndo I object to it as the scientific definition of what a proposition\nmeans? Because, though the mere collocation which makes the proposition\na proposition, conveys no more than this scanty amount of meaning, that\nsame collocation combined with other circumstances, that _form_\ncombined with other _matter_, does convey more, and much more.\n\nThe only propositions of which Hobbes' principle is a sufficient\naccount, are that limited and unimportant class in which both the\npredicate and the subject are proper names. For, as has already been\nremarked, proper names have strictly no meaning; they are mere marks for\nindividual objects: and when a proper name is predicated of another\nproper name, all the signification conveyed is, that both the names are\nmarks for the same object. But this is precisely what Hobbes produces as\na theory of predication in general. His doctrine is a full explanation\nof such predications as these: Hyde was Clarendon, or, Tully is Cicero.\nIt exhausts the meaning of those propositions. But it is a sadly\ninadequate theory of any others. That it should ever have been thought\nof as such, can be accounted for only by the fact, that Hobbes, in\ncommon with the other Nominalists, bestowed little or no attention upon\nthe _connotation_ of words; and sought for their meaning exclusively in\nwhat they _denote_: as if all names had been (what none but proper names\nreally are) marks put upon individuals; and as if there were no\ndifference between a proper and a general name, except that the first\ndenotes only one individual, and the last 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\nanalysing the meaning of any proposition in which the predicate and the\nsubject, or either of them, are connotative names, it is to the\nconnotation of those terms that we must exclusively look, and not to\nwhat they _denote_, or in the language of Hobbes (language so far\ncorrect) are names of.\n\nIn asserting that the truth of a proposition depends on the conformity\nof import between its terms, as, for instance, that the proposition,\nSocrates is wise, is a true proposition, because Socrates and wise are\nnames applicable to, or, as he expresses it, names of, the same person;\nit is very remarkable that so powerful a thinker should not have asked\nhimself the question, But how came they to be names of the same person?\nSurely not because such was the intention of those who invented the\nwords. When mankind fixed the meaning of the word wise, they were not\nthinking of Socrates, nor, when his parents gave him the name of\nSocrates, were they thinking of wisdom. The names _happen_ to fit the\nsame person because of a certain _fact_, which fact was not known, nor\nin being, when the names were invented. If we want to know what the fact\nis, we shall find the clue to it in the _connotation_ of the names.\n\nA bird or a stone, a man, or a wise man, means simply, an object having\nsuch and such attributes. The real meaning of the word man, is those\nattributes, and not Smith, Brown, and the remainder of the individuals.\nThe word _mortal_, in like manner connotes a certain attribute or\nattributes; and when we say, All men are mortal, the meaning of the\nproposition is, that all beings which possess the one set of attributes,\npossess also the other. If, in our experience, the attributes connoted\nby _man_ are always accompanied by the attribute connoted by _mortal_,\nit will follow as a consequence, that the class _man_ will be wholly\nincluded in the class _mortal_, and that _mortal_ will be a name of all\nthings of which _man_ is a name: but why? Those objects are brought\nunder the name, by possessing the attributes connoted by it: but their\npossession of the attributes is the real condition on which the truth of\nthe proposition depends; not their being called by the name. Connotative\nnames do not precede, but follow, the attributes which they connote. If\none attribute happens to be always found in conjunction with another\nattribute, the concrete names which answer to those attributes will of\ncourse be predicable of the same subjects, and may be said, in Hobbes'\nlanguage, (in the propriety of which on this occasion I fully concur,)\nto be two names for the same things. But the possibility of a concurrent\napplication of the two names, is a mere consequence of the conjunction\nbetween the two attributes, and was, in most cases, never thought of\nwhen the names were introduced and their signification fixed. That the\ndiamond is combustible, was a proposition certainly not dreamt of when\nthe words Diamond and Combustible first received their meaning; and\ncould not have been discovered by the most ingenious and refined\nanalysis of the signification of those words. It was found out by a very\ndifferent process, namely, by exerting the senses, and learning from\nthem, that the attribute of combustibility existed in the diamonds upon\nwhich the experiment was tried; the number or character of the\nexperiments being such, that what was true of those individuals might be\nconcluded to be true of all substances \"called by the name,\" that is, of\nall substances possessing the attributes which the name connotes. The\nassertion, therefore, when analysed, is, that wherever we find certain\nattributes, there will be found a certain other attribute: which is not\na question of the signification of names, but of laws of nature; the\norder existing among phenomena.\n\n\n\u00a7 3. Although Hobbes' theory of Predication has not, in the terms in\nwhich he 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\nto this view of it, that the class man is included in the class mortal.\n\"Plato is a philosopher,\" 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\nthe theory of Hobbes. For a class _is_ absolutely nothing but an\nindefinite number of individuals denoted by a general name. The name\ngiven to them in common, is what makes them a class. To refer anything\nto a class, therefore, is to look upon it as one of the things which are\nto be called by that common name. To exclude it from a class, is to say\nthat the common name 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\nnullo_. When the syllogism is resolved, by all who treat of it, into an\ninference that what is true of a class is true of all things whatever\nthat belong to the class; and when this is laid down by almost all\nprofessed logicians as the ultimate principle to which all reasoning\nowes its validity; it is clear that in the general estimation of\nlogicians, the propositions of which reasonings are composed can be the\nexpression of nothing but the process of dividing things into classes,\nand referring everything to its proper class.\n\nThis theory appears to me a signal example of a logical error very often\ncommitted in logic, that of [Greek: hysteron proteron], or explaining a\nthing by something which presupposes it. When I say that snow is white,\nI may and ought to be thinking of snow as a class, because I am\nasserting a proposition as true of all snow: but I am certainly not\nthinking of white objects as a class; I am thinking of no white object\nwhatever except snow, but only of that, and of the sensation of white\nwhich it gives me. When, indeed, I have judged, or assented to the\npropositions, that snow is white, and that several other things are also\nwhite, I gradually begin to think of white objects as a class, including\nsnow and those other things. But this is a conception which followed,\nnot preceded, those judgments, and therefore cannot be given as an\nexplanation of them. Instead of explaining the effect by the cause, this\ndoctrine explains the cause by the effect, and is, I conceive, founded\non a latent misconception of the nature of classification.\n\nThere is a sort of language very generally prevalent in these\ndiscussions, which seems to suppose that classification is an\narrangement and grouping of definite and known individuals: that when\nnames were imposed, mankind took into consideration all the individual\nobjects in the universe, distributed them into parcels or lists, and\ngave to the objects of each list a common name, repeating this operation\n_toties quoties_ until they had invented all the general names of which\nlanguage consists; which having been once done, if a question\nsubsequently arises whether a certain general name can be truly\npredicated of a certain particular object, we have only (as it were) to\nread the roll of the objects upon which that name was conferred, and see\nwhether the object about which the question arises is to be found among\nthem. The framers of language (it would seem to be supposed) have\npredetermined all the objects that are to compose each class, and we\nhave only to refer to the record of an antecedent decision.\n\nSo absurd a doctrine will be owned by nobody when thus nakedly stated;\nbut if the commonly received explanations of classification and naming\ndo not imply this theory, it requires to be shown how they admit of\nbeing reconciled 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.\nThe objects which compose any given class are perpetually fluctuating.\nWe may frame a class without knowing the individuals, or even any of the\nindividuals, of which it may be composed; we may do so while believing\nthat no such individuals exist. If by the _meaning_ of a general name\nare to be understood the things which it is the name of, no general\nname, except by accident, has a fixed meaning at all, or ever long\nretains the same meaning. The only mode in which any general name has a\ndefinite meaning, is by being a name of an indefinite variety of things;\nnamely, of all things, known or unknown, past, present, or future, which\npossess certain definite attributes. When, by studying not the meaning\nof words, but the phenomena of nature, we discover that these attributes\nare possessed by some object not previously known to possess them, (as\nwhen chemists found that the diamond was combustible), we include this\nnew object in the class; but it did not already belong to the class. We\nplace the 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\nof that 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,\nthe minds which have been entangled in this net are precisely those\nwhich have escaped the other cardinal error commented upon in the\nbeginning of the present chapter. Since the revolution which dislodged\nAristotle from the schools, logicians may almost be divided into those\nwho have looked upon reasoning as essentially an affair of Ideas, and\nthose who have looked upon it as essentially an affair of Names.\n\nAlthough, however, Hobbes' theory of Predication, according to the\nwell-known remark of Leibnitz, and the avowal of Hobbes himself,[18]\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\nconsider the distinction between truth and error as less real, or\nattached less importance to it, than other people. To suppose that they\ndid so would argue total unacquaintance with their other speculations.\nBut this shows how little hold their doctrine possessed over their own\nminds. No person, at bottom, ever imagined that there was nothing more\nin truth than propriety of expression; than using language in conformity\nto a previous convention. When the inquiry was brought down from\ngenerals to a particular case, it has always been acknowledged that\nthere is a distinction between verbal and real questions; that some\nfalse propositions are uttered from ignorance of the meaning of words,\nbut that in others the source of the error is a misapprehension of\nthings; that a person who has not the use of language at all may form\npropositions mentally, and that they may be untrue, that is, he may\nbelieve as matters of fact what are not really so. This last admission\ncannot be made in stronger terms than it is by Hobbes himself;[19]\nthough he will not allow such erroneous belief to be called falsity, but\nonly error. And he has himself laid down, in other places, doctrines in\nwhich the true theory of predication is by implication contained. He\ndistinctly says that general names are given to things on account of\ntheir attributes, and that abstract names are the names of those\nattributes. \"Abstract is that which in any subject denotes the cause of\nthe concrete name.... And these causes of names are the same with the\ncauses of our conceptions, namely, some power of action, or affection,\nof the thing conceived, which some call the manner by which anything\nworks upon our senses, but by most men they are called _accidents_.\"[20]\nIt is strange that having gone so far, he should not have gone one step\nfarther, and seen that what he calls the cause of the concrete name, is\nin reality the meaning of it; and that when we predicate of any subject\na name which is given _because_ of an attribute (or, as he calls it, an\naccident), our object is not to affirm the name, but, by means of the\nname, to affirm the attribute.\n\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: \"The\nsummit of Chimborazo is white.\" The word white connotes an attribute\nwhich is possessed by the individual object designated by the words\n\"summit of Chimborazo;\" which attribute consists in the physical fact,\nof its exciting in human beings the sensation which we call a sensation\nof white. It will be admitted that, by asserting the proposition, we\nwish to communicate information of that physical fact, and are not\nthinking of the names, except as the necessary means of making that\ncommunication. The meaning of the proposition, therefore, is, that the\nindividual thing denoted by the subject, has the attributes connoted by\nthe 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\ncomplication. Let us first suppose the proposition to be universal, as\nwell as affirmative: \"All men are mortal.\" In this case, as in the last,\nwhat the proposition asserts (or expresses a belief of) is, of course,\nthat the objects denoted by the subject (man) possess the attributes\nconnoted by the predicate (mortal). But the characteristic of this case\nis, that the objects are no longer _individually_ designated. They are\npointed out only by some of their attributes: they are the objects\ncalled men, that is, possessing the attributes connoted by the name man;\nand the only thing known of them may be those attributes: indeed, as the\nproposition is general, and the objects denoted by the subject are\ntherefore indefinite in number, most of them are not known individually\nat all. The assertion, therefore, is not, as before, that the attributes\nwhich the predicate connotes are possessed by any given individual, or\nby any number of individuals previously known as John, Thomas, &c., but\nthat those attributes are possessed by each and every individual\npossessing certain other attributes; that whatever has the attributes\nconnoted by the subject, has also those connoted by the predicate; that\nthe latter set of attributes _constantly accompany_ the former set.\nWhatever has the attributes of man has the attribute of mortality;\nmortality constantly accompanies the attributes of man.[21]\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\nattributes which we ascribe to a certain kind of living creatures, on\nthe ground of certain phenomena which they exhibit, and which are partly\nphysical phenomena, namely the impressions made on our senses by their\nbodily form and structure, and partly mental phenomena, namely the\nsentient and intellectual life which they have of their own. All this is\nunderstood when we utter the word man, by any one to whom the meaning of\nthe word is known. Now, when we say, Man is mortal, we mean that\nwherever these various physical and mental phenomena are all found,\nthere we have assurance that the other physical and mental phenomenon,\ncalled death, will not fail to take place. The proposition does not\naffirm _when_; for the connotation of the word _mortal_ goes no farther\nthan to the occurrence of the phenomenon at some time or other, leaving\nthe precise time undecided.\n\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,\nas in the cases which we have examined, either the co-existence or the\nsequence of two phenomena. At the very commencement of our inquiry, we\nfound that every act of belief implied two Things: we have now\nascertained what, in the most frequent case, these two things are,\nnamely two Phenomena, in other words, two states of consciousness; and\nwhat it is which the proposition affirms (or denies) to subsist between\nthem, namely either succession or co-existence. And this case includes\ninnumerable instances which no one, previous to reflection, would think\nof referring to it. Take the following example: A generous person is\nworthy of honour. Who would expect to recognise here a case of\nco-existence between phenomena? But so it is. The attribute which causes\na person to be termed generous, is ascribed to him on the ground of\nstates of his mind, and particulars of his conduct: both are phenomena:\nthe former are facts of internal consciousness; the latter, so far as\ndistinct from the former, are physical facts, or perceptions of the\nsenses. Worthy of honour admits of a similar analysis. Honour, as here\nused, means a state of approving and admiring emotion, followed on\noccasion by corresponding outward acts. \"Worthy of honour\" connotes all\nthis, together with our approval of the act of showing honour. All these\nare phenomena; states of internal consciousness, accompanied or followed\nby physical facts. When we say, A generous person is worthy of honour,\nwe affirm co-existence between the two complicated phenomena connoted by\nthe two terms respectively. We affirm, that wherever and whenever the\ninward feelings and outward facts implied in the word generosity have\nplace, then and there the existence and manifestation of an inward\nfeeling, honour, would be followed in our minds by another inward\nfeeling, 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\nthe extremely complicated connotation of many words; the immense\nmultitude and prolonged series of facts which often constitute the\nphenomenon connoted by a name. But where it is seen what the phenomenon\nis, there is seldom any difficulty in seeing that the assertion conveyed\nby the proposition is, the co-existence of one such phenomenon with\nanother; or the succession of one such phenomenon to another: their\n_conjunction_, in short, so that where the one is found, we may\ncalculate 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 co-existences are not only asserted respecting Phenomena; we make\npropositions also respecting those hidden causes of phenomena, which are\nnamed substances and attributes. A substance, however, being to us\nnothing but either that which causes, or that which is conscious of,\nphenomena; and the same being true, _mutatis mutandis_, of attributes;\nno assertion can be made, at least with a meaning, concerning these\nunknown and unknowable entities, except in virtue of the Phenomena by\nwhich alone they manifest themselves to our faculties. When we say,\nSocrates was cotemporary with the Peloponnesian war, the foundation of\nthis assertion, as of all assertions concerning substances, is an\nassertion concerning the phenomena which they exhibit,--namely, that the\nseries of facts by which Socrates manifested himself to mankind, and the\nseries of mental states which constituted his sentient existence, went\non simultaneously with the series of facts known by the name of the\nPeloponnesian war. Still, the proposition does not assert that alone; it\nasserts that the Thing in itself, the _noumenon_ Socrates, was existing,\nand doing or experiencing those various facts during the same time.\nCo-existence and sequence, therefore, may be affirmed or denied not only\nbetween phenomena, but between noumena, or between a noumenon and\nphenomena. And both of noumena and of phenomena we may affirm simple\nexistence. But what is a noumenon? An unknown cause. In affirming,\ntherefore, the existence of a noumenon, we affirm causation. Here,\ntherefore, are two additional kinds of fact, capable of being asserted\nin a proposition. Besides the propositions which assert Sequence or\nCoexistence, there are some which assert simple Existence; and others\nassert Causation, which, subject to the explanations which will follow\nin the Third Book, must be considered provisionally as a distinct and\npeculiar kind of assertion.\n\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\na sequence or co-existence between two phenomena, there are therefore\nalso propositions which assert resemblance between them: as, This colour\nis like that colour;--The heat of to-day is _equal_ to the heat of\nyesterday. It is true that such an assertion might with some\nplausibility be brought within the description of an affirmation of\nsequence, by considering it as an assertion that the simultaneous\ncontemplation of the two colours is _followed_ by a specific feeling\ntermed the feeling of resemblance. But there would be nothing gained by\nencumbering ourselves, especially in this place, with a generalization\nwhich may be looked upon as strained. Logic does not undertake to\nanalyse mental facts into their ultimate elements. Resemblance between\ntwo phenomena is more intelligible in itself than any explanation could\nmake it, and under any classification must remain specifically distinct\nfrom the ordinary cases of sequence and co-existence.\n\nIt is sometimes said, that all propositions whatever, of which the\npredicate is a general name, do, in point of fact, affirm or deny\nresemblance. All such propositions affirm that a thing belongs to a\nclass; but 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\ngold resembles other metals, and Socrates other men, more nearly than\nthey resemble the objects contained in any other of the classes\nco-ordinate with 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\nthe class _metal_, or the class _man_, is grounded indeed on a\nresemblance among the things which are placed in the same class, but not\non a mere general resemblance: the resemblance it is grounded on\nconsists in the possession by all those things, of certain common\npeculiarities; and those peculiarities it is which the terms connote,\nand which the propositions consequently assert; not the resemblance: for\nthough when I say, Gold is a metal, I say by implication that if there\nbe any other metals it must resemble them, yet if there were no other\nmetals I might still assert the proposition with the same meaning as at\npresent, namely, that gold has the various properties implied in the\nword metal; just as it might be said, Christians are men, even if there\nwere no men who were not Christians. Propositions, therefore, in which\nobjects are referred to a class because they possess the attributes\nconstituting the class, are so far from asserting nothing but\nresemblance, that they do not, properly speaking, assert resemblance at\nall.\n\nBut we remarked some time ago (and the reasons of the remark will be\nmore fully entered into in a subsequent Book[22]) that there is\nsometimes a convenience in extending the boundaries of a class so as to\ninclude things which possess in a very inferior degree, if in any, some\nof the characteristic properties of the class,--provided they resemble\nthat class more than any other, insomuch that the general propositions\nwhich are true of the class, will be nearer to being true of those\nthings than any other equally general propositions. For instance, there\nare substances called metals which have very few of the properties by\nwhich metals are commonly recognised; and almost every great family of\nplants or animals has a few anomalous genera or species on its borders,\nwhich are admitted into it by a sort of courtesy, and concerning which\nit has been matter of discussion to what family they properly belonged.\nNow when the class-name is predicated of any object of this description,\nwe do, by so predicating it, affirm resemblance and nothing more. And in\norder to be scrupulously correct it ought to be said, that in every case\nin which we predicate a general name, we affirm, not absolutely that the\nobject possesses the properties designated by the name, but that it\n_either_ possesses those properties, or if it does not, at any rate\nresembles the things which do so, more than it resembles any other\nthings. In most cases, however, it is unnecessary to suppose any such\nalternative, the latter of the two grounds being very seldom that on\nwhich the assertion is made: and when it is, there is generally some\nslight difference in the form of the expression, as, This species (or\ngenus) is _considered_, or _may be ranked_, as belonging to such and\nsuch a family: we should hardly say positively that it does belong to\nit, unless it possessed unequivocally the properties of which the\nclass-name is scientifically significant.\n\nThere is still another exceptional case, in which, though the predicate\nis the 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\none of tightness, in both cases the attribute I affirm of the colour or\nof the other sensation is mere resemblance--simple _likeness_ to\nsensations which I have had before, and which have had those names\nbestowed upon them. The names of feelings, like other concrete general\nnames, are connotative; but they connote a mere resemblance. When\npredicated of any individual feeling, the information they convey is\nthat of its likeness to the other feelings which we have been accustomed\nto call by the same name. Thus much may suffice in illustration of the\nkind of propositions in which the matter-of-fact asserted (or denied) is\nsimple Resemblance.\n\nExistence, Coexistence, Sequence, Causation, Resemblance: one or other\nof these is asserted (or denied) in every proposition which is not\nmerely verbal. This five-fold division is an exhaustive classification\nof matters-of-fact; of all things that can be believed, or tendered for\nbelief; of all questions that can be propounded, and all answers that\ncan be returned to them. Instead of Coexistence and Sequence, we shall\nsometimes say, for greater particularity, Order in Place, and Order in\nTime: Order in Place being the specific mode of coexistence, not\nnecessary to be more particularly analysed here; while the mere fact of\ncoexistence, or simultaneousness, may be classed, together with\nSequence, under the head of Order in Time.\n\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,\nin doing 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\nto signify; for the real signification of a concrete general name is, as\nwe have so often said, its connotation; and what the concrete term\nconnotes, forms the entire meaning of the abstract name. Since there is\nnothing in the import of an abstract name which is not in the import of\nthe corresponding concrete, it is natural to suppose that neither can\nthere be anything in the import of a proposition of which the terms are\nabstract, but what there is in some proposition which can be framed of\nconcrete terms.\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\norder to express, their possessing that attribute, or that combination\nof attributes. When, therefore, we predicate of anything a concrete\nname, the attribute is what we in reality predicate of it. But it has\nnow been shown that in all propositions of which the predicate is a\nconcrete name, what is really predicated is one of five things:\nExistence, Coexistence, Causation, Sequence, or Resemblance. An\nattribute, therefore, is necessarily either an existence, a coexistence,\na causation, a sequence, or a resemblance. When a proposition consists\nof a subject and predicate which are abstract terms, it consists of\nterms which must necessarily signify one or other of these things. When\nwe predicate of anything an abstract name, we affirm of the thing that\nit is one or other of these five things; that it is a case of Existence,\nor of Coexistence, or of Causation, 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, \"Thoughtlessness is dangerous.\"\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: \"Whiteness is a colour;\" or \"The\ncolour of snow is a whiteness.\" 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,--The\nsensation of sight, caused by looking at snow, is one of the sensations\ncalled sensations of white. In these propositions, as we have before\nseen, the matter-of-fact asserted is a Resemblance. In the following\nexamples, the concrete terms are those which directly correspond to the\nabstract names; connoting the attribute which these denote. \"Prudence\nis a virtue:\" this may be rendered, \"All prudent persons, _in so far as_\nprudent, are virtuous:\" \"Courage is deserving of honour,\" thus, \"All\ncourageous persons are deserving of honour _in so far_ as they are\ncourageous:\" which is equivalent to this--\"All courageous persons\ndeserve an addition to the honour, or a diminution of the disgrace,\nwhich would attach to them on other grounds.\"\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:--\"Prudence is a virtue.\" Let us substitute for the word\nvirtue an equivalent but more definite expression, such as \"a mental\nquality beneficial to society,\" or \"a mental quality pleasing to God,\"\nor whatever else we adopt as the definition of virtue. What the\nproposition asserts is a sequence, accompanied with causation; namely,\nthat benefit to society, or that the approval of God, is consequent on,\nand caused by, prudence. Here is a sequence; but between what? We\nunderstand the consequent of the sequence, but we have yet to analyse\nthe antecedent. Prudence is an attribute; and, in connexion with it, two\nthings besides itself are to be considered; prudent persons, who are the\n_subjects_ of the attribute, and prudential conduct, which may be called\nthe _foundation_ of it. Now is either of these the antecedent? and,\nfirst, is it meant, that the approval of God, or benefit to society, is\nattendant upon all prudent _persons_? No; except _in so far_ as they are\nprudent; for prudent persons who are scoundrels can seldom on the whole\nbe beneficial to society, nor can they be acceptable to a good being. Is\nit upon prudential _conduct_, then, that divine approbation and benefit\nto mankind are supposed to be invariably consequent? Neither is this the\nassertion meant, when it is said that prudence is a virtue; except with\nthe same reservation as before, and for the same reason, namely, that\nprudential conduct, although in _so far as_ it is prudential it is\nbeneficial to society, may yet, by reason of some other of its\nqualities, be productive of an injury outweighing the benefit, and\ndeserve a displeasure exceeding the approbation which would be due to\nthe prudence. Neither the substance, therefore, (viz. the person,) nor\nthe phenomenon, (the conduct,) is an antecedent on which the other term\nof the sequence is universally consequent. But the proposition,\n\"Prudence is a virtue,\" 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\nwhen the action, though prudent, is wicked; namely, a correct foresight\nof consequences, a just estimation of their importance to the object in\nview, and repression of any unreflecting impulse at variance with the\ndeliberate purpose. These, which are states of the person's mind, are\nthe real antecedent in the sequence, the real cause in the causation,\nasserted by the proposition. But these are also the real ground, or\nfoundation, of the attribute Prudence; since wherever these states of\nmind exist we may predicate prudence, even before we know whether any\nconduct has followed. And in this manner every assertion respecting an\nattribute, may be transformed into an assertion exactly equivalent\nrespecting the fact or phenomenon which is the ground of the attribute.\nAnd no case can be assigned, where that which is predicated of the fact\nor phenomenon, does not belong to one or other of the five species\nformerly enumerated: it is either simple Existence, or it is some\nSequence, Coexistence, Causation, or Resemblance.\n\nAnd as these five are the only things which can be affirmed, so are they\nthe only things which can be denied. \"No horses are web-footed\" denies\nthat the attributes of a horse ever coexist with web-feet. It is\nscarcely necessary to apply the same analysis to Particular affirmations\nand negations. \"Some birds are web-footed,\" affirms that, with the\nattributes connoted by _bird_, the phenomenon web-feet is sometimes\nco-existent: \"Some birds are not web-footed,\" asserts that there are\nother instances in which this coexistence does not have place. Any\nfurther explanation of a thing which, if the previous exposition has\nbeen assented to, is so obvious, may here be spared.\n\n\n\n\nCHAPTER VI.\n\nOF PROPOSITIONS MERELY VERBAL.\n\n\n\u00a7 1. As a preparation for the inquiry which is the proper object of\nLogic, namely, in what manner propositions are to be proved, we have\nfound it necessary to inquire what they contain which requires, or is\nsusceptible of, proof; or (which is the same thing) what they assert. In\nthe course of this preliminary investigation into the import of\nPropositions, we examined the opinion of the Conceptualists, that a\nproposition is the expression of a relation between two ideas; and the\ndoctrine of the Nominalists, that it is the expression of an agreement\nor disagreement between the meanings of two names. We decided that, as\ngeneral theories, both of these are erroneous; and that, though\npropositions may be made both respecting names and respecting ideas,\nneither the one nor the other are the subject-matter of Propositions\nconsidered generally. We then examined the different kinds of\nPropositions, and found that, with the exception of those which are\nmerely verbal, they assert five different kinds of matters of fact,\nnamely, Existence, Order in Place, Order in Time, Causation, and\nResemblance; that in every proposition one of these five is either\naffirmed, or denied, of some fact or phenomenon, or of some object the\nunknown 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\ndo not relate to any matter of fact, in the proper sense of the term, at\nall, but to the meaning of names. Since names and their signification\nare entirely 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\nof usage; 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\ntheir nature and characteristics are of as much importance in logic, as\nthose of any of the other classes of propositions previously adverted\nto.\n\nIf all propositions respecting the signification of words were as simple\nand unimportant as those which served us for examples when examining\nHobbes' 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\nwill perceive that I allude to the distinction on which so much stress\nwas laid by the schoolmen, and which has been retained either under the\nsame or under other names by most metaphysicians to the present day,\nviz. between what were called _essential_, and what were called\n_accidental_, propositions, and between essential and accidental\nproperties or attributes.\n\n\n\u00a7 2. Almost all metaphysicians prior to Locke, as well as many since his\ntime, have made a great mystery of Essential Predication, and of\npredicates which are said to be of the _essence_ of the subject. The\nessence of a thing, they said, was that without which the thing could\nneither be, nor be conceived to be. Thus, rationality was of the essence\nof man, because without rationality, man could not be conceived to\nexist. The different attributes which made up the essence of the thing\nwere called its essential properties; and a proposition in which any of\nthese were 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\ndo. All properties, not of the essence of the thing, were called its\naccidents; were supposed to have nothing at all, or nothing\ncomparatively, to do with its inmost nature; and the propositions in\nwhich any of these were predicated of it were called Accidental\nPropositions. A connexion may be traced between this distinction, which\noriginated with the schoolmen, and the well-known dogmas of _substanti\u00e6\nsecund\u00e6_ or general substances, and _substantial forms_, doctrines which\nunder varieties of language pervaded alike the Aristotelian and the\nPlatonic schools, and of which more of the spirit has come down to\nmodern times than might be conjectured from the disuse of the\nphraseology. The false views of the nature of classification and\ngeneralization which prevailed among the schoolmen, and of which these\ndogmas were the technical expression, afford the only explanation which\ncan be given of their having misunderstood the real nature of those\nEssences which held so conspicuous a place in their philosophy. They\nsaid, truly, that _man_ cannot be conceived without rationality. But\nthough _man_ cannot, a being may be conceived exactly like a man in all\npoints except that one quality, and those others which are the\nconditions or consequences of it. All therefore which is really true in\nthe assertion that man cannot be conceived without rationality, is only,\nthat if he had not rationality, he would not be reputed a man. There is\nno 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\nwhich is reserved for rational beings. Rationality, in short, is\ninvolved in the meaning of the word man: is one of the attributes\nconnoted by the name. The essence of man, simply means the whole of the\nattributes connoted by the word; and any one of those attributes taken\nsingly, is an essential property of man.\n\nBut these reflections, so easy to us, would have been difficult to\npersons who thought, as most of the later Aristotelians did, that\nobjects were made what they were called, that gold (for instance) was\nmade gold, not by the possession of certain properties to which mankind\nhave chosen to attach that name, but by participation in the nature of\na certain general substance, called gold in general, which substance,\ntogether with all the properties that belonged to it, _inhered_ in every\nindividual piece of gold.[23] As they did not consider these universal\nsubstances to be attached to all general names, but only to some, they\nthought that an object borrowed only a part of its properties from an\nuniversal substance, and that the rest belonged to it individually: the\nformer they called its essence, and the latter its accidents. The\nscholastic doctrine of essences long survived the theory on which it\nrested, that of the existence of real entities corresponding to general\nterms; and it was reserved for Locke at the end of the seventeenth\ncentury, to convince philosophers that the supposed essences of classes\nwere merely the signification of their names; nor, among the signal\nservices which his writings rendered to philosophy, was there one more\nneedful or more valuable.\n\nNow, as the most familiar of the general names by which an object is\ndesignated usually connotes not one only, but several attributes of the\nobject, each of which attributes separately forms also the bond of union\nof some class, and the meaning of some general name; we may predicate of\na name which connotes a variety of attributes, another name which\nconnotes only one of these attributes, or some smaller number of them\nthan all. In such cases, the universal affirmative proposition will be\ntrue; since whatever possesses the whole of any set of attributes, must\npossess any part of that same set. A proposition of this sort, however,\nconveys no information to any one who previously understood the whole\nmeaning of the terms. The propositions, Every man is a corporeal being,\nEvery man is a living creature, Every man is rational, convey no\nknowledge to any one who was already aware of the entire meaning of the\nword _man_, for the meaning of the word includes all this: and that\nevery _man_ has the attributes connoted by all these predicates, is\nalready asserted when he is called a man. Now, of this nature are all\nthe propositions which have been called essential. They are, in fact,\nidentical propositions.\n\nIt is true that a proposition which predicates any attribute, even\nthough it be one implied in the name, is in most cases understood to\ninvolve a tacit assertion that there _exists_ a thing corresponding to\nthe name, and possessing the attributes connoted by it; and this implied\nassertion may convey information, even to those who understood the\nmeaning of the name. But all information of this sort, conveyed by all\nthe essential propositions of which man can be made the subject, is\nincluded in the assertion, Men exist. And this assumption of real\nexistence is, after all, the result of an imperfection of language. It\narises from the ambiguity of the copula, which, in addition to its\nproper office of a mark to show that an assertion is made, is also, as\nformerly remarked, a concrete word connoting existence. The actual\nexistence of the subject of the proposition is therefore only\napparently, not really, implied in the predication, if an essential one:\nwe may say, A ghost is a disembodied spirit, without believing in\nghosts. But an accidental, or non-essential, affirmation, does imply the\nreal existence of the subject, because in the case of a non-existent\nsubject there is nothing for the proposition to assert. Such a\nproposition as, The ghost of a murdered person haunts the couch of the\nmurderer, can only have a meaning if understood as implying a belief in\nghosts; for since the signification of the word ghost implies nothing of\nthe kind, the speaker either means nothing, or means to assert a thing\nwhich he wishes to be believed to have really taken place.\n\nIt will be hereafter seen that when any important consequences seem to\nfollow, as in mathematics, from an essential proposition, or, in other\nwords, from a proposition involved in the meaning of a name, what they\nreally flow from is the tacit assumption of the real existence of the\nobjects so named. Apart from this assumption of real existence, the\nclass of propositions in which the predicate is of the essence of the\nsubject (that is, in which the predicate connotes the whole or part of\nwhat the subject connotes, but nothing besides) answer no purpose but\nthat of unfolding the whole or some part of the meaning of the name, to\nthose who did not previously know it. Accordingly, the most useful, and\nin strictness 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,\nand the purposes to which they are respectively subservient, will be\nminutely considered in the proper place.\n\n\n\u00a7 3. According to the above view of essential propositions, no\nproposition can be reckoned such which relates to an individual by name,\nthat is, in which the subject is a proper name. Individuals have no\nessences. When the schoolmen talked of the essence of an individual,\nthey did not mean the properties implied in its name, for the names of\nindividuals imply no properties. They regarded as of the essence of an\nindividual, whatever was of the essence of the species in which they\nwere accustomed to place that individual; _i.e._ of the class to which\nit was most familiarly referred, and to which, therefore, they conceived\nthat it by nature belonged. Thus, because the proposition Man is a\nrational being, was an essential proposition, they affirmed the same\nthing of the proposition, Julius C\u00e6sar is a rational being. This\nfollowed very naturally if genera and species were to be considered as\nentities, distinct from, but _inhering_ in, the individuals composing\nthem. If _man_ was a substance inhering in each individual man, the\n_essence_ of man (whatever that might mean) was naturally supposed to\naccompany it; to inhere in John Thompson, and to form the _common\nessence_ of Thompson and Julius C\u00e6sar. It might then be fairly said,\nthat rationality, being of the essence of Man, was of the essence also\nof Thompson. But if Man altogether be only the individual men and a name\nbestowed upon them in consequence of certain common properties, what\nbecomes of John Thompson's essence?\n\nA fundamental error is seldom expelled from philosophy by a single\nvictory. It retreats slowly, defends every inch of ground, and often,\nafter it has been driven from the open country, retains a footing in\nsome remote fastness. The essences of individuals were an unmeaning\nfigment arising from a misapprehension of the essences of classes, yet\neven Locke, when he extirpated the parent error, could not shake himself\nfree from that which was its fruit. He distinguished two sorts of\nessences, Real and Nominal. His nominal essences were the essences of\nclasses, explained nearly as we have now explained them. Nor is anything\nwanting to render the third book of Locke's Essay a nearly\nunexceptionable treatise on the connotation of names, except to free its\nlanguage from the assumption of what are called Abstract Ideas, which\nunfortunately is involved in the phraseology, though not necessarily\nconnected with the thoughts contained in that immortal Third Book.[24]\nBut, besides nominal essences, he admitted real essences, or essences of\nindividual objects, which he supposed to be the causes of the sensible\nproperties of those objects. We know not (said he) what these are; (and\nthis acknowledgment rendered the fiction comparatively innocuous;) but\nif we did, we could, from them alone, demonstrate the sensible\nproperties of the object, as the properties of the triangle are\ndemonstrated from the definition of the triangle. I shall have occasion\nto revert to this theory in treating of Demonstration, and of the\nconditions under which one property of a thing admits of being\ndemonstrated from another property. It is enough here to remark that,\naccording to this definition, the real essence of an object has, in the\nprogress of physics, come to be conceived as nearly equivalent, in the\ncase of bodies, to their corpuscular structure: what it is now supposed\nto mean in the case of any other entities, I would not take upon myself\nto define.\n\n\n\u00a7 4. An essential proposition, then, is one which is purely verbal;\nwhich asserts of a thing under a particular name, only what is asserted\nof it in the fact of calling it by that name; and which therefore either\ngives no information, or gives it respecting the name, not the thing.\nNon-essential, or accidental propositions, on the contrary, may be\ncalled Real Propositions, in opposition to Verbal. They predicate of a\nthing some fact not involved in the signification of the name by which\nthe proposition speaks of it; some attribute not connoted by that name.\nSuch are all propositions concerning things individually designated, and\nall general or particular propositions in which the predicate connotes\nany attribute not connoted by the subject. All these, if true, add to\nour knowledge: they convey information, not already involved in the\nnames employed. When I am told that all, or even that some objects,\nwhich have certain qualities, or which stand in certain relations, have\nalso certain other qualities, or stand in certain other relations, I\nlearn from this proposition a new fact; a fact not included in my\nknowledge of the meaning of the words, nor even of the existence of\nThings answering to the signification of those words. It is this class\nof propositions only which are in themselves instructive, or from which\nany instructive propositions can be inferred.[25]\n\nNothing has probably contributed more to the opinion so long prevalent\nof the futility of the school logic, than the circumstance that almost\nall the examples used in the common school books to illustrate the\ndoctrine of predication and that of the syllogism, consist of essential\npropositions. They were usually taken either from the branches or from\nthe main trunk of the Predicamental Tree, which included nothing but\nwhat was of the _essence_ of the species: _Omne corpus est substantia_,\n_Omne animal est corpus_, _Omnis homo est corpus_, _Omnis homo est\nanimal_, _Omnis homo est rationalis_, and so forth. It is far from\nwonderful that the syllogistic art should have been thought to be of no\nuse in assisting correct reasoning, when almost the only propositions\nwhich, in the hands of its professed teachers, it was employed to prove,\nwere such as every one assented to without proof the moment he\ncomprehended the meaning of the words; and stood exactly on a level, in\npoint of evidence, with the premises from which they were drawn. I have,\ntherefore, throughout this work, avoided the employment of essential\npropositions as examples, except where the nature of the principle to be\nillustrated specifically required them.\n\n\n\u00a7 5. With respect to propositions which do convey information--which\nassert something of a Thing, under a name that does not already\npresuppose what is about to be asserted; there are two different aspects\nin which these, or rather such of them as are general propositions, may\nbe considered: we may either look at them as portions of speculative\ntruth, or as memoranda for practical use. According as we consider\npropositions in one or the other of these lights, their import may be\nconveniently expressed in one or 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\nour theoretical knowledge, All men are mortal, means that the attributes\nof man are always accompanied by the attribute mortality: No men are\ngods, means that the attributes of man are never accompanied by the\nattributes, or at least never by all the attributes, signified by the\nword god. But when the proposition is considered as a memorandum for\npractical use, we shall find a different mode of expressing the same\nmeaning better adapted to indicate the office which the proposition\nperforms. The practical use of a proposition is, to apprise or remind us\nwhat we have to expect, in any individual case which comes within the\nassertion contained in the proposition. In reference to this purpose,\nthe proposition, All men are mortal, means that the attributes of man\nare _evidence of_, are a _mark_ of, mortality; an indication by which\nthe presence of that attribute is made manifest. No men are gods, means\nthat the attributes of man are a mark or evidence that some or all of\nthe attributes understood to belong to a god are not there; that where\nthe former are, we need not expect to find the latter.\n\nThese two forms of expression are at bottom equivalent; but the one\npoints the attention more directly to what a proposition means, the\nlatter to the manner in which it is to be used.\n\nNow it is to be observed that Reasoning (the subject to which we are\nnext to proceed) is a process into which propositions enter not as\nultimate results, but as means to the establishment of other\npropositions. We may expect, therefore, that the mode of exhibiting the\nimport of a general proposition which shows it in its application to\npractical use, will best express the function which propositions perform\nin Reasoning. And accordingly, in the theory of Reasoning, the mode of\nviewing the subject which considers a Proposition as asserting that one\nfact or phenomenon is a _mark_ or _evidence_ of another fact or\nphenomenon, will be found almost indispensable. For the purposes of that\nTheory, the best mode of defining the import of a proposition is not the\nmode which shows most clearly what it is in itself, but that which most\ndistinctly suggests the manner in which it may be made available for\nadvancing from it to other propositions.\n\n\n\n\nCHAPTER VII.\n\nOF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.\n\n\n\u00a7 1. In examining into the nature of general propositions, we have\nadverted much less than is usual with logicians to the ideas of a Class,\nand Classification; ideas which, since the Realist doctrine of General\nSubstances went out of vogue, have formed the basis of almost every\nattempt at a philosophical theory of general terms and general\npropositions. We have considered general names as having a meaning,\nquite independently of their being the names of classes. That\ncircumstance is in truth accidental, it being wholly immaterial to the\nsignification of the name whether there are many objects, or only one,\nto which it happens to be applicable, or whether there be any at all.\nGod is as much a general term to the Christian or Jew as to the\nPolytheist; and dragon, hippogriff, chimera, mermaid, ghost, are as much\nso as if real objects existed, corresponding to those names. Every name\nthe signification of which is constituted by attributes, is potentially\na name of an indefinite number of objects; but it needs not be actually\nthe name of any; and if of any, it may be the name of only one. As soon\nas we employ a name to connote attributes, the things, be they more or\nfewer, which happen to possess those attributes, are constituted _ipso\nfacto_ a class. But in predicating the name we predicate only the\nattributes; and the fact of belonging to a class does not, in many\ncases, come into view at all.\n\nAlthough, however, Predication does not presuppose Classification, and\nthough the theory of Names and of Propositions is not cleared up, but\nonly encumbered, by intruding the idea of classification into it, there\nis nevertheless a close connexion between Classification and the\nemployment of General Names. By every general name which we introduce,\nwe create a class, if there be any things, real or imaginary, to compose\nit; that is, any Things corresponding to the signification of the name.\nClasses, therefore, mostly owe their existence to general language. But\ngeneral language, also, though that is not the most common case,\nsometimes owes its existence to classes. A general, which is as much as\nto say a significant, name, is indeed mostly introduced because we have\na signification to express by it; because we need a word by means of\nwhich to predicate the attributes which it connotes. But it is also true\nthat a name is sometimes introduced because we have found it convenient\nto create a class; because we have thought it useful for the regulation\nof our mental operations, that a certain group of objects should be\nthought of together. A naturalist, for purposes connected with his\nparticular science, sees reason to distribute the animal or vegetable\ncreation into certain groups rather than into any others, and he\nrequires a name to bind, as it were, each of his groups together. It\nmust not however be supposed that such names, when introduced, differ in\nany respect, as to their mode of signification, from other connotative\nnames. The classes which they denote are, as much as any other classes,\nconstituted by certain common attributes, and their names are\nsignificant of those attributes, and of nothing else. The names of\nCuvier's classes and orders, _Plantigrades_, _Digitigrades_, &c., are as\nmuch the expression of attributes as if those names had preceded,\ninstead of grown out of, his classification of animals. The only\npeculiarity of the case is, that the convenience of classification was\nhere the primary motive for introducing the names; while in other cases\nthe name is introduced as a means of predication, and the formation of a\nclass denoted by it is only an indirect consequence.\n\nThe principles which ought to regulate Classification as a logical\nprocess subservient to the investigation of truth, cannot be discussed\nto any purpose until a much later stage of our inquiry. But, of\nClassification as resulting from, and implied in, the fact of employing\ngeneral language, we cannot forbear to treat here, without leaving the\ntheory of general names and of their employment in predication,\nmutilated and formless.\n\n\n\u00a7 2. This portion of the theory of general language is the subject of\nwhat is termed the doctrine of the Predicables; a set of distinctions\nhanded down from Aristotle, and his follower Porphyry, many of which\nhave taken a firm root in scientific, and some of them even in popular,\nphraseology. The predicables are a five-fold division of General Names,\nnot grounded as usual on a difference in their meaning, that is, in the\nattribute which they connote, but on a difference in the kind of class\nwhich they denote. We may predicate of a thing five different varieties\nof class-name:--\n\n A _genus_ of the thing ([Greek: genos]).\n A _species_ ([Greek: eidos]).\n A _differentia_ ([Greek: diaphora]).\n A _proprium_ ([Greek: idion]).\n An _accidens_ ([Greek: symbeb\u00eakos]).\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\nto one or another predicable, according to the subject of which it is\npredicated on the particular occasion. _Animal_, for instance, is a\ngenus with respect to man, or John; a species with respect to Substance,\nor Being. _Rectangular_ is one of the Differenti\u00e6 of a geometrical\nsquare; it is merely one of the Accidentia of the table at which I am\nwriting. The words genus, species, &c. are therefore relative terms;\nthey are names applied to certain predicates, to express the relation\nbetween them and some given subject: a relation grounded, as we shall\nsee, not on what the predicate connotes, but on the class which it\ndenotes, and on the place which, in some given classification, that\nclass occupies relatively to the particular subject.\n\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,\nmuch more general than either. In this popular sense any two classes,\none of which includes the whole of the other and more, may be called a\nGenus and a Species. Such, for instance, are Animal and Man; Man and\nMathematician. Animal is a Genus; Man and Brute are its two species; or\nwe may divide it into a greater number of species, as man, horse, dog,\n&c. _Biped_, or _two-footed animal_, may also be considered a genus, of\nwhich man and bird are two species. _Taste_ is a genus, of which sweet\ntaste, sour taste, salt taste, &c. are species. _Virtue_ is a genus;\njustice, prudence, courage, 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\ncommon discourse. And it should be observed that in ordinary parlance,\nnot the name of the class, but the class itself, is said to be the genus\nor species; not, of course, the class in the sense of each individual of\nthe class, but the individuals collectively, considered as an aggregate\nwhole; the name by which the class is designated being then called not\nthe genus or species, but the generic or specific name. And this is an\nadmissible form of expression; nor is it of any importance which of the\ntwo modes of speaking we adopt, provided the rest of our language is\nconsistent with it; but, if we call the class itself the genus, we must\nnot talk of predicating the genus. We predicate of man the _name_\nmortal; and by predicating the name, we may be said, in an intelligible\nsense, to predicate what the name expresses, the _attribute_ mortality;\nbut in no allowable sense of the word predication do we predicate of man\nthe _class_ mortal. We predicate of him the fact of belonging to the\nclass.\n\nBy the Aristotelian logicians, the terms genus and species were used in\na more 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\nconsidered a genus; man and brute co-ordinate species under that genus:\n_biped_, however, would not have been admitted to be a genus with\nreference to man, but a _proprium_ or _accidens_ only. It was requisite,\naccording to their theory, that genus and species should be of the\n_essence_ of the subject. Animal was of the essence of man; biped was\nnot. And in every classification they considered some one class as the\nlowest or _infima_ species. Man, for instance, was a lowest species. Any\nfurther divisions into which the class might be capable of being broken\ndown, as man into white, black, and red man, or into priest and layman,\nthey did not admit to be species.\n\nIt has been seen, however, in the preceding chapter, that the\ndistinction between the essence of a class, and the attributes or\nproperties which are not of its essence--a distinction which has given\noccasion to so much abstruse speculation, and to which so mysterious a\ncharacter was formerly, and by many writers is still, attached,--amounts\nto nothing more than the difference between those attributes of the\nclass which are, and those which are not, involved in the signification\nof the class-name. As applied to individuals, the word Essence, we\nfound, has no meaning, except in connexion with the exploded tenets of\nthe Realists; and what the schoolmen chose to call the essence of an\nindividual, was simply the essence of the class to which that individual\nwas 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\nto which 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\nmean something by this distinction, and something important; but which,\nbeing but indistinctly conceived, was inadequately expressed by the\nphraseology of essences, and the various other modes of speech to which\nthey had recourse.\n\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\nactual classes (either of real or of imaginary things) as there are\ngeneral names, positive and negative together.\n\nBut if we contemplate any one of the classes so formed, such as the\nclass animal or plant, or the class sulphur or phosphorus, or the class\nwhite or red, and consider in what particulars the individuals included\nin the class differ from those which do not come within it, we find a\nvery remarkable diversity in this respect between some classes and\nothers. There are some classes, the things contained in which differ\nfrom other things only in certain particulars which may be numbered,\nwhile others differ in more than can be numbered, more even than we need\never expect to know. Some classes have little or nothing in common to\ncharacterize them by, except precisely what is connoted by the name:\nwhite things, for example, are not distinguished by any common\nproperties, except whiteness; or if they are, it is only by such as are\nin some way dependent on, or connected with, whiteness. But a hundred\ngenerations have not exhausted the common properties of animals or of\nplants, of sulphur or of phosphorus; nor do we suppose them to be\nexhaustible, but proceed to new observations and experiments, in the\nfull confidence of discovering new properties which were by no means\nimplied in those we previously knew. While, if any one were to propose\nfor investigation the common properties of all things which are of the\nsame colour, the same shape, or the same specific gravity, the absurdity\nwould be palpable. We have no ground to believe that any such common\nproperties exist, except such as may be shown to be involved in the\nsupposition itself, or to be derivable from it by some law of causation.\nIt appears, therefore, that the properties, on which we ground our\nclasses, sometimes exhaust all that the class has in common, or contain\nit all by some mode of implication; but in other instances we make a\nselection of a few properties from among not only a greater number, but\na number inexhaustible by us, and to which as we know no bounds, they\nmay, so far as we are concerned, be regarded as infinite.\n\nThere is no impropriety in saying that, of these two classifications,\nthe one answers to a much more radical distinction in the things\nthemselves, than the other does. And if any one even chooses to say that\nthe one classification is made by nature, the other by us for our\nconvenience, he will be right; provided he means no more than this:\nWhere a certain apparent difference between things (though perhaps in\nitself of little moment) answers to we know not what number of other\ndifferences, pervading not only their known properties, but properties\nyet undiscovered, it is not optional but imperative to recognise this\ndifference as the foundation of a specific distinction; while, on the\ncontrary, differences that are merely finite and determinate, like those\ndesignated by the words white, black, or red, may be disregarded if the\npurpose for which the classification is made does not require attention\nto those particular properties. The differences, however, are made by\nnature, in both cases; while the recognition of those differences as\ngrounds of classification and of naming, is, equally in both cases, the\nact of man: only in the one case, the ends of language and of\nclassification would be subverted if no notice were taken of the\ndifference, while in the other case, the necessity of taking notice of\nit depends on the importance or unimportance of the particular qualities\nin which the difference happens to consist.\n\nNow, these classes, distinguished by unknown multitudes of properties,\nand not solely by a few determinate ones--which are parted off from one\nanother by an unfathomable chasm, instead of a mere ordinary ditch with\na visible bottom--are the only classes which, by the Aristotelian\nlogicians, were considered as genera or species. Differences which\nextended only to a certain property or properties, and there terminated,\nthey considered as differences only in the _accidents_ of things; but\nwhere any class differed from other things by an infinite series of\ndifferences, known and unknown, they considered the distinction as one\nof _kind_, and spoke of it as being an _essential_ difference, which is\nalso one of the current meanings of that vague expression at the present\nday.\n\nConceiving the schoolmen to have been justified in drawing a broad line\nof separation between these two kinds of classes and of\nclass-distinctions, I shall not only retain the division itself, but\ncontinue to express it in their language. According to that language,\nthe proximate (or lowest) Kind to which any individual is referrible, is\ncalled its species. Conformably to this, Sir Isaac Newton would be said\nto be of the species man. There are indeed numerous sub-classes included\nin the class man, to which Newton also belongs; for example, Christian,\nand Englishman, and Mathematician. But these, though distinct classes,\nare not, in our sense of the term, distinct Kinds of men. A Christian,\nfor example, differs from other human beings; but he differs only in the\nattribute which the word expresses, namely, belief in Christianity, and\nwhatever else that implies, either as involved in the fact itself, or\nconnected with it through some law of cause and effect. We should never\nthink of inquiring what properties, unconnected with Christianity either\nas cause or effect, are common to all Christians and peculiar to them;\nwhile in regard to all Men, physiologists are perpetually carrying on\nsuch an inquiry; nor is the answer ever likely to be completed. Man,\ntherefore, we may call a species; Christian, or Mathematician, we\ncannot.\n\nNote here, that it is by no means intended to imply that there may not\nbe different Kinds, or logical species, of man. The various races and\ntemperaments, the two sexes, and even the various ages, may be\ndifferences of kind, within our meaning of the term. I do not say that\nthey are so. For in the progress of physiology it may almost be said to\nbe made out, that the differences which really exist between different\nraces, sexes, &c., follow as consequences, under laws of nature, from a\nsmall number of primary differences which can be precisely determined,\nand which, as the phrase is, _account for_ all the rest. If this be so,\nthese are not distinctions in kind; no more than Christian, Jew,\nMussulman, and Pagan, a difference which also carries many consequences\nalong with it. And in this way classes are often mistaken for real\nKinds, which are afterwards proved not to be so. But if it turned out\nthat the differences were not capable of being thus accounted for, then\nCaucasian, Mongolian, Negro, &c. would be really different Kinds of\nhuman beings, and entitled to be ranked as species by the logician;\nthough not by the naturalist. For (as already noticed) the word species\nis used in a different signification in logic and in natural history. By\nthe naturalist, organized beings are not usually said to be of different\nspecies, if it is supposed that they could possibly have descended from\nthe same stock. That, however, is a sense artificially given to the\nword, for the technical purposes of a particular science. To the\nlogician, if a negro and a white man differ in the same manner (however\nless in degree) as a horse and a camel do, that is, if their differences\nare inexhaustible, and not referrible to any common cause, they are\ndifferent species, whether they are descended from common ancestors or\nnot. But if their differences can all be traced to climate and habits,\nor to some one or a few special differences in structure, they are not,\nin the logician's view, specially distinct.\n\nWhen the _infima species_, or proximate Kind, to which an individual\nbelongs, has been ascertained, the properties common to that Kind\ninclude necessarily the whole of the common properties of every other\nreal Kind to which the individual can be referrible. Let the individual,\nfor example, be Socrates, and the proximate Kind, man. Animal, or living\ncreature, is also a real Kind, and includes Socrates; but, since it\nlikewise includes man, or in other words, since all men are animals, the\nproperties common to animals form a portion of the common properties of\nthe sub-class, man. And if there be any class which includes Socrates\nwithout including man, that class is not a real Kind. Let the class for\nexample, be _flat-nosed_; that being a class which includes Socrates,\nwithout including all men. To determine whether it is a real Kind, we\nmust ask ourselves this question: Have all flat-nosed animals, in\naddition to whatever is implied in their flat noses, any common\nproperties, other than those which are common to all animals whatever?\nIf they had; if a flat nose were a mark or index to an indefinite number\nof other peculiarities, not deducible from the former by an\nascertainable law, then out of the class man we might cut another class,\nflat-nosed man, which according to our definition, would be a Kind. But\nif we could do this, man would not be, as it was assumed to be, the\nproximate Kind. Therefore, the properties of the proximate Kind do\ncomprehend those (whether known or unknown) of all other Kinds to which\nthe individual belongs; which was the point we undertook to prove. And\nhence, every other Kind which is predicable of the individual, will be\nto the proximate Kind in the relation of a genus, according to even the\npopular acceptation of the terms genus and species; that is, it will be\na 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\none another, is either a genus or a species. A Kind which is not\ndivisible into other Kinds, cannot be a genus, because it has no\nspecies under it; but it is itself a species, both with reference to the\nindividuals below and to the genera above (Species Pr\u00e6dicabilis and\nSpecies Subjicibilis.) But every Kind which admits of division into real\nKinds (as animal into mammal, bird, fish, &c., or bird into various\nspecies of birds) is a genus to all below it, a species to all genera in\nwhich it is itself included. And here we may close this part of the\ndiscussion, and pass to the three remaining predicables, Differentia,\nProprium, and Accidens.\n\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\ngenus. This is so far clear: but we may still ask, which of the\ndistinguishing attributes it signifies. For we have seen that every Kind\n(and a species must be a Kind) is distinguished from other Kinds not by\nany one attribute, but by an indefinite number. Man, for instance, is a\nspecies of the genus animal: Rational (or rationality, for it is of no\nconsequence here whether we use the concrete or the abstract form) is\ngenerally assigned by logicians as the Differentia; and doubtless this\nattribute serves the purpose of distinction: but it has also been\nremarked of man, that he is a cooking animal; the only animal that\ndresses its food. This, therefore, is another of the attributes by which\nthe species man is distinguished from other species of the same genus:\nwould this attribute serve equally well for a differentia? The\nAristotelians say No; having laid it down that the differentia must,\nlike the genus and species, be of the _essence_ of the subject.\n\nAnd here we lose even that vestige of a meaning grounded in the nature\nof the things themselves, which may be supposed to be attached to the\nword essence when it is said that genus and species must be of the\nessence of the thing. There can be no doubt that when the schoolmen\ntalked of the essences of things as opposed to their accidents, they had\nconfusedly in view the distinction between differences of kind, and the\ndifferences which are not of kind; they meant to intimate that genera\nand species must be Kinds. Their notion of the essence of a thing was a\nvague notion of a something which makes it what it is, _i. e._ which\nmakes it the Kind of thing that it is--which causes it to have all that\nvariety of properties which distinguish its Kind. But when the matter\ncame to be looked at more closely, nobody could discover what caused the\nthing to have all those properties, nor even that there was anything\nwhich caused it to have them. Logicians, however, not liking to admit\nthis, and being unable to detect what made the thing to be what it was,\nsatisfied themselves with what made it to be what it was called. Of the\ninnumerable properties, known and unknown, that are common to the class\nman, a portion only, and of course a very small portion, are connoted by\nits name; these few, however, will naturally have been thus\ndistinguished from the rest either for their greater obviousness, or for\ngreater supposed importance. These properties, then, which were connoted\nby the name, logicians seized upon, and called them the essence of the\nspecies; and not stopping there, they affirmed them, in the case of the\n_infima species_, to be the essence of the individual too; for it was\ntheir maxim, that the species contained the \"whole essence\" of the\nthing. Metaphysics, that fertile field of delusion propagated by\nlanguage, does not afford a more signal instance of such delusion. On\nthis account it was that rationality, being connoted by the name man,\nwas allowed to be a differentia of the class; but the peculiarity of\ncooking their food, not being connoted, was relegated to the class of\naccidental properties.\n\nThe distinction, therefore, between Differentia, Proprium, and Accidens,\nis not grounded in the nature of things, but in the connotation of\nnames; and 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\ngenus. It must connote all the attributes which the genus connotes, or\nthere would be nothing to prevent it from denoting individuals not\nincluded in the genus. And it must connote something besides, otherwise\nit would include the whole genus. Animal denotes all the individuals\ndenoted by man, and many more. Man, therefore, must connote all that\nanimal connotes, otherwise there might be men who are not animals; and\nit must connote something more than animal connotes, otherwise all\nanimals would be men. This surplus of connotation--this which the\nspecies connotes over and above the connotation of the genus--is the\nDifferentia, or specific difference; or, to state the same proposition\nin other words, the Differentia is that which must be added to the\nconnotation of the genus, to complete the connotation of the species.\n\nThe word man, for instance, exclusively of what it connotes in common\nwith animal, also connotes rationality, and at least some approximation\nto that external form which we all know, but which as we have no name\nfor it considered in itself, we are content to call the human. The\nDifferentia, or specific difference, therefore, of man, as referred to\nthe genus animal, is that outward form and the possession of reason. The\nAristotelians said, the possession of reason, without the outward form.\nBut if they adhered to this, they would have been obliged to call the\nHouyhnhnms men. The question never arose, and they were never called\nupon to decide how such a case would have affected their notion of\nessentiality. However this may be, they were satisfied with taking such\na portion of the differentia as sufficed to distinguish the species from\nall other _existing_ things, though by so doing they might not exhaust\nthe connotation of the name.\n\n\n\u00a7 6. And here, to prevent the notion of differentia from being\nrestricted within too narrow limits, it is necessary to remark, that a\nspecies, even as referred to the same genus, will not always have the\nsame differentia, but a different one, according to the principle and\npurpose which preside over the particular classification. For example, a\nnaturalist surveys the various kinds of animals, and looks out for the\nclassification of them most in accordance with the order in which, for\nzoological purposes, he considers it desirable that we should think of\nthem. With this view he finds it advisable that one of his fundamental\ndivisions should be into warm-blooded and cold-blooded animals; or into\nanimals which breathe with lungs and those which breathe with gills; or\ninto carnivorous, and frugivorous or graminivorous; or into those which\nwalk on the flat part and those which walk on the extremity of the foot,\na distinction on which two of Cuvier's families are founded. In doing\nthis, the naturalist creates as many new classes; which are by no means\nthose to which the individual animal is familiarly and spontaneously\nreferred; nor should we ever think of assigning to them so prominent a\nposition in our arrangement of the animal kingdom, unless for a\npreconceived purpose of scientific convenience. And to the liberty of\ndoing this there is no limit. In the examples we have given, most of the\nclasses are real Kinds, since each of the peculiarities is an index to a\nmultitude of properties belonging to the class which it characterizes:\nbut even if the case were otherwise--if the other properties of those\nclasses could all be derived, by any process known to us, from the one\npeculiarity on which the class is founded--even then, if these\nderivative properties were of primary importance for the purposes of the\nnaturalist, he would be warranted in founding his primary divisions on\nthem.\n\nIf, however, practical convenience is a sufficient warrant for making\nthe main 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\ngenera and species _are_ real genera and species, in marking the\ndistinction between them by those of their properties which\nconsiderations of practical convenience most strongly recommend. If we\ncut a species out of a given genus--the species man, for instance, out\nof the genus animal--with an intention on our part that the peculiarity\nby which we are to be guided in the application of the name man should\nbe rationality, then rationality is the differentia of the species man.\nSuppose, however, that being naturalists, we, for the purposes of our\nparticular study, cut out of the genus animal the same species man, but\nwith an intention that the distinction between man and all other species\nof animal should be, not rationality, but the possession of \"four\nincisors in each jaw, tusks solitary, and erect posture.\" It is evident\nthat the word man, when used by us as naturalists, no longer connotes\nrationality, but connotes the three other properties specified; for that\nwhich we have expressly in view when we impose a name, assuredly forms\npart of the meaning of that name. We may, therefore, lay it down as a\nmaxim, that wherever there is a Genus, and a Species marked out from\nthat genus by an assignable differentia, the name of the species must be\nconnotative, and must connote the differentia; but the connotation may\nbe special--not involved in the signification of the term as ordinarily\nused, but given to it when employed as a term of art or science. The\nword Man in common use, connotes rationality and a certain form, but\ndoes not connote the number or character of the teeth; in the Linn\u00e6an\nsystem it connotes the number of incisor and canine teeth, but does not\nconnote rationality nor any particular form. The word _man_ has,\ntherefore, two different meanings; though not commonly considered as\nambiguous, because it happens in both cases to _de_note the same\nindividual objects. But a case is conceivable in which the ambiguity\nwould become evident: we have only to imagine that some new kind of\nanimal were discovered, having Linn\u00e6us's three characteristics of\nhumanity, but not rational, or not of the human form. In ordinary\nparlance, these animals would not be called men; but in natural history\nthey must still be called so by those, if any there be, who adhere to\nthe Linn\u00e6an classification; and the question would arise, whether the\nword should continue to be used in two senses, or the classification be\ngiven up, and the technical sense of the term be abandoned along with\nit.\n\nWords not otherwise connotative may, in the mode just adverted to,\nacquire a special or technical connotation. Thus the word whiteness, as\nwe have so often remarked, connotes nothing; it merely denotes the\nattribute corresponding to a certain sensation: but if we are making a\nclassification of colours, and desire to justify, or even merely to\npoint out, the particular place assigned to whiteness in our\narrangement, we may define it \"the colour produced by the mixture of all\nthe simple rays;\" and this fact, though by no means implied in the\nmeaning of the word whiteness as ordinarily used, but only known by\nsubsequent scientific investigation, is part of its meaning in the\nparticular essay or treatise, and becomes the differentia of the\nspecies.[26]\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\nreferring it.\n\n\n\u00a7 7. Having disposed of Genus, Species, and Differentia, we shall not\nfind much difficulty in attaining a clear conception of the distinction\nbetween the other two predicables, as well as between them and the first\nthree.\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\nthat the 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\nby whatever comes under that definition. Accidens, on the contrary, has\nno connexion whatever with the essence, but may come and go, and the\nspecies still remain what it was before. If a species could exist\nwithout its Propria, it must be capable of existing without that on\nwhich its Propria are necessarily consequent, and therefore without its\nessence, without that which constitutes it a species. But an Accidens,\nwhether separable or inseparable from the species in actual experience,\nmay be supposed separated, without the necessity of supposing any other\nalteration; or at least, without supposing any of the essential\nproperties of the species to be altered, since with them an Accidens has\nno connexion.\n\nA Proprium, therefore, of the species, may be defined, any attribute\nwhich belongs to all the individuals included in the species, and which,\nthough 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\nthe name 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\nfollows premises, or it may follow as an effect follows a cause. Thus,\nthe attribute of having the opposite sides equal, which is not one of\nthose connoted by the word Parallelogram, nevertheless follows from\nthose connoted by it, namely, from having the opposite sides straight\nlines and parallel, and the number of sides four. The attribute,\ntherefore, of having the opposite sides equal, is a Proprium of the\nclass parallelogram; and a Proprium of the first kind, which follows\nfrom the connoted attributes by way of _demonstration_. The attribute of\nbeing capable of understanding language, is a Proprium of the species\nman, since without being connoted by the word, it follows from an\nattribute which the word does connote, viz. from the attribute of\nrationality. But this is a Proprium of the second kind, which follows by\nway of _causation_. How it is that one property of a thing follows, or\ncan be inferred, from another; under what conditions this is possible,\nand what is the exact meaning of the phrase; are among the questions\nwhich will occupy us in the two succeeding Books. At present it needs\nonly be said, that whether a Proprium follows by demonstration or by\ncausation, it follows _necessarily_; that is to say, its not following\nwould be inconsistent with some law which we regard as a part of the\nconstitution either of our thinking faculty or of the universe.\n\n\n\u00a7 8. Under the remaining predicable, Accidens, are included all\nattributes of a thing which are neither involved in the signification of\nthe name (whether ordinarily or as a term of art), nor have, so far as\nwe know, any necessary connexion with attributes which are so involved.\nThey are commonly divided into Separable and Inseparable Accidents.\nInseparable accidents are those which--although we know of no connexion\nbetween them and the attributes constitutive of the species, and\nalthough, therefore, so far as we are aware, they might be absent\nwithout making the name inapplicable and the species a different\nspecies--are yet never in fact known to be absent. A concise mode of\nexpressing the same meaning is, that inseparable accidents are\nproperties which are universal to the species, but not necessary to it.\nThus, blackness is an attribute of a crow, and, as far as we know, an\nuniversal one. But if we were to discover a race of white birds, in\nother respects resembling crows, we should not say, These are not crows;\nwe should say, These are white crows. Crow, therefore, does not connote\nblackness; nor, from any of the attributes which it does connote,\nwhether as a word in popular use or as a term of art, could blackness be\ninferred. Not only, therefore, can we conceive a white crow, but we know\nof no reason why such an animal should not exist. Since, however, none\nbut black crows are known to exist, blackness, in the present state of\nour knowledge, ranks as an accident, but an inseparable accident, of\nthe 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\nof the species, but only to some individuals; or if to all, not at all\ntimes. Thus the colour of an European is one of the separable accidents\nof the species man, because it is not an attribute of all human\ncreatures. Being born, is also (speaking in the logical sense) a\nseparable accident of the species man, because, though an attribute of\nall human beings, it is so only at one particular time. _\u00c0 fortiori_\nthose attributes which are not constant even in the same individual, as,\nto be in one or in another place, to be hot or cold, sitting or walking,\nmust be ranked as separable accidents.\n\n\n\n\nCHAPTER VIII.\n\nOF DEFINITION.\n\n\n\u00a7 1. One necessary part of the theory of Names and of Propositions\nremains to be treated of in this place: the theory of Definitions. As\nbeing the most important of the class of propositions which we have\ncharacterized as purely verbal, they have already received some notice\nin the chapter preceding the last. But their fuller treatment was at\nthat time postponed, because definition is so closely connected with\nclassification, that, until the nature of the latter process is in some\nmeasure understood, the former 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\nit bears in common acceptation, or that which the speaker or writer, for\nthe particular 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 \"John Thomson\" to say he is \"the son of General Thomson;\" for the\nname John Thomson does not express this. Neither is it any definition of\n\"John Thomson\" to say he is \"the man now crossing the street.\" These\npropositions may serve to make known who is the particular man to whom\nthe name belongs, but that may be done still more unambiguously by\npointing to him, which, however, has not been esteemed one of the modes\nof definition.\n\nIn the case of connotative names, the meaning, as has been so often\nobserved, is the connotation; and the definition of a connotative name,\nis the proposition which declares its connotation. This might be done\neither directly or indirectly. The direct mode would be by a proposition\nin this form: \"Man\" (or whatsoever the word may be) \"is a name connoting\nsuch and such attributes,\" or \"is a name which, when predicated of\nanything, signifies the possession of such and such attributes by that\nthing.\" Or thus: Man is everything which possesses such and such\nattributes: Man is everything which possesses corporeity, organization,\nlife, rationality, and certain peculiarities of external form.\n\nThis form of definition is the most precise and least equivocal of any;\nbut it is not brief enough, and is besides too technical for common\ndiscourse. The more usual mode of declaring the connotation of a name,\nis to predicate of it another name or names of known signification,\nwhich connote the same aggregation of attributes. This may be done\neither by predicating of the name intended to be defined, another\nconnotative name exactly synonymous, as, \"Man is a human being,\" which\nis not commonly accounted a definition at all; or by predicating two or\nmore connotative names, which make up among them the whole connotation\nof the name to be defined. In this last case, again, we may either\ncompose our definition of as many connotative names as there are\nattributes, each attribute being connoted by one, as, Man is a\ncorporeal, organized, animated, rational being, shaped so and so; or we\nmay employ names which connote several of the attributes at once, as,\nMan 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\nfor their subject. All propositions the truth of which is implied in the\nname, all those which we are made aware of by merely hearing the name,\nare included in the definition, if complete, and may be evolved from it\nwithout the aid of any other premises; whether the definition expresses\nthem in two or three words, or in a larger number. It is, therefore, not\nwithout reason that Condillac and other writers have affirmed a\ndefinition to be an _analysis_. To resolve any complex whole into the\nelements of which it is compounded, is the meaning of analysis: and this\nwe do when we replace one word which connotes a set of attributes\ncollectively, by two or more which connote the same attributes singly,\nor in smaller groups.\n\n\n\u00a7 2. From this, however, the question naturally arises, in what manner\nare we to define a name which connotes only a single attribute: for\ninstance, \"white,\" which connotes nothing but whiteness; \"rational,\"\nwhich connotes nothing but the possession of reason. It might seem that\nthe meaning of such names could only be declared in two ways; by a\nsynonymous term, if any such can be found; or in the direct way already\nalluded to: \"White is a name connoting the attribute whiteness.\" Let us\nsee, however, whether the analysis of the meaning of the name, that is,\nthe breaking down of that meaning into several parts, admits of being\ncarried farther. Without at present deciding this question as to the\nword _white_, it is obvious that in the case of _rational_ some further\nexplanation may be given of its meaning than is contained in the\nproposition, \"Rational is that which possesses the attribute of reason;\"\nsince the attribute reason itself admits of being defined. And here we\nmust turn our attention to the definitions of attributes, or rather of\nthe names of attributes, that is, of 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, \"a quality productive of evil or\ninconvenience.\" 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\nconcrete name form the entire signification of the corresponding\nabstract name, the same enumeration will serve for the definition of\nboth. Thus, if the definition of _a human being_ be this, \"a being,\ncorporeal, animated, rational, shaped so and so,\" the definition of\n_humanity_ will be corporeity and animal life, combined with\nrationality, and with such and such a shape.\n\nWhen, on the other hand, the abstract name does not express a\ncomplication of attributes, but a single attribute, we must remember\nthat every attribute is grounded on some fact or phenomenon, from which,\nand which alone, it derives its meaning. To that fact or phenomenon,\ncalled in a former chapter the foundation of the attribute, we must,\ntherefore, have recourse for its definition. Now, the foundation of the\nattribute may be a phenomenon of any degree of complexity, consisting of\nmany different parts, either coexistent or in succession. To obtain a\ndefinition of the attribute, we must analyse the phenomenon into these\nparts. Eloquence, for example, is the name of one attribute only; but\nthis attribute is grounded on external effects of a complicated nature,\nflowing from acts of the person to whom we ascribed the attribute; and\nby resolving this phenomenon of causation into its two parts, the cause\nand the effect, we obtain a definition of eloquence, viz. the power of\ninfluencing the feelings by speech 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\npower of exciting the sensation of white. A white object may be defined,\nan object 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 recal 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\ndirect appeal to the personal experience of the individual whom we\naddress.\n\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\nwhich declares the facts, and the whole of the facts, which the name\ninvolves in its signification. But with most persons the object of a\ndefinition does not embrace so much; they look for nothing more, in a\ndefinition, than a guide to the correct use of the term--a protection\nagainst applying it in a manner inconsistent with custom and convention.\nAnything, therefore, is to them a sufficient definition of a term, which\nwill serve as a correct index to what the term denotes; though not\nembracing the whole, and sometimes, perhaps, not even any part, of what\nit connotes. This gives rise to two sorts of imperfect, or unscientific\ndefinition; Essential but incomplete Definitions, and Accidental\nDefinitions, or Descriptions. In the former, a connotative name is\ndefined by a part only of its connotation; in the latter, by something\nwhich forms no part of the connotation at all.\n\nAn example of the first kind of imperfect definitions is the\nfollowing:--Man is a rational animal. It is impossible to consider this\nas a complete definition of the word Man, since (as before remarked) if\nwe adhered to it we should be obliged to call the Houyhnhnms men; but as\nthere happen to be no Houyhnhnms, this imperfect definition is\nsufficient to mark out and distinguish from all other things, the\nobjects at present denoted by \"man;\" all the beings actually known to\nexist, of whom the name is predicable. Though the word is defined by\nsome only among the attributes which it connotes, not by all, it happens\nthat all known objects which possess the enumerated attributes, possess\nalso those which are omitted; so that the field of predication which the\nword covers, and the employment of it which is conformable to usage, are\nas well indicated by the inadequate definition as by an adequate one.\nSuch definitions, however, are always liable to be overthrown by the\ndiscovery of new objects in nature.\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\ngenus et differentiam_. Differentia being seldom taken to mean the whole\nof the peculiarities 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\nname of the superior genus, not merely _some_ attribute which\ndistinguishes the species intended to be defined from all other species\nof the same genus, but _all_ the attributes implied in the name of the\nspecies, which the name of the superior genus has not already implied.\nThe assertion, however, that a definition must of necessity consist of a\ngenus and differenti\u00e6, is not tenable. It was early remarked by\nlogicians, that the _summum genus_ in any classification, having no\ngenus superior to itself, could not be defined in this manner. Yet we\nhave seen that all names, except those of our elementary feelings, are\nsusceptible of definition in the strictest sense; by setting forth in\nwords the constituent parts of the fact or phenomenon, of which the\nconnotation of every word is ultimately composed.\n\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\nsufficient to mark out correctly the boundaries of its denotation,) has\nbeen considered by the ancients, and by logicians in general, as a\ncomplete definition; it has always been deemed necessary that the\nattributes employed should really form part of the connotation; for the\nrule was that the definition must be drawn from the _essence_ of the\nclass; and this would not have been the case if it had been in any\ndegree made up of attributes not connoted by the name. The second kind\nof imperfect definition, therefore, in which the name of a class is\ndefined by any of its accidents,--that is, by attributes which are not\nincluded in its connotation,--has been rejected from the rank of genuine\nDefinition by all logicians, 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\nstating any (no matter what) of the attributes which are common to the\nwhole of the class, and peculiar to it; or any combination of attributes\nwhich happens to be peculiar to it, though separately each of those\nattributes may be common to it with some other things. It is only\nnecessary that the definition (or description) thus formed, should be\n_convertible_ with the name which it professes to define; that is,\nshould be exactly co-extensive with it, being predicable of everything\nof which it is predicable, and of nothing of which it is not predicable;\nthough the attributes specified may have no connexion with those which\nmankind had in view when they formed or recognised the class, and gave\nit a name. The following are correct definitions of Man, according to\nthis test: Man is a mammiferous animal, having (by nature) two hands\n(for the human species answers to this description, and no other animal\ndoes): Man is an animal who cooks his food: Man is a featherless biped.\n\nWhat would otherwise be a mere description, may be raised to the rank of\na real definition by the peculiar purpose which the speaker or writer\nhas in view. As was seen in the preceding chapter, it may, for the ends\nof a particular art or science, or for the more convenient statement of\nan author's particular doctrines, be advisable to give to some general\nname, without altering its denotation, a special connotation, different\nfrom its ordinary one. When this is done, a definition of the name by\nmeans of the attributes which make up the special connotation, though in\ngeneral a mere accidental definition or description, becomes on the\nparticular occasion and for the particular purpose a complete and\ngenuine definition. This actually occurs with respect to one of the\npreceding examples, \"Man is a mammiferous animal having two hands,\"\nwhich is the scientific definition of man, considered as one of the\nspecies in Cuvier's distribution of the animal kingdom.\n\nIn cases of this sort, though 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 a\nclassification. The special meaning which Cuvier assigned to the word\nMan, (quite foreign to its ordinary meaning, though involving no change\nin the denotation of the word,) was incidental to a plan of arranging\nanimals into classes on a certain principle, that is, according to a\ncertain set of distinctions. And since the definition of Man according\nto the ordinary connotation of the word, though it would have answered\nevery other purpose of a definition, would not have pointed out the\nplace 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\nanimated nature.\n\nScientific definitions, whether they are definitions of scientific\nterms, or of common terms used in a scientific sense, are almost always\nof the kind last spoken of: their main purpose is to serve as the\nlandmarks of scientific classification. And since the classifications in\nany science are continually modified as scientific knowledge advances,\nthe definitions in the sciences are also constantly varying. A striking\ninstance is afforded by the words Acid and Alkali, especially the\nformer. As experimental discovery advanced, the substances classed with\nacids have been constantly multiplying, and by a natural consequence the\nattributes connoted by the word have receded and become fewer. At first\nit connoted the attributes, of combining with an alkali to form a\nneutral substance (called a salt); being compounded of a base and\noxygen; causticity to the taste and touch; fluidity, &c. The true\nanalysis of muriatic acid, into chlorine and hydrogen, caused the second\nproperty, composition from a base and oxygen, to be excluded from the\nconnotation. The same discovery fixed the attention of chemists upon\nhydrogen as an important element in acids; and more recent discoveries\nhaving led to the recognition of its presence in sulphuric, nitric, and\nmany other acids, where its existence was not previously suspected,\nthere is now a tendency to include the presence of this element in the\nconnotation of the word. But carbonic acid, silica, sulphurous acid,\nhave no hydrogen in their composition; that property cannot therefore be\nconnoted by the term, unless those substances are no longer to be\nconsidered acids. Causticity and fluidity have long since been excluded\nfrom the characteristics of the class, by the inclusion of silica and\nmany other substances in it; and the formation of neutral bodies by\ncombination with alkalis, together with such electro-chemical\npeculiarities as this is supposed to imply, are now the only\n_differenti\u00e6_ which form the fixed connotation of the word Acid, as a\nterm of chemical science.\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\nor alteration in the current opinions respecting the subject matter, may\nlead to a change more or less extensive in the particulars included in\nthe science; and its composition being thus altered, it may easily\nhappen that a different set of characteristics will be found better\nadapted as differenti\u00e6 for defining its name.\n\nIn the same manner in which a special or technical definition has for\nits object to expound the artificial classification out of which it\ngrows; the Aristotelian logicians seem to have imagined that it was also\nthe business of ordinary definition to expound the ordinary, and what\nthey deemed the natural, classification of things, namely, the division\nof them into Kinds; and to show the place which each Kind occupies, as\nsuperior, collateral, or subordinate, among other Kinds. This notion\nwould account for the rule that all definition must necessarily be _per\ngenus et differentiam_, and would also explain why a single differentia\nwas deemed sufficient. But to expound, or express in words, a\ndistinction of Kind, has already been shown to be an impossibility: the\nvery meaning of a Kind is, that the properties which distinguish it do\nnot grow out of one another, and cannot therefore be set forth in words,\neven by implication, otherwise than by enumerating them all: and all are\nnot known, nor are ever likely to be so. It is idle, therefore, to look\nto this as one of the purposes of a definition: while, if it be only\nrequired that the definition of a Kind should indicate what Kinds\ninclude it or are included by it, any definitions which expound the\nconnotation of the names will do this: for the name of each class must\nnecessarily connote enough of its properties to fix the boundaries of\nthe class. If the definition, therefore, be a full statement of the\nconnotation, it is all that a definition can be required to be.\n\n\n\u00a7 5. Of the two incomplete and popular modes of definition, and in what\nthey differ from the complete or philosophical mode, enough has now been\nsaid. We shall next examine an ancient doctrine, once generally\nprevalent and still by no means exploded, which I regard as the source\nof a great part of the obscurity hanging over some of the most important\nprocesses of the understanding in the pursuit of truth. According to\nthis, the definitions of which we have now treated are only one of two\nsorts into which definitions may be divided, viz. definitions of names,\nand definitions of things. The former are intended to explain the\nmeaning of a term; the latter, the nature of a thing; the last being\nincomparably the most important.\n\nThis opinion was held by the ancient philosophers, and by their\nfollowers, with the exception of the Nominalists; but as the spirit of\nmodern metaphysics, until a recent period, has been on the whole a\nNominalist spirit, the notion of definitions of things has been to a\ncertain extent in abeyance, still continuing, however, to breed\nconfusion in logic, by its consequences indeed rather than by itself.\nYet the doctrine in its own proper form now and then breaks out, and has\nappeared (among other places) where it was scarcely to be expected, in a\njustly admired work, Archbishop Whately's _Logic_.[27] In a review of\nthat work published by me in the _Westminster Review_ for January 1828,\nand containing some opinions which I no longer entertain, I find the\nfollowing observations on the question now before us; observations with\nwhich my present view of that question is still sufficiently in\naccordance.\n\n\"The distinction between nominal and real definitions, between\ndefinitions of words and what are called definitions of things, though\nconformable to the ideas of most of the Aristotelian logicians, cannot,\nas it appears to us, be maintained. We apprehend that no definition is\never intended to 'explain and unfold the nature of a thing.' It is some\nconfirmation of our opinion, that none of those writers who have thought\nthat there were definitions of things, have ever succeeded in\ndiscovering any criterion by which the definition of a thing can be\ndistinguished from any other proposition relating to the thing. The\ndefinition, they say, unfolds the nature of the thing: but no definition\ncan unfold its whole nature; and every proposition in which any quality\nwhatever is predicated of the thing, unfolds some part of its nature.\nThe true state of the case we take to be this. All definitions are of\nnames, and of names only; but, in some definitions, it is clearly\napparent, that nothing is intended except to explain the meaning of the\nword; while in others, besides explaining the meaning of the word, it is\nintended to be implied that there exists a thing, corresponding to the\nword. Whether this be or be not implied in any given case, cannot be\ncollected from the mere form of the expression. 'A centaur is an animal\nwith the upper parts of a man and the lower parts of a horse,' and 'A\ntriangle is a rectilineal figure with three sides,' are, in form,\nexpressions precisely similar; although in the former it is not implied\nthat any _thing_, conformable to the term, really exists, while in the\nlatter it is; as may be seen by substituting, in both definitions, the\nword _means_ for _is_. In the first expression, 'A centaur means an\nanimal,' &c., the sense would remain unchanged: in the second, 'A\ntriangle means,' &c., the meaning would be altered, since it would be\nobviously impossible to deduce any of the truths of geometry from a\nproposition expressive only of the manner in which we intend to employ a\nparticular sign.\n\n\"There are, therefore, expressions, commonly passing for definitions,\nwhich include in themselves more than the mere explanation of the\nmeaning of a term. But it is not correct to call an expression of this\nsort a peculiar kind of definition. Its difference from the other kind\nconsists in this, that it is not a definition, but a definition and\nsomething more. The definition above given of a triangle, obviously\ncomprises not one, but two propositions, perfectly distinguishable. The\none is, 'There may exist a figure, bounded by three straight lines;' the\nother, 'And this figure may be termed a triangle.' The former of these\npropositions is not a definition at all: the latter is a mere nominal\ndefinition, or explanation of the use and application of a term. The\nfirst is susceptible of truth or falsehood, and may therefore be made\nthe foundation of a train of reasoning. The latter can neither be true\nnor false; the only character it is susceptible of is that of conformity\nor disconformity to the ordinary usage of language.\"\n\nThere is a real distinction, then, between definitions of names, and\nwhat are erroneously called definitions of things; but it is, that the\nlatter, along with the meaning of a name, covertly asserts a matter of\nfact. This covert assertion is not a definition, but a postulate. The\ndefinition is a mere identical proposition, which gives information only\nabout the use of language, and from which no conclusions affecting\nmatters of fact can possibly be drawn. The accompanying postulate, on\nthe other hand, affirms a fact, which may lead to consequences of every\ndegree of importance. It affirms the actual or possible existence of\nThings possessing the combination of attributes set forth in the\ndefinition; and this, if true, may be foundation sufficient on which to\nbuild a whole fabric of scientific truth.\n\nWe have already made, and shall often have to repeat, the remark, that\nthe philosophers who overthrew Realism by no means got rid of the\nconsequences of Realism, but retained long afterwards, in their own\nphilosophy, numerous propositions which could only have a rational\nmeaning as part of a Realistic system. It had been handed down from\nAristotle, and probably from earlier times, as an obvious truth, that\nthe science of Geometry is deduced from definitions. This, so long as a\ndefinition was considered to be a proposition \"unfolding the nature of\nthe thing,\" did well enough. But Hobbes followed, and rejected utterly\nthe notion that a definition declares the nature of the thing, or does\nanything but state the meaning of a name; yet he continued to affirm as\nbroadly as any of his predecessors, that the [Greek: archai],\n_principia_, or original premises of mathematics, and even of all\nscience, are definitions; producing the singular paradox, that systems\nof scientific truth, nay, all truths whatever at which we arrive by\nreasoning, are deduced from the arbitrary conventions of mankind\nconcerning the signification of words.\n\nTo save the credit of the doctrine that definitions are the premises of\nscientific knowledge, the proviso is sometimes added, that they are so\nonly under a certain condition, namely, that they be framed conformably\nto the phenomena of nature; that is, that they ascribe such meanings to\nterms as shall suit objects actually existing. But this is only an\ninstance of the attempt so often made, to escape from the necessity of\nabandoning old language after the ideas which it expresses have been\nexchanged for contrary ones. From the meaning of a name (we are told) it\nis possible to infer physical facts, provided the name has corresponding\nto it an existing thing. But if this proviso be necessary, from which of\nthe two is the inference really drawn? From the existence of a thing\nhaving the properties, or from the existence of a name meaning them?\n\nTake, for instance, any of the definitions laid down as premises in\nEuclid's Elements; the definition, let us say, of a circle. This, being\nanalysed, consists of two propositions; the one an assumption with\nrespect to a matter of fact, the other a genuine definition. \"A figure\nmay exist, having all the points in the line which bounds it equally\ndistant from a single point within it:\" \"Any figure possessing this\nproperty is called a circle.\" Let us look at one of the demonstrations\nwhich are said to depend on this definition, and observe to which of the\ntwo propositions contained in it the demonstration really appeals.\n\"About the centre A, describe the circle B C D.\" Here is an assumption\nthat a figure, such as the definition expresses, _may_ be described;\nwhich is no other than the postulate, or covert assumption, involved in\nthe so-called definition. But whether that figure be called a circle or\nnot is quite immaterial. The purpose would be as well answered, in all\nrespects except brevity, were we to say, \"Through the point B, draw a\nline returning into itself, of which every point shall be at an equal\ndistance from the point A.\" By this the definition of a circle would be\ngot rid of, and rendered needless; but not the postulate implied in it;\nwithout that the demonstration could not stand. The circle being now\ndescribed, let us proceed to the consequence. \"Since B C D is a circle,\nthe radius B A is equal to the radius C A.\" B A is equal to C A, not\nbecause B C D is a circle, but because B C D is a figure with the radii\nequal. Our warrant for assuming that such a figure about the centre A,\nwith the radius B A, may be made to exist, is the postulate. Whether the\nadmissibility of these postulates rests on intuition, or on proof, may\nbe a matter of dispute; but in either case they are the premises on\nwhich the theorems depend; and while these are retained it would make no\ndifference in the certainty of geometrical truths, though every\ndefinition in Euclid, and every technical term therein defined, were\nlaid 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,\nhas been confounded, and by powerful intellects, it is better to say too\nmuch than too little for the purpose of rendering such mistakes\nimpossible in future. I will, therefore, detain the reader while I point\nout one of the absurd consequences flowing from the supposition that\ndefinitions, as such, are the premises in any of our reasonings, except\nsuch as relate to words only. If this supposition were true, we might\nargue correctly from true premises, and arrive at a false conclusion. We\nshould only have to assume as a premise the definition of a nonentity;\nor rather of a name which has no entity corresponding to it. Let this,\nfor instance, be our definition:\n\n A 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\nto the definition, would, in the present instance, be false. Out of this\ndefinition we may carve the premises of the following syllogism:\n\n A dragon is a thing which breathes flame:\n A dragon is a serpent:\n\nFrom which the conclusion is,\n\n Therefore some serpent or serpents breathe flame:--\n\nan unexceptionable syllogism in the first mode of the third figure, in\nwhich both premises are true and yet the conclusion false; which every\nlogician knows to be an absurdity. The conclusion being false and the\nsyllogism correct, the premises cannot be true. But the premises,\nconsidered as parts of a definition, are true. Therefore, the premises\nconsidered as parts of a definition cannot be the real ones. The real\npremises must be--\n\n A dragon is a _really existing_ thing which breathes flame:\n A dragon is a _really existing_ serpent:\n\nwhich implied premises being false, the falsity of the conclusion\npresents no absurdity.\n\nIf we would determine what conclusion follows from the same ostensible\npremises when the tacit assumption of real existence is left out, let\nus, according to the recommendation in a previous page, substitute\n_means_ for _is_. We then have--\n\n Dragon is _a word meaning_ a thing which breathes flame:\n Dragon is _a word meaning_ a serpent:\n\nFrom which the conclusion is,\n\n Some _word or words which mean_ a serpent, also mean a thing which\n breathes flame:\n\nwhere the conclusion (as well as the premises) is true, and is the only\nkind of conclusion which can ever follow from a definition, namely, a\nproposition relating to the meaning of words.\n\nThere is still another shape into which we may transform this syllogism.\nWe may suppose the middle term to be the designation neither of a thing\nnor of a name, but of an idea. We then have--\n\n The _idea of_ a dragon is _an idea of_ a thing which breathes\n flame:\n The _idea of_ a dragon is _an idea of_ a serpent:\n Therefore, there is _an idea of_ a serpent, which is _an idea of_\n a thing breathing flame.\n\nHere the conclusion is true, and also the premises; but the premises are\nnot definitions. They are propositions affirming that an idea existing\nin the mind, includes certain ideal elements. The truth of the\nconclusion follows from the existence of the psychological phenomenon\ncalled the idea of a dragon; and therefore still from the tacit\nassumption of a matter of fact.[28]\n\nWhen, as in this last syllogism, the conclusion is a proposition\nrespecting an idea, the assumption on which it depends may be merely\nthat of the existence of an idea. But when the conclusion is a\nproposition concerning a Thing, the postulate involved in the definition\nwhich stands as the apparent premise, is the existence of a thing\nconformable to the definition, and not merely of an idea conformable to\nit. This assumption of real existence will always convey the impression\nthat we intend to make, when we profess to define any name which is\nalready known to be a name of really existing objects. On this account\nit is, that the assumption was not necessarily implied in the definition\nof a dragon, while there was no doubt of its being included in the\ndefinition of a circle.\n\n\n\u00a7 6. One of the circumstances which have contributed to keep up the\nnotion, that demonstrative truths follow from definitions rather than\nfrom the postulates implied in those definitions, is, that the\npostulates, even in those sciences which are considered to surpass all\nothers in demonstrative certainty, are not always exactly true. It is\nnot true that a circle exists, or can be described, which has all its\nradii _exactly_ equal. Such accuracy is ideal only; it is not found in\nnature, still less can it be realized by art. People had a difficulty,\ntherefore, in conceiving that the most certain of all conclusions could\nrest on premises which, instead of being certainly true, are certainly\nnot true to the full extent asserted. This apparent paradox will be\nexamined when we come to treat of Demonstration; where we shall be able\nto show that as much of the postulate is true, as is required to support\nas much as is true of the conclusion. Philosophers, however, to whom\nthis view had not occurred, or whom it did not satisfy, have thought it\nindispensable that there should be found in definitions something _more_\ncertain, or at least more accurately true, than the implied postulate of\nthe real existence of a corresponding object. And this something they\nflattered themselves they had found, when they laid it down that a\ndefinition is a statement and analysis not of the mere meaning of a\nword, nor yet of the nature of a thing, but of an idea. Thus, the\nproposition, \"A circle is a plane figure bounded by a line all the\npoints of which are at an equal distance from a given point within it,\"\nwas considered by them, not as an assertion that any real circle has\nthat property, (which would not be exactly true,) but that we _conceive_\na circle as having it; that our abstract idea of a circle is an idea of\na 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\nwithout breadth; but no such line exists in nature; it is a notion\nmerely suggested to the mind by its experience of nature. The definition\n(it is said) is a definition of this mental line, not of any actual\nline: and it is only of the mental line, not of any line existing in\nnature, that the theorems of geometry are accurately true.\n\nAllowing this doctrine respecting the nature of demonstrative truth to\nbe correct (which, in a subsequent place, I shall endeavour to prove\nthat it is not;) even on that supposition, the conclusions which seem to\nfollow from a definition, do not follow from the definition as such, but\nfrom an implied postulate. Even if it be true that there is no object in\nnature answering to the definition of a line, and that the geometrical\nproperties of lines are not true of any lines in nature, but only of the\nidea of a line; the definition, at all events, postulates the real\nexistence of such an idea: it assumes that the mind can frame, or rather\nhas framed, the notion of length without breadth, and without any other\nsensible property whatever. To me, indeed, it appears that the mind\ncannot form any such notion; it cannot conceive length without breadth;\nit can only, in contemplating objects, attend to their length,\nexclusively of their other sensible qualities, and so determine what\nproperties may be predicated of them in virtue of their length alone. If\nthis be true, the postulate involved in the geometrical definition of a\nline, is the real existence, not of length without breadth, but merely\nof length, that is, of long objects. This is quite enough to support all\nthe truths of geometry, since every property of a geometrical line is\nreally a property of all physical objects in so far as possessing\nlength. But even what I hold to be the false doctrine on the subject,\nleaves the conclusion that our reasonings are grounded on the matters of\nfact postulated in definitions, and not on the definitions themselves,\nentirely unaffected; and accordingly this conclusion is one which I have\nin common with Dr. Whewell, in his _Philosophy of the Inductive\nSciences_: though, on the nature of demonstrative truth, Dr. Whewell's\nopinions are greatly at variance with mine. And here, as in many other\ninstances, I gladly acknowledge that his writings are eminently\nserviceable in clearing from confusion the initial steps in the analysis\nof the mental processes, even where his views respecting the ultimate\nanalysis are such as (though with unfeigned respect) I cannot but regard\nas fundamentally erroneous.\n\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\ndenoted by the name. Such, for instance, are the inquiries which form\nthe subjects of the most important of Plato's Dialogues; as, \"What is\nrhetoric?\" the topic of the Gorgias, or \"What is justice?\" that of the\nRepublic. Such, also, is the question scornfully asked by Pilate, \"What\nis truth?\" and the fundamental question with speculative moralists in\nall ages, \"What is virtue?\"\n\nIt would be a mistake to represent these difficult and noble inquiries\nas having nothing in view beyond ascertaining the conventional meaning\nof a name. They are inquiries not so much to determine what is, as what\nshould be, the meaning of a name; which, like other practical questions\nof terminology, requires for its solution that we should enter, and\nsometimes enter very deeply, into the properties not merely of names but\nof the things 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\nnames are mostly compounds or other derivatives of the concrete names\nwhich correspond to them. Connotative names, therefore, were, after\nproper names, the first which were used: and in the simpler cases, no\ndoubt, a distinct connotation was present to the minds of those who\nfirst used the name, and was distinctly intended by them to be conveyed\nby it. The first person who used the word white, as applied to snow or\nto any other object, knew, no doubt, very well what quality he intended\nto predicate, and had a perfectly distinct conception in his mind of the\nattribute signified 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\neasily discriminated, and referred each to its true source; it often\nhappens that names are applied to nameable objects, with no distinct\nconnotation present to the minds of those who apply them. They are only\ninfluenced by a general resemblance between the new object and all or\nsome of the old familiar objects which they have been accustomed to call\nby that name. This, as we have seen, is the law which even the mind of\nthe philosopher must follow, in giving names to the simple elementary\nfeelings of our nature: but, where the things to be named are complex\nwholes, a philosopher is not content with noticing a general\nresemblance; he examines what the resemblance consists in: and he only\ngives the same name to things which resemble one another in the same\ndefinite particulars. The philosopher, therefore, habitually employs his\ngeneral names with a definite connotation. But language was not made,\nand can only in some small degree be mended, by philosophers. In the\nminds of the real arbiters of language, general names, especially where\nthe classes they denote cannot be brought before the tribunal of the\noutward senses to be identified and discriminated, connote little more\nthan a vague gross resemblance to the things which they were earliest,\nor have been most, accustomed to call by those names. When, for\ninstance, ordinary persons predicate the words _just_ or _unjust_ of any\naction, _noble_ or _mean_ of any sentiment, expression, or demeanour,\n_statesman_ or _charlatan_ of any personage figuring in politics, do\nthey mean to affirm of those various subjects any determinate\nattributes, of whatever kind? No: they merely recognise, as they think,\nsome likeness, more or less vague and loose, between these and some\nother things which they have been accustomed to denominate or to hear\ndenominated by those appellations.\n\nLanguage, as Sir James Mackintosh used to say of governments, \"is not\nmade, but grows.\" 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\none object to another, until it becomes applied to things having nothing\nin common with the first things to which the name was given; which,\nhowever, do not, for that reason, drop the name; so that it at last\ndenotes a confused huddle of objects, having nothing whatever in common;\nand connotes nothing, not even a vague and general resemblance. When a\nname has fallen into this state, in which by predicating it of any\nobject we assert literally nothing about the object, it has become unfit\nfor the purposes either of thought or of the communication of thought;\nand can only be made serviceable by stripping it of some part of its\nmultifarious denotation, and confining it to objects possessed of some\nattributes in common, which it may be made to connote. Such are the\ninconveniences of a language which \"is not made, but grows.\" Like the\ngovernments which are in a similar case, it may be compared to a road\nwhich is not made but has made itself: it requires continual mending in\norder 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\nwhich mankind mean to predicate when they call an action just? To which\nthe first answer is, that having come to no precise agreement on the\npoint, they do not mean to predicate distinctly any attribute at all.\nNevertheless, all believe that there is some common attribute belonging\nto all the actions which they are in the habit of calling just. The\nquestion then must be, whether there is any such common attribute? and,\nin the first place, whether mankind agree sufficiently with one another\nas to the particular actions which they do or do not call just, to\nrender the inquiry, what quality those actions have in common, a\npossible one: if so, whether the actions really have any quality in\ncommon; and if they have, what it is. Of these three, the first alone is\nan inquiry into usage and convention; the other two are inquiries into\nmatters of fact. And if the second question (whether the actions form a\nclass at all) has been answered negatively, there remains a fourth,\noften more arduous than all the rest, namely, how best to form a class\nartificially, which the name may denote.\n\nAnd here it is fitting to remark, that the study of the spontaneous\ngrowth of languages is of the utmost importance to those who would\nlogically remodel them. The classifications rudely made by established\nlanguage, when retouched, as they almost all require to be, by the hands\nof the logician, are often in themselves excellently suited to his\npurposes. As compared with the classifications of a philosopher, they\nare like the customary law of a country, which has grown up as it were\nspontaneously, compared with laws methodized and digested into a code:\nthe former are a far less perfect instrument than the latter; but being\nthe result of a long, though unscientific, course of experience, they\ncontain a mass of materials which may be made very usefully available in\nthe formation of the systematic body of written law. In like manner, the\nestablished grouping of objects under a common name, even when founded\nonly on a gross and general resemblance, is evidence, in the first\nplace, that the resemblance is obvious, and therefore considerable;\nand, in the next place, that it is a resemblance which has struck great\nnumbers of persons during a series of years and ages. Even when a name,\nby successive extensions, has come to be applied to things among which\nthere does not exist this gross resemblance common to them all, still at\nevery step in its progress we shall find such a resemblance. And these\ntransitions of the meaning of words are often an index to real\nconnexions between the things denoted by them, which might otherwise\nescape the notice of thinkers; of those at least who, from using a\ndifferent language, or from any difference in their habitual\nassociations, have fixed their attention in preference on some other\naspect of the things. The history of philosophy abounds in examples of\nsuch oversights, committed for want of perceiving the hidden link that\nconnected together the seemingly disparate meanings of some ambiguous\nword.[29]\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\nwith its continuing to denote, if possible all, but at any rate the\ngreater or the more important part, of the things of which it is\ncommonly predicated. The inquiry, therefore, into the definition, is an\ninquiry into the resemblances and differences among those things:\nwhether there be any resemblance running through them all; if not,\nthrough what portion of them such a general resemblance can be traced:\nand finally, what are the common attributes, the possession of which\ngives to them all, or to that portion of them, the character of\nresemblance which has led to their being classed together. When these\ncommon attributes have been ascertained and specified, the name which\nbelongs in common to the resembling objects acquires a distinct instead\nof a vague connotation; and by possessing this distinct connotation,\nbecomes susceptible of definition.\n\nIn giving a distinct connotation to the general name, the philosopher\nwill endeavour to fix upon such attributes as, while they are common to\nall the things usually denoted by the name, are also of greatest\nimportance in themselves; either directly, or from the number, the\nconspicuousness, or the interesting character, of the consequences to\nwhich they lead. He will select, as far as possible, such _differenti\u00e6_\nas lead to the greatest number of interesting _propria_. For these,\nrather than the more obscure and recondite qualities on which they often\ndepend, give that general character and aspect to a set of objects,\nwhich determine the groups into which they naturally fall. But to\npenetrate to the more hidden agreement on which these obvious and\nsuperficial agreements depend, is often one of the most difficult of\nscientific problems. As it is among the most difficult, so it seldom\nfails to be among the most important. And since upon the result of this\ninquiry respecting the causes of the properties of a class of things,\nthere incidentally depends the question what shall be the meaning of a\nword; some of the most profound and most valuable investigations which\nphilosophy presents to us, have been introduced by, and have offered\nthemselves under the guise of, inquiries into the definition of a name.\n\nFOOTNOTES:\n\n[1] _Computation or Logic_, chap. ii.\n\n[2] In the original \"had, _or had not_.\" These last words, as involving\na subtlety foreign to our present purpose, I have forborne to quote.\n\n[3] Vide infra, note at the end of \u00a7 3, book ii. ch. ii.\n\n[4] _Notare_, to mark; _con_notare, to mark _along with_; to mark one\nthing _with_ or _in addition to_ another.\n\n[5] Archbishop Whately, who, in the later editions of his _Elements of\nLogic_, aided in reviving the important distinction treated of in the\ntext, proposes the term \"Attributive\" as a substitute for \"Connotative\"\n(p. 22, 9th ed.) The expression is, in itself, appropriate; but as it\nhas not the advantage of being connected with any verb, of so markedly\ndistinctive a character as \"to connote,\" it is not, I think, fitted to\nsupply the place of the word Connotative in scientific use.\n\n[6] A writer who entitles his book _Philosophy; or, the Science of\nTruth_, charges me in his very first page (referring at the foot of it\nto this passage) with asserting that _general_ names have properly no\nsignification. And he repeats this statement many times in the course of\nhis volume, with comments, not at all flattering, thereon. It is well to\nbe now and then reminded to how great a length perverse misquotation\n(for, strange as it appears, I do not believe that the writer is\ndishonest) can sometimes go. It is a warning to readers, when they see\nan author accused, with volume and page referred to, and the apparent\nguarantee of inverted commas, of maintaining something more than\ncommonly absurd, not to give implicit credence to the assertion without\nverifying the reference.\n\n[7] Before quitting the subject of connotative names, it is proper to\nobserve, that the first writer who, in our times, has adopted from the\nschoolmen the word _to connote_, Mr. James Mill, in his _Analysis of the\nPhenomena of the Human Mind_, employs it in a signification different\nfrom that in which it is here used. He uses the word in a sense\ncoextensive with its etymology, applying it to every case in which a\nname, while pointing directly to one thing, (which is consequently\ntermed its signification,) includes also a tacit reference to some other\nthing. In the case considered in the text, that of concrete general\nnames, his language and mine are the converse of one another.\nConsidering (very justly) the signification of the name to lie in the\nattribute, he speaks of the word as _noting_ the attribute, and\n_connoting_ the things possessing the attribute. And he describes\nabstract names as being properly concrete names with their connotation\ndropped: whereas, in my view, it is the _de_notation which would be said\nto be dropped, what was previously connoted becoming the whole\nsignification.\n\nIn adopting a phraseology at variance with that which so high an\nauthority, and one which I am less likely than any other person to\nundervalue, has deliberately sanctioned, I have been influenced by the\nurgent necessity for a term exclusively appropriated to express the\nmanner in which a concrete general name serves to mark the attributes\nwhich are involved in its signification. This necessity can scarcely be\nfelt in its full force by any one who has not found by experience how\nvain is the attempt to communicate clear ideas on the philosophy of\nlanguage without such a word. It is hardly an exaggeration to say, that\nsome of the most prevalent of the errors with which logic has been\ninfected, and a large part of the cloudiness and confusion of ideas\nwhich have enveloped it, would, in all probability, have been avoided,\nif a term had been in common use to express exactly what I have\nsignified by the term to connote. And the schoolmen, to whom we are\nindebted for the greater part of our logical language, gave us this\nalso, and in this very sense. For though some of their general\nexpressions countenance the use of the word in the more extensive and\nvague acceptation in which it is taken by Mr. Mill, yet when they had to\ndefine it specifically as a technical term, and to fix its meaning as\nsuch, with that admirable precision which always characterizes their\ndefinitions, they clearly explained that nothing was said to be connoted\nexcept _forms_, which word may generally, in their writings, be\nunderstood as synonymous with _attributes_.\n\nNow, if the word _to connote_, so well suited to the purpose to which\nthey applied it, be diverted from that purpose by being taken to fulfil\nanother, for which it does not seem to me to be at all required; I am\nunable to find any expression to replace it, but such as are commonly\nemployed in a sense so much more general, that it would be useless\nattempting to associate them peculiarly with this precise idea. Such are\nthe words, to involve, to imply, &c. By employing these, I should fail\nof attaining the object for which alone the name is needed, namely, to\ndistinguish this particular kind of involving and implying from all\nother kinds, and to assure to it the degree of habitual attention which\nits importance demands.\n\n[8] Or rather, all objects except itself and the percipient mind; for,\nas we shall see hereafter, to ascribe any attribute to an object,\nnecessarily implies a mind to perceive it.\n\nThe simple and clear explanation given in the text, of relation and\nrelative names, a subject so long the opprobrium of metaphysics, was\ngiven (as far as I know) for the first time, by Mr. James Mill, in his\nAnalysis of the Phenomena of the Human Mind.\n\n[9] _Philosophy of the Inductive Sciences_, vol. i. p. 40.\n\n[10] _Discussions on Philosophy_, &c. Appendix I. pp. 643-4.\n\n[11] It is to be regretted that Sir William Hamilton, though he often\nstrenuously insists on this doctrine, and though, in the passage quoted,\nhe states it with a comprehensiveness and force which leave nothing to\nbe desired, did not consistently adhere to his own doctrine, but\nmaintained along with it opinions with which it is utterly\nirreconcileable. See the third and other chapters of _An Examination of\nSir William Hamilton's Philosophy_.\n\n[12] \"Nous savons qu'il existe quelque chose hors de nous, parceque nous\nne pouvons expliquer nos perceptions sans les rattacher \u00e0 des causes\ndistinctes de nous-m\u00eames; nous savons de plus que ces causes, dont nous\nne connaissons pas d'ailleurs l'essence, produisent les effets les plus\nvariables, les plus divers, et m\u00eame les plus contraires, selon qu'elles\nrencontrent telle nature ou telle disposition du sujet. Mais savons-nous\nquelque chose de plus? et m\u00eame, vu le caract\u00e8re ind\u00e9termin\u00e9 des causes\nque nous concevons dans les corps, y a-t-il quelque chose de plus \u00e0\nsavoir? Y a-t-il lieu de nous enqu\u00e9rir si nous percevons les choses\ntelles qu'elles sont? Non \u00e9videmment.... Je ne dis pas que le probl\u00e8me\nest insoluble, _je dis qu'il est absurde et enferme une contradiction_.\nNous _ne savons pas ce que ces causes sont en elles-m\u00eames_, et la raison\nnous d\u00e9fend de chercher \u00e0 le conna\u00eetre: mais il est bien \u00e9vident _\u00e0\npriori_, qu'_elles ne sont pas en elles-m\u00eames ce qu'elles sont par\nrapport \u00e0 nous_, puisque la pr\u00e9sence du sujet modifie n\u00e9cessairement\nleur action. Supprimez tout sujet sentant, il est certain que ces causes\nagiraient encore puisqu'elles continueraient d'exister; mais elles\nagiraient autrement; elles seraient encore des qualit\u00e9s et des\npropri\u00e9t\u00e9s, mais qui ne ressembleraient \u00e0 rien de ce que nous\nconnaissons. Le feu ne manifesterait plus aucune des propri\u00e9t\u00e9s que nous\nlui connaissons: que serait-il? C'est ce que nous ne saurons jamais.\n_C'est d'ailleurs peut-\u00eatre un probl\u00e8me qui ne r\u00e9pugne pas seulement \u00e0\nla nature de notre esprit, mais \u00e0 l'essence m\u00eame des choses._ Quand m\u00eame\nen effet on supprimerait par la pens\u00e9e tous les sujets sentants, il\nfaudrait encore admettre que nul corps ne manifesterait ses propri\u00e9t\u00e9s\nautrement qu'en relation avec un sujet quelconque, et dans ce cas _ses\npropri\u00e9t\u00e9s ne seraient encore que relatives_: en sorte qu'il me para\u00eet\nfort raisonnable d'admettre que les propri\u00e9t\u00e9s d\u00e9termin\u00e9es des corps\nn'existent pas ind\u00e9pendamment d'un sujet quelconque, et que quand on\ndemande si les propri\u00e9t\u00e9s de la mati\u00e8re sont telles que nous les\npercevons, il faudrait voir auparavant si elles sont en tant que\nd\u00e9termin\u00e9es, et dans quel sens il est vrai de dire qu'elles\nsont.\"--_Cours d'Histoire de la Philosophie Morale au 18me si\u00e8cle_, 8me\nle\u00e7on.\n\n[13] An attempt, indeed, has been made by Reid and others, to establish\nthat although some of the properties we ascribe to objects exist only in\nour sensations, others exist in the things themselves, being such as\ncannot possibly be copies of any impression upon the senses; and they\nask, from what sensations our notions of extension and figure have been\nderived? The gauntlet thrown down by Reid was taken up by Brown, who,\napplying greater powers of analysis than had previously been applied to\nthe notions of extension and figure, pointed out that the sensations\nfrom which those notions are derived, are sensations of touch, combined\nwith sensations of a class previously too little adverted to by\nmetaphysicians, those which have their seat in our muscular frame. His\nanalysis, which was adopted and followed up by James Mill, has been\nfurther and greatly improved upon in Professor Bain's profound work,\n_The Senses and the Intellect_, and in the chapters on \"Perception\" of a\nwork of eminent analytic power, Mr. Herbert Spencer's _Principles of\nPsychology_.\n\nOn this point M. Cousin may again be cited in favour of the better\ndoctrine. M. Cousin recognises, in opposition to Reid, the essential\nsubjectivity of our conceptions of what are called the primary qualities\nof matter, as extension, solidity, &c., equally with those of colour,\nheat, and the remainder of the so-called secondary qualities.--_Cours_,\nut supra, 9me le\u00e7on.\n\n[14] This doctrine, which is the most complete form of the philosophical\ntheory known as the Relativity of Human Knowledge, has, since the recent\nrevival in this country of an active interest in metaphysical\nspeculation, been the subject of a greatly increased amount of\ndiscussion and controversy; and dissentients have manifested themselves\nin considerably greater number than I had any knowledge of when the\npassage in the text was written. The doctrine has been attacked from two\nsides. Some thinkers, among whom are the late Professor Ferrier, in his\n_Institutes of Metaphysic_, and Professor John Grote in his _Exploratio\nPhilosophica_, appear to deny altogether the reality of Noumena, or\nThings in themselves--of an unknowable substratum or support for the\nsensations which we experience, and which, according to the theory,\nconstitute all our knowledge of an external world. It seems to me,\nhowever, that in Professor Grote's case at least, the denial of Noumena\nis only apparent, and that he does not essentially differ from the other\nclass of objectors, including Mr. Bailey in his valuable _Letters on the\nPhilosophy of the Human Mind_, and (in spite of the striking passage\nquoted in the text) also Sir William Hamilton, who contend for a direct\nknowledge by the human mind of more than the sensations--of certain\nattributes or properties as they exist not in us, but in the Things\nthemselves.\n\nWith the first of these opinions, that which denies Noumena, I have, as\na metaphysician, no quarrel; but, whether it be true or false, it is\nirrelevant to Logic. And since all the forms of language are in\ncontradiction to it, nothing but confusion could result from its\nunnecessary introduction into a treatise, every essential doctrine of\nwhich could stand equally well with the opposite and accredited opinion.\nThe other and rival doctrine, that of a direct perception or intuitive\nknowledge of the outward object as it is in itself, considered as\ndistinct from the sensations we receive from it, is of far greater\npractical moment. But even this question, depending on the nature and\nlaws of Intuitive Knowledge, is not within the province of Logic. For\nthe grounds of my own opinion concerning it, I must content myself with\nreferring to a work already mentioned--_An Examination of Sir William\nHamilton's Philosophy_; several chapters of which are devoted to a full\ndiscussion of the questions and theories relating to the supposed direct\nperception of external objects.\n\n[15] _Analysis of the Human Mind_, i. 126 et seq.\n\n[16] It may, however, be considered as equivalent to an universal\nproposition with a different predicate, viz. \"All wine is good _qu\u00e2_\nwine,\" or \"is good in respect of the qualities which constitute it\nwine.\"\n\n[17] Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this\nstatement, and asks, \"Are we to say that a mole cannot dig the ground,\nexcept he has an idea of the ground, and of the snout and paws with\nwhich he digs it?\" I do not know what passes in a mole's mind, nor what\namount of mental apprehension may or may not accompany his instinctive\nactions. But a human being does not use a spade by instinct; and he\ncertainly could not use it unless he had knowledge of a spade, and of\nthe earth which he uses it upon.\n\n[18] \"From hence also this may be deduced, that the first truths were\narbitrarily made by those that first of all imposed names upon things,\nor received them from the imposition of others. For it is true (for\nexample) that _man is a living creature_, but it is for this reason,\nthat it pleased men to impose both these names on the same\nthing.\"--_Computation or Logic_, ch. iii. sect. 8.\n\n[19] \"Men are subject to err not only in affirming and denying, but also\nin perception, and in silent cogitation.... Tacit errors, or the errors\nof sense and cogitation, are made by passing from one imagination to the\nimagination of another different thing; or by feigning that to be past,\nor future, which never was, nor ever shall be; as when by seeing the\nimage of the sun in water, we imagine the sun itself to be there; or by\nseeing swords, that there has been, or shall be, fighting, because it\nuses to be so for the most part; or when from promises we feign the mind\nof the promiser to be such and such; or, lastly, when from any sign we\nvainly imagine something to be signified which is not. And errors of\nthis sort are common to all things that have sense.\"--_Computation or\nLogic_, ch. v. sect. 1.\n\n[20] Ch. iii. sect. 3.\n\n[21] To the preceding statement it has been objected, that \"we naturally\nconstrue the subject of a proposition in its extension, and the\npredicate (which therefore may be an adjective) in its intension,\n(connotation): and that consequently coexistence of attributes does not,\nany more than the opposite theory of equation of groups, correspond with\nthe living processes of thought and language.\" I acknowledge the\ndistinction here drawn, which, indeed, I had myself laid down and\nexemplified a few pages back (p. 104). But though it is true that we\nnaturally \"construe the subject of a proposition in its extension,\" this\nextension, or in other words, the extent of the class denoted by the\nname, is not apprehended or indicated directly. It is both apprehended\nand indicated solely through the attributes. In the \"living processes of\nthought and language\" the extension, though in this case really thought\nof (which in the case of the predicate it is not), is thought of only\nthrough the medium of what my acute and courteous critic terms the\n\"intension.\"\n\nFor further illustrations of this subject, see _Examination of Sir\nWilliam Hamilton's Philosophy_, ch. xxii.\n\n[22] Book iv. ch. vii.\n\n[23] The doctrines which prevented the real meaning of Essences from\nbeing understood, had not assumed so settled a shape in the time of\nAristotle and his immediate followers, as was afterwards given to them\nby the Realists of the middle ages. Aristotle himself (in his Treatise\non the Categories) expressly denies that the [Greek: deuterai ousiai],\nor Substanti\u00e6 Secund\u00e6, inhere in a subject. They are only, he says,\npredicated of it.\n\n[24] The always acute and often profound author of _An Outline of\nSematology_ (Mr. B. H. Smart) justly says, \"Locke will be much more\nintelligible if, in the majority of places, we substitute 'the knowledge\nof' for what he calls 'the Idea of'\" (p. 10). Among the many criticisms\non Locke's use of the word Idea, this is the one which, as it appears to\nme, most nearly hits the mark; and I quote it for the additional reason\nthat it precisely expresses the point of difference respecting the\nimport of Propositions, between my view and what I have spoken of as the\nConceptualist view of them. Where a Conceptualist says that a name or a\nproposition expresses our Idea of a thing, I should generally say\n(instead of our Idea) our Knowledge, or Belief, concerning the thing\nitself.\n\n[25] This distinction corresponds to that which is drawn by Kant and\nother metaphysicians between what they term _analytic_, and _synthetic_,\njudgments; the former being those which can be evolved from the meaning\nof the terms used.\n\n[26] If we allow a differentia to what is not really a species. For the\ndistinction of Kinds, in the sense explained by us, not being in any way\napplicable to attributes, it of course follows that although attributes\nmay be put into classes, those classes can be admitted to be genera or\nspecies only by courtesy.\n\n[27] In the fuller discussion which Archbishop Whately has given to this\nsubject in his later editions, he almost ceases to regard the\ndefinitions of names and those of things as, in any important sense,\ndistinct. He seems (9th ed. p. 145) to limit the notion of a Real\nDefinition to one which \"explains anything _more_ of the nature of the\nthing than is implied in the name;\" (including under the word \"implied,\"\nnot only what the name connotes, but everything which can be deduced by\nreasoning from the attributes connoted). Even this, as he adds, is\nusually called, not a Definition, but a Description; and (as it seems to\nme) rightly so called. A Description, I conceive, can only be ranked\namong Definitions, when taken (as in the case of the zoological\ndefinition of man) to fulfil the true office of a Definition, by\ndeclaring the connotation given to a word in some special use, as a term\nof science or art: which special connotation of course would not be\nexpressed by the proper definition of the word in its ordinary\nemployment.\n\nMr. De Morgan, exactly reversing the doctrine of Archbishop Whately,\nunderstands by a Real Definition one which contains _less_ than the\nNominal Definition, provided only that what it contains is sufficient\nfor distinction. \"By _real_ definition I mean such an explanation of the\nword, be it the whole of the meaning or only part, as will be sufficient\nto separate the things contained under that word from all others. Thus\nthe following, I believe, is a complete definition of an elephant: An\nanimal which naturally drinks by drawing the water into its nose, and\nthen spurting it into its mouth.\"--_Formal Logic_, p. 36. Mr. De\nMorgan's general proposition and his example are at variance; for the\npeculiar mode of drinking of the elephant certainly forms no part of the\nmeaning of the word elephant. It could not be said, because a person\nhappened to be ignorant of this property, that he did not know what an\nelephant means.\n\n[28] In the only attempt which, so far as I know, has been made to\nrefute the preceding argumentation, it is maintained that in the first\nform 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\"there is just as much truth in the conclusion as there is in the\npremises, or rather, no more in the latter than in the former. If the\ngeneral name serpent includes both real and imaginary serpents, there is\nno falsity in the conclusion; if not, there is falsity in the minor\npremise.\"\n\nLet us, then, try to set out the syllogism on the hypothesis that the\nname serpent includes imaginary serpents. We shall find that it is now\nnecessary to alter the predicates; for it cannot be asserted that an\nimaginary creature breathes flame: in predicating of it such a fact, we\nassert by the most positive implication that it is real and not\nimaginary. The conclusion must run thus, \"Some serpent or serpents\neither do or are _imagined_ to breathe flame.\" And to prove this\nconclusion by the instance of dragons, the premises must be, A dragon is\n_imagined_ as breathing flame, A dragon is a (real or imaginary)\nserpent: from which it undoubtedly follows, that there are serpents\nwhich are imagined to breathe flame; but the major premise is not a\ndefinition, nor part of a definition; which is all that I am concerned\nto prove.\n\nLet us now examine the other assertion--that if the word serpent stands\nfor none but real serpents, the minor premise (a dragon is a serpent) is\nfalse. This is exactly what I have myself said of the premise,\nconsidered as a statement of fact: but it is not false as part of the\ndefinition of a dragon; and since the premises, or one of them, must be\nfalse, (the conclusion being so,) the real premise cannot be the\ndefinition, which is true, but the statement of fact, which is false.\n\n[29] \"Few people\" (I have said in another place) \"have reflected how\ngreat a knowledge of Things is required to enable a man to affirm that\nany given argument turns wholly upon words. There is, perhaps, not one\nof the leading terms of philosophy which is not used in almost\ninnumerable shades of meaning, to express ideas more or less widely\ndifferent from one another. Between two of these ideas a sagacious and\npenetrating mind will discern, as it were intuitively, an unobvious link\nof connexion, upon which, though perhaps unable to give a logical\naccount of it, he will found a perfectly valid argument, which his\ncritic, not having so keen an insight into the Things, will mistake for\na fallacy turning on the double meaning of a term. And the greater the\ngenius of him who thus safely leaps over the chasm, the greater will\nprobably be the crowing and vain-glory of the mere logician, who,\nhobbling after him, evinces his own superior wisdom by pausing on its\nbrink, and giving up as desperate his proper business of bridging it\nover.\"\n\n\n\n\nBOOK II.\n\nOF REASONING.\n\n\n[Greek: Di\u00f4rismen\u00f4n de tout\u00f4n leg\u00f4men \u00ead\u00ea, dia tin\u00f4n, kai pote, kai p\u00f4s\nginetai pas syllogismos hysteron de lekteon peri apodeixe\u00f4s. Proteron\ngar peri syllogismou lekteon, \u00ea peri apodeixe\u00f4s, dia to katholou mallon\neinai ton syllogismon. H\u00ea men gar apodeixis, syllogismos tis; ho\nsyllogismos de ou pas, apodeixis.]\n\n ARIST. _Analyt. Prior._ l. i. cap. 4.\n\n\n\n\nCHAPTER I.\n\nOF INFERENCE, OR REASONING, IN GENERAL.\n\n\n\u00a7 1. In the preceding Book, we have been occupied not with the nature of\nProof, but with the nature of Assertion: the import conveyed by a\nProposition, whether that Proposition be true or false; not the means by\nwhich to discriminate true from false Propositions. The proper subject,\nhowever, of Logic is Proof. Before we could understand what Proof is, it\nwas necessary to understand what that is to which proof is applicable;\nwhat that is which can be a subject of belief or disbelief, of\naffirmation or denial; what, in short, the different kinds of\nPropositions assert.\n\nThis preliminary inquiry we have prosecuted to a definite result.\nAssertion, in the first place, relates either to the meaning of words,\nor to some property of the things which words signify. Assertions\nrespecting the meaning of words, among which definitions are the most\nimportant, hold a place, and an indispensable one, in philosophy; but as\nthe meaning of words is essentially arbitrary, this class of assertions\nare not susceptible of truth or falsity, nor therefore of proof or\ndisproof. Assertions respecting Things, or what may be called Real\nPropositions, in contradistinction to verbal ones, are of various sorts.\nWe have analysed the import of each sort, and have ascertained the\nnature of the things they relate to, and the nature of what they\nseverally assert respecting those things. We found that whatever be the\nform of the proposition, and whatever its nominal subject or predicate,\nthe real subject of every proposition is some one or more facts or\nphenomena of consciousness, or some one or more of the hidden causes or\npowers to which we ascribe those facts; and that what is predicated or\nasserted, either in the affirmative or negative, of those phenomena or\nthose powers, is always either Existence, Order in Place, Order in Time,\nCausation, or Resemblance. This, then, is the theory of the Import of\nPropositions, reduced to its ultimate elements: but there is another and\na less abstruse expression for it, which, though stopping short in an\nearlier stage of the analysis, is sufficiently scientific for many of\nthe purposes for which such a general expression is required. This\nexpression recognises the commonly received distinction between Subject\nand Attribute, and gives the following as the analysis of the meaning of\npropositions:--Every Proposition asserts, that some given subject does\nor does not possess some attribute; or that some attribute is or is not\n(either in all or in some portion of the subjects in which it is met\nwith) 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\non their own evidence, but on the ground of something previously\nassented to, from which they are said to be _inferred_. To infer a\nproposition from a previous proposition or propositions; to give\ncredence to it, or claim credence for it, as a conclusion from something\nelse; is to _reason_, in the most extensive sense of the term. There is\na narrower sense, in which the name reasoning is confined to the form of\ninference which is termed ratiocination, and of which the syllogism is\nthe general type. The reasons for not conforming to this restricted use\nof the term were stated in an earlier stage of our inquiry, and\nadditional motives will be suggested by the considerations on which we\nare now about to enter.\n\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\nin which 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\nwe were not proving the proposition, but only appealing to another mode\nof wording it, which may or may not be more readily comprehensible by\nthe hearer, or better adapted to suggest the real proof, but which\ncontains in itself 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,\nis not to conclude one proposition from another, but to repeat a second\ntime something which had been asserted at first; with the difference,\nthat we do not here repeat the whole of the previous assertion, but only\nan indefinite 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,\ntherefore Socrates is a living creature; where all that is connoted by\nliving creature was affirmed of Socrates when he was asserted to be a\nman. If the propositions are negative, we must invert their order, thus:\nSocrates is not a living creature, therefore he is not a man; for if we\ndeny the less, the greater, which includes it, is already denied by\nimplication. These, therefore, are not really cases of inference; and\nyet the trivial examples by which, in manuals of Logic, the rules of the\nsyllogism are illustrated, are often of this ill-chosen kind; formal\ndemonstrations of conclusions to which whoever understands the terms\nused in the statement of the data, has already, and consciously,\nassented.\n\nThe most complex case of this sort of apparent inference is what is\ncalled the Conversion of propositions; which consists in turning the\npredicate into a subject, and the subject into a predicate, and framing\nout of the same terms thus reversed, another proposition, which must be\ntrue if the former is true. Thus, from the particular affirmative\nproposition, Some A is B, we may infer that Some B is A. From the\nuniversal negative, No A is B, we may conclude that No B is A. From the\nuniversal affirmative proposition, All A is B, it cannot be inferred\nthat all B is A; though all water is liquid, it is not implied that all\nliquid is water; but it is implied that some liquid is so; and hence the\nproposition, All A is B, is legitimately convertible into Some B is A.\nThis process, which converts an universal proposition into a particular,\nis termed conversion _per accidens_. From the proposition, Some A is not\nB, we cannot even infer that some B is not A; though some men are not\nEnglishmen, it does not follow that some Englishmen are not men. The\nonly mode usually recognised of converting a particular negative\nproposition, is in the form, Some A is not B, therefore, something which\nis not B is A; and this is termed conversion by contraposition. In this\ncase, however, the predicate and subject are not merely reversed, but\none of them is changed. Instead of [A] and [B], the terms of the new\nproposition are [a thing which is not B], and [A]. The original\nproposition, Some A _is not_ B, is first changed into a proposition\n\u00e6quipollent with it, Some A _is_ \"a thing which is not B;\" and the\nproposition, being now no longer a particular negative, but a particular\naffirmative, _admits_ of conversion in the first mode, or as it is\ncalled, _simple_ conversion.[1]\n\nIn all these cases there is not really any inference; there is in the\nconclusion no new truth, nothing but what was already asserted in the\npremises, and obvious to whoever apprehends them. The fact asserted in\nthe conclusion is either the very same fact, or part of the fact\nasserted in the original proposition. This follows from our previous\nanalysis of the Import of Propositions. When we say, for example, that\nsome lawful sovereigns are tyrants, what is the meaning of the\nassertion? That the attributes connoted by the term \"lawful sovereign,\"\nand the attributes connoted by the term \"tyrant,\" sometimes coexist in\nthe same individual. Now this is also precisely what we mean, when we\nsay that some tyrants are lawful sovereigns; which, therefore, is not a\nsecond proposition inferred from the first, any more than the English\ntranslation of Euclid's Elements is a collection of theorems different\nfrom, and consequences of, those contained in the Greek original. Again,\nif we assert that no great general is a rash man, we mean that the\nattributes connoted by \"great general,\" and those connoted by \"rash,\"\nnever coexist in the same subject; which is also the exact meaning which\nwould be expressed by saying, that no rash man is a great general. When\nwe say that all quadrupeds are warm-blooded, we assert, not only that\nthe attributes connoted by \"quadruped\" and those connoted by\n\"warm-blooded\" sometimes coexist, but that the former never exist\nwithout the latter: now the proposition, Some warm-blooded creatures are\nquadrupeds, 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_\nwarm-blooded creatures are quadrupeds, or, in other words, that the\nattributes connoted by \"warm-blooded\" never exist without those connoted\nby \"quadruped,\" has not been asserted, and cannot be inferred. In order\nto reassert, in an inverted form, the whole of what was affirmed in the\nproposition, All quadrupeds are warm-blooded, we must convert it by\ncontraposition, thus, Nothing which is not warm-blooded is a quadruped.\nThis proposition, and the one from which it is derived, are exactly\nequivalent, and either of them may be substituted for the other; for,\nto say that when the attributes of a quadruped are present, those of a\nwarm-blooded creature are present, is to say that when the latter are\nabsent the former are absent.\n\nIn a manual for young students, it would be proper to dwell at greater\nlength on the conversion and \u00e6quipollency of propositions. For, though\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\nmore strictly within the province of the art of logic, than that of\ndiscerning rapidly and surely the identity of an assertion when\ndisguised under diversity of language. That important chapter in logical\ntreatises which relates to the Opposition of Propositions, and the\nexcellent technical language which logic provides for distinguishing the\ndifferent kinds or modes of opposition, are of use chiefly for this\npurpose. Such considerations as these, that contrary propositions may\nboth be false, but cannot both be true; that subcontrary propositions\nmay both be true, but cannot both be false; that of two contradictory\npropositions one must be true and the other false; that of two\nsubalternate propositions the truth of the universal proves the truth of\nthe particular, and the falsity of the particular proves the falsity of\nthe universal, but not _vice vers\u00e2_;[2] are apt to appear, at first\nsight, very technical and mysterious, but when explained, seem almost\ntoo obvious to require so formal a statement, since the same amount of\nexplanation which is necessary to make the principles intelligible,\nwould enable the truths which they convey to be apprehended in any\nparticular case which can occur. In this respect, however, these axioms\nof logic are on a level with those of mathematics. That things which are\nequal to the same thing are equal to one another, is as obvious in any\nparticular case as it is in the general statement: and if no such\ngeneral maxim had ever been laid down, the demonstrations in Euclid\nwould never have halted for any difficulty in stepping across the gap\nwhich this axiom at present serves to bridge over. Yet no one has ever\ncensured writers on geometry, for placing a list of these elementary\ngeneralizations at the head of their treatises, as a first exercise to\nthe learner of the faculty which will be required in him at every step,\nthat of apprehending a _general_ truth. And the student of logic, in the\ndiscussion even of such truths as we have cited above, acquires habits\nof circumspect interpretation of words, and of exactly measuring the\nlength and breadth of his assertions, which are among the most\nindispensable conditions of any considerable mental attainment, and\nwhich it is one of the primary objects of logical discipline to\ncultivate.\n\n\n\u00a7 3. Having noticed, in order to exclude from the province of Reasoning\nor Inference properly so called, the cases in which the progression from\none truth to another is only apparent, the logical consequent being a\nmere repetition of the logical antecedent; we now pass to those which\nare cases of inference in the proper acceptation of the term, those in\nwhich we set out from known truths, to arrive at others really distinct\nfrom them.\n\nReasoning, in the extended sense in which I use the term, and in which\nit is 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\nof reasoning, which falls under neither of these descriptions, and\nwhich, nevertheless, is not only valid, but is the foundation of both\nthe 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\nby these expressions is, that Induction is inferring a proposition from\npropositions _less general_ than itself, and Ratiocination is inferring\na proposition from propositions _equally_ or _more_ general. When, from\nthe observation of a number of individual instances, we ascend to a\ngeneral proposition, or when, by combining a number of general\npropositions, we conclude from them another proposition still more\ngeneral, the process, which is substantially the same in both instances,\nis called Induction. When from a general proposition, not alone (for\nfrom a single proposition nothing can be concluded which is not involved\nin the terms), but by combining it with other propositions, we infer a\nproposition of the same degree of generality with itself, or a less\ngeneral proposition, or a proposition merely individual, the process is\nRatiocination. When, in short, the conclusion is more general than the\nlargest of the premises, the argument is commonly called Induction; when\nless general, or equally general, it is Ratiocination.\n\nAs all experience begins with individual cases, and proceeds from them\nto generals, it might seem most conformable to the natural order of\nthought that Induction should be treated of before we touch upon\nRatiocination. It will, however, be advantageous, in a science which\naims at tracing our acquired knowledge to its sources, that the inquirer\nshould commence with the latter rather than with the earlier stages of\nthe process of constructing our knowledge; and should trace derivative\ntruths backward to the truths from which they are deduced, and on which\nthey depend for their evidence, before attempting to point out the\noriginal spring from which both ultimately take their rise. The\nadvantages of this order of proceeding in the present instance will\nmanifest themselves as we advance, in a manner superseding the necessity\nof any further justification or explanation.\n\nOf Induction, therefore, we shall say no more at present, than that it\nat least is, without doubt, a process of real inference. The conclusion\nin an induction embraces more than is contained in the premises. The\nprinciple or law collected from particular instances, the general\nproposition in which we embody the result of our experience, covers a\nmuch larger extent of ground than the individual experiments which form\nits basis. A principle ascertained by experience, is more than a mere\nsumming up of what has been specifically observed in the individual\ncases which have been examined; it is a generalization grounded on those\ncases, and expressive of our belief, that what we there found true is\ntrue in an indefinite number of cases which we have not examined, and\nare never likely to examine. The nature and grounds of this inference,\nand the conditions necessary to make it legitimate, will be the subject\nof discussion in the Third Book: but that such inference really takes\nplace is not susceptible of question. In every induction we proceed from\ntruths which we knew, to truths which we did not know; from facts\ncertified by observation, to facts which we have not observed, and even\nto facts not capable of being now observed; future facts, for example;\nbut which we do not hesitate to believe on the sole evidence of the\ninduction itself.\n\nInduction, then, is a real process of Reasoning or Inference. Whether,\nand in what sense, as much can be said of the Syllogism, remains to be\ndetermined by the examination into which we are about to enter.\n\n\n\n\nCHAPTER II.\n\nOF RATIOCINATION, OR SYLLOGISM.\n\n\n\u00a7 1. The analysis of the Syllogism has been so accurately and fully\nperformed in the common manuals of Logic, that in the present work,\nwhich is not designed as a manual, it is sufficient to recapitulate,\n_memori\u00e6 caus\u00e2_, the leading results of that analysis, as a foundation\nfor the remarks to be afterwards made on the functions of the syllogism,\nand the place which it holds in science.\n\nTo a legitimate syllogism it is essential that there should be three,\nand no more than three, propositions, namely, the conclusion, or\nproposition to be proved, and two other propositions which together\nprove it, and which are called the premises. It is essential that there\nshould be three, and no more than three, terms, namely, the subject and\npredicate of the conclusion, and another called the middleterm, which\nmust be found in both premises, since it is by means of it that the\nother two terms are to be connected together. The predicate of the\nconclusion is called the major term of the syllogism; the subject of the\nconclusion is called the minor term. As there can be but three terms,\nthe major and minor terms must each be found in one, and only one, of\nthe premises, together with the middleterm which is in them both. The\npremise which contains the middleterm and the major term is called the\nmajor premise; that which contains the middleterm and the minor term is\ncalled the minor premise.\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 premises, the predicate in both, or the subject\nin one and the predicate in the other. The most common case is that in\nwhich the middleterm is the subject of the major premise and the\npredicate of the minor. This is reckoned as the first figure. When the\nmiddleterm is the predicate in both premises, the syllogism belongs to\nthe second figure; when it is the subject in both, to the third. In the\nfourth figure the middleterm is the subject of the minor premise and the\npredicate of the major. Those writers who reckon no more than three\nfigures, include this case in the first.\n\nEach figure is divided into _moods_, according to what are called the\n_quantity_ and _quality_ of the propositions, that is, according as they\nare universal or particular, affirmative or negative. The following are\nexamples of all the legitimate moods, that is, all those in which the\nconclusion correctly follows from the premises. A is the minor term, C\nthe major, B the middleterm.\n\nFIRST FIGURE.\n\n All B is C No B is C All B is C No B is C\n All A is B All A is B Some A is B Some A is B\n therefore therefore therefore therefore\n All A is C No A is C Some A is C Some A is not C\n\nSECOND FIGURE.\n\n No C is B All C is B No C is B All C is B\n All A is B No A is B Some A is B Some A is not B\n therefore therefore therefore therefore\n No A is C No A is C Some A is not C Some A is not C\n\nTHIRD FIGURE.\n\n All B is C No B is C Some B is C All B is C Some B No B is C\n is not C\n All B is A All B is A All B is A Some B is A All B is A Some B is A\n therefore therefore therefore therefore therefore therefore\n Some A is C Some A Some A is C Some A is C Some A Some A\n is not C is not C is not C\n\nFOURTH FIGURE.\n\n All C is B All C is B Some C is B No C is B No C is B\n All B is A No B is A All B is A All B is A Some B is A\n therefore therefore therefore therefore therefore\n Some A is C Some A is not C Some A is C Some A is not C Some A is not C\n\nIn these exemplars, or blank forms for making syllogisms, no place is\nassigned to _singular_ propositions; not, of course, because such\npropositions are not used in ratiocination, but because, their predicate\nbeing affirmed or denied of the whole of the subject, they are ranked,\nfor the purposes of the syllogism, with universal propositions. Thus,\nthese two syllogisms--\n\n All men are mortal, All men are mortal,\n All kings are men, Socrates is a man,\n therefore therefore\n All kings are mortal, Socrates is mortal,\n\nare arguments precisely similar, and are both ranked in the first mood\nof the first figure.\n\nThe reasons why syllogisms in any of the above forms are legitimate,\nthat is, why, if the premises are true, the conclusion must inevitably\nbe so, and why this is not the case in any other possible mood, (that\nis, in any other combination of universal and particular, affirmative\nand negative propositions,) any person taking interest in these\ninquiries may be presumed to have either learned from the common school\nbooks of the syllogistic logic, or to be capable of discovering for\nhimself. The reader may, however, be referred, for every needful\nexplanation, to Archbishop Whately's _Elements of Logic_, where he will\nfind stated with philosophical precision, and explained with remarkable\nperspicuity, the whole of the common doctrine of the syllogism.\n\nAll valid ratiocination; all reasoning by which, from general\npropositions previously admitted, other propositions equally or less\ngeneral are inferred; may be exhibited in some of the above forms. The\nwhole of Euclid, for example, might be thrown without difficulty into a\nseries of syllogisms, regular in mood and figure.\n\nThough a syllogism framed according to any of these formul\u00e6 is a valid\nargument, all correct ratiocination admits of being stated in syllogisms\nof the first figure alone. The rules for throwing an argument in any of\nthe other figures into the first figure, are called rules for the\n_reduction_ of syllogisms. It is done by the _conversion_ of one or\nother, or both, of the premises. Thus an argument in the first mood of\nthe second figure, as--\n\n No C is B\n All A is B\n therefore\n No A is C,\n\nmay be reduced as follows. The proposition, No C is B, being an\nuniversal negative, admits of simple conversion, and may be changed into\nNo B is C, which, as we showed, is the very same assertion in other\nwords--the same fact differently expressed. This transformation having\nbeen effected, the argument assumes the following form:--\n\n No B is C\n All A is B\n therefore\n No A is C,\n\nwhich is a good syllogism in the second mood of the first figure. Again,\nan argument in the first mood of the third figure must resemble the\nfollowing:--\n\n All B is C\n All B is A\n therefore\n Some A is C,\n\nwhere the minor premise, All B is A, conformably to what was laid down\nin the last chapter respecting universal affirmatives, does not admit of\nsimple conversion, but may be converted _per accidens_, thus, Some A is\nB; which, though it does not express the whole of what is asserted in\nthe proposition All B is A, expresses, as was formerly shown, part of\nit, and must therefore be true if the whole is true. We have, then, as\nthe result of the reduction, the following syllogism in the third mood\nof the first figure:--\n\n All B is C\n Some A is B,\n\nfrom which it obviously follows, that\n\n Some A is C.\n\nIn the same manner, or in a manner on which after these examples it is\nnot necessary to enlarge, every mood of the second, third, and fourth\nfigures may be reduced to some one of the four moods of the first. In\nother words, every conclusion which can be proved in any of the last\nthree figures, may be proved in the first figure from the same premises,\nwith a slight alteration in the mere manner of expressing them. Every\nvalid ratiocination, therefore, may be stated in the first figure, that\nis, in one of the following forms:--\n\n Every B is C No B is C\n All A } is B, All A } is B,\n Some A } Some A }\n therefore therefore\n All A } is C. No A is } C.\n Some A } Some A is not }\n\nOr if more significant symbols are preferred:--\n\nTo prove an affirmative, the argument must admit of being stated in this\nform:--\n\n All animals are mortal;\n All men }\n Some men } are animals;\n Socrates }\n therefore\n All men }\n Some men } are mortal.\n Socrates }\n\nTo prove a negative, the argument must be capable of being expressed in\nthis form:--\n\n No one who is capable of self-control is necessarily vicious;\n All negroes }\n Some negroes } are capable of self-control;\n Mr. A's negro }\n therefore\n No negroes are }\n Some negroes are not } necessarily vicious.\n Mr. A's negro is not }\n\nThough all ratiocination admits of being thrown into one or the other of\nthese forms, and sometimes gains considerably by the transformation,\nboth in clearness and in the obviousness of its consequence; there are,\nno doubt, cases in which the argument falls more naturally into one of\nthe other three figures, and in which its conclusiveness is more\napparent at the first glance in those figures, than when reduced to the\nfirst. Thus, if the proposition were that pagans may be virtuous, and\nthe evidence to prove it were the example of Aristides; a syllogism in\nthe third figure,\n\n Aristides was virtuous,\n Aristides was a pagan,\n therefore\n Some 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\ninto the first figure, thus--\n\n Aristides was virtuous,\n Some pagan was Aristides,\n therefore\n Some pagan was virtuous.\n\nA German philosopher, Lambert, whose _Neues Organon_ (published in the\nyear 1764) contains among other things one of the most elaborate and\ncomplete expositions which had ever been made of the syllogistic\ndoctrine, has expressly examined what sort of arguments fall most\nnaturally and suitably into each of the four figures; and his\ninvestigation is characterized by great ingenuity and clearness of\nthought.[3] The argument, however, is one and the same, in whichever\nfigure it is expressed; since, as we have already seen, the premises of\na syllogism in the second, third, or fourth figure, and those of the\nsyllogism in the first figure to which it may be reduced, are the same\npremises in everything except language, or, at least, as much of them as\ncontributes to the proof of the conclusion is the same. We are\ntherefore at liberty, in conformity with the general opinion of\nlogicians, to consider the two elementary forms of the first figure as\nthe universal types of all correct ratiocination; the one, when the\nconclusion to be proved is affirmative, the other, when it is negative;\neven though certain arguments may have a tendency to clothe themselves\nin the forms of the second, third, and fourth figures; which, however,\ncannot possibly happen with the only class of arguments which are of\nfirst-rate scientific importance, those in which the conclusion is an\nuniversal affirmative, such conclusions being susceptible of proof in\nthe first figure alone.[4]\n\n\n\u00a7 2. On examining, then, these two general formul\u00e6, we find that in\nboth of them, one premise, 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\naffirmed or denied of an entire class; that is, in which some attribute,\nor the negation of some attribute, is asserted of an indefinite number\nof objects distinguished by a common characteristic, and designated in\nconsequence, by a common name.\n\nThe other premise is always affirmative, and asserts that something\n(which may be either an individual, a class, or part of a class)\nbelongs to, or is included in, the class respecting which something was\naffirmed or denied in the major premise. It follows that the attribute\naffirmed or denied of the entire class may (if that affirmation or\ndenial was correct) be affirmed or denied of the object or objects\nalleged to be included in the class: and this is precisely the assertion\nmade in the conclusion.\n\nWhether or not the foregoing is an adequate account of the constituent\nparts of the syllogism, will be presently considered; but as far as it\ngoes it is a true account. It has accordingly been generalized, and\nerected into a logical maxim, on which all ratiocination is said to be\nfounded, insomuch that to reason, and to apply the maxim, are supposed\nto be one and the same thing. The maxim is, That whatever can be\naffirmed (or denied) of a class, may be affirmed (or denied) of\neverything included in the class. This axiom, supposed to be the basis\nof the syllogistic theory, is termed by logicians the _dictum de omni et\nnullo_.\n\nThis maxim, however, when considered as a principle of reasoning,\nappears suited to a system of metaphysics once indeed generally\nreceived, but which for the last two centuries has been considered as\nfinally abandoned, though there have not been wanting in our own day\nattempts at its revival. So long as what are termed Universals were\nregarded as a peculiar kind of substances, having an objective existence\ndistinct from the individual objects classed under them, the _dictum de\nomni_ conveyed an important meaning; because it expressed the\nintercommunity of nature, which it was necessary on that theory that we\nshould suppose to exist between those general substances and the\nparticular substances which were subordinated to them. That everything\npredicable of the universal was predicable of the various individuals\ncontained under it, was then no identical proposition, but a statement\nof what was conceived as a fundamental law of the universe. The\nassertion that the entire nature and properties of the _substantia\nsecunda_ formed part of the nature and properties of each of the\nindividual substances called by the same name; that the properties of\nMan, for example, were properties of all men; was a proposition of real\nsignificance when man did not _mean_ all men, but something inherent in\nmen, and vastly superior to them in dignity. Now, however, when it is\nknown that a class, an universal, a genus or species, is not an entity\n_per se_, but neither more nor less than the individual substances\nthemselves which are placed in the class, and that there is nothing real\nin the matter except those objects, a common name given to them, and\ncommon attributes indicated by the name; what, I should be glad to know,\ndo we learn by being told, that whatever can be affirmed of a class, may\nbe affirmed of every object contained in the class? The class is nothing\nbut the objects contained in it: and the _dictum de omni_ merely amounts\nto the identical proposition, that whatever is true of certain objects,\nis true of each of those objects. If all ratiocination were no more than\nthe application of this maxim to particular cases, the syllogism would\nindeed be, what it has so often been declared to be, solemn trifling.\nThe _dictum de omni_ is on a par with another truth, which in its time\nwas also reckoned of great importance, \"Whatever is, is.\" To give any\nreal meaning to the _dictum de omni_, we must consider it not as an\naxiom, but as a definition; we must look upon it as intended to explain,\nin a circuitous and paraphrastic manner, the meaning of the word,\n_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\nperpetual flux, knowledge, which necessarily imports stability, can only\nhave relation to those general substances or universals, and not to the\nfacts or particulars included under them. Yet, though nominally\nrejected, this very doctrine, whether disguised under the Abstract Ideas\nof Locke (whose speculations, however, it has less vitiated than those\nof perhaps any other writer who has been infected with it), under the\nultra-nominalism of Hobbes and Condillac, or the ontology of the later\nKantians, has never ceased to poison philosophy. Once accustomed to\nconsider scientific investigation as essentially consisting in the study\nof universals, men did not drop this habit of thought when they ceased\nto regard universals as possessing an independent existence: and even\nthose who went the length of considering them as mere names, could not\nfree themselves from the notion that the investigation of truth\nconsisted entirely or partly in some kind of conjuration or juggle with\nthose names. When a philosopher adopted fully the Nominalist view of the\nsignification of general language, retaining along with it the _dictum\nde omni_ as the foundation of all reasoning, two such premises fairly\nput together were likely, if he was a consistent thinker, to land him in\nrather startling conclusions. Accordingly it has been seriously held, by\nwriters of deserved celebrity, that the process of arriving at new\ntruths by reasoning consists in the mere substitution of one set of\narbitrary signs for another; a doctrine which they suppose to derive\nirresistible confirmation from the example of algebra. If there were any\nprocess in sorcery or necromancy more preternatural than this, I should\nbe much surprised. The culminating point of this philosophy is the noted\naphorism of Condillac, that a science is nothing, or scarcely anything,\nbut _une langue bien faite_; in other words, that the one sufficient\nrule for discovering the nature and properties of objects is to name\nthem properly: as if the reverse were not the truth, that it is\nimpossible to name them properly except in proportion as we are already\nacquainted with their nature and properties. Can it be necessary to say,\nthat none, not even the most trivial knowledge with respect to Things,\never was or could be originally got at by any conceivable manipulation\nof mere names, as such; and that what can be learned from names, is only\nwhat somebody who used the names knew before? Philosophical analysis\nconfirms the indication of common sense, that the function of names is\nbut that of enabling us to _remember_ and to _communicate_ our thoughts.\nThat they also strengthen, even to an incalculable extent, the power of\nthought itself, is most true: but they do this by no intrinsic and\npeculiar virtue; they do it by the power inherent in an artificial\nmemory, an instrument of which few have adequately considered the\nimmense potency. As an artificial memory, language truly is, what it has\nso often been called, an instrument of thought; but it is one thing to\nbe the instrument, and another to be the exclusive subject upon which\nthe instrument is exercised. We think, indeed, to a considerable extent,\nby means of names, but what we think of, are the things called by those\nnames; and there cannot be a greater error than to imagine that thought\ncan be carried on with nothing in our mind but names, or that we can\nmake the names think for us.\n\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\nhis definition might be rigorously universal, defined a proposition as\nif no propositions declared anything except the meaning of words. If\nHobbes was right; if no further account than this could be given of the\nimport of propositions; no theory could be given but the commonly\nreceived one, of the combination of propositions in a syllogism. If the\nminor premise asserted nothing more than that something belongs to a\nclass, and if the major premise asserted nothing of that class except\nthat it is included in another class, the conclusion would only be that\nwhat was included in the lower class is included in the higher, and the\nresult, therefore, nothing except that the classification is consistent\nwith itself. But we have seen that it is no sufficient account of the\nmeaning of a proposition, to say that it refers something to, or\nexcludes something from, a class. Every proposition which conveys real\ninformation asserts a matter of fact, dependent on the laws of nature,\nand not on classification. It asserts that a given object does or does\nnot possess a given attribute; or it asserts that two attributes, or\nsets of attributes, do or do not (constantly or occasionally) coexist.\nSince such is the purport of all propositions which convey any real\nknowledge, and since ratiocination is a mode of acquiring real\nknowledge, any theory of ratiocination which does not recognise this\nimport of propositions, cannot, we may be sure, be the true one.\n\nApplying this view of propositions to the two premises of a syllogism,\nwe obtain the following results. The major premise, which, as already\nremarked, is always universal, asserts, that all things which have a\ncertain attribute (or attributes) have or have not along with it, a\ncertain other attribute (or attributes). The minor premise asserts that\nthe thing or set of things which are the subject of that premise, have\nthe first-mentioned attribute; and the conclusion is, that they have (or\nthat they have not) the second. Thus in our former example,\n\n All men are mortal,\n Socrates is a man,\n therefore\n Socrates is mortal,\n\nthe subject and predicate of the major premise are connotative terms,\ndenoting objects and connoting attributes. The assertion in the major\npremise is, that along with one of the two sets of attributes, we always\nfind the other: that the attributes connoted by \"man\" never exist unless\nconjoined with the attribute called mortality. The assertion in the\nminor premise is that the individual named Socrates possesses the former\nattributes; and it is concluded that he possesses also the attribute\nmortality. Or if both the premises are general propositions, as\n\n All men are mortal,\n All kings are men,\n therefore\n All kings are mortal,\n\nthe minor premise asserts that the attributes denoted by kingship only\nexist in conjunction with those signified by the word man. The major\nasserts as before, that the last-mentioned attributes are never found\nwithout the attribute of mortality. The conclusion is, that wherever the\nattributes of kingship are found, that of mortality is found also.\n\nIf the major premise were negative, as, No men are omnipotent, it would\nassert, not that the attributes connoted by \"man\" never exist without,\nbut that they never exist with, those connoted by \"omnipotent:\" from\nwhich, together with the minor premise, it is concluded, that the same\nincompatibility exists between the attribute omnipotence and those\nconstituting a king. In a similar manner we might 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,\nthe propositions of which are anything more than merely verbal; we find,\nnot the unmeaning _dictum de omni et nullo_, but a fundamental\nprinciple, or rather two principles, strikingly resembling the axioms of\nmathematics. The first, which is the principle of affirmative\nsyllogisms, is, that things which coexist with the same thing, coexist\nwith one another. The second is the principle of negative syllogisms,\nand is to this effect: that a thing which coexists with another thing,\nwith which other a third thing does not coexist, is not coexistent with\nthat third thing. These axioms manifestly relate to facts, and not to\nconventions; and one or other of them is the ground of the legitimacy of\nevery argument in which facts and not conventions are the matter treated\nof.[5]\n\n\n\u00a7 4. It remains to translate this exposition of the syllogism from the\none into the other of the two languages in which we formerly\nremarked[6] that all propositions, and of course therefore all\ncombinations of propositions, might be expressed. We observed that a\nproposition might be considered in two different lights; as a portion of\nour knowledge of nature, or as a memorandum for our guidance. Under the\nformer, or speculative aspect, an affirmative general proposition is an\nassertion of a speculative truth, viz. that whatever has a certain\nattribute has a certain other attribute. Under the other aspect, it is\nto be regarded not as a part of our knowledge, but as an aid for our\npractical exigencies, by enabling us, when we see or learn that an\nobject possesses one of the two attributes, to infer that it possesses\nthe other; thus employing the first attribute as a mark or evidence of\nthe second. Thus regarded, every syllogism comes within the following\ngeneral formula:--\n\n Attribute A is a mark of attribute B,\n The given object has the mark A,\n therefore\n The given object has the attribute B.\n\nReferred to this type, the arguments which we have lately cited as\nspecimens of the syllogism, will express themselves in the following\nmanner:--\n\n The attributes of man are a mark of the attribute mortality,\n Socrates has the attributes of man,\n therefore\n Socrates has the attribute mortality.\n\nAnd again,\n\n The attributes of man are a mark of the attribute mortality,\n The attributes of a king are a mark of the attributes of man,\n therefore\n The attributes of a king are a mark of the attribute mortality.\n\nAnd, lastly,\n\n The attributes of man are a mark of the absence of\n the attribute omnipotence,\n The attributes of a king are a mark of the attributes of man,\n therefore\n The attributes of a king are a mark of the absence of\n the attribute signified by the word omnipotent\n (or, are evidence of the absence of that 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\nwhatever has any mark, has that which it is a mark of. Or, when the\nminor premise 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\nlaid down, may be left to the intelligent reader. We shall find, as we\nproceed, the great convenience of the phraseology into which we have\nlast thrown them, and which is better adapted than any I am acquainted\nwith, to express 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.\n\nOF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.\n\n\n\u00a7 1. We have shown what is the real nature of the truths with which the\nSyllogism is conversant, in contradistinction to the more superficial\nmanner in which their import is conceived in the common theory; and what\nare the fundamental axioms on which its probative force or\nconclusiveness depends. We have now to inquire, whether the syllogistic\nprocess, that of reasoning from generals to particulars, is, or is not,\na process of inference; a progress from the known to the unknown: a\nmeans of coming to a knowledge of something which we did not know\nbefore.\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 premises. But\nthis is, in fact, to say, that nothing ever was, or can be, proved by\nsyllogism, which was not known, or assumed to be known, before. Is\nratiocination, then, not a process of inference? And is the syllogism,\nto which the word reasoning has so often been represented to be\nexclusively appropriate, not really entitled to be called reasoning at\nall? This seems an inevitable consequence of the doctrine, admitted by\nall writers on the subject, that a syllogism can prove no more than is\ninvolved in the premises. Yet the acknowledgment so explicitly made, has\nnot prevented one set of writers from continuing to represent the\nsyllogism as the correct analysis of what the mind actually performs in\ndiscovering and proving the larger half of the truths, whether of\nscience or of daily life, which we believe; while those who have avoided\nthis inconsistency, and followed out the general theorem respecting the\nlogical value of the syllogism to its legitimate corollary, have been\nled to impute uselessness and frivolity to the syllogistic theory\nitself, on the ground of the _petitio principii_ which they allege to be\ninherent in every syllogism. As I believe both these opinions to be\nfundamentally erroneous, I must request the attention of the reader to\ncertain considerations, without which any just appreciation of the true\ncharacter of the syllogism, and the functions it performs in philosophy,\nappears to me impossible; but which seem to have been either overlooked,\nor insufficiently adverted to, both by the defenders of the syllogistic\ntheory and by its assailants.\n\n\n\u00a7 2. It must be granted that in every syllogism, considered as an\nargument to prove the conclusion, there is a _petitio principii_. When\nwe say,\n\n All men are mortal,\n Socrates is a man,\n therefore\n Socrates 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 we choose to name, be mortal or not, the same\ndegree of uncertainty must hang over the assertion, All men are mortal:\nthat the general principle, instead of being given as evidence of the\nparticular case, cannot itself be taken for true without exception,\nuntil every shadow of doubt which could affect any case comprised with\nit, is dispelled by evidence _aliund\u00e8_; and then what remains for the\nsyllogism to prove? That, in short, no reasoning from generals to\nparticulars can, as such, prove anything: since from a general principle\nwe cannot infer any particulars, but those which the principle itself\nassumes as known.\n\nThis doctrine appears to me irrefragable; and if logicians, though\nunable to dispute it, have usually exhibited a strong disposition to\nexplain it away, this was not because they could discover any flaw in\nthe argument itself, but because the contrary opinion seemed to rest on\narguments equally indisputable. In the syllogism last referred to, for\nexample, or in any of those which we previously constructed, is it not\nevident that the conclusion may, to the person to whom the syllogism is\npresented, be actually and _bon\u00e2 fide_ a new truth? Is it not matter of\ndaily experience that truths previously unthought of, facts which have\nnot been, and cannot be, directly observed, are arrived at by way of\ngeneral reasoning? We believe that the Duke of Wellington is mortal. We\ndo not know this by direct observation, so long as he is not yet dead.\nIf we were asked how, this being the case, we know the duke to be\nmortal, we should probably answer, Because all men are so. Here,\ntherefore, we arrive at the knowledge of a truth not (as yet)\nsusceptible of observation, by a reasoning which admits of being\nexhibited in the following syllogism:--\n\n All men are mortal,\n The Duke of Wellington is a man,\n therefore\n The 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\nor proof; though none of them has cleared up the difficulty which arises\nfrom the inconsistency between that assertion, and the principle, that\nif there be anything in the conclusion which was not already asserted in\nthe premises, the argument is vicious. For it is impossible to attach\nany serious scientific value to such a mere salvo, as the distinction\ndrawn between being involved _by implication_ in the premises, and being\ndirectly asserted in them. When Archbishop Whately says[7] that the\nobject of reasoning is \"merely to expand and unfold the assertions wrapt\nup, as it were, and implied in those with which we set out, and to bring\na person to perceive and acknowledge the full force of that which he\nhas admitted,\" he does not, I think, meet the real difficulty requiring\nto be explained, namely, how it happens that a science, like geometry,\n_can_ be all \"wrapt up\" in a few definitions and axioms. Nor does this\ndefence of the syllogism differ much from what its assailants urge\nagainst it as an accusation, when they charge it with being of no use\nexcept to those who seek to press the consequences of an admission into\nwhich a person has been entrapped without having considered and\nunderstood its full force. When you admitted the major premise, you\nasserted the conclusion; but, says Archbishop Whately, you asserted it\nby implication merely: this, however, can here only mean that you\nasserted it unconsciously; that you did not know you were asserting it;\nbut, if so, the difficulty revives in this shape--Ought you not to have\nknown? Were you warranted in asserting the general proposition without\nhaving satisfied yourself of the truth of everything which it fairly\nincludes? And if not, is not the syllogistic art _prim\u00e2 facie_ what its\nassailants affirm it to be, a contrivance for catching you in a trap,\nand holding you fast in it?[8]\n\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,\nin reality, conclude it from the proposition, All men are mortal? I\nanswer, no.\n\nThe error committed is, I conceive, that of overlooking the distinction\nbetween two parts of the process of philosophizing, the inferring part,\nand the registering part; and ascribing to the latter the functions of\nthe 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\nto a memorandum which he carries about with him. But if he were asked,\nhow the fact came to his knowledge, he would scarcely answer, because it\nwas set down in his note-book: unless the book was written, like the\nKoran, with 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;\nwhence do 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;\na comprehensive 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.\nWe then, by that valuable contrivance of language which enables us to\nspeak of many as if they were one, record all that we have observed,\ntogether with all that we infer from our observations, in one concise\nexpression; and have thus only one proposition, instead of an endless\nnumber, to remember or to communicate. The results of many observations\nand inferences, 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\nevery other person we ever heard of in whose case the experiment had\nbeen fairly tried, that the Duke of Wellington is mortal like the rest;\nwe may, indeed, pass through the generalization, All men are mortal, as\nan intermediate stage; but it is not in the latter half of the process,\nthe descent from all men to the Duke of Wellington, that the _inference_\nresides. The inference is finished when we have asserted that all men\nare mortal. What remains to be performed afterwards is merely\ndecyphering our own notes.\n\nArchbishop Whately has contended that syllogizing, or reasoning from\ngenerals to particulars, is not, agreeably to the vulgar idea, a\npeculiar _mode_ of reasoning, but the philosophical analysis of _the_\nmode in which all men reason, and must do so if they reason at all. With\nthe deference due to so high an authority, I cannot help thinking that\nthe vulgar notion is, in this case, the more correct. If, from our\nexperience of John, Thomas, &c., who once were living, but are now dead,\nwe are entitled to conclude that all human beings are mortal, we might\nsurely without any logical inconsequence have concluded at once from\nthose instances, that the Duke of Wellington is mortal. The mortality of\nJohn, Thomas, and company is, after all, the whole evidence we have for\nthe mortality of the Duke of Wellington. Not one iota is added to the\nproof by interpolating a general proposition. Since the individual cases\nare all the evidence we can possess, evidence which no logical form into\nwhich we choose to throw it can make greater than it is; and since that\nevidence is either sufficient in itself, or, if insufficient for the one\npurpose, cannot be sufficient for the other; I am unable to see why we\nshould be forbidden to take the shortest cut from these sufficient\npremises to the conclusion, and constrained to travel the \"high priori\nroad,\" by the arbitrary fiat of logicians. I cannot perceive why it\nshould be impossible to journey from one place to another unless we\n\"march up a hill, and then march down again.\" It may be the safest road,\nand there may be a resting-place at the top of the hill, affording a\ncommanding view of the surrounding country; but for the mere purpose of\narriving at our journey's end, our taking that road is perfectly\noptional; 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\ndraw inferences, but years elapse before we learn the use of general\nlanguage. The child, who, having burnt his fingers, avoids to thrust\nthem again into the fire, has reasoned or inferred, though he has never\nthought of the general maxim, Fire burns. He knows from memory that he\nhas been burnt, and on this evidence believes, when he sees a candle,\nthat if he puts his finger into the flame of it, he will be burnt again.\nHe believes this in every case which happens to arise; but without\nlooking, in each instance, beyond the present case. He is not\ngeneralizing; he is inferring a particular from particulars. In the same\nway, also, brutes reason. There is no ground for attributing to any of\nthe lower animals the use of signs, of such a nature as to render\ngeneral propositions possible. But those animals profit by experience,\nand avoid what they have found to cause them pain, in the same manner,\nthough not always with the same skill, as a human creature. Not only the\nburnt child, but the burnt dog, dreads the fire.\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\nproposition. We are constantly reasoning from ourselves to other people,\nor from one person to another, without giving ourselves the trouble to\nerect our observations into general maxims of human or external nature.\nWhen we conclude that some person will, on some given occasion, feel or\nact so and so, we sometimes judge from an enlarged consideration of the\nmanner in which human beings in general, or persons of some particular\ncharacter, are accustomed to feel and act: but much oftener from merely\nrecollecting the feelings and conduct of the same person in some\nprevious instance, or from considering how we should feel or act\nourselves. It is not only the village matron, who, when called to a\nconsultation upon the case of a neighbour's child, pronounces on the\nevil and its remedy simply on the recollection and authority of what she\naccounts the similar case of her Lucy. We all, where we have no definite\nmaxims to steer by, guide ourselves in the same way: and if we have an\nextensive experience, and retain its impressions strongly, we may\nacquire in this manner a very considerable power of accurate judgment,\nwhich we may be utterly incapable of justifying or of communicating to\nothers. Among the higher order of practical intellects there have been\nmany of whom it was remarked how admirably they suited their means to\ntheir ends, without being able to give any sufficient reasons for what\nthey did; and applied, or seemed to apply, recondite principles which\nthey were wholly unable to state. This is a natural consequence of\nhaving a mind stored with appropriate particulars, and having been long\naccustomed to reason at once from these to fresh particulars, without\npractising the habit of stating to oneself or to others the\ncorresponding general propositions. An old warrior, on a rapid glance at\nthe outlines of the ground, is able at once to give the necessary orders\nfor a skilful arrangement of his troops; though if he has received\nlittle theoretical instruction, and has seldom been called upon to\nanswer 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\nanalogies in his mind, the most appropriate of which, instantly\nsuggesting itself, determines him to a judicious arrangement.\n\nThe skill of an uneducated person in the use of weapons, or of tools,\nis of 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\nand distance of the object, the action of the wind, &c., owes this power\nto a long series of previous experiments, the results of which he\ncertainly never framed into any verbal theorems or rules. The same thing\nmay generally be said of any other extraordinary manual dexterity. Not\nlong ago a Scotch manufacturer procured from England, at a high rate of\nwages, a working dyer, famous for producing very fine colours, with the\nview of teaching to his other workmen the same skill. The workman came;\nbut his mode of proportioning the ingredients, in which lay the secret\nof the effects he produced, was by taking them up in handfuls, while the\ncommon method was to weigh them. The manufacturer sought to make him\nturn his handling system into an equivalent weighing system, that the\ngeneral principle of his peculiar mode of proceeding might be\nascertained. This, however, the man found himself quite unable to do,\nand therefore could impart his skill to nobody. He had, from the\nindividual cases of his own experience, established a connexion in his\nmind between fine effects of colour, and tactual perceptions in handling\nhis dyeing materials; and from these perceptions he could, in any\nparticular case, infer the means to be employed, and the effects which\nwould be produced, but could not put others in possession of the grounds\non which he proceeded, from having never generalized them in his own\nmind, or expressed them in language.\n\nAlmost every one knows Lord Mansfield's advice to a man of practical\ngood sense, who, being appointed governor of a colony, had to preside in\nits court of justice, without previous judicial practice or legal\neducation. The advice was to give his decision boldly, for it would\nprobably be right; but never to venture on assigning reasons, for they\nwould almost infallibly be wrong. In cases like this, which are of no\nuncommon occurrence, it would be absurd to suppose that the bad reason\nwas the source of the good decision. Lord Mansfield knew that if any\nreason were assigned it would be necessarily an afterthought, the judge\nbeing _in fact_ guided by impressions from past experience, without the\ncircuitous process of framing general principles from them, and that if\nhe attempted to frame any such he would assuredly fail. Lord Mansfield,\nhowever, would not have doubted that a man of equal experience who had\nalso a mind stored with general propositions derived by legitimate\ninduction from that experience, would have been greatly preferable as a\njudge, to one, however sagacious, who could not be trusted with the\nexplanation and justification of his own judgments. The cases of men of\ntalent performing wonderful things they know not how, are examples of\nthe rudest and most spontaneous form of the operations of superior\nminds. It is a defect in them, and often a source of errors, not to have\ngeneralized as they went on; but generalization, though a help, the most\nimportant indeed of all helps, is not 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\nto apply that experience to a new case. It is justly remarked by Dugald\nStewart, that though the reasonings in mathematics depend entirely on\nthe axioms, it is by no means necessary to our seeing the conclusiveness\nof the proof, that the axioms should be expressly adverted to. When it\nis inferred that AB is equal to CD because each of them is equal to EF,\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 \"things which are equal to the same thing are\nequal to one another.\" This remark of Stewart, consistently followed\nout, goes to the root, as I conceive, of the philosophy of\nratiocination; and it is to be regretted that he himself stopt short at\na much more limited application of it. He saw that the general\npropositions on which a reasoning is said to depend, may, in certain\ncases, be altogether omitted, without impairing its probative force.\nBut he imagined this to be a peculiarity belonging to axioms; and argued\nfrom it, that axioms are not the foundations or first principles of\ngeometry, from which all the other truths of the science are\nsynthetically deduced (as the laws of motion and of the composition of\nforces in dynamics, the equal mobility of fluids in hydrostatics, the\nlaws of reflection and refraction in optics, are the first principles of\nthose sciences); but are merely necessary assumptions, self-evident\nindeed, and the denial of which would annihilate all demonstration, but\nfrom which, as premises, nothing can be demonstrated. In the present, as\nin many other instances, this thoughtful and elegant writer has\nperceived an important truth, but only by halves. Finding, in the case\nof geometrical axioms, that general names have not any talismanic virtue\nfor conjuring new truths out of the well where they lie hid, and not\nseeing that this is equally true in every other case of generalization,\nhe contended that axioms are in their nature barren of consequences, and\nthat the really fruitful truths, the real first principles of geometry,\nare the definitions; that the definition, for example, of the circle is\nto the properties of the circle, what the laws of equilibrium and of the\npressure of the atmosphere are to the rise of the mercury in the\nTorricellian tube. Yet all that he had asserted respecting the function\nto which the axioms are confined in the demonstrations of geometry,\nholds equally true of the definitions. Every demonstration in Euclid\nmight be carried on without them. This is apparent from the ordinary\nprocess of proving a proposition of geometry by means of a diagram. What\nassumption, in fact, do we set out from, to demonstrate by a diagram any\nof the properties of the circle? Not that in all circles the radii are\nequal, but only that they are so in the circle ABC. As our warrant for\nassuming this, we appeal, it is true, to the definition of a circle in\ngeneral; but it is only necessary that the assumption be granted in the\ncase of the particular circle supposed. From this, which is not a\ngeneral but a singular proposition, combined with other propositions of\na similar kind, some of which _when generalized_ are called definitions,\nand others axioms, we prove that a certain conclusion is true, not of\nall circles, but of the particular circle ABC; or at least would be so,\nif the facts precisely accorded with our assumptions. The enunciation,\nas it is called, that is, the general theorem which stands at the head\nof the demonstration, is not the proposition actually demonstrated. One\ninstance only is demonstrated: but the process by which this is done, is\na process which, when we consider its nature, we perceive might be\nexactly copied in an indefinite number of other instances; in every\ninstance which conforms to certain conditions. The contrivance of\ngeneral language furnishing us with terms which connote these\nconditions, we are able to assert this indefinite multitude of truths in\na single expression, and this expression is the general theorem. By\ndropping the use of diagrams, and substituting, in the demonstrations,\ngeneral phrases for the letters of the alphabet, we might prove the\ngeneral theorem directly, that is, we might demonstrate all the cases at\nonce; and to do this we must, of course, employ as our premises, the\naxioms and definitions in their general form. But this only means, that\nif we can prove an individual conclusion by assuming an individual fact,\nthen in whatever case we are warranted in making an exactly similar\nassumption, we may draw an exactly similar conclusion. The definition is\na sort of notice to ourselves and others, what assumptions we think\nourselves entitled to make. And so in all cases, the general\npropositions, whether called definitions, axioms, or laws of nature,\nwhich we lay down at the beginning of our reasonings, are merely\nabridged statements, in a kind of short-hand, of the particular facts,\nwhich, as occasion arises, we either think we may proceed on as proved,\nor intend to assume. In any one demonstration it is enough if we assume\nfor a particular case suitably selected, what by the statement of the\ndefinition or principle we announce that we intend to assume in all\ncases which may arise. The definition of the circle, therefore, is to\none of Euclid's demonstrations, exactly what, according to Stewart, the\naxioms are; that is, the demonstration does not depend on it, but yet if\nwe deny it the demonstration fails. The proof does not rest on the\ngeneral assumption, but on a similar assumption confined to the\nparticular case: that case, however, being chosen as a specimen or\nparadigm of the whole class of cases included in the theorem, there can\nbe no ground for making the assumption in that case which does not exist\nin every other; and to deny the assumption as a general truth, is to\ndeny the right of making 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\ngeneral proposition, is manifest from the difficulty they find in\napplying a theorem to a case in which the configuration of the diagram\nis extremely unlike that of the diagram by which the original theorem\nwas demonstrated. A difficulty which, except in cases of unusual mental\npower, long practice can alone remove, and removes chiefly by rendering\nus familiar with all the configurations consistent with the general\nconditions of the theorem.\n\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\nmade, and short formul\u00e6 for making more: The major premise of a\nsyllogism, consequently, is a formula of this description: and the\nconclusion is not an inference drawn _from_ the formula, but an\ninference drawn _according_ to the formula: the real logical antecedent,\nor premise, being the particular facts from which the general\nproposition was collected by induction. Those facts, and the individual\ninstances which supplied them, may have been forgotten: but a record\nremains, not indeed descriptive of the facts themselves, but showing how\nthose cases may be distinguished, respecting which the facts, when\nknown, were considered to warrant a given inference. According to the\nindications of this record we draw our conclusion; which is, to all\nintents and purposes, a conclusion from the forgotten facts. For this\nit is essential that we should read the record correctly: and the rules\nof the syllogism are a set of precautions to ensure 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\nleast favourable to it, namely, those in which ratiocination is\nindependent of any previous induction. We have already observed that the\nsyllogism, in the ordinary course of our reasoning, is only the latter\nhalf of the process of travelling from premises to a conclusion. There\nare, however, some peculiar cases in which it is the whole process.\nParticulars alone are capable of being subjected to observation; and all\nknowledge which is derived from observation, begins, therefore, of\nnecessity, in particulars; but our knowledge may, in cases of certain\ndescriptions, be conceived as coming to us from other sources than\nobservation. It may present itself as coming from testimony, which, on\nthe occasion and for the purpose in hand, is accepted as of an\nauthoritative character: and the information thus communicated, may be\nconceived to comprise not only particular facts but general\npropositions, as when a scientific doctrine is accepted without\nexamination on the authority of writers, or a theological doctrine on\nthat of Scripture. Or the generalization may not be, in the ordinary\nsense, an assertion at all, but a command; a law, not in the\nphilosophical, 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\nfar as this asserts a fact, namely, a volition of the legislator, that\nfact is an individual fact, and the proposition, therefore, is not a\ngeneral proposition. But the description therein contained of the\nconduct which it is the will of the legislator that his subjects should\nobserve, is general. The proposition asserts, not that all men _are_\nanything, but that 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\nothers, or not. This is ascertained by examining whether the case\npossesses the marks by which, as those authorities have signified, the\ncases which they meant to certify or to influence may be known. The\nobject of the inquiry is to make out the witness's or the legislator's\nintention, through the indication given by their words. This is a\nquestion, as the Germans express it, of hermeneutics. The operation is\nnot a process of inference, but a process of interpretation.\n\nIn this last phrase we have obtained an expression which appears to me\nto characterize, more aptly than any other, the functions of the\nsyllogism in all cases. When the premises are given by authority, the\nfunction of Reasoning is to ascertain the testimony of a witness, or the\nwill of a legislator, by interpreting the signs in which the one has\nintimated his assertion and the other his command. In like manner, when\nthe premises are derived from observation, the function of Reasoning is\nto ascertain what we (or our predecessors) formerly thought might be\ninferred from the observed facts, and to do this by interpreting a\nmemorandum of ours, or of theirs. The memorandum reminds us, that from\nevidence, more or less carefully weighed, it formerly appeared that a\ncertain attribute might be inferred wherever we perceive a certain mark.\nThe proposition, All men are mortal (for instance) shows that we have\nhad experience from which we thought it followed that the attributes\nconnoted by the term man, are a mark of mortality. But when we conclude\nthat the Duke of Wellington is mortal, we do not infer this from the\nmemorandum, but from the former experience. All that we infer from the\nmemorandum is our own previous belief, (or that of those who transmitted\nto us the proposition), concerning the inferences which that former\nexperience would warrant.\n\nThis view of the nature of the syllogism renders consistent and\nintelligible what otherwise remains obscure and confused in the theory\nof Archbishop Whately and other enlightened defenders of the syllogistic\ndoctrine, respecting the limits to which its functions are confined.\nThey affirm in as explicit terms as can be used, that the sole office of\ngeneral reasoning is to prevent inconsistency in our opinions; to\nprevent us from assenting to anything, the truth of which would\ncontradict something to which we had previously on good grounds given\nour assent. And they tell us, that the sole ground which a syllogism\naffords for assenting to the conclusion, is that the supposition of its\nbeing false, combined with the supposition that the premises are true,\nwould lead to a contradiction in terms. Now this would be but a lame\naccount of the real grounds which we have for believing the facts which\nwe learn from reasoning, in contradistinction to observation. The true\nreason why we believe that the Duke of Wellington will die, is that his\nfathers, and our fathers, and all other persons who were cotemporary\nwith them, have died. Those facts are the real premises of the\nreasoning. But we are not led to infer the conclusion from those\npremises, by the necessity of avoiding any verbal inconsistency. There\nis no contradiction in supposing that all those persons have died, and\nthat the Duke of Wellington may, notwithstanding, live for ever. But\nthere would be a contradiction if we first, on the ground of those same\npremises, made a general assertion including and covering the case of\nthe Duke of Wellington, and then refused to stand to it in the\nindividual case. There is an inconsistency to be avoided between the\nmemorandum we make of the inferences which may be justly drawn in future\ncases, and the inferences we actually draw in those cases when they\narise. With this view we interpret our own formula, precisely as a judge\ninterprets a law: in order that we may avoid drawing any inferences not\nconformable to our former intention, as a judge avoids giving any\ndecision not conformable to the legislator's intention. The rules for\nthis interpretation are the rules of the syllogism: and its sole purpose\nis to maintain consistency between the conclusions we draw in every\nparticular case, and the previous general directions for drawing them;\nwhether those general directions were framed by ourselves as the result\nof induction, or were received by us from an authority competent to give\nthem.\n\n\n\u00a7 5. In the above observations it has, I think, been shown, that, though\nthere is always a process of reasoning or inference where a syllogism is\nused, the syllogism is not a correct analysis of that process of\nreasoning 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\nof particular 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\ntherefore hold in time to come, it will hold not merely in some\nindividual case, but in all cases of some given description. Every\ninduction, therefore, which suffices to prove one fact, proves an\nindefinite multitude of facts: the experience which justifies a single\nprediction must be such as will suffice to bear out a general theorem.\nThis theorem it is extremely important to ascertain and declare, in its\nbroadest form of generality; and thus to place before our minds, in its\nfull extent, the whole of what our evidence must prove if it proves\nanything.\n\nThis throwing of the whole body of possible inferences from a given set\nof particulars, into one general expression, operates as a security for\ntheir being just inferences, in more ways than one. First, the general\nprinciple presents a larger object to the imagination than any of the\nsingular propositions which it contains. A process of thought which\nleads to a comprehensive generality, is felt as of greater importance\nthan one which terminates in an insulated fact; and the mind is, even\nunconsciously, led to bestow greater attention upon the process, and to\nweigh more carefully the sufficiency of the experience appealed to, for\nsupporting the inference grounded upon it. There is another, and a more\nimportant, advantage. In reasoning from a course of individual\nobservations to some new and unobserved case, which we are but\nimperfectly acquainted with (or we should not be inquiring into it), and\nin which, since we are inquiring into it, we probably feel a peculiar\ninterest; there is very little to prevent us from giving way to\nnegligence, or to any bias which may affect our wishes or our\nimagination, and, under that influence, accepting insufficient evidence\nas sufficient. But if, instead of concluding straight to the particular\ncase, we place before ourselves an entire class of facts--the whole\ncontents of a general proposition, every tittle of which is legitimately\ninferrible from our premises, if that one particular conclusion is so;\nthere is then a considerable likelihood that if the premises are\ninsufficient, and the general inference, therefore, groundless, it will\ncomprise within it some fact or facts the reverse of which we already\nknow to be true; and we shall thus discover the error in our\ngeneralization by a _reductio ad impossibile_.\n\nThus if, during the reign of Marcus Aurelius, a subject of the Roman\nempire, under the bias naturally given to the imagination and\nexpectations by the lives and characters of the Antonines, had been\ndisposed to expect that Commodus would be a just ruler; supposing him to\nstop there, he might only have been undeceived by sad experience. But if\nhe reflected that this expectation could not be justifiable unless from\nthe same evidence he was warranted in concluding some general\nproposition, as, for instance, that all Roman emperors are just rulers;\nhe would immediately have thought of Nero, Domitian, and other\ninstances, which, showing the falsity of the general conclusion, and\ntherefore the insufficiency of the premises, would have warned him that\nthose premises could not prove in the instance of Commodus, what they\nwere inadequate to prove in any collection of cases in which his was\nincluded.\n\nThe advantage, in judging whether any controverted inference is\nlegitimate, of referring to a parallel case, is universally\nacknowledged. But by ascending to the general proposition, we bring\nunder our view not one parallel case only, but all possible parallel\ncases at once; all cases to which the same set of evidentiary\nconsiderations 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,\nthis mode of stating the argument causes us to know or to suspect that\nthe original observations, which are the real grounds of our conclusion,\nare not sufficient to support it. And in proportion to the greater\nchance of our detecting the inconclusiveness of our evidence, will be\nthe increased reliance we are entitled to place in it if no such\nevidence of defect shall appear.\n\nThe value, therefore, of the syllogistic form, and of the rules for\nusing it correctly, does not consist in their being the form and the\nrules according to which our reasonings are necessarily, or even\nusually, made; but in their furnishing us with a mode in which those\nreasonings may always be represented, and which is admirably calculated,\nif they are inconclusive, to bring their inconclusiveness to light. An\ninduction from particulars to generals, followed by a syllogistic\nprocess from those generals to other particulars, is a form in which we\nmay always state our reasonings if we please. It is not a form in which\nwe _must_ reason, but it is a form in which we _may_ reason, and into\nwhich it is indispensable to throw our reasoning, when there is any\ndoubt of its validity: though when the case is familiar and little\ncomplicated, and there is no suspicion of error, we may, and do, reason\nat once from the known particular cases to unknown ones.[9]\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\nthis, that the inductions may be made once for all: a single careful\ninterrogation of experience may suffice, and the result may be\nregistered in the form of a general proposition, which is committed to\nmemory or to writing, and from which afterwards we have only to\nsyllogize. The particulars of our experiments may then be dismissed from\nthe memory, in which it would be impossible to retain so great a\nmultitude of details; while the knowledge which those details afforded\nfor future use, and which would otherwise be lost as soon as the\nobservations were forgotten, or as their record became too bulky for\nreference, is retained in a commodious and immediately available shape\nby means of general language.\n\nAgainst this advantage is to be set the countervailing inconvenience,\nthat inferences originally made on insufficient evidence, become\nconsecrated, and, as it were, hardened into general maxims; and the mind\ncleaves to them from habit, after it has outgrown any liability to be\nmisled by similar fallacious appearances if they were now for the first\ntime presented; but having forgotten the particulars, it does not think\nof revising its own former decision. An inevitable drawback, which,\nhowever considerable in itself, forms evidently but a small set-off\nagainst the immense benefits of general language.\n\nThe use of the syllogism is in truth no other than the use of general\npropositions in reasoning. We _can_ reason without them; in simple and\nobvious cases we habitually do so; minds of great sagacity can do it in\ncases not simple and obvious, provided their experience supplies them\nwith instances essentially similar to every combination of circumstances\nlikely to arise. But other minds, and the same minds where they have not\nthe same pre-eminent advantages of personal experience, are quite\nhelpless without the aid of general propositions, wherever the case\npresents the smallest complication; and if we made no general\npropositions, few persons would get much beyond those simple inferences\nwhich are drawn by the more intelligent of the brutes. Though not\nnecessary to reasoning, general propositions are necessary to any\nconsiderable progress in reasoning. It is, therefore, natural and\nindispensable to separate the process of investigation into two parts;\nand obtain general formul\u00e6 for determining what inferences may be drawn,\nbefore the occasion arises for drawing the inferences. The work of\ndrawing them is then that of applying the formul\u00e6; and the rules of\nsyllogism are a system of securities for the correctness of the\napplication.\n\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\nthe nature of the minor premise, and in what manner it contributes to\nestablish the conclusion: for as to the major, we now fully understand,\nthat the place which it nominally occupies in our reasonings, properly\nbelongs to the individual facts or observations of which it expresses\nthe general result; the major itself being no real part of the argument,\nbut an intermediate halting-place for the mind, interposed by an\nartifice of language between the real premises and the conclusion, by\nway of a security, which it is in a most material degree, for the\ncorrectness of the process. The minor, however, being an indispensable\npart of the syllogistic expression of an argument, without doubt either\nis, or corresponds to, an equally indispensable part of the argument\nitself, and we have only to inquire what part.\n\nIt is perhaps worth while to notice here a speculation of a philosopher\nto whom mental science is much indebted, but who, though a very\npenetrating, 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\nfact it is, an assertion of the existence of evidence sufficient to\nprove any conclusion of a given description. Seeing this, Dr. Brown not\nonly failed to see the immense advantage, in point of security for\ncorrectness, which is gained by interposing this step between the real\nevidence and the conclusion; but he thought it incumbent on him to\nstrike out the major altogether from the reasoning process, without\nsubstituting anything else, and maintained that our reasonings consist\nonly of the minor premise and the conclusion, Socrates is a man,\ntherefore Socrates is mortal: thus actually suppressing, as an\nunnecessary step in the argument, the appeal to former experience. The\nabsurdity of this was disguised from him by the opinion he adopted, that\nreasoning is merely analysing our own general notions, or abstract\nideas; and that the proposition, Socrates is mortal, is evolved from the\nproposition, Socrates is a man, simply by recognising the notion of\nmortality as already contained in the notion we form of a man.\n\nAfter the explanations so fully entered into on the subject of\npropositions, much further discussion cannot be necessary to make the\nradical error of this view of ratiocination apparent. If the word man\nconnoted mortality; if the meaning of \"mortal\" were involved in the\nmeaning of \"man;\" we might, undoubtedly, evolve the conclusion from the\nminor alone, because the minor would have already asserted it. But if,\nas is in fact the case, the word man does not connote mortality, how\ndoes it appear that in the mind of every person who admits Socrates to\nbe a man, the idea of man must include the idea of mortality? Dr. Brown\ncould not help seeing this difficulty, and in order to avoid it, was\nled, contrary to his intention, to re-establish, under another name,\nthat step in the argument which corresponds to the major, by affirming\nthe necessity of _previously perceiving_ the relation between the idea\nof man and the idea of mortal. If the reasoner has not previously\nperceived this relation, he will not, says Dr. Brown, infer because\nSocrates is a man, that Socrates is mortal. But even this admission,\nthough amounting to a surrender of the doctrine that an argument\nconsists of the minor and the conclusion alone, will not save the\nremainder of Dr. Brown's theory. The failure of assent to the argument\ndoes not take place merely because the reasoner, for want of due\nanalysis, does not perceive that his idea of man includes the idea of\nmortality; it takes place, much more commonly, because in his mind that\nrelation between the two ideas has never existed. And in truth it never\ndoes exist, except as the result of experience. Consenting, for the sake\nof the argument, to discuss the question on a supposition of which we\nhave recognised the radical incorrectness, namely, that the meaning of a\nproposition relates to the ideas of the things spoken of, and not to\nthe things themselves; I must yet observe, that the idea of man, as an\nuniversal idea, the common property of all rational creatures, cannot\ninvolve anything but what is strictly implied in the name. If any one\nincludes in his own private idea of man, as no doubt is always the case,\nsome other attributes, such for instance as mortality, he does so only\nas the consequence of experience, after having satisfied himself that\nall men possess that attribute: so that whatever the idea contains, in\nany person's mind, beyond what is included in the conventional\nsignification of the word, has been added to it as the result of assent\nto a proposition; while Dr. Brown's theory requires us to suppose, on\nthe contrary, that assent to the proposition is produced by evolving,\nthrough an analytic process, this very element out of the idea. This\ntheory, therefore, may be considered as sufficiently refuted; and the\nminor premise must be regarded as totally insufficient to prove the\nconclusion, except with the assistance of the major, or of that which\nthe major represents, namely, the various singular propositions\nexpressive of the series of observations, of which the generalization\ncalled the major premise is the result.\n\nIn the argument, then, which proves that Socrates is mortal, one\nindispensable part of the premises will be as follows: \"My father, and\nmy father's father, A, B, C, and an indefinite number of other persons,\nwere mortal;\" which is only an expression in different words of the\nobserved fact that they have died. This is the major premise divested of\nthe _petitio principii_, and cut down to as much as is really known by\ndirect evidence.\n\nIn order to connect this proposition with the conclusion Socrates is\nmortal, the additional link necessary is such a proposition as the\nfollowing: \"Socrates resembles my father, and my father's father, and\nthe other individuals specified.\" This proposition we assert when we say\nthat Socrates is a man. By saying so we likewise assert in what respect\nhe resembles them, namely, in the attributes connoted by the word man.\nAnd we conclude that he further resembles them in the attribute\nmortality.\n\n\n\u00a7 7. We have thus obtained what we were seeking, an universal type of\nthe reasoning process. We find it resolvable in all cases into the\nfollowing elements: Certain individuals have a given attribute; an\nindividual or individuals resemble the former in certain other\nattributes; therefore they resemble them also in the given attribute.\nThis type of ratiocination does not claim, like the syllogism, to be\nconclusive, from the mere form of the expression; nor can it possibly be\nso. That one proposition does or does not assert the very fact which was\nalready asserted in another, may appear from the form of the expression,\nthat is, from a comparison of the language; but when the two\npropositions assert facts which are _bon\u00e2 fide_ different, whether the\none fact proves the other or not can never appear from the language, but\nmust depend on other considerations. Whether, from the attributes in\nwhich Socrates resembles those men who have heretofore died, it is\nallowable to infer that he resembles them also in being mortal, is a\nquestion of Induction; and is to be decided by the principles or canons\nwhich we shall hereafter recognise as tests of the correct performance\nof that great mental operation.\n\nMeanwhile, however, it is certain, as before remarked, that if this\ninference can be drawn as to Socrates, it can be drawn as to all others\nwho resemble the observed individuals in the same attributes in which he\nresembles them; that is (to express the thing concisely) of all mankind.\nIf, therefore, the argument be admissible in the case of Socrates, we\nare at liberty, once for all, to treat the possession of the attributes\nof man as a mark, or satisfactory evidence, of the attribute of\nmortality. This we do by laying down the universal proposition, All men\nare mortal, and interpreting this, as occasion arises, in its\napplication to Socrates and others. By this means we establish a very\nconvenient division of the entire logical operation into two steps;\nfirst, that of ascertaining what attributes are marks of mortality; and,\nsecondly, whether any given individuals possess those marks. And it will\ngenerally be advisable, in our speculations on the reasoning process, to\nconsider this double operation as in fact taking place, and all\nreasoning as carried on in the form into which it must necessarily be\nthrown to enable us to apply to it any test of its correct performance.\n\nAlthough, therefore, all processes of thought in which the ultimate\npremises are particulars, whether we conclude from particulars to a\ngeneral formula, or from particulars to other particulars according to\nthat formula, are equally Induction: we shall yet, conformably to usage,\nconsider the name Induction as more peculiarly belonging to the process\nof establishing the general proposition, and the remaining operation,\nwhich is substantially that of interpreting the general proposition, we\nshall call by its usual name, Deduction. And we shall consider every\nprocess by which anything is inferred respecting an unobserved case, as\nconsisting of an Induction followed by a Deduction; because, although\nthe process needs not necessarily be carried on in this form, it is\nalways susceptible of the form, and must be thrown into it when\nassurance of scientific accuracy is needed and desired.\n\n\n\u00a7 8. The theory of the syllogism, laid down in the preceding pages, has\nobtained, among other important adhesions, three of peculiar value;\nthose of Sir John Herschel,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir\nJohn Herschel considering the doctrine, though not strictly \"a\ndiscovery,\"[13] to be \"one of the greatest steps which have yet been\nmade in the philosophy of Logic.\" \"When we consider\" (to quote the\nfurther words of the same authority) \"the inveteracy of the habits and\nprejudices which it has cast to the winds,\" there is no cause for\nmisgiving in the fact that other thinkers, no less entitled to\nconsideration, have formed a very different estimate of it. Their\nprincipal objection cannot be better or more succinctly stated than by\nborrowing a sentence from Archbishop Whately.[14] \"In every case where\nan inference is drawn from Induction (unless that name is to be given to\na mere random guess without any grounds at all) we must form a judgment\nthat the instance or instances adduced are _sufficient_ to authorize the\nconclusion; that it is _allowable_ to take these instances as a sample\nwarranting an inference respecting the whole class;\" and the expression\nof this judgment in words (it has been said by several of my critics)\n_is_ the major premise.\n\nI quite admit that the major is an affirmation of the sufficiency of the\nevidence on which the conclusion rests. That it is so, is the very\nessence of my own theory. And whoever admits that the major premise is\n_only_ this, adopts the theory in its essentials.\n\nBut I cannot concede that this recognition of the sufficiency of the\nevidence--that is, of the correctness of the induction--is a part of the\ninduction itself; unless we ought to say that it is a part of everything\nwe do, to satisfy ourselves that it has been done rightly. We conclude\nfrom known instances to unknown by the impulse of the generalizing\npropensity; and (until after a considerable amount of practice and\nmental discipline) the question of the sufficiency of the evidence is\nonly raised by a retrospective act, turning back upon our own footsteps,\nand examining whether we were warranted in doing what we have already\ndone. To speak of this reflex operation as part of the original one,\nrequiring to be expressed in words in order that the verbal formula may\ncorrectly represent the psychological process, appears to me false\npsychology.[15] We review our syllogistic as well as our inductive\nprocesses, and recognise that they have been correctly performed; but\nlogicians do not add a third premise to the syllogism, to express this\nact of recognition. A careful copyist verifies his transcript by\ncollating it with the original; and if no error appears, he recognises\nthat the transcript has been correctly made. But we do not call the\nexamination of the copy a part of the act of copying.\n\nThe conclusion in an induction is inferred from the evidence itself, and\nnot from a recognition of the sufficiency of the evidence; as I infer\nthat my friend is walking towards me because I see him, and not because\nI recognise that my eyes are open, and that eyesight is a means of\nknowledge. In all operations which require care, it is good to assure\nourselves that the process has been performed accurately; but the\ntesting of the process is not the process itself; and, besides, may have\nbeen omitted altogether, and yet the process be correct. It is precisely\nbecause that operation is omitted in ordinary unscientific reasoning,\nthat there is anything gained in certainty by throwing reasoning into\nthe syllogistic form. To make sure, as far as possible, that it shall\nnot be omitted, we make the testing operation a part of the reasoning\nprocess itself. We insist that the inference from particulars to\nparticulars shall pass through a general proposition. But this is a\nsecurity for good reasoning, not a condition of all reasoning; and in\nsome cases not even a security. Our most familiar inferences are all\nmade before we learn the use of general propositions; and a person of\nuntutored sagacity will skilfully apply his acquired experience to\nadjacent cases, though he would bungle grievously in fixing the limits\nof the appropriate general theorem. But though he may conclude rightly,\nhe never, properly speaking, knows whether he has done so or not; he has\nnot tested his reasoning. Now, this is precisely what forms of reasoning\ndo for us. We do not need them to enable us to reason, but to enable us\nto know whether we reason correctly.\n\nIn still further answer to the objection, it may be added that, even\nwhen the test has been applied, and the sufficiency of the evidence\nrecognised,--if it is sufficient to support the general proposition, it\nis sufficient also to support an inference from particulars to\nparticulars without passing through the general proposition. The\ninquirer who has logically satisfied himself that the conditions of\nlegitimate induction were realized in the cases A, B, C, would be as\nmuch justified in concluding directly to the Duke of Wellington as in\nconcluding to all men. The general conclusion is never legitimate,\nunless the particular one would be so too; and in no sense, intelligible\nto me, can the particular conclusion be said to be drawn from the\ngeneral one. Whenever there is ground for drawing any conclusion at all\nfrom particular instances, there is ground for a general conclusion; but\nthat this general conclusion should be actually drawn, however useful,\ncannot be an indispensable condition of the validity of the inference in\nthe particular case. A man gives away sixpence by the same power by\nwhich he disposes of his whole fortune; but it is not necessary to the\nlegality of the smaller act, that he should make a formal assertion of\nhis right to the greater one.\n\nSome additional remarks, in reply to minor objections, are appended.[16]\n\n\n\u00a7 9. The preceding considerations enable us to understand the true\nnature of what is termed, by recent writers, Formal Logic, and the\nrelation between it and Logic in the widest sense. Logic, as I conceive\nit, is the entire theory of the ascertainment of reasoned or inferred\ntruth. Formal Logic, therefore, which Sir William Hamilton from his own\npoint of view, and Archbishop Whately from his, have represented as the\nwhole of Logic properly so called, is really a very subordinate part of\nit, not being directly concerned with the process of Reasoning or\nInference in the sense in which that process is a part of the\nInvestigation of Truth. What, then, is Formal Logic? The name seems to\nbe properly applied to all that portion of doctrine which relates to the\nequivalence of different modes of expression; the rules for determining\nwhen assertions in a given form imply or suppose the truth or falsity of\nother assertions. This includes the theory of the Import of\nPropositions, and of their Conversion, \u00c6quipollence, and Opposition; of\nthose falsely called Inductions (to be hereafter spoken of[17]), in\nwhich the apparent generalization is a mere abridged statement of cases\nknown individually; and finally, of the syllogism: while the theory of\nNaming, and of (what is inseparably connected with it) Definition,\nthough belonging still more to the other and larger kind of logic than\nto this, is a necessary preliminary to this. The end aimed at by Formal\nLogic, and attained by the observance of its precepts, is not truth, but\nconsistency. It has been seen that this is the only direct purpose of\nthe rules of the syllogism; the intention and effect of which is simply\nto keep our inferences or conclusions in complete consistency with our\ngeneral formul\u00e6 or directions for drawing them. The Logic of Consistency\nis a necessary auxiliary to the logic of truth, not only because what is\ninconsistent with itself or with other truths cannot be true, but also\nbecause truth can only be successfully pursued by drawing inferences\nfrom experience, which, if warrantable at all, admit of being\ngeneralized, and, to test their warrantableness, require to be exhibited\nin a generalized form; after which the correctness of their application\nto particular cases is a question which specially concerns the Logic of\nConsistency. This Logic, not requiring any preliminary knowledge of the\nprocesses or conclusions of the various sciences, may be studied with\nbenefit in a much earlier stage of education than the Logic of Truth:\nand the practice which has empirically obtained of teaching it apart,\nthrough elementary treatises which do not attempt to include anything\nelse, though the reasons assigned for the practice are in general very\nfar from philosophical, admits of a philosophical justification.\n\n\n\n\nCHAPTER IV.\n\nOF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.\n\n\n\u00a7 1. In our analysis of the syllogism, it appeared that the minor\npremise always affirms a resemblance between a new case and some cases\npreviously known; while the major premise asserts something which,\nhaving been found true of those known cases, we consider ourselves\nwarranted in holding true of any other case resembling the former in\ncertain given particulars.\n\nIf all ratiocinations resembled, as to the minor premise, the examples\nwhich were exclusively employed in the preceding chapter; if the\nresemblance, which that premise asserts, were obvious to the senses, as\nin the proposition \"Socrates is a man,\" 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\nnot only cannot directly observe what is to be proved, but cannot\ndirectly observe even the mark which is to prove it.\n\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,\nis obviously so: the only premise the establishment of which requires\nany anterior process of inquiry, is the major; and provided the\ninduction of which that premise is the expression was correctly\nperformed, the conclusion respecting the animal now present will be\ninstantly drawn; because, as soon as she is compared with the formula,\nshe will be identified as being included in it. But suppose the\nsyllogism to be the following:--All arsenic is poisonous, the substance\nwhich is before me is arsenic, therefore it is poisonous. The truth of\nthe minor may not here be obvious at first sight; it may not be\nintuitively evident, but may itself be known only by inference. It may\nbe the conclusion of another argument, which, thrown into the\nsyllogistic form, would stand thus:--Whatever when lighted produces a\ndark spot on a piece of white porcelain held in the flame, which spot is\nsoluble in hypochlorite of calcium, is arsenic; the substance before me\nconforms to this condition; therefore it is arsenic. To establish,\ntherefore, the ultimate conclusion, The substance before me is\npoisonous, requires a process, which, in order to be syllogistically\nexpressed, stands in need of two syllogisms; and we have a Train of\nReasoning.\n\nWhen, however, we thus add syllogism to syllogism, we are really adding\ninduction to induction. Two separate inductions must have taken place to\nrender this chain of inference possible; inductions founded, probably,\non different sets of individual instances, but which converge in their\nresults, so that the instance which is the subject of inquiry comes\nwithin the range of them both. The record of these inductions is\ncontained in the majors of the two syllogisms. First, we, or others for\nus, have examined various objects which yielded under the given\ncircumstances a dark spot with the given property, and found that they\npossessed the properties connoted by the word arsenic; they were\nmetallic, volatile, their vapour had a smell of garlic, and so forth.\nNext, we, or others for us, have examined various specimens which\npossessed this metallic and volatile character, whose vapour had this\nsmell, &c., and have invariably found that they were poisonous. The\nfirst observation we judge that we may extend to all substances whatever\nwhich yield that particular kind of dark spot; 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\nnot, as in the simple case, _seen_ to resemble them in the material\npoints, but _inferred_ to do so, because resembling them in something\nelse, which we have been led by quite a different set of instances to\nconsider as a mark of the former resemblance.\n\nThis first example of a train of reasoning is still extremely simple,\nthe series consisting of only two syllogisms. The following is somewhat\nmore complicated:--No government, which earnestly seeks the good of its\nsubjects, is likely to be overthrown; some particular government\nearnestly seeks the good of its subjects, therefore it is not likely to\nbe overthrown. The major premise in this argument we shall suppose not\nto be derived from considerations _\u00e0 priori_, but to be a generalization\nfrom history, which, whether correct or erroneous, must have been\nfounded on observation of governments concerning whose desire of the\ngood of their subjects there was no doubt. It has been found, or thought\nto be found, that these were not easily overthrown, and it has been\ndeemed that those instances warranted an extension of the same predicate\nto any and every government which resembles them in the attribute of\ndesiring earnestly the good of its subjects. But _does_ the government\nin question thus resemble them? This may be debated _pro_ and _con_ by\nmany arguments, and must, in any case, be proved by another induction;\nfor we cannot directly observe the sentiments and desires of the persons\nwho carry on the government. To prove the minor, therefore, we require\nan argument in this form: Every government which acts in a certain\nmanner, desires the good of its subjects; the supposed government acts\nin that particular manner, therefore it desires the good of its\nsubjects. But is it true that the government acts in the manner\nsupposed? This minor also may require proof; still another induction, as\nthus:--What is asserted by intelligent and disinterested witnesses, may\nbe believed to be true; that the government acts in this manner, is\nasserted by such witnesses, therefore it may be believed to be true. The\nargument hence consists of three steps. Having the evidence of our\nsenses that the case of the government under consideration resembles a\nnumber of former cases, in the circumstance of having something asserted\nrespecting it by intelligent and disinterested witnesses, we infer,\nfirst, that, as in those former instances, so in this instance, the\nassertion is true. Secondly, what was asserted of the government being\nthat it acts in a particular manner, and other governments or persons\nhaving been observed to act in the same manner, the government in\nquestion is brought into known resemblance with those other governments\nor persons; and since they were known to desire the good of the people,\nit is thereupon, by a second induction, inferred that the particular\ngovernment spoken of, desires the good of the people. This brings that\ngovernment into known resemblance with the other governments which were\nthought likely to escape revolution, and thence, by a third induction,\nit is concluded that this particular government is also likely to\nescape. 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\nperceive the new one to be similar; but from that similarity we\ninductively infer that it has the attribute by which it is assimilated\nto the next set, and brought within the corresponding induction; after\nwhich by a repetition of the same operation we infer it to be similar to\nthe third set, and hence a third induction conducts us to the ultimate\nconclusion.\n\n\n\u00a7 3. Notwithstanding the superior complication of these examples,\ncompared with those by which in the preceding chapter we illustrated the\ngeneral theory of reasoning, every doctrine which we then laid down\nholds equally true in these more intricate cases. The successive general\npropositions are not steps in the reasoning, are not intermediate links\nin the chain of inference, between the particulars observed and those to\nwhich we apply the observation. If we had sufficiently capacious\nmemories, and a sufficient power of maintaining order among a huge mass\nof details, the reasoning could go on without any general propositions;\nthey are mere formul\u00e6 for inferring particulars from particulars. The\nprinciple of general reasoning is (as before explained), that if from\nobservation of certain known particulars, what was seen to be true of\nthem can be inferred to be true of any others, it may be inferred of all\nothers which are of a certain description. And in order that we may\nnever fail to draw this conclusion in a new case when it can be drawn\ncorrectly, and may avoid drawing it when it cannot, we determine once\nfor all what are the distinguishing marks by which such cases may be\nrecognised. The subsequent process is merely that of identifying an\nobject, and ascertaining it to have those marks; whether we identify it\nby the very marks themselves, or by others which we have ascertained\n(through another and a similar process) to be marks of those marks. The\nreal inference is always from particulars to particulars, from the\nobserved instances to an unobserved one: but in drawing this inference,\nwe conform to a formula which we have adopted for our guidance in such\noperations, and which is a record of the criteria by which we thought we\nhad ascertained that we might distinguish when the inference could, and\nwhen it could not, be drawn. The real premises are the individual\nobservations, even though they may have been forgotten, or, being the\nobservations of others and not of ourselves, may, to us, never have been\nknown: but we have before us proof that we or others once thought them\nsufficient for an induction, and we have marks to show whether any new\ncase is one of those to which, if then known, the induction would have\nbeen deemed to extend. These marks we either recognise at once, or by\nthe aid of other marks, which by another previous induction we collected\nto be marks of the first. Even these marks of marks may only be\nrecognised through a third set of marks; and we may have a train of\nreasoning, of any length, to bring a new case within the scope of an\ninduction 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,\nthat a certain government was not likely to be overthrown; this\ninference was drawn according to a formula in which desire of the public\ngood was set down as a mark of not being likely to be overthrown; a mark\nof this mark was, acting in a particular manner; and a mark of acting in\nthat manner was, being asserted to do so by intelligent and\ndisinterested witnesses: this mark, the government under discussion was\nrecognised by the senses as possessing. Hence that government fell\nwithin the last induction, and by it was brought within all the others.\nThe perceived resemblance of the case to one set of observed particular\ncases, brought it into known resemblance with another set, and that with\na third.\n\nIn the more complex branches of knowledge, the deductions seldom\nconsist, as in the examples hitherto exhibited, of a single chain, _a_ a\nmark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They\nconsist (to carry on the same metaphor) of several chains united at the\nextremity, as thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_\nof _n_, therefore _a b c_ a mark of _n_. Suppose, for example, the\nfollowing combination of circumstances; 1st, rays of light impinging on\na reflecting surface; 2nd, that surface parabolic; 3rd, those rays\nparallel to each other and to the axis of the surface. It is to be\nproved that the concourse of these three circumstances is a mark that\nthe reflected rays will pass through the focus of the parabolic surface.\nNow, each of the three circumstances is singly a mark of something\nmaterial to the case. Rays of light impinging on a reflecting surface,\nare a mark that those rays will be reflected at an angle equal to the\nangle of incidence. The parabolic form of the surface is a mark that,\nfrom any point of it, a line drawn to the focus and a line parallel to\nthe axis will make equal angles with the surface. And finally, the\nparallelism of the rays to the axis is a mark that their angle of\nincidence coincides with one of these equal angles. The three marks\ntaken together are therefore a mark of all these three things united.\nBut the three united are evidently a mark that the angle of reflection\nmust coincide with the other of the two equal angles, that formed by a\nline drawn to the focus; and this again, by the fundamental axiom\nconcerning 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: \"_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,\" &c.\n\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 reconcileable 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\ngenius in those who contributed to its creation, and calling for a most\ncontinued and vigorous exertion of intellect in order to appropriate it\nwhen created, may seem hard to be accounted for on the foregoing theory.\nBut the considerations more recently adduced remove the mystery, by\nshowing, that even when the inductions themselves are obvious, there may\nbe much difficulty in finding whether the particular case which is the\nsubject of inquiry comes within them; and ample room for scientific\ningenuity in so combining various inductions, as, by means of one within\nwhich the case evidently falls, to bring it within others in which it\ncannot be directly seen 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\none of 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\ngeometry: and as it is taken only for illustration, let the reader\nconcede to us for the present, what we shall endeavour to prove in the\nnext chapter, that the first principles of geometry are results of\ninduction. Our example shall be the fifth proposition of the first book\nof Euclid. The inquiry is, Are the angles at the base of an isosceles\ntriangle equal or unequal? The first thing to be considered is, what\ninductions we have, from which we can infer equality or inequality. For\ninferring equality we have the following formul\u00e6:--Things which being\napplied to each other coincide, are equals. Things which are equal to\nthe same thing are equals. A whole and the sum of its parts are equals.\nThe sums of equal things are equals. The differences of equal things are\nequals. There are no other original formul\u00e6 to prove equality. For\ninferring inequality we have the following:--A whole and its parts are\nunequals. The sums of equal things and unequal things are unequals. The\ndifferences of equal things and unequal things are unequals. In all,\neight formul\u00e6. The angles at the base of an isosceles triangle do not\nobviously come within any of these. The formul\u00e6 specify certain marks of\nequality and of inequality, but the angles cannot be perceived\nintuitively to have any of those marks. On examination it appears that\nthey have; and we ultimately succeed in bringing them within the\nformula, \"The differences of equal things are equal.\" Whence comes the\ndifficulty of recognising these angles as the differences of equal\nthings? Because each of them is the difference not of one pair only, but\nof innumerable pairs of angles; and out of these we had to imagine and\nselect two, which could either be intuitively perceived to be equals, or\npossessed some of the marks of equality set down in the various formul\u00e6.\nBy an exercise of ingenuity, which, on the part of the first inventor,\ndeserves to be regarded as considerable, two pairs of angles were hit\nupon, which united these requisites. First, it could be perceived\nintuitively that their differences were the angles at the base; and,\nsecondly, they possessed one of the marks of equality, namely,\ncoincidence when applied to one another. This coincidence, however, was\nnot perceived intuitively, but inferred, in conformity to another\nformula.\n\nFor greater clearness, I subjoin an analysis of the demonstration.\nEuclid, it will be remembered, demonstrates his fifth proposition by\nmeans of the fourth. This it is not allowable for us to do, because we\nare undertaking to trace deductive truths not to prior deductions, but\nto their original inductive foundation. We must therefore use the\npremises of the fourth proposition instead of its conclusion, and prove\nthe fifth directly from first principles. To do so requires six\nformulas. (We must begin, as in Euclid, by prolonging the equal sides\nAB, AC, to equal distances, and joining the extremities BE, DC.)\n\n[Illustration]\n\nFIRST FORMULA. _The sums of equals are equal._\n\nAD and AE are sums of equals by the supposition. Having that mark of\nequality, they are concluded by this formula to be equal.\n\nSECOND FORMULA. _Equal straight lines being applied to one another\ncoincide._\n\nAC, AB, are within this formula by supposition; AD, AE, 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\nBE and CD 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 BE and CD coincide, and the second\nthat AB, AC, coincide, the angles ABE and ACD are thereby brought within\nthe fourth formula, and accordingly coincide.\n\nFIFTH FORMULA. _Things which coincide are equal._\n\nThe angles ABE and ACD are brought within this formula by the induction\nimmediately preceding. This train of reasoning being also applicable,\n_mutatis mutandis_, to the angles EBC, DCB, these also are brought\nwithin the fifth formula. And, finally,\n\nSIXTH FORMULA. _The differences of equals are equal._\n\nThe angle ABC being the difference of ABE, CBE, and the angle ACB being\nthe difference of ACD, DCB; which have been proved to be equals; ABC and\nACB are brought within the last formula by the whole of the previous\nprocess.\n\nThe difficulty here encountered is chiefly that of figuring to ourselves\nthe two angles at the base of the triangle ABC as remainders made by\ncutting one pair of angles out of another, while each pair shall be\ncorresponding angles of triangles which have two sides and the\nintervening angle equal. It is by this happy contrivance that so many\ndifferent inductions are brought to bear upon the same particular case.\nAnd this not being at all an obvious thought, it may be seen from an\nexample so near the threshold of mathematics, how much scope there may\nwell be for scientific dexterity in the higher branches of that and\nother sciences, in order so to combine a few simple inductions, as to\nbring within each of them innumerable cases which are not obviously\nincluded in it; and how long, and numerous, and complicated may be the\nprocesses necessary for bringing the inductions together, even when each\ninduction may itself be very easy and simple. All the inductions\ninvolved in all geometry are comprised in those simple ones, the formul\u00e6\nof which are the Axioms, and a few of the so-called Definitions. The\nremainder of the science is made up of the processes employed for\nbringing unforeseen cases within these inductions; or (in syllogistic\nlanguage) for proving the minors necessary to complete the syllogisms;\nthe majors being the definitions and axioms. In those definitions and\naxioms are laid down the whole of the marks, by an artful combination of\nwhich it has been found possible to discover and prove all that is\nproved in geometry. The marks being so few, and the inductions which\nfurnish them being so obvious and familiar; the connecting of several of\nthem together, which constitutes Deductions, or Trains of Reasoning,\nforms the whole difficulty of the science, and with a trifling\nexception, its whole bulk; and hence Geometry is a Deductive Science.\n\n\n\u00a7 5. It will be seen hereafter[18] that there are weighty scientific\nreasons for giving to every science as much of the character of a\nDeductive Science as possible; for endeavouring to construct the science\nfrom the fewest and the simplest possible inductions, and to make these,\nby any combinations however complicated, suffice for proving even such\ntruths, relating to complex cases, as could be proved, if we chose, by\ninductions from specific experience. Every branch of natural philosophy\nwas originally experimental; each generalization rested on a special\ninduction, and was derived from its own distinct set of observations and\nexperiments. From being sciences of pure experiment, as the phrase is,\nor, to speak more correctly, sciences in which the reasonings mostly\nconsist of no more than one step, and are expressed by single\nsyllogisms, all these sciences have become to some extent, and some of\nthem in nearly the whole of their extent, sciences of pure reasoning;\nwhereby multitudes of truths, already known by induction from as many\ndifferent sets of experiments, have come to be exhibited as deductions\nor corollaries from inductive propositions of a simpler and more\nuniversal character. Thus mechanics, hydrostatics, optics, acoustics,\nthermology, have successively been rendered mathematical; and astronomy\nwas brought by Newton within the laws of general mechanics. Why it is\nthat the substitution of this circuitous mode of proceeding for a\nprocess apparently much easier and more natural, is held, and justly, to\nbe the greatest triumph of the investigation of nature, we are not, in\nthis stage of our inquiry, prepared to examine. But it is necessary to\nremark, that although, by this progressive transformation, all sciences\ntend to become more and more Deductive, they are not, therefore, the\nless Inductive; every step in the Deduction is still an Induction. The\nopposition is not between the terms Deductive and Inductive, but between\nDeductive and Experimental. A science is experimental, in proportion as\nevery new case, which presents any peculiar features, stands in need of\na new set of observations and experiments--a fresh induction. It is\ndeductive, in proportion as it can draw conclusions, respecting cases of\na new kind, by processes which bring those cases under old inductions;\nby ascertaining that cases which cannot be observed to have the\nrequisite marks, have, however, marks of those marks.\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\nyet able, to discover marks of marks. If by our various inductions we\nhave been able to proceed no further than to such propositions as these,\n_a_ a mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of\n_d_, or _c_ and _d_ marks of one another, without anything to connect\n_a_ or _b_ with _c_ or _d_; we have a science of detached and mutually\nindependent generalizations, such as these, that acids redden vegetable\nblues, and that alkalies colour them green; from neither of which\npropositions could we, directly or indirectly, infer the other: and a\nscience, so far as it is composed of such propositions, is purely\nexperimental. Chemistry, in the present state of our knowledge, has not\nyet thrown off this character. There are other sciences, however, of\nwhich the propositions are of this kind: _a_ a mark of _b_, _b_ a mark\nof _c_, _c_ of _d_, _d_ of _e_, &c. In these sciences we can mount the\nladder from _a_ to _e_ by a process of ratiocination; we can conclude\nthat _a_ is a mark of _e_, and that every object which has the mark _a_\nhas the property _e_, although, perhaps, we never were able to observe\n_a_ and _e_ together, and although even _d_, our only direct mark of\n_e_, may not be perceptible in those objects, but only inferrible. Or,\nvarying the first metaphor, we may be said to get from _a_ to _e_\nunderground: the marks _b_, _c_, _d_, which indicate the route, must all\nbe possessed somewhere by the objects concerning which we are inquiring;\nbut they are below the surface: _a_ is the only mark that is visible,\nand by it we are able to trace in succession all the rest.\n\n\n\u00a7 6. We can now understand how an experimental may transform itself into\na deductive science by the mere progress of experiment. In an\nexperimental science, the inductions, as we have said, lie detached, as,\n_a_ a mark of _b_, _c_ a mark of _d_, _e_ a mark of _f_, and so on: now,\na new set of instances, and a consequent new induction, may at any time\nbridge over the interval between two of these unconnected arches; _b_,\nfor example, may be ascertained to be a mark of _c_, which enables us\nthenceforth to prove deductively that _a_ is a mark of _c_. Or, as\nsometimes happens, some comprehensive induction may raise an arch high\nin the air, which bridges over hosts of them at once: _b_, _d_, _f_, and\nall the rest, turning out to be marks of some one thing, or of things\nbetween which a connexion has already been traced. As when Newton\ndiscovered that the motions, whether regular or apparently anomalous, of\nall the bodies of the solar system, (each of which motions had been\ninferred by a separate logical operation, from separate marks,) were all\nmarks of moving round a common centre, with a centripetal force varying\ndirectly as the mass, and inversely as the square of the distance from\nthat centre. This is the greatest example which has yet occurred of the\ntransformation, at one stroke, of a science which was still to a great\ndegree merely experimental, into a deductive science.\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\nby Liebig, that all blue colouring matters which are reddened by acids\n(as well as, reciprocally, all red colouring matters which are rendered\nblue by 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 antagonistic action of\nacids and alkalies in producing or destroying the colour blue, is the\nresult of some one, more general, law. Although this connecting of\ndetached generalizations is so much gain, it tends but little to give a\ndeductive character to any science as a whole; because the new courses\nof observation and experiment, which thus enable us to connect together\na few general 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,\nwhich, like Newton's, shall connect a vast number of the smaller known\ninductions together, and change the whole method of the science at once.\nChemistry has already one great generalization, which, though relating\nto one of the subordinate aspects of chemical phenomena, possesses\nwithin its limited sphere this comprehensive character; the principle of\nDalton, called the atomic theory, or the doctrine of chemical\nequivalents: which by enabling us to a certain extent to foresee the\nproportions in which two substances will combine, before the experiment\nhas been tried, constitutes undoubtedly a source of new chemical truths\nobtainable by deduction, as well as a connecting principle for all\ntruths of the same description previously obtained by experiment.\n\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\ncoexistence which obtained between phenomena of the more known class,\nobtained also between the phenomena which corresponded to them in the\nother class. Every sound, being a mark of a particular oscillatory\nmotion, became a mark of everything which, by the laws of dynamics, was\nknown to be inferrible from that motion; and everything which by those\nsame laws was a mark of any oscillatory motion among the particles of an\nelastic medium, became a mark of the corresponding sound. And thus many\ntruths, not before suspected, concerning sound, become deducible from\nthe known laws of the propagation of motion through an elastic medium;\nwhile facts already empirically known respecting sound, become an\nindication of corresponding properties of vibrating bodies, previously\nundiscovered.\n\nBut the grand agent for transforming experimental into deductive\nsciences, is the science of number. The properties of numbers, alone\namong all known phenomena, are, in the most rigorous sense, properties\nof all things whatever. All things are not coloured, or ponderable, or\neven extended; but all things are numerable. And if we consider this\nscience in its whole extent, from common arithmetic up to the calculus\nof variations, the truths already ascertained seem all but infinite, and\nadmit of indefinite extension.\n\nThese truths, though affirmable of all things whatever, of course apply\nto them only in respect of their quantity. But if it comes to be\ndiscovered that variations of quality in any class of phenomena,\ncorrespond regularly to variations of quantity either in those same or\nin some other phenomena; every formula of mathematics applicable to\nquantities which vary in that particular manner, becomes a mark of a\ncorresponding general truth respecting the variations in quality which\naccompany them: and the science of quantity being (as far as any science\ncan be) altogether deductive, the theory of that particular kind of\nqualities becomes, to this extent, deductive 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\nmathematicians pointed out the importance of the fact, that to every\nvariety of position in points, direction in lines, or form in curves or\nsurfaces (all of which are Qualities), there corresponds a peculiar\nrelation of quantity between either two or three rectilineal\nco-ordinates; insomuch that if the law were known according to which\nthose co-ordinates vary relatively to one another, every other\ngeometrical property of the line or surface in question, whether\nrelating to quantity or quality, would be capable of being inferred.\nHence it followed that every geometrical question could be solved, if\nthe corresponding algebraical one could; and geometry received an\naccession (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\nphysical phenomena with which those sciences are conversant, have been\nfound to answer to determinable varieties in the quantity of some\ncircumstance or other; or at least to varieties of form or position, for\nwhich corresponding equations of quantity had already been, or were\nsusceptible of 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 facts 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 vers\u00e2_, 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\na mark of it.\n\n\n\n\nCHAPTER V.\n\nOF DEMONSTRATION, AND NECESSARY TRUTHS.\n\n\n\u00a7 1. If, as laid down in the two preceding chapters, the foundation of\nall sciences, even deductive or demonstrative sciences, is Induction; if\nevery step in the ratiocinations even of geometry is an act of\ninduction; and if a train of reasoning is but bringing many inductions\nto bear upon the same subject of inquiry, and drawing a case within one\ninduction by means of another; wherein lies the peculiar certainty\nalways ascribed to the sciences which are entirely, or almost entirely,\ndeductive? Why are they called the Exact Sciences? Why are mathematical\ncertainty, and the evidence of demonstration, common phrases to express\nthe very highest degree of assurance attainable by reason? Why are\nmathematics by almost all philosophers, and (by some) even those\nbranches of natural philosophy which, through the medium of mathematics,\nhave been converted into deductive sciences, considered to be\nindependent of the evidence of experience and observation, and\ncharacterized as systems of Necessary Truth?\n\nThe answer I conceive to be, that this character of necessity, ascribed\nto the truths of mathematics, and even (with some reservations to be\nhereafter made) the peculiar certainty attributed to them, is an\nillusion; in order to sustain which, it is necessary to suppose that\nthose truths relate to, and express the properties of, purely imaginary\nobjects. It is acknowledged that the conclusions of geometry are\ndeduced, partly at least, from the so-called Definitions, and that those\ndefinitions are assumed to be correct representations, as far as they\ngo, of the objects with which geometry is conversant. Now we have\npointed out that, from a definition as such, no proposition, unless it\nbe one concerning the meaning of a word, can ever follow; and that what\napparently follows from a definition, follows in reality from an\nimplied assumption that there exists a real thing conformable thereto.\nThis assumption, in the case of the definitions of geometry, is false:\nthere exist no real things exactly conformable to the definitions. There\nexist no points without magnitude; no lines without breadth, nor\nperfectly straight; no circles with all their radii exactly equal, nor\nsquares with all their angles perfectly right. It will perhaps be said\nthat the assumption does not extend to the actual, but only to the\npossible, existence of such things. I answer that, according to any test\nwe have of possibility, they are not even possible. Their existence, so\nfar as we can form any judgment, would seem to be inconsistent with the\nphysical constitution of our planet at least, if not of the universe. To\nget rid of this difficulty, and at the same time to save the credit of\nthe supposed system of necessary truth, it is customary to say that the\npoints, lines, circles, and squares which are the subject of geometry,\nexist in our conceptions merely, and are part of our minds; which minds,\nby working on their own materials, construct an _\u00e0 priori_ science, the\nevidence of which is purely mental, and has nothing whatever to do with\noutward experience. By howsoever high authorities this doctrine may have\nbeen sanctioned, it appears to me psychologically incorrect. The points,\nlines, circles, and squares, which any one has in his mind, are (I\napprehend) simply copies of the points, lines, circles, and squares\nwhich he has known in his experience. Our idea of a point, I apprehend\nto be simply our idea of the _minimum visibile_, the smallest portion of\nsurface which we can see. A line, as defined by geometers, is wholly\ninconceivable. We can reason about a line as if it had no breadth;\nbecause we have a power, which is the foundation of all the control we\ncan exercise over the operations of our minds; the power, when a\nperception is present to our senses, or a conception to our intellects,\nof _attending_ to a part only of that perception or conception, instead\nof the whole. But we cannot _conceive_ a line without breadth; we can\nform no mental picture of such a line: all the lines which we have in\nour minds are lines possessing breadth. If any one doubts this, we may\nrefer him to his own experience. I much question if any one who fancies\nthat he can conceive what is called a mathematical line, thinks so from\nthe evidence of his consciousness: I suspect it is rather because he\nsupposes that unless such a conception were possible, mathematics could\nnot exist as a science: a supposition which there will be no difficulty\nin showing to be entirely groundless.\n\nSince, then, neither in nature, nor in the human mind, do there exist\nany objects exactly corresponding to the definitions of geometry, while\nyet that 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\nthose generalizations, as generalizations, is without a flaw: the\nequality of all the radii of a circle is true of all circles, so far as\nit is true of any one: but it is not exactly true of any circle; it is\nonly nearly true; so nearly that no error of any importance in practice\nwill be incurred by feigning it to be exactly true. When we have\noccasion to extend these inductions, or their consequences, to cases in\nwhich the error would be appreciable--to lines of perceptible breadth or\nthickness, parallels which deviate sensibly from equidistance, and the\nlike--we correct our conclusions, by combining with them a fresh set of\npropositions relating to the aberration; just as we also take in\npropositions relating to the physical or chemical properties of the\nmaterial, if those properties happen to introduce any modification into\nthe result; which they easily may, even with respect to figure and\nmagnitude, as in the case, for instance, of expansion by heat. So long,\nhowever, as there exists no practical necessity for attending to any of\nthe properties of the object except its geometrical properties, or to\nany of the natural irregularities in those, it is convenient to neglect\nthe consideration of the other properties and of the irregularities, and\nto reason as if these did not exist: accordingly, we formally announce\nin the definitions, that we intend to proceed on this plan. But it is\nan error to suppose, because we resolve to confine our attention to a\ncertain number of the properties of an object, that we therefore\nconceive, or have an idea of, the object, denuded of its other\nproperties. We are thinking, all the time, of precisely such objects as\nwe have seen and touched, and with all the properties which naturally\nbelong to them; but, for scientific convenience, we feign them to be\ndivested of all properties, except those which are material to our\npurpose, and in regard to which we design to consider them.\n\nThe peculiar accuracy, supposed to be characteristic of the first\nprinciples of geometry, thus appears to be fictitious. The assertions on\nwhich the reasonings of the science are founded, do not, any more than\nin other sciences, exactly correspond with the fact; but we suppose that\nthey do so, for the sake of tracing the consequences which follow from\nthe supposition. The opinion of Dugald Stewart respecting the\nfoundations of geometry, is, I conceive, substantially correct; that it\nis built on hypotheses; that it owes to this alone the peculiar\ncertainty supposed to distinguish it; and that in any science whatever,\nby reasoning from a set of hypotheses, we may obtain a body of\nconclusions as certain as those of geometry, that is, as strictly in\naccordance with the hypotheses, and as irresistibly compelling assent,\n_on condition_ that those hypotheses are true.\n\nWhen, therefore, it is affirmed that the conclusions of geometry are\nnecessary truths, the necessity consists in reality only in this, that\nthey correctly follow from the suppositions from which they are deduced.\nThose suppositions are so far from being necessary, that they are not\neven true; they purposely depart, more or less widely, from the truth.\nThe only sense in which necessity can be ascribed to the conclusions of\nany scientific investigation, is that of legitimately following from\nsome assumption, 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\n\u00a7 2. The important doctrine of Dugald Stewart, which I have endeavoured\nto enforce, has been contested by Dr. Whewell, both in the dissertation\nappended to his excellent _Mechanical Euclid_, and in his elaborate work\non the _Philosophy of the Inductive Sciences_; in which last he also\nreplies to an article in the Edinburgh Review, (ascribed to a writer of\ngreat scientific eminence), in which Stewart's opinion was defended\nagainst his former strictures. The supposed refutation of Stewart\nconsists in proving against him (as has also been done in this work)\nthat the premises of geometry are not definitions, but assumptions of\nthe real existence of things corresponding to those definitions. This,\nhowever, is doing little for Dr. Whewell's purpose; for it is these very\nassumptions which are asserted to be hypotheses, and which he, if he\ndenies that geometry is founded on hypotheses, must show to be absolute\ntruths. All he does, however, is to observe, that they at any rate, are\nnot _arbitrary_ hypotheses; that we should not be at liberty to\nsubstitute other hypotheses for them; that not only \"a definition, to be\nadmissible, must necessarily refer to and agree with some conception\nwhich we can distinctly frame in our thoughts,\" but that the straight\nlines, for instance, which we define, must be \"those by which angles are\ncontained, those by which triangles are bounded, those of which\nparallelism may be predicated, and the like.\"[19] And this is true; but\nthis has never been contradicted. Those who say that the premises of\ngeometry are hypotheses, are not bound to maintain them to be hypotheses\nwhich have no relation whatever to fact. Since an hypothesis framed for\nthe purpose of scientific inquiry must relate to something which has\nreal existence, (for there can be no science respecting non-entities,)\nit follows that any hypothesis we make respecting an object, to\nfacilitate our study of it, must not involve anything which is\ndistinctly false, and repugnant to its real nature: we must not ascribe\nto the thing any property which it has not; our liberty extends only to\nslightly exaggerating some of those which it has, (by assuming it to be\ncompletely what it really is very nearly,) and suppressing others, under\nthe indispensable obligation of restoring them whenever, and in as far\nas, their presence or absence would make any material difference in the\ntruth of our conclusions. Of this nature, accordingly, are the first\nprinciples involved in the definitions of geometry. That the hypotheses\nshould be of this particular character, is however no further necessary,\nthan inasmuch as no others could enable us to deduce conclusions which,\nwith due corrections, would be true of real objects: and in fact, when\nour aim is only to illustrate truths, and not to investigate them, we\nare not under any such restriction. We might suppose an imaginary\nanimal, and work out by deduction, from the known laws of physiology,\nits natural history; or an imaginary commonwealth, and from the elements\ncomposing it, might argue what would be its fate. And the conclusions\nwhich we might thus draw from purely arbitrary hypotheses, might form a\nhighly useful intellectual exercise: but as they could only teach us\nwhat _would_ be the properties of objects which do not really exist,\nthey would not constitute any addition to our knowledge of nature: while\non the contrary, if the hypothesis merely divests a real object of some\nportion of its properties, without clothing it in false ones, the\nconclusions will always express, under known liability to correction,\nactual truth.\n\n\n\u00a7 3. But though Dr. Whewell has not shaken Stewart's doctrine as to the\nhypothetical character of that portion of the first principles of\ngeometry which are involved in the so-called definitions, he has, I\nconceive, greatly the advantage of Stewart on another important point in\nthe theory of geometrical reasoning; the necessity of admitting, among\nthose first principles, axioms as well as definitions. Some of the\naxioms of Euclid might, no doubt, be exhibited in the form of\ndefinitions, or might be deduced, by reasoning, from propositions\nsimilar to what are so called. Thus, if instead of the axiom, Magnitudes\nwhich can be made to coincide are equal, we introduce a definition,\n\"Equal magnitudes are those which may be so applied to one another as to\ncoincide;\" the three axioms which follow (Magnitudes which are equal to\nthe same are equal to one another--If equals are added to equals the\nsums are equal--If equals are taken from equals the remainders are\nequal,) may be proved by an imaginary superposition, resembling that by\nwhich the fourth proposition of the first book of Euclid is\ndemonstrated. But though these and several others may be struck out of\nthe list of first principles, because, though not requiring\ndemonstration, they are susceptible of it; there will be found in the\nlist of axioms two or three fundamental truths, not capable of being\ndemonstrated: among which must be reckoned the proposition that two\nstraight lines cannot inclose a space, (or its equivalent, Straight\nlines which coincide in two points coincide altogether,) and some\nproperty of parallel lines, other than that which constitutes their\ndefinition: one of the most suitable for the purpose being that selected\nby Professor Playfair: \"Two straight lines which intersect each other\ncannot both of them be parallel to a third straight line.\"[20]\n\nThe axioms, as well those which are indemonstrable as those which admit\nof being demonstrated, differ from that other class of fundamental\nprinciples which are involved in the definitions, in this, that they\nare true without any mixture of hypothesis. That things which are equal\nto the same thing are equal to one another, is as true of the lines and\nfigures in nature, as it would be of the imaginary ones assumed in the\ndefinitions. In this respect, however, mathematics are only on a par\nwith most other sciences. In almost all sciences there are some general\npropositions which are exactly true, while the greater part are only\nmore or less distant approximations to the truth. Thus in mechanics, the\nfirst law of motion (the continuance of a movement once impressed, until\nstopped or slackened by some resisting force) is true without\nqualification or error. The rotation of the earth in twenty-four hours,\nof the same length as in our time, has gone on since the first accurate\nobservations, without the increase or diminution of one second in all\nthat period. These are inductions which require no fiction to make them\nbe received as accurately true: but along with them there are others, as\nfor instance the propositions respecting the figure of the earth, which\nare but approximations to the truth; and in order to use them for the\nfurther advancement of our knowledge, we must feign that they are\nexactly true, though they really want something of being so.\n\n\n\u00a7 4. It remains to inquire, what is the ground of our belief in\naxioms--what 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--or in other words, Two\nstraight lines which have once met, do not meet again, but continue to\ndiverge--is an induction from the evidence of our senses.\n\nThis opinion runs counter to a scientific prejudice of long standing and\ngreat strength, and there is probably no proposition enunciated in this\nwork for which a more unfavourable reception is to be expected. It is,\nhowever, no new opinion; and even if it were so, would be entitled to be\njudged, not by its novelty, but by the strength of the arguments by\nwhich it can be supported. I consider it very fortunate that so eminent\na champion of the contrary opinion as Dr. Whewell, has found occasion\nfor 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.\nWhoever is anxious that a discussion should go to the bottom of the\nsubject, must rejoice to see the opposite side of the question worthily\nrepresented. If what is said by Dr. Whewell, in support of an opinion\nwhich he has made the foundation of a systematic work, can be shown not\nto be conclusive, enough will have been done, without going further in\nquest of stronger arguments 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\nknown that two straight lines cannot inclose a space if we had never\nseen a straight line: thus much being admitted by Dr. Whewell, and by\nall, in recent times, who have taken his view of the subject. But they\ncontend, that it is not experience which _proves_ the axiom; but that\nits truth is perceived _\u00e0 priori_, by the constitution of the mind\nitself, from the first moment when the meaning of the proposition is\napprehended; and without any necessity for verifying it by repeated\ntrials, as is requisite in the case of truths really ascertained by\nobservation.\n\nThey cannot, however, but allow that the truth of the axiom, Two\nstraight lines cannot inclose a space, even if evident independently of\nexperience, is also evident from experience. Whether the axiom needs\nconfirmation or not, it receives confirmation in almost every instant of\nour lives; since we cannot look at any two straight lines which\nintersect one another, without seeing that from that point they continue\nto diverge more and more. Experimental proof crowds in upon us in such\nendless profusion, and without one instance in which there can be even a\nsuspicion of an exception to the rule, that we should soon have stronger\nground for believing the axiom, even as an experimental truth, than we\nhave for almost any of the general truths which we confessedly learn\nfrom the evidence of our senses. Independently of _\u00e0 priori_ evidence,\nwe should certainly believe it with an intensity of conviction far\ngreater than we accord to any ordinary physical truth: and this too at a\ntime of life much earlier than that from which we date almost any part\nof our acquired knowledge, and much too early to admit of our retaining\nany recollection of the history of our intellectual operations at that\nperiod. Where then is the necessity for assuming that our recognition of\nthese truths has a different origin from the rest of our knowledge, when\nits existence is perfectly accounted for by supposing its origin to be\nthe same? when the causes which produce belief in all other instances,\nexist in this instance, and in a degree of strength as much superior to\nwhat exists in other cases, as the intensity of the belief itself is\nsuperior? The burden of proof lies on the advocates of the contrary\nopinion: it is for them to point out some fact, inconsistent with the\nsupposition that this part of our knowledge of nature is derived from\nthe same sources as every other part.[21]\n\nThis, for instance, they would be able to do, if they could prove\nchronologically that we had the conviction (at least practically) so\nearly in infancy as to be anterior to those impressions on the senses,\nupon which, on the other theory, the conviction is founded. This,\nhowever, cannot be proved: the point being too far back to be within the\nreach of memory, and too obscure for external observation. The advocates\nof the _\u00e0 priori_ theory are obliged to have recourse to other\narguments. These are reducible to two, which I shall endeavour to state\nas clearly and as forcibly as possible.\n\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\nis, by seeing or feeling the straight lines; whereas in fact it is seen\nto be true by merely thinking of them. That a stone thrown into water\ngoes to the bottom, may be perceived by our senses, but mere thinking of\na stone thrown into the water would never have led us to that\nconclusion: not so, however, with the axioms relating to straight lines:\nif I could be made to conceive what a straight line is, without having\nseen one, I should at once recognise that two such lines cannot inclose\na space. Intuition is \"imaginary looking;\"[22] but experience must be\nreal looking: if we see a property of straight lines to be true by\nmerely fancying ourselves to be looking at them, the ground of our\nbelief cannot be the senses, or experience; 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\nof it 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\nprolonged to infinity they do not meet, but continue to diverge from one\nanother. How can this, in any single case, be proved by actual\nobservation? We may follow the lines to any distance we please; but we\ncannot follow them to infinity: for aught our senses can testify, they\nmay, immediately beyond the farthest point to which we have traced them,\nbegin to approach, and at last meet. Unless, therefore, we had some\nother proof of the impossibility than observation affords us, we should\nhave no ground for believing the axiom 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\nthe characteristic properties of geometrical forms--their capacity of\nbeing painted in the imagination with a distinctness equal to reality:\nin other words, the exact resemblance of our ideas of form to the\nsensations which suggest them. This, in the first place, enables us to\nmake (at least with a little practice) mental pictures of all possible\ncombinations of lines and angles, which resemble the realities quite as\nwell as any which we could make on paper; and in the next place, make\nthose pictures just as fit subjects of geometrical experimentation as\nthe realities themselves; inasmuch as pictures, if sufficiently\naccurate, exhibit of course all the properties which would be manifested\nby the realities at one given instant, and on simple inspection: and in\ngeometry we are concerned only with such properties, and not with that\nwhich pictures could not exhibit, the mutual action of bodies one upon\nanother. The foundations of geometry would therefore be laid in direct\nexperience, even if the experiments (which in this case consist merely\nin attentive contemplation) were practised solely upon what we call our\nideas, that is, upon the diagrams in our minds, and not upon outward\nobjects. For in all systems of experimentation we take some objects to\nserve as representatives of all which resemble them; and in the present\ncase the conditions which qualify a real object to be the representative\nof its class, are completely fulfilled by an object existing only in our\nfancy. Without denying, therefore, the possibility of satisfying\nourselves that two straight lines cannot inclose a space, by merely\nthinking of straight lines without actually looking at them; I contend,\nthat we do not believe this truth on the ground of the imaginary\nintuition simply, but because we know that the imaginary lines exactly\nresemble real ones, and that we may conclude from them to real ones with\nquite as much certainty as we could conclude from one real line to\nanother. The conclusion, therefore, is still an induction from\nobservation. And we should not be authorized to substitute observation\nof the image in our mind, for observation of the reality, if we had not\nlearnt by long-continued experience that the properties of the reality\nare faithfully represented in the image; just as we should be\nscientifically warranted in describing an animal which we have never\nseen, from a picture made of it with a daguerreotype; but not until we\nhad learnt 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\nnever meet, it would be necessary to follow them to infinity; yet\nwithout doing so we may know that if they ever do meet, or if, after\ndiverging from one another, they begin again to approach, this must take\nplace not at an infinite, but at a finite distance. Supposing,\ntherefore, such to be the case, we can transport ourselves thither in\nimagination, and can frame a mental image of the appearance which one or\nboth of the lines must present at that point, which we may rely on as\nbeing precisely similar to the reality. Now, whether we fix our\ncontemplation upon this imaginary picture, or call to mind the\ngeneralizations we have had occasion to make from former ocular\nobservation, we learn by the evidence of experience, that a line which,\nafter diverging from another straight line, begins to approach to it,\nproduces the impression on our senses which we describe by the\nexpression, \"a bent line,\" not by the expression, \"a straight line.\"[23]\n\n\n\u00a7 6. The first of the two arguments in support of the theory that\naxioms are _\u00e0 priori_ truths, having, I think, been sufficiently\nanswered; I proceed to the second, which is usually the most relied on.\nAxioms (it is asserted) are conceived by us not only as true, but as\nuniversally and necessarily true. Now, experience cannot possibly give\nto any proposition this character. I may have seen snow a hundred\ntimes, and may have seen that it was white, but this cannot give me\nentire assurance even that all snow is white; much less that snow _must_\nbe white. \"However many instances we may have observed of the truth of a\nproposition, there is nothing to assure us that the next case shall not\nbe an exception to the rule. If it be strictly true that every ruminant\nanimal yet known has cloven hoofs, we still cannot be sure that some\ncreature will not hereafter be discovered which has the first of these\nattributes, without having the other.... Experience must always consist\nof a limited number of observations; and, however numerous these may be,\nthey can show nothing with regard to the infinite number of cases in\nwhich the experiment has not been made.\" Besides, Axioms are not only\nuniversal, they are also necessary. Now \"experience cannot offer the\nsmallest ground for the necessity of a proposition. She can observe and\nrecord what has happened; but she cannot find, in any case, or in any\naccumulation of cases, any reason for what _must_ happen. She may see\nobjects side by side; but she cannot see a reason why they must ever be\nside by side. She finds certain events to occur in succession; but the\nsuccession supplies, in its occurrence, no reason for its recurrence.\nShe contemplates external objects; but she cannot detect any internal\nbond, which indissolubly connects the future with the past, the possible\nwith the real. To learn a proposition by experience, and to see it to be\nnecessarily true, are two altogether different processes of\nthought.\"[24] And Dr. Whewell adds, \"If any one does not clearly\ncomprehend this distinction of necessary and contingent truths, he will\nnot be able to go along with us in our researches into the foundations\nof human knowledge; nor, indeed, to pursue with success any speculation\non the subject.\"[25]\n\nIn the following passage, we are told what the distinction is, the\nnon-recognition of which incurs this denunciation. \"Necessary 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.\"[26]\n\nAlthough Dr. Whewell has naturally and properly employed a variety of\nphrases to bring his meaning more forcibly home, he would, I presume,\nallow that they are all equivalent; and that what he means by a\nnecessary truth, would be sufficiently defined, a proposition the\nnegation of which is not only false but inconceivable. I am unable to\nfind in any of his expressions, turn them what way you will, a meaning\nbeyond this, and I do not believe he would contend that they mean\nanything 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\nand more cogent description than any which experience can afford.\n\nNow I cannot but wonder that so much stress should be laid on the\ncircumstance of inconceivableness, when there is such ample experience\nto show, 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\ntruth very much an affair of accident, and depends on the past history\nand habits of our own minds. There is no more generally acknowledged\nfact in human nature, than the extreme difficulty at first felt in\nconceiving anything as possible, which is in contradiction to long\nestablished and familiar experience; or even to old familiar habits of\nthought. And this difficulty is a necessary result of the fundamental\nlaws of the human mind. When we have often seen and thought of two\nthings together, and have never in any one instance either seen or\nthought of them separately, there is by the primary law of association\nan increasing difficulty, which may in the end become insuperable, of\nconceiving the two things apart. This is most of all conspicuous in\nuneducated persons, who are in general utterly unable to separate any\ntwo ideas which have once become firmly associated in their minds; and\nif persons of cultivated intellect have any advantage on the point, it\nis only because, having seen and heard and read more, and being more\naccustomed to exercise their imagination, they have experienced their\nsensations 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\nnot exempt from the universal laws of our conceptive faculty. If daily\nhabit presents to any one for a long period two facts in combination,\nand if he is not led during that period either by accident or by his\nvoluntary mental operations to think of them apart, he will probably in\ntime become incapable of doing so even by the strongest effort; and the\nsupposition that the two facts can be separated in nature, will at last\npresent itself to his mind with all the characters of an inconceivable\nphenomenon.[27] There are remarkable instances of this in the history of\nscience: instances in which the most instructed men rejected as\nimpossible, because inconceivable, things which their posterity, by\nearlier practice and longer perseverance in the attempt, found it quite\neasy to conceive, and which everybody now knows to be true. There was a\ntime when men of the most cultivated intellects, and the most\nemancipated from the dominion of early prejudice, could not credit the\nexistence of antipodes; were unable to conceive, in opposition to old\nassociation, the force of gravity acting upwards instead of downwards.\nThe Cartesians long rejected the Newtonian doctrine of the\ngravitation of all bodies towards one another, on the faith of\na general proposition, the reverse of which seemed to them to be\ninconceivable--the proposition that a body cannot act where it is not.\nAll the cumbrous machinery of imaginary vortices, assumed without the\nsmallest particle of evidence, appeared to these philosophers a more\nrational mode of explaining the heavenly motions, than one which\ninvolved what seemed to them so great an absurdity.[28] And they no\ndoubt found it as impossible to conceive that a body should act upon the\nearth at the distance of the sun or moon, as we find it to conceive an\nend to space or time, or two straight lines inclosing a space. Newton\nhimself had not been able to realize the conception, or we should not\nhave had his hypothesis of a subtle ether, the occult cause of\ngravitation; and his writings prove, that though he deemed the\nparticular nature of the intermediate agency a matter of conjecture, the\nnecessity of _some_ such agency appeared to him indubitable. It would\nseem that even now the majority of scientific men have not completely\ngot over this very difficulty; for though they have at last learnt to\nconceive the sun _attracting_ the earth without any intervening fluid,\nthey cannot yet conceive the sun _illuminating_ the earth without some\nsuch 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\nproved to be true; what wonder if in cases where the association is\nstill older, more confirmed, and more familiar, and in which nothing\never occurs to shake our conviction, or even suggest to us any\nconception at variance with the association, the acquired incapacity\nshould continue, and be mistaken for a natural incapacity? It is true,\nour experience of the varieties in nature enables us, within certain\nlimits, to conceive other varieties analogous to them. We can conceive\nthe sun or moon falling; for though we never saw them fall, nor ever\nperhaps imagined them falling, we have seen so many other things fall,\nthat we have innumerable familiar analogies to assist the conception;\nwhich, after all, we should probably have some difficulty in framing,\nwere we not well accustomed to see the sun and moon move (or appear to\nmove,) so that we are only called upon to conceive a slight change in\nthe direction of motion, a circumstance familiar to our experience. But\nwhen experience affords no model on which to shape the new conception,\nhow is it possible for us to form it? How, for example, can we imagine\nan end to space or time? We never saw any object without something\nbeyond it, nor experienced any feeling without something following it.\nWhen, therefore, we attempt to conceive the last point of space, we have\nthe idea irresistibly raised of other points beyond it. When we try to\nimagine the last instant of time, we cannot help conceiving another\ninstant after it. Nor is there any necessity to assume, as is done by a\nmodern school of metaphysicians, a peculiar fundamental law of the mind\nto account for the feeling of infinity inherent in our conceptions of\nspace and time; that apparent infinity is sufficiently accounted for by\nsimpler 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,--a truth which is testified to us\nby our very earliest impressions of the external world,--how is it\npossible (whether those external impressions be or be not the ground of\nour belief) that the reverse of the proposition _could_ be otherwise\nthan inconceivable to us? What analogy have we, what similar order of\nfacts in any other branch of our experience, to facilitate to us the\nconception of two straight lines inclosing a space? Nor is even this\nall. I have already called attention to the peculiar property of our\nimpressions of form, that the ideas or mental images exactly resemble\ntheir prototypes, and adequately represent them for the purposes of\nscientific observation. From this, and from the intuitive character of\nthe observation, which in this case reduces itself to simple inspection,\nwe cannot so much as call up in our imagination two straight lines, in\norder to attempt to conceive them inclosing a space, without by that\nvery act repeating the scientific experiment which establishes the\ncontrary. Will it really be contended that the inconceivableness of the\nthing, in such circumstances, proves anything against the experimental\norigin of the conviction? Is it not clear that in whichever mode our\nbelief in the proposition may have originated, the impossibility of our\nconceiving the negative of it must, on either hypothesis, be the same?\nAs, then, Dr. Whewell exhorts those who have any difficulty in\nrecognising the distinction held by him between necessary and contingent\ntruths, to study geometry,--a condition which I can assure him I have\nconscientiously fulfilled,--I, in return, with equal confidence, exhort\nthose who agree with him, to study the general laws of association;\nbeing convinced that nothing more is requisite than a moderate\nfamiliarity with those laws, to dispel the illusion which ascribes a\npeculiar necessity to our earliest inductions from experience, and\nmeasures the possibility of things in themselves, by the human capacity\nof 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\nto an experimental truth the appearance of a necessary one, and afforded\na striking 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,\nbut for historical proof, it would have been impossible to conceive that\nthey had not been recognised from the first by all persons in a sound\nstate of their faculties. \"We now despise those who, in the Copernican\ncontroversy, could not conceive the apparent motion of the sun on the\nheliocentric hypothesis; or those who, in opposition to Galileo, thought\nthat a uniform force might be that which generated a velocity\nproportional to the space; or those who held there was something absurd\nin Newton's doctrine of the different refrangibility of differently\ncoloured rays; or those who imagined that when elements combine, their\nsensible qualities must be manifest in the compound; or those who were\nreluctant to give up the distinction of vegetables into herbs, shrubs,\nand trees. We cannot help thinking that men must have been singularly\ndull of comprehension, to find a difficulty in admitting what is to us\nso plain and simple. We have a latent persuasion that we in their place\nshould have been wiser and more clear-sighted; that we should have taken\nthe right side, and given our assent at once to the truth. Yet in\nreality such a persuasion is a mere delusion. The persons who, in such\ninstances as the above, were on the losing side, were very far, in most\ncases, from being persons more prejudiced, or stupid, or narrow-minded,\nthan the greater part of mankind now are; and the cause for which they\nfought was far from being a manifestly bad one, till it had been so\ndecided by the result of the war.... So complete has been the victory of\ntruth in most of these instances, that at present we can hardly imagine\nthe struggle to have been necessary. _The very essence of these triumphs\nis, that they lead us to regard the views we reject as not only false\nbut inconceivable._\"[29]\n\nThis last proposition is precisely what I contend for; and I ask no\nmore, in order to overthrow the whole theory of its author on the nature\nof the evidence of axioms. For what is that theory? That the truth of\naxioms cannot have been learnt from experience, because their falsity is\ninconceivable. But Dr. Whewell himself says, that we are continually\nled, by the natural progress of thought, to regard as inconceivable what\nour forefathers not only conceived but believed, nay even (he might\nhave added) were unable to conceive the reverse of. He cannot intend to\njustify this mode of thought: he cannot mean to say, that we can be\nright 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\nof the 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\nof the atomic theory.\n\nWith respect to the laws of motion, Dr. Whewell says: \"No one can doubt\nthat, in historical fact, these laws were collected from experience.\nThat such is the case, is no matter of conjecture. We know the time, the\npersons, the circumstances, belonging to each step of each\ndiscovery.\"[30] After this testimony, to adduce evidence of the fact\nwould be superfluous. And not only were these laws by no means\nintuitively evident, but some of them were originally paradoxes. The\nfirst law was especially so. That a body, once in motion, would continue\nfor ever to move in the same direction with undiminished velocity unless\nacted upon by some new force, was a proposition which mankind found for\na long time the greatest difficulty in crediting. It stood opposed to\napparent experience of the most familiar kind, which taught that it was\nthe nature of motion to abate gradually, and at last terminate of\nitself. Yet when once the contrary doctrine was firmly established,\nmathematicians, as Dr. Whewell observes, speedily began to believe that\nlaws, thus contradictory to first appearances, and which, even after\nfull proof had been obtained, it had required generations to render\nfamiliar to the minds of the scientific world, were under \"a\ndemonstrable necessity, compelling them to be such as they are and no\nother;\" and he himself, though not venturing \"absolutely to pronounce\"\nthat _all_ these laws \"can be rigorously traced to an absolute necessity\nin the nature of things,\"[31] does actually so think of the law just\nmentioned; of which he says: \"Though the discovery of the first law of\nmotion was made, historically speaking, by means of experiment, we have\nnow attained a point of view in which we see that it might have been\ncertainly known to be true, independently of experience.\"[32] Can there\nbe a more striking exemplification than is here afforded, of the effect\nof association which we have described? Philosophers, for generations,\nhave the most extraordinary difficulty in putting certain ideas\ntogether; they at last succeed in doing so; and after a sufficient\nrepetition of the process, they first fancy a natural bond between the\nideas, then experience a growing difficulty, which at last, by the\ncontinuation of the same progress, becomes an impossibility, of severing\nthem from one another. If such be the progress of an experimental\nconviction of which the date is of yesterday, and which is in opposition\nto first appearances, how must it fare with those which are conformable\nto appearances familiar from the first dawn of intelligence, and of the\nconclusiveness of which, from the earliest records of human thought, no\nsceptic has suggested even a momentary doubt?\n\nThe other instance which I shall quote is a truly astonishing one, and\nmay be called the _reductio ad absurdum_ of the theory of\ninconceivableness. Speaking of the laws of chemical composition, Dr.\nWhewell says:[33] \"That they could never have been clearly understood,\nand therefore never firmly established, without laborious and exact\nexperiments, is certain; but yet we may venture to say, that being once\nknown, they possess an evidence beyond that of mere experiment. _For how\nin fact can we conceive combinations, otherwise than as definite in kind\nand quality?_ If we were to suppose each element ready to combine with\nany other indifferently, and indifferently in any quantity, we should\nhave a world in which all would be confusion and indefiniteness. There\nwould be no fixed kinds of bodies. Salts, and stones, and ores, would\napproach to and graduate into each other by insensible degrees. Instead\nof this, we know that the world consists of bodies distinguishable from\neach other by definite differences, capable of being classified and\nnamed, and of having general propositions asserted concerning them. And\nas _we cannot conceive a world in which this should not be the case_, it\nwould appear that we cannot conceive a state of things in which the laws\nof the combination of elements should not be of that definite and\nmeasured kind which we have above asserted.\"\n\nThat a philosopher of Dr. Whewell's eminence should gravely assert that\nwe cannot conceive a world in which the simple elements should combine\nin other than definite proportions; that by dint of meditating on a\nscientific truth, the original discoverer of which was still living, he\nshould have rendered the association in his own mind between the idea of\ncombination and that of constant proportions so familiar and intimate as\nto be unable to conceive the one fact without the other; is so signal an\ninstance of the mental law for which I am contending, that one word more\nin illustration must be superfluous.\n\nIn the latest and most complete elaboration of his metaphysical system\n(the _Philosophy of Discovery_), as well as in the earlier discourse on\nthe _Fundamental Antithesis of Philosophy_, reprinted as an appendix to\nthat work, Dr. Whewell, while very candidly admitting that his language\nwas open to misconception, disclaims having intended to say that mankind\nin general can _now_ perceive the law of definite proportions in\nchemical combination to be a necessary truth. All he meant was that\nphilosophical chemists in a future generation may possibly see this.\n\"Some truths may be seen by intuition, but yet the intuition of them may\nbe a rare and a difficult attainment.\"[34] And he explains that the\ninconceivableness which, according to his theory, is the test of\naxioms, \"depends entirely upon the clearness of the Ideas which the\naxioms involve. So long as those Ideas are vague and indistinct, the\ncontrary of an Axiom may be assented to, though it cannot be distinctly\nconceived. It may be assented to, not because it is possible, but\nbecause we do not see clearly what is possible. To a person who is only\nbeginning to think geometrically, there may appear nothing absurd in the\nassertion, that two straight lines may inclose a space. And in the same\nmanner, to a person who is only beginning to think of mechanical truths,\nit may not appear to be absurd, that in mechanical processes, Reaction\nshould be greater or less than Action; and so, again, to a person who\nhas not thought steadily about Substance, it may not appear\ninconceivable, that by chemical operations, we should generate new\nmatter, or destroy matter which already exists.\"[35] Necessary truths,\ntherefore, are not those of which we cannot conceive, but \"those of\nwhich we cannot _distinctly_ conceive, the contrary.\"[36] So long as our\nideas are indistinct altogether, we do not know what is or is not\ncapable of being distinctly conceived; but, by the ever increasing\ndistinctness with which scientific men apprehend the general conceptions\nof science, they in time come to perceive that there are certain laws of\nnature, which, though historically and as a matter of fact they were\nlearnt from experience, we cannot, now that we know them, distinctly\nconceive to be other than they are.\n\nThe account which I should give of this progress of the scientific mind\nis somewhat different. After a general law of nature has been\nascertained, men's minds do not at first acquire a complete facility of\nfamiliarly representing to themselves the phenomena of nature in the\ncharacter which that law assigns to them. The habit which constitutes\nthe scientific cast of mind, that of conceiving facts of all\ndescriptions conformably to the laws which regulate them--phenomena of\nall descriptions according to the relations which have been ascertained\nreally to exist between them; this habit, in the case of newly\ndiscovered relations, comes only by degrees. So long as it is not\nthoroughly formed, no necessary character is ascribed to the new truth.\nBut in time, the philosopher attains a state of mind in which his mental\npicture of nature spontaneously represents to him all the phenomena with\nwhich the new theory is concerned, in the exact light in which the\ntheory regards them: all images or conceptions derived from any other\ntheory, or from the confused view of the facts which is anterior to any\ntheory, having entirely disappeared from his mind. The mode of\nrepresenting facts which results from the theory, has now become, to his\nfaculties, the only natural mode of conceiving them. It is a known\ntruth, that a prolonged habit of arranging phenomena in certain groups,\nand explaining them by means of certain principles, makes any other\narrangement or explanation of these facts be felt as unnatural: and it\nmay at last become as difficult to him to represent the facts to himself\nin any other mode, as it often was, originally, to represent them in\nthat mode.\n\nBut, further, if the theory is true, as we are supposing it to be, any\nother mode in which he tries, or in which he was formerly accustomed, to\nrepresent the phenomena, will be seen by him to be inconsistent with the\nfacts that suggested the new theory--facts which now form a part of his\nmental picture of nature. And since a contradiction is always\ninconceivable, his imagination rejects these false theories, and\ndeclares itself incapable of conceiving them. Their inconceivableness to\nhim does not, however, result from anything in the theories themselves,\nintrinsically and _\u00e0 priori_ repugnant to the human faculties; it\nresults from the repugnance between them and a portion of the facts;\nwhich facts as long as he did not know, or did not distinctly realize in\nhis mental representations, the false theory did not appear other than\nconceivable; it becomes inconceivable, merely from the fact that\ncontradictory elements cannot be combined in the same conception.\nAlthough, then, his real reason for rejecting theories at variance with\nthe true one, is no other than that they clash with his experience, he\neasily falls into the belief, that he rejects them because they are\ninconceivable, and that he adopts the true theory because it is\nself-evident, and does not need the evidence of experience at all.\n\nThis I take to be the real and sufficient explanation of the paradoxical\ntruth, on which so much stress is laid by Dr. Whewell, that a\nscientifically cultivated mind is actually, in virtue of that\ncultivation, unable to conceive suppositions which a common man\nconceives without the smallest difficulty. For there is nothing\ninconceivable in the suppositions themselves; the impossibility is in\ncombining them with facts inconsistent with them, as part of the same\nmental picture; an obstacle of course only felt by those who know the\nfacts, and are able to perceive the inconsistency. As far as the\nsuppositions themselves are concerned, in the case of many of Dr.\nWhewell's necessary truths the negative of the axiom is, and probably\nwill be as long as the human race lasts, as easily conceivable as the\naffirmative. There is no axiom (for example) to which Dr. Whewell\nascribes a more thorough character of necessity and self-evidence, than\nthat of the indestructibility of matter. That this is a true law of\nnature I fully admit; but I imagine there is no human being to whom the\nopposite supposition is inconceivable--who has any difficulty in\nimagining a portion of matter annihilated: inasmuch as its apparent\nannihilation, in no respect distinguishable from real by our unassisted\nsenses, takes place every time that water dries up, or fuel is consumed.\nAgain, the law that bodies combine chemically in definite proportions is\nundeniably true; but few besides Dr. Whewell have reached the point\nwhich he seems personally to have arrived at, (though he only dares\nprophesy similar success to the multitude after the lapse of\ngenerations,) that of being unable to conceive a world in which the\nelements are ready to combine with one another \"indifferently in any\nquantity;\" nor is it likely that we shall ever rise to this sublime\nheight of inability, so long as all the mechanical mixtures in our\nplanet, whether solid, liquid, or a\u00ebriform, exhibit to our daily\nobservation the very phenomenon declared to be inconceivable.\n\nAccording to Dr. Whewell, these and similar laws of nature cannot be\ndrawn from experience, inasmuch as they are, on the contrary, assumed\nin the interpretation of experience. Our inability to \"add to or\ndiminish the quantity of matter in the world,\" is a truth which \"neither\nis nor can be derived from experience; for the experiments which we make\nto verify it presuppose its truth.... When men began to use the balance\nin chemical analysis, they did not prove by trial, but took for granted,\nas self-evident, that the weight of the whole must be found in the\naggregate weight of the elements.\"[37] True, it is assumed; but, I\napprehend, no otherwise than as all experimental inquiry assumes\nprovisionally some theory or hypothesis, which is to be finally held\ntrue or not, according as the experiments decide. The hypothesis chosen\nfor this purpose will naturally be one which groups together some\nconsiderable number of facts already known. The proposition that the\nmaterial of the world, as estimated by weight, is neither increased nor\ndiminished by any of the processes of nature or art, had many\nappearances in its favour to begin with. It expressed truly a great\nnumber of familiar facts. There were other facts which it had the\nappearance of conflicting with, and which made its truth, as an\nuniversal law of nature, at first doubtful. Because it was doubtful,\nexperiments were devised to verify it. Men assumed its truth\nhypothetically, and proceeded to try whether, on more careful\nexamination, the phenomena which apparently pointed to a different\nconclusion, would not be found to be consistent with it. This turned out\nto be the case; and from that time the doctrine took its place as an\nuniversal truth, but as one proved to be such by experience. That the\ntheory itself preceded the proof of its truth--that it had to be\nconceived before it could be proved, and in order that it might be\nproved--does not imply that it was self-evident, and did not need proof.\nOtherwise all the true theories in the sciences are necessary and\nself-evident; for no one knows better than Dr. Whewell that they all\nbegan by being assumed, for the purpose of connecting them by deductions\nwith those facts of experience on which, as evidence, they now\nconfessedly rest.[38]\n\n\n\n\nCHAPTER VI.\n\nTHE SAME SUBJECT CONTINUED.\n\n\n\u00a7 1. In the examination which formed the subject of the last chapter,\ninto the nature of the evidence of those deductive sciences which are\ncommonly represented to be systems of necessary truth, we have been led\nto the following conclusions. The results of those sciences are indeed\nnecessary, in the sense of necessarily following from certain first\nprinciples, commonly called axioms and definitions; that is, of being\ncertainly true if those axioms and definitions are so; for the word\nnecessity, even in this acceptation of it, means no more than certainty.\nBut their claim to the character of necessity in any sense beyond this,\nas implying an evidence independent of and superior to observation and\nexperience, must depend on the previous establishment of such a claim in\nfavour of the definitions and axioms themselves. With regard to axioms,\nwe found that, considered as experimental truths, they rest on\nsuperabundant and obvious evidence. We inquired, whether, since this is\nthe case, it be imperative to suppose any other evidence of those truths\nthan experimental evidence, any other origin for our belief of them than\nan experimental origin. We decided, that the burden of proof lies with\nthose who maintain the affirmative, and we examined, at considerable\nlength, such arguments as they have produced. The examination having led\nto the rejection of those arguments, we have thought ourselves warranted\nin concluding that axioms are but a class, the most universal class, of\ninductions from experience; the simplest and easiest cases of\ngeneralization from the facts furnished to us by our senses or by our\ninternal 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\nproperties which observation shows to belong to it, we at the same time\ndeny that it possesses any other properties, though in truth other\nproperties do in every individual instance accompany, and in almost all\ninstances modify, the property thus exclusively predicated. The denial,\ntherefore, is a mere fiction, or supposition, made for the purpose of\nexcluding the consideration of those modifying circumstances, when their\ninfluence is of too trifling amount to be worth considering, or\nadjourning it, when important, to a more convenient moment.\n\nFrom these considerations it would appear that Deductive or\nDemonstrative Sciences are all, without exception, Inductive Sciences;\nthat their evidence is that of experience; but that they are also, in\nvirtue of the peculiar character of one indispensable portion of the\ngeneral formul\u00e6 according to which their inductions are made,\nHypothetical Sciences. Their conclusions are only true on certain\nsuppositions, which are, or ought to be, approximations to the truth,\nbut are seldom, if ever, exactly true; and to this hypothetical\ncharacter is to be ascribed the peculiar certainty, which is supposed to\nbe inherent in demonstration.\n\nWhat we have now asserted, however, cannot be received as universally\ntrue of Deductive or Demonstrative Sciences, until verified by being\napplied to the most remarkable of all those sciences, that of Numbers;\nthe theory of the Calculus; Arithmetic and Algebra. It is harder to\nbelieve of the doctrines of this science than of any other, either that\nthey are not truths _\u00e0 priori_, but experimental truths, or that their\npeculiar certainty is owing to their being not absolute but only\nconditional truths. This, therefore, is a case which merits examination\napart; and the more so, because on this subject we have a double set of\ndoctrines to contend with; that of the _\u00e0 priori_ philosophers on one\nside; and on the other, a theory the most opposite to theirs, which was\nat one time very generally received, and is still far from being\naltogether exploded, among metaphysicians.\n\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\none are equal to three, according to these writers, is not a truth, is\nnot the assertion of a really existing fact, but a definition of the\nword three; a statement that mankind have agreed to use the name three\nas a sign exactly equivalent to two and one; to call by the former name\nwhatever is called by the other more clumsy phrase. According to this\ndoctrine, the longest process in algebra is but a succession of changes\nin terminology, by which equivalent expressions are substituted one for\nanother; a series of translations of the same fact, from one into\nanother language; though how, after such a series of translations, the\nfact itself comes out changed (as when we demonstrate a new geometrical\ntheorem by algebra,) they have not explained; and it is a difficulty\nwhich 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\nplausible, and have not unnaturally made those sciences the stronghold\nof Nominalism. The doctrine that we can discover facts, detect the\nhidden processes of nature, by an artful manipulation of language, is so\ncontrary to common sense, that a person must have made some advances in\nphilosophy to believe it: men fly to so paradoxical a belief to avoid,\nas they think, some even greater difficulty, which the vulgar do not\nsee. What has led many to believe that reasoning is a mere verbal\nprocess, is, that no other theory seemed reconcileable with the nature\nof the Science of Numbers. For we do not carry any ideas along with us\nwhen we use the symbols of arithmetic or of algebra. In a geometrical\ndemonstration we have a mental diagram, if not one on paper; AB, AC, are\npresent to our imagination as lines, intersecting other lines, forming\nan angle with one another, and the like; but not so _a_ and _b_. These\nmay represent lines or any other magnitudes, but those magnitudes are\nnever thought of; nothing is realized in our imagination but _a_ and\n_b_. The ideas which, on the particular occasion, they happen to\nrepresent, are banished from the mind during every intermediate part of\nthe process, between the beginning, when the premises are translated\nfrom things into signs, and the end, when the conclusion is translated\nback from signs into things. Nothing, then, being in the reasoner's mind\nbut the symbols, what can seem more inadmissible than to contend that\nthe reasoning process has to do with anything more? We seem to have come\nto one of Bacon's Prerogative Instances; an _experimentum crucis_ on the\nnature 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\nan arithmetical or algebraical calculation a real induction, a real\ninference of facts from facts; and that what disguises the induction is\nsimply its comprehensive nature, and the consequent extreme generality\nof the language. All numbers must be numbers of something: there are no\nsuch things as numbers in the abstract. _Ten_ must mean ten bodies, or\nten sounds, or ten beatings of the pulse. But though numbers must be\nnumbers of something, they may be numbers of anything. Propositions,\ntherefore, concerning numbers, have the remarkable peculiarity that they\nare propositions concerning all things whatever; all objects, all\nexistences of every kind, known to our experience. All things possess\nquantity; consist of parts which can be numbered; and in that character\npossess all the properties which are called properties of numbers. That\nhalf of four is two, must be true whatever the word four represents,\nwhether four hours, four miles, or four pounds weight. We need only\nconceive a thing divided into four equal parts, (and all things may be\nconceived as so divided,) to be able to predicate of it every property\nof the number four, that is, every arithmetical proposition in which the\nnumber four stands on one side of the equation. Algebra extends the\ngeneralization still farther: every number represents that particular\nnumber of all things without distinction, but every algebraical symbol\ndoes more, it represents all numbers without distinction. As soon as we\nconceive a thing divided into equal parts, without knowing into what\nnumber of parts, we may call it _a_ or _x_, and apply to it, without\ndanger of error, every algebraical formula in the books. The\nproposition, _2(a + b) = 2a + 2b_, is a truth co-extensive with all\nnature. Since then algebraical truths are true of all things whatever,\nand not, like those of geometry, true of lines only or angles only, it\nis no wonder that the symbols should not excite in our minds ideas of\nany things in particular. When we demonstrate the forty-seventh\nproposition of Euclid, it is not necessary that the words should raise\nin us an image of all right-angled triangles, but only of some one\nright-angled triangle: so in algebra we need not, under the symbol _a_,\npicture to ourselves all things whatever, but only some one thing; why\nnot, then, the letter itself? The mere written characters, _a_, _b_,\n_x_, _y_, _z_, serve as well for representatives of Things in general,\nas any more complex and apparently more concrete conception. That we are\nconscious of them however in their character of things, and not of mere\nsigns, is evident from the fact that our whole process of reasoning is\ncarried on by predicating of them the properties of things. In resolving\nan algebraic equation, by what rules do we proceed? By applying at each\nstep to _a_, _b_, and _x_, the proposition that equals added to equals\nmake 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\nall things. The inferences, therefore, which are successively drawn, are\ninferences concerning things, not symbols; though 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\nthought, when they have been performed often, will do if permitted,\nnamely, to become entirely mechanical. Hence the general language of\nalgebra comes to be used familiarly without exciting ideas, as all\nother general language is prone to do from mere habit, though in no\nother case than this can it be done with complete safety. But when we\nlook back to see from whence the probative force of the process is\nderived, we find that at every single step, unless we suppose ourselves\nto be thinking and talking of the things, and not the mere symbols, the\nevidence fails.\n\nThere is another circumstance, which, still more than that which we have\nnow mentioned, gives plausibility to the notion that the propositions of\narithmetic and algebra are merely verbal. That is, that when considered\nas propositions 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 \"Two\npebbles and one pebble are equal to three pebbles,\" 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\nassertion that \"objects are themselves\" being insignificant, it seems\nbut natural to consider the proposition, Two and one are equal to three,\nas asserting mere identity of signification between the two names.\n\nThis, however, though it looks so plausible, will not bear examination.\nThe expression \"two pebbles and one pebble,\" and the expression, \"three\npebbles,\" stand indeed for the same aggregation of objects, but they by\nno means 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\npebbles in two separate parcels, and three pebbles in one parcel, do not\nmake the same impression on our senses; and the assertion that the very\nsame pebbles may by an alteration of place and arrangement be made to\nproduce either the one set of sensations or the other, though a very\nfamiliar proposition, is not an identical one. It is a truth known to us\nby early and constant experience: an inductive truth; and such truths\nare the foundation of the science of Number. The fundamental truths of\nthat science all rest on the evidence of sense; they are proved by\nshowing to our eyes and our fingers that any given number of objects,\nten balls for example, may by separation and re-arrangement exhibit to\nour senses all the different sets of numbers the sum of which is equal\nto ten. All the improved methods of teaching arithmetic to children\nproceed on a knowledge of this fact. All who wish to carry the child's\n_mind_ along with them in learning arithmetic; all who wish to teach\nnumbers, and not mere ciphers--now teach it through the evidence of the\nsenses, in the manner we have described.\n\nWe may, if we please, call the proposition, \"Three is two and one,\" a\ndefinition of the number three, and assert that arithmetic, as it has\nbeen asserted that geometry, is a science founded on definitions. But\nthey are definitions in the geometrical sense, not the logical;\nasserting not the meaning of a term only, but along with it an observed\nmatter of fact. The proposition, \"A circle is a figure bounded by a line\nwhich has all its points equally distant from a point within it,\" is\ncalled the definition of a circle; but the proposition from which so\nmany consequences follow, and which is really a first principle in\ngeometry, is, that figures answering to this description exist. And thus\nwe may call \"Three is two and one\" a definition of three; but the\ncalculations which depend on that proposition do not follow from the\ndefinition itself, but from an arithmetical theorem presupposed in it,\nnamely, that collections of objects exist, which while they impress the\nsenses thus,\n\n o o\n o,\n\nmay be separated into two parts, thus,\n\n o o o.\n\nThis proposition being granted, we term all such parcels Threes, after\nwhich the enunciation of the above mentioned physical fact will serve\nalso for a definition of the word Three.\n\nThe Science of Number is thus no exception to the conclusion we\npreviously arrived at, that the processes even of deductive sciences are\naltogether inductive, and that their first principles are\ngeneralizations from experience. It remains to be examined whether this\nscience resembles geometry in the further circumstance, that some of its\ninductions are not exactly true; and that the peculiar certainty\nascribed to it, on account of which its propositions are called\nNecessary Truths, is fictitious and hypothetical, being true in no other\nsense than that those propositions legitimately follow from the\nhypothesis of the truth of premises which are avowedly mere\napproximations to truth.\n\n\n\u00a7 3. The inductions of arithmetic are of two sorts: first, those which\nwe have just expounded, such as One and one are two, Two and one are\nthree, &c., which may be called the definitions of the various numbers,\nin the improper or geometrical sense of the word Definition; and\nsecondly, the two following axioms: The sums of equals are equal, The\ndifferences of equals are equal. These two are sufficient; for the\ncorresponding propositions respecting unequals may be proved from these,\nby a _reductio ad absurdum_.\n\nThese axioms, and likewise the so-called definitions, are, as has\nalready been said, results of induction; true of all objects whatever,\nand, as it may seem, exactly true, without the hypothetical assumption\nof unqualified truth where an approximation to it is all that exists.\nThe conclusions, therefore, it will naturally be inferred, are exactly\ntrue, and the science of number is an exception to other demonstrative\nsciences in this, that the categorical certainty which is predicable of\nits demonstrations is independent of all hypothesis.\n\nOn more accurate investigation, however, it will be found that, even in\nthis case, there is one hypothetical element in the ratiocination. In\nall propositions concerning numbers, a condition is implied, without\nwhich none of them would be true; and that condition is an assumption\nwhich maybe false. The condition, is that 1 = 1; that all the numbers\nare numbers of the same or of equal units. Let this be doubtful, and not\none of the propositions of arithmetic will hold true. How can we know\nthat one pound and one pound make two pounds, if one of the pounds may\nbe troy, and the other avoirdupois? They may not make two pounds of\neither, or of any weight. How can we know that a forty-horse power is\nalways equal to itself, unless we assume that all horses are of equal\nstrength? It is certain that 1 is always equal in _number_ to 1; and\nwhere the mere number of objects, or of the parts of an object, without\nsupposing them to be equivalent in any other respect, is all that is\nmaterial, the conclusions of arithmetic, so far as they go to that\nalone, are true without mixture of hypothesis. There are a few such\ncases; as, for instance, an inquiry into the amount of the population of\nany country. It is indifferent to that inquiry whether they are grown\npeople or children, strong or weak, tall or short; the only thing we\nwant to ascertain is their number. But whenever, from equality or\ninequality of number, equality or inequality in any other respect is to\nbe inferred, arithmetic carried into such inquiries becomes as\nhypothetical a science as geometry. All units must be assumed to be\nequal in that other respect; and this is never accurately true, for one\nactual pound weight is not exactly equal to another, nor one measured\nmile's 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\ncomprises the twofold conception of unconditional truth and perfect\naccuracy, is not an attribute of all mathematical truths, but of those\nonly which relate to pure Number, as distinguished from Quantity in the\nmore enlarged sense; and only so long as we abstain from supposing that\nthe numbers are a precise index to actual quantities. The certainty\nusually ascribed to the conclusions of geometry, and even to those of\nmechanics, is nothing whatever but certainty of inference. We can have\nfull assurance of particular results under particular suppositions, but\nwe cannot have the same assurance that these suppositions are accurately\ntrue, nor that they include all the data which may exercise an influence\nover the result in any given instance.\n\n\n\u00a7 4. It appears, therefore, that the method of all Deductive Sciences is\nhypothetical. They proceed by tracing the consequences of certain\nassumptions; leaving for separate consideration whether the assumptions\nare true or not, and if not exactly true, whether they are a\nsufficiently near approximation to the truth. The reason is obvious.\nSince it is only in questions of pure number that the assumptions are\nexactly true, and even there, only so long as no conclusions except\npurely numerical ones are to be founded on them; it must, in all other\ncases of deductive investigation, form a part of the inquiry, to\ndetermine how much the assumptions want of being exactly true in the\ncase in hand. This is generally a matter of observation, to be repeated\nin every fresh case; or if it has to be settled by argument instead of\nobservation, may require in every different case different evidence, and\npresent every degree of difficulty from the lowest to the highest. But\nthe other part of the process--namely, to determine what else may be\nconcluded if we find, and in proportion as we find, the assumptions to\nbe true--may be performed once for all, and the results held ready to be\nemployed as the occasions turn up for use. We thus do all beforehand\nthat can be so done, and leave the least possible work to be performed\nwhen cases arise and press for a decision. This inquiry into the\ninferences which can be drawn from assumptions, is what properly\nconstitutes 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\ninferences in this form--_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_,\ntherefore _a_ is a mark of _d_, which last may be a truth inaccessible\nto direct observation. In like manner it is allowable to say, _suppose_\nthat _a_ were a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a\nmark of _d_, which last conclusion was not thought of by those who laid\ndown the premises. A system of propositions as complicated as geometry\nmight be deduced from assumptions which are false; as was done by\nPtolemy, Descartes, and others, in their attempts to explain\nsynthetically the phenomena of the solar system on the supposition that\nthe apparent motions of the heavenly bodies were the real motions, or\nwere produced in some way more or less different from the true one.\nSometimes the same thing is knowingly done, for the purpose of showing\nthe falsity of the assumption; which is called a _reductio ad absurdum_.\nIn such cases, the reasoning is as follows: _a_ is a mark of _b_, and\n_b_ of _c_; now if _c_ were also a mark of _d_, _a_ would be a mark of\n_d_; but _d_ is known to be a mark of the absence of _a_; consequently\n_a_ would be a mark of its own absence, which is a contradiction;\ntherefore _c_ is not a mark of _d_.\n\n\n\u00a7 5. It has even been held by some writers, that all ratiocination rests\nin the last resort on a _reductio ad absurdum_; since the way to enforce\nassent to it, in case of obscurity, would be to show that if the\nconclusion be denied we must deny some one at least of the premises,\nwhich, as they are all supposed true, would be a contradiction. And in\naccordance with this, many have thought that the peculiar nature of the\nevidence of ratiocination consisted in the impossibility of admitting\nthe premises and rejecting the conclusion without a contradiction in\nterms. This theory, however, is inadmissible as an explanation of the\ngrounds on which ratiocination itself rests. If any one denies the\nconclusion notwithstanding his admission of the premises, he is not\ninvolved in any direct and express contradiction until he is compelled\nto deny some premise; and he can only be forced to do this by a\n_reductio ad absurdum_, that is, by another ratiocination: now, if he\ndenies the validity of the reasoning process itself, he can no more be\nforced to assent to the second syllogism than to the first. In truth,\ntherefore, no one is ever forced to a contradiction in terms: he can\nonly be forced to a contradiction (or rather an infringement) of the\nfundamental maxim of ratiocination, namely, that whatever has a mark,\nhas what it is a mark of; or, (in the case of universal propositions,)\nthat whatever is a mark of anything, is a mark of whatever else that\nthing is a mark of. For in the case of every correct argument, as soon\nas thrown into the syllogistic form, it is evident without the aid of\nany other syllogism, that he who, admitting the premises, fails to draw\nthe conclusion, does not conform to the above axiom.\n\nWe have now proceeded as far in the theory of Deduction as we can\nadvance in the present stage of our inquiry. Any further insight into\nthe subject requires that the foundation shall have been laid of the\nphilosophic theory of Induction itself; in which theory that of\ndeduction, as a mode of induction, which we have now shown it to be,\nwill assume spontaneously the place which belongs to it, and will\nreceive its share of whatever light may be thrown upon the great\nintellectual operation of which it forms so important a part.\n\n\n\n\nCHAPTER VII.\n\nEXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES.\n\n\n\u00a7 1. Polemical discussion is foreign to the plan of this work. But an\nopinion which stands in need of much illustration, can often receive it\nmost effectually, and least tediously, in the form of a defence against\nobjections. And on subjects concerning which speculative minds are still\ndivided, a writer does but half his duty by stating his own doctrine, if\nhe does not also examine, and to the best of his ability judge, those of\nother thinkers.\n\nIn the dissertation which Mr. Herbert Spencer has prefixed to his, in\nmany respects, highly philosophical treatise on the Mind,[39] he\ncriticises some of the doctrines of the two preceding chapters, and\npropounds a theory of his own on the subject of first principles. Mr.\nSpencer agrees with me in considering axioms to be \"simply our earliest\ninductions from experience.\" But he differs from me \"widely as to the\nworth of the test of inconceivableness.\" He thinks that it is the\nultimate test of all beliefs. He arrives at this conclusion by two\nsteps. First, we never can have any stronger ground for believing\nanything, than that the belief of it \"invariably exists.\" Whenever any\nfact or proposition is invariably believed; that is, if I understand Mr.\nSpencer rightly, believed by all persons, and by oneself at all times;\nit is entitled to be received as one of the primitive truths, or\noriginal premises of our knowledge. Secondly, the criterion by which we\ndecide whether anything is invariably believed to be true, is our\ninability to conceive it as false. \"The inconceivability of its negation\nis the test by which we ascertain whether a given belief invariably\nexists or not.\" \"For our primary beliefs, the fact of invariable\nexistence, tested by an abortive effort to cause their non-existence, is\nthe only reason assignable.\" He thinks this the sole ground of our\nbelief in our own sensations. If I believe that I feel cold, I only\nreceive this as true because I cannot conceive that I am not feeling\ncold. \"While the proposition remains true, the negation of it remains\ninconceivable.\" There are numerous other beliefs which Mr. Spencer\nconsiders to rest on the same basis; being chiefly those, or a part of\nthose, which the metaphysicians of the Reid and Stewart school consider\nas truths of immediate intuition. That there exists a material world;\nthat this is the very world which we directly and immediately perceive,\nand not merely the hidden cause of our perceptions; that Space, Time,\nForce, Extension, Figure, are not modes of our consciousness, but\nobjective realities; are regarded by Mr. Spencer as truths known by the\ninconceivableness of their negatives. We cannot, he says, by any effort,\nconceive these objects of thought as mere states of our mind; as not\nhaving an existence external to us. Their real existence is, therefore,\nas certain as our sensations themselves. The truths which are the\nsubject of direct knowledge, being, according to this doctrine, known to\nbe truths only by the inconceivability of their negation; and the truths\nwhich are not the object of direct knowledge, being known as inferences\nfrom those which are; and those inferences being believed to follow from\nthe premises, only because we cannot conceive them not to follow;\ninconceivability is thus the ultimate ground of all assured beliefs.\n\nThus far, there is no very wide difference between Mr. Spencer's\ndoctrine and the ordinary one of philosophers of the intuitive school,\nfrom Descartes to Dr. Whewell; but at this point Mr. Spencer diverges\nfrom them. For he does not, like them, set up the test of\ninconceivability as infallible. On the contrary, he holds that it may be\nfallacious, not from any fault in the test itself, but because \"men have\nmistaken for inconceivable things, some things which were not\ninconceivable.\" And he himself, in this very book, denies not a few\npropositions usually regarded as among the most marked examples of\ntruths whose negations are inconceivable. But occasional failure, he\nsays, is incident to all tests. If such failure vitiates \"the test of\ninconceivableness,\" it \"must similarly vitiate all tests whatever. We\nconsider an inference logically drawn from established premises to be\ntrue. Yet in millions of cases men have been wrong in the inferences\nthey have thought thus drawn. Do we therefore argue that it is absurd to\nconsider an inference true on no other ground than that it is logically\ndrawn from established premises? No: we say that though men may have\ntaken for logical inferences, inferences that were not logical, there\nnevertheless _are_ logical inferences, and that we are justified in\nassuming the truth of what seem to us such, until better instructed.\nSimilarly, though men may have thought some things inconceivable which\nwere not so, there may still be inconceivable things; and the inability\nto conceive the negation of a thing, may still be our best warrant for\nbelieving it.... Though occasionally it may prove an imperfect test,\nyet, as our most certain beliefs are capable of no better, to doubt any\none belief because we have no higher guarantee for it, is really to\ndoubt all beliefs.\" Mr. Spencer's doctrine, therefore, does not erect\nthe curable, but only the incurable limitations of the human conceptive\nfaculty, into laws of the outward universe.\n\n\n\u00a7 2. The doctrine, that \"a belief which is proved by the\ninconceivableness of its negation to invariably exist, is true,\" Mr.\nSpencer enforces by two arguments, one of which may be distinguished as\npositive, and the other as negative.\n\nThe positive argument is, that every such belief represents the\naggregate of all past experience. \"Conceding the entire truth of\" the\n\"position, that during any phase of human progress, the ability or\ninability to form a specific conception wholly depends on the\nexperiences men have had; and that, by a widening of their experiences,\nthey may, by and by, be enabled to conceive things before inconceivable\nto them; it may still be argued that as, at any time, the best warrant\nmen can have for a belief is the perfect agreement of all pre-existing\nexperience in support of it, it follows that, at any time, the\ninconceivableness of its negation is the deepest test any belief admits\nof.... Objective facts are ever impressing themselves upon us; our\nexperience is a register of these objective facts; and the\ninconceivableness of a thing implies that it is wholly at variance with\nthe register. Even were this all, it is not clear how, if every truth is\nprimarily inductive, any better test of truth could exist. But it must\nbe remembered that whilst many of these facts, impressing themselves\nupon us, are occasional; whilst others again are very general; some are\nuniversal and unchanging. These universal and unchanging facts are, by\nthe hypothesis, certain to establish beliefs of which the negations are\ninconceivable; whilst the others are not certain to do this; and if they\ndo, subsequent facts will reverse their action. Hence if, after an\nimmense accumulation of experiences, there remain beliefs of which the\nnegations are still inconceivable, most, if not all of them, must\ncorrespond to universal objective facts. If there be ... certain\nabsolute uniformities in nature; if these uniformities produce, as they\nmust, absolute uniformities in our experience; and if ... these absolute\nuniformities in our experience disable us from conceiving the negations\nof them; then answering to each absolute uniformity in nature which we\ncan cognize, there must exist in us a belief of which the negation is\ninconceivable, and which is absolutely true. In this wide range of cases\nsubjective inconceivableness must correspond to objective impossibility.\nFurther experience will produce correspondence where it may not yet\nexist; and we may expect the correspondence to become ultimately\ncomplete. In nearly all cases this test of inconceivableness must be\nvalid now;\" (I wish I could think we were so nearly arrived at\nomniscience) \"and where it is not, it still expresses the net result of\nour experience up to the present time; which is the most that any test\ncan do.\"\n\nTo this I answer: Even if it were true that inconceivableness represents\n\"the net result\" of all past experience, why should we stop at the\nrepresentative when we can get at the thing represented? If our\nincapacity to conceive the negation of a given supposition is proof of\nits truth, because proving that our experience has hitherto been\nuniform in its favour, the real evidence for the supposition is not the\ninconceivableness, but the uniformity of experience. Now this, which is\nthe substantial and only proof, is directly accessible. We are not\nobliged to presume it from an incidental consequence. If all past\nexperience is in favour of a belief, let this be stated, and the belief\nopenly rested on that ground: after which the question arises, what that\nfact may be worth as evidence of its truth? For uniformity of experience\nis evidence in very different degrees: in some cases it is strong\nevidence, in others weak, in others it scarcely amounts to evidence at\nall. That all metals sink in water, was an uniform experience, from the\norigin of the human race to the discovery of potassium in the present\ncentury by Sir Humphry Davy. That all swans are white, was an uniform\nexperience down to the discovery of Australia. In the few cases in which\nuniformity of experience does amount to the strongest possible proof, as\nwith such propositions as these, Two straight lines cannot inclose a\nspace, Every event has a cause, it is not because their negations are\ninconceivable, which is not always the fact; but because the experience,\nwhich has been thus uniform, pervades all nature. It will be shown in\nthe following Book that none of the conclusions either of induction or\nof deduction can be considered certain, except as far as their truth is\nshown to be inseparably bound up with truths of this class.\n\nI maintain then, first, that uniformity of past experience is very far\nfrom being universally a criterion of truth. But secondly,\ninconceivableness is still farther from being a test even of that test.\nUniformity of contrary experience is only one of many causes of\ninconceivability. Tradition handed down from a period of more limited\nknowledge, is one of the commonest. The mere familiarity of one mode of\nproduction of a phenomenon, often suffices to make every other mode\nappear inconceivable. Whatever connects two ideas by a strong\nassociation may, and continually does, render their separation in\nthought impossible; as Mr. Spencer, in other parts of his speculations,\nfrequently recognises. It was not for want of experience that the\nCartesians were unable to conceive that one body could produce motion\nin another without contact. They had as much experience of other modes\nof producing motion, as they had of that mode. The planets had revolved,\nand heavy bodies had fallen, every hour of their lives. But they fancied\nthese phenomena to be produced by a hidden machinery which they did not\nsee, because without it they were unable to conceive what they did see.\nThe inconceivableness, instead of representing their experience,\ndominated and overrode their experience. It is needless to dwell farther\non what I have termed the positive argument of Mr. Spencer in support of\nhis criterion of truth. I pass to his negative argument, on which he\nlays more stress.\n\n\n\u00a7 3. The negative argument is, that, whether inconceivability be good\nevidence or bad, no stronger evidence is to be obtained. That what is\ninconceivable cannot be true, is postulated in every act of thought. It\nis the foundation of all our original premises. Still more it is assumed\nin all conclusions from those premises. The invariability of belief,\ntested by the inconceivableness of its negation, \"is our sole warrant\nfor every demonstration. Logic is simply a systematization of the\nprocess by which we indirectly obtain this warrant for beliefs that do\nnot directly possess it. To gain the strongest conviction possible\nrespecting any complex fact, we either analytically descend from it by\nsuccessive steps, each of which we unconsciously test by the\ninconceivableness of its negation, until we reach some axiom or truth\nwhich we have similarly tested; or we synthetically ascend from such\naxiom or truth by such steps. In either case we connect some isolated\nbelief, with a belief which invariably exists, by a series of\nintermediate beliefs which invariably exist.\" The following passage sums\nup the whole theory: \"When we perceive that the negation of the belief\nis inconceivable, we have all possible warrant for asserting the\ninvariability of its existence: and in asserting this, we express alike\nour logical justification of it, and the inexorable necessity we are\nunder of holding it.... We have seen that this is the assumption on\nwhich every conclusion whatever ultimately rests. We have no other\nguarantee for the reality of consciousness, of sensations, of personal\nexistence; we have no other guarantee for any axiom; we have no other\nguarantee for any step in a demonstration. Hence, as being taken for\ngranted in every act of the understanding, it must be regarded as the\nUniversal Postulate.\" But as this postulate which we are under an\n\"inexorable necessity\" of holding true, is sometimes false; as \"beliefs\nthat once were shown by the inconceivableness of their negations to\ninvariably exist, have since been found untrue,\" and as \"beliefs that\nnow possess this character may some day share the same fate;\" the canon\nof belief laid down by Mr. Spencer is, that \"the most certain\nconclusion\" is that \"which involves the postulate the fewest times.\"\nReasoning, therefore, never ought to prevail against one of the\nimmediate beliefs (the belief in Matter, in the outward reality of\nExtension, Space, and the like), because each of these involves the\npostulate only once; while an argument, besides involving it in the\npremises, involves it again in every step of the ratiocination, no one\nof the successive acts of inference being recognised as valid except\nbecause we cannot conceive the conclusion not to follow from the\npremises.\n\nIt will be convenient to take the last part of this argument first. In\nevery reasoning, according to Mr. Spencer, the assumption of the\npostulate is renewed at every step. At each inference we judge that the\nconclusion follows from the premises, our sole warrant for that judgment\nbeing that we cannot conceive it not to follow. Consequently if the\npostulate is fallible, the conclusions of reasoning are more vitiated by\nthat uncertainty than direct intuitions; and the disproportion is\ngreater, the more numerous the steps of the argument.\n\nTo test this doctrine, let us first suppose an argument consisting only\nof a single step, which would be represented by one syllogism. This\nargument does rest on an assumption, and we have seen in the preceding\nchapters what the assumption is. It is, that whatever has a mark, has\nwhat it is a mark of. The evidence of this axiom I shall not consider at\npresent;[40] let us suppose it (with Mr. Spencer) to be the\ninconceivableness of its reverse.\n\nLet us now add a second step to the argument: we require, what? Another\nassumption? No: the same assumption a second time; and so on to a third,\nand a fourth. I confess I do not see how, on Mr. Spencer's own\nprinciples, the repetition of the assumption at all weakens the force of\nthe argument. If it were necessary the second time to assume some other\naxiom, the argument would no doubt be weakened, since it would be\nnecessary to its validity that both axioms should be true, and it might\nhappen that one was true and not the other: making two chances of error\ninstead of one. But since it is the _same_ axiom, if it is true once it\nis true every time; and if the argument, being of a hundred links,\nassumed the axiom a hundred times, these hundred assumptions would make\nbut one chance of error among them all. It is satisfactory that we are\nnot obliged to suppose the deductions of pure mathematics to be among\nthe most uncertain of argumentative processes, which on Mr. Spencer's\ntheory they could hardly fail to be, since they are the longest. But the\nnumber of steps in an argument does not subtract from its reliableness,\nif no new _premises_, of an uncertain character, are taken up by the\nway.\n\nTo speak next of the premises. Our assurance of their truth, whether\nthey be generalities or individual facts, is grounded, in Mr. Spencer's\nopinion, on the inconceivableness of their being false. It is necessary\nto advert to a double meaning of the word inconceivable, which Mr.\nSpencer is aware of, and would sincerely disclaim founding an argument\nupon, but from which his case derives no little advantage\nnotwithstanding. By inconceivableness is sometimes meant, inability to\nform or get rid of an _idea_; sometimes, inability to form or get rid of\na _belief_. The former meaning is the most conformable to the analogy of\nlanguage; for a conception always means an idea, and never a belief.\nThe wrong meaning of \"inconceivable\" is, however, fully as frequent in\nphilosophical discussion as the right meaning, and the intuitive school\nof metaphysicians could not well do without either. To illustrate the\ndifference, we will take two contrasted examples. The early physical\nspeculators considered antipodes incredible, because inconceivable. But\nantipodes were not inconceivable in the primitive sense of the word. An\nidea of them could be formed without difficulty: they could be\ncompletely pictured to the mental eye. What was difficult, and as it\nthen seemed, impossible, was to apprehend them as believable. The idea\ncould be put together, of men sticking on by their feet to the under\nside of the earth; but the belief _would_ follow, that they must fall\noff. Antipodes were not unimaginable, but they were unbelievable.\n\nOn the other hand, when I endeavour to conceive an end to extension, the\ntwo ideas refuse to come together. When I attempt to form a conception\nof the last point of space, I cannot help figuring to myself a vast\nspace beyond that last point. The combination is, under the conditions\nof our experience, unimaginable. This double meaning of inconceivable it\nis very important to bear in mind, for the argument from\ninconceivableness almost always turns on the alternate substitution of\neach of those meanings for the other.\n\nIn which of these two senses does Mr. Spencer employ the term, when he\nmakes it a test of the truth of a proposition that its negation is\ninconceivable? Until Mr. Spencer expressly stated the contrary, I\ninferred from the course of his argument, that he meant unbelievable. He\nhas, however, in a paper published in the fifth number of the\n_Fortnightly Review_, disclaimed this meaning, and declared that by an\ninconceivable proposition he means, now and always, \"one of which the\nterms cannot, by any effort, be brought before consciousness in that\nrelation which the proposition asserts between them--a proposition of\nwhich the subject and predicate offer an insurmountable resistance to\nunion in thought.\" We now, therefore, know positively that Mr. Spencer\nalways endeavours to use the word inconceivable in this, its proper,\nsense: but it may yet be questioned whether his endeavour is always\nsuccessful; whether the other, and popular use of the word does not\nsometimes creep in with its associations, and prevent him from\nmaintaining a clear separation between the two. When, for example, he\nsays, that when I feel cold, I cannot conceive that I am not feeling\ncold, this expression cannot be translated into, \"I cannot conceive\nmyself not feeling cold,\" for it is evident that I can: the word\nconceive, therefore, is here used to express the recognition of a matter\nof fact--the perception of truth or falsehood; which I apprehend to be\nexactly the meaning of an act of belief, as distinguished from simple\nconception. Again, Mr. Spencer calls the attempt to conceive something\nwhich is inconceivable, \"an abortive effort to cause the non-existence\"\nnot of a conception or mental representation, but of a belief. There is\nneed, therefore, to revise a considerable part of Mr. Spencer's\nlanguage, if it is to be kept always consistent with his definition of\ninconceivability. But in truth the point is of little importance; since\ninconceivability, in Mr. Spencer's theory, is only a test of truth,\ninasmuch as it is a test of believability. The inconceivableness of a\nsupposition is the extreme case of its unbelievability. This is the very\nfoundation of Mr. Spencer's doctrine. The invariability of the belief is\nwith him the real guarantee. The attempt to conceive the negative, is\nmade in order to test the inevitableness of the belief. It should be\ncalled, an attempt to _believe_ the negative. When Mr. Spencer says that\nwhile looking at the sun a man cannot conceive that he is looking into\ndarkness, he should have said that a man cannot _believe_ that he is\ndoing so. For it is surely possible, in broad daylight, to _imagine_\noneself looking into darkness.[41] As Mr. Spencer himself says, speaking\nof the belief of our own existence: \"That he _might_ not exist, he can\nconceive well enough; but that he _does_ not exist, he finds it\nimpossible to conceive,\" _i.e._ to believe. So that the statement\nresolves itself into this: That I exist, and that I have sensations, I\nbelieve, because I cannot believe otherwise. And in this case every one\nwill admit that the necessity is real. Any one's present sensations, or\nother states of subjective consciousness, that one person inevitably\nbelieves. They are facts known _per se_: it is impossible to ascend\nbeyond them. Their negative is really unbelievable, and therefore there\nis never any question about believing it. Mr. Spencer's theory is not\nneeded for these truths.\n\nBut according to Mr. Spencer there are other beliefs, relating to other\nthings than our own subjective feelings, for which we have the same\nguarantee--which are, in a similar manner, invariable and necessary.\nWith regard to these other beliefs, they cannot be necessary, since they\ndo not always exist. There have been, and are, many persons who do not\nbelieve the reality of an external world, still less the reality of\nextension and figure as the forms of that external world; who do not\nbelieve that space and time have an existence independent of the\nmind--nor any other of Mr. Spencer's objective intuitions. The negations\nof these alleged invariable beliefs are not unbelievable, for they are\nbelieved. It may be maintained, without obvious error, that we cannot\n_imagine_ tangible objects as mere states of our own and other people's\nconsciousness; that the perception of them irresistibly suggests to us\nthe _idea_ of something external to ourselves: and I am not in a\ncondition to say that this is not the fact (though I do not think any\none is entitled to affirm it of any person besides himself). But many\nthinkers have believed, whether they could conceive it or not, that what\nwe represent to ourselves as material objects, are mere modifications of\nconsciousness; complex feelings of touch and of muscular action. Mr.\nSpencer may think the inference correct from the unimaginable to the\nunbelievable, because he holds that belief itself is but the persistence\nof an idea, and that what we can succeed in imagining, we cannot at the\nmoment help apprehending as believable. But of what consequence is it\nwhat we apprehend at the moment, if the moment is in contradiction to\nthe permanent state of our mind? A person who has been frightened when\nan infant by stories of ghosts, though he disbelieves them in after\nyears (and perhaps disbelieved them at first), may be unable all his\nlife to be in a dark place, in circumstances stimulating to the\nimagination, without mental discomposure. The idea of ghosts, with all\nits attendant terrors, is irresistibly called up in his mind by the\noutward circumstances. Mr. Spencer may say, that while he is under the\ninfluence of this terror he does not disbelieve in ghosts, but has a\ntemporary and uncontrollable belief in them. Be it so; but allowing it\nto be so, which would it be truest to say of this man on the whole--that\nhe believes in ghosts, or that he does not believe in them? Assuredly\nthat he does not believe in them. The case is similar with those who\ndisbelieve a material world. Though they cannot get rid of the idea;\nthough while looking at a solid object they cannot help having the\nconception, and therefore, according to Mr. Spencer's metaphysics, the\nmomentary belief, of its externality; even at that moment they would\nsincerely deny holding that belief: and it would be incorrect to call\nthem other than disbelievers of the doctrine. The belief therefore is\nnot invariable; and the test of inconceivableness fails in the only\ncases to which there could ever be any occasion to apply it.\n\nThat a thing may be perfectly believable, and yet may not have become\nconceivable, and that we may habitually believe one side of an\nalternative, and conceive only in the other, is familiarly exemplified\nin the state of mind of educated persons respecting sunrise and sunset.\nAll educated persons either know by investigation, or believe on the\nauthority of science, that it is the earth and not the sun which moves:\nbut there are probably few who habitually _conceive_ the phenomenon\notherwise than as the ascent or descent of the sun. Assuredly no one can\ndo so without a prolonged trial; and it is probably not easier now than\nin the first generation after Copernicus. Mr. Spencer does not say, \"In\nlooking at sunrise it is impossible not to conceive that it is the sun\nwhich moves, therefore this is what everybody believes, and we have all\nthe evidence for it that we can have for any truth.\" Yet this would be\nan exact parallel to his doctrine about the belief in matter.\n\nThe existence of matter, and other Noumena, as distinguished from the\nphenomenal world, remains a question of argument, as it was before; and\nthe very general, but neither necessary nor universal, belief in them,\nstands as a psychological phenomenon to be explained, either on the\nhypothesis of its truth, or on some other. The belief is not a\nconclusive proof of its own truth, unless there are no such things as\n_idola trib\u00fbs_; but, being a fact, it calls on antagonists to show, from\nwhat except the real existence of the thing believed, so general and\napparently spontaneous a belief can have originated. And its opponents\nhave never hesitated to accept this challenge.[42] The amount of their\nsuccess in meeting it will probably determine the ultimate verdict of\nphilosophers on the question.\n\n\n\u00a7 4. Sir William Hamilton holds as I do, that inconceivability is no\ncriterion of impossibility. \"There is no ground for inferring a certain\nfact to be impossible, merely from our inability to conceive its\npossibility.\" \"Things there are which _may_, nay _must_, be true, of\nwhich the understanding is wholly unable to construe to itself the\npossibility.\"[43] Sir William Hamilton is however a firm believer in the\n_\u00e0 priori_ character of many axioms, and of the sciences deduced from\nthem; and is so far from considering those axioms to rest on the\nevidence of experience, that he declares certain of them to be true even\nof Noumena--of the Unconditioned--of which it is one of the principal\naims of his philosophy to prove that the nature of our faculties debars\nus from having any knowledge. The axioms to which he attributes this\nexceptional emancipation from the limits which confine all our other\npossibilities of knowledge; the chinks through which, as he represents,\none ray of light finds its way to us from behind the curtain which veils\nfrom us the mysterious world of Things in themselves,--are the two\nprinciples, which he terms, after the schoolmen, the Principle of\nContradiction, and the Principle of Excluded Middle: the first, that two\ncontradictory propositions cannot both be true; the second, that they\ncannot both be false. Armed with these logical weapons, we may boldly\nface Things in themselves, and tender to them the double alternative,\nsure that they must absolutely elect one or the other side, though we\nmay be for ever precluded from discovering which. To take his favourite\nexample, we cannot conceive the infinite divisibility of matter, and we\ncannot conceive a minimum, or end to divisibility: yet one or the other\nmust be true.\n\nAs I have hitherto said nothing of the two axioms in question, those of\nContradiction and of Excluded Middle, it is not unseasonable to consider\nthem here. The former asserts that an affirmative proposition and the\ncorresponding negative proposition cannot both be true; which has\ngenerally been held to be intuitively evident. Sir William Hamilton and\nthe Germans consider it to be the statement in words of a form or law of\nour thinking faculty. Other philosophers, not less deserving of\nconsideration, deem it to be an identical proposition; an assertion\ninvolved in the meaning of terms; a mode of defining Negation, and the\nword Not.\n\nI am able to go one step with these last. An affirmative assertion and\nits negative are not two independent assertions, connected with each\nother only as mutually incompatible. That if the negative be true, the\naffirmative must be false, really is a mere identical proposition; for\nthe negative proposition asserts nothing but the falsity of the\naffirmative, and has no other sense or meaning whatever. The Principium\nContradictionis should therefore put off the ambitious phraseology which\ngives it the air of a fundamental antithesis pervading nature, and\nshould be enunciated in the simpler form, that the same proposition\ncannot at the same time be false and true. But I can go no farther with\nthe Nominalists; for I cannot look upon this last as a merely verbal\nproposition. I consider it to be, like other axioms, one of our first\nand most familiar generalizations from experience. The original\nfoundation of it I take to be, that Belief and Disbelief are two\ndifferent mental states, excluding one another. This we know by the\nsimplest observation of our own minds. And if we carry our observation\noutwards, we also find that light and darkness, sound and silence,\nmotion and quiescence, equality and inequality, preceding and following,\nsuccession and simultaneousness, any positive phenomenon whatever and\nits negative, are distinct phenomena, pointedly contrasted, and the one\nalways absent where the other is present. I consider the maxim in\nquestion to be a generalization from all these facts.\n\nIn like manner as the Principle of Contradiction (that one of two\ncontradictories must be false) means that an assertion cannot be _both_\ntrue and false, so the Principle of Excluded Middle, or that one of two\ncontradictories must be true, means that an assertion must be _either_\ntrue or false: either the affirmative is true, or otherwise the negative\nis true, which means that the affirmative is false. I cannot help\nthinking this principle a surprising specimen of a so-called necessity\nof Thought, since it is not even true, unless with a large\nqualification. A proposition must be either true or false, _provided_\nthat the predicate be one which can in any intelligible sense be\nattributed to the subject; (and as this is always assumed to be the case\nin treatises on logic, the axiom is always laid down there as of\nabsolute truth). \"Abracadabra is a second intention\" is neither true nor\nfalse. Between the true and the false there is a third possibility, the\nUnmeaning: and this alternative is fatal to Sir William Hamilton's\nextension of the maxim to Noumena. That Matter must either have a\nminimum of divisibility or be infinitely divisible, is more than we can\never know. For in the first place, Matter, in any other than the\nphenomenal sense of the term, may not exist: and it will scarcely be\nsaid that a non-entity must be either infinitely or finitely\ndivisible.[44] In the second place, though matter, considered as the\noccult cause of our sensations, do really exist, yet what we call\ndivisibility may be an attribute only of our sensations of sight and\ntouch, and not of their uncognizable cause. Divisibility may not be\npredicable at all, in any intelligible sense, of Things in themselves,\nnor therefore of Matter in itself; and the assumed necessity of being\neither infinitely or finitely divisible, may be an inapplicable\nalternative.\n\nOn this question I am happy to have the full concurrence of Mr. Herbert\nSpencer, from whose paper in the _Fortnightly Review_ I extract the\nfollowing passage. The germ of an idea identical with that of Mr.\nSpencer may be found in the present chapter, about a page back, but in\nMr. Spencer it is not an undeveloped thought, but a philosophical\ntheory.\n\n\"When remembering a certain thing as in a certain place, the place and\nthe thing are mentally represented together; while to think of the\nnon-existence of the thing in that place, implies a consciousness in\nwhich the place is represented, but not the thing. Similarly, if instead\nof thinking of an object as colourless, we think of its having colour,\nthe change consists in the addition to the concept of an element that\nwas before absent from it--the object cannot be thought of first as red\nand then as not red, without one component of the thought being totally\nexpelled from the mind by another. The law of the Excluded Middle, then,\nis simply a generalization of the universal experience that some mental\nstates are directly destructive of other states. It formulates a certain\nabsolutely constant law, that the appearance of any positive mode of\nconsciousness cannot occur without excluding a correlative negative\nmode; and that the negative mode cannot occur without excluding the\ncorrelative positive mode: the antithesis of positive and negative\nbeing, indeed, merely an expression of this experience. Hence it follows\nthat if consciousness is not in one of the two modes it must be in the\nother.\"[45]\n\nI must here close this supplementary chapter, and with it the Second\nBook. The theory of Induction, in the most comprehensive sense of the\nterm, will form the subject of the Third.\n\nFOOTNOTES:\n\n[1] As Sir William Hamilton has pointed out, \"Some A is not B\" may also\nbe converted in the following form: \"No B is _some_ A.\" Some men are not\nnegroes; therefore, No negroes are _some_ men (_e.g._ Europeans).\n\n[2]\n All A is B } contraries.\n No A is B }\n\n Some A is B } subcontraries.\n Some A is not B }\n\n All A is B } contradictories.\n Some A is not B }\n\n No A is B } also contradictories.\n Some A is B }\n\n All A is B } and No A is B } respectively subalternate.\n Some A is B } Some A is not B }\n\n[3] His conclusions are, \"The first figure is suited to the discovery or\nproof of the properties of a thing; the second to the discovery or proof\nof the distinctions between things; the third to the discovery or proof\nof instances and exceptions; the fourth to the discovery, or exclusion,\nof the different species of a genus.\" The reference of syllogisms in the\nlast three figures to the _dictum de omni et nullo_ is, in Lambert's\nopinion, strained and unnatural: to each of the three belongs, according\nto him, a separate axiom, co-ordinate and of equal authority with that\n_dictum_, and to which he gives the names of _dictum de diverso_ for the\nsecond figure, _dictum de exemplo_ for the third, and _dictum de\nreciproco_ for the fourth. See part i. or _Dianoiologie_, chap. iv. \u00a7\n229 _et seqq._ Mr. Bailey, (_Theory of Reasoning_, 2nd ed. pp. 70-74)\ntakes a similar view of the subject.\n\n[4] Since this chapter was written, two treatises have appeared (or\nrather a treatise and a fragment of a treatise), which aim at a further\nimprovement in the theory of the forms of ratiocination: Mr. De Morgan's\n\"Formal Logic; or, the Calculus of Inference, Necessary and Probable;\"\nand the \"New Analytic of Logical Forms,\" attached as an Appendix to Sir\nWilliam Hamilton's _Discussions on Philosophy_, and at greater length,\nto his posthumous _Lectures on Logic_.\n\nIn Mr. De Morgan's volume--abounding, in its more popular parts, with\nvaluable observations felicitously expressed--the principal feature of\noriginality is an attempt to bring within strict technical rules the\ncases in which a conclusion can be drawn from premises of a form usually\nclassed as particular. Mr. De Morgan observes, very justly, that from\nthe premises Most Bs are Cs, most Bs are As, it may be concluded with\ncertainty that some As are Cs, since two portions of the class B, each\nof them comprising more than half, must necessarily in part consist of\nthe same individuals. Following out this line of thought, it is equally\nevident that if we knew exactly what proportion the \"most\" in each of\nthe premises bear to the entire class B, we could increase in a\ncorresponding degree the definiteness of the conclusion. Thus if 60 per\ncent of B are included in C, and 70 per cent in A, 30 per cent at least\nmust be common to both; in other words, the number of As which are Cs,\nand of Cs which are As, must be at least equal to 30 per cent of the\nclass B. Proceeding on this conception of \"numerically definite\npropositions,\" and extending it to such forms as these:--\"45 Xs (or\nmore) are each of them one of 70 Ys,\" or \"45 Xs (or more) are no one of\nthem to be found among 70 Ys,\" and examining what inferences admit of\nbeing drawn from the various combinations which may be made of premises\nof this description, Mr. De Morgan establishes universal formul\u00e6 for\nsuch inferences; creating for that purpose not only a new technical\nlanguage, but a formidable array of symbols analogous to those of\nalgebra.\n\nSince it is undeniable that inferences, in the cases examined by Mr. De\nMorgan, can legitimately be drawn, and that the ordinary theory takes no\naccount of them, I will not say that it was not worth while to show in\ndetail how these also could be reduced to formul\u00e6 as rigorous as those\nof Aristotle. What Mr. De Morgan has done was worth doing once (perhaps\nmore than once, as a school exercise); but I question if its results are\nworth studying and mastering for any practical purpose. The practical\nuse of technical forms of reasoning is to bar out fallacies: but the\nfallacies which require to be guarded against in ratiocination properly\nso called, arise from the incautious use of the common forms of\nlanguage; and the logician must track the fallacy into that territory,\ninstead of waiting for it on a territory of his own. While he remains\namong propositions which have acquired the numerical precision of the\nCalculus of Probabilities, the enemy is left in possession of the only\nground on which he can be formidable. And since the propositions (short\nof universal) on which a thinker has to depend, either for purposes of\nspeculation or of practice, do not, except in a few peculiar cases,\nadmit of any numerical precision; common reasoning cannot be translated\ninto Mr. De Morgan's forms, which therefore cannot serve any purpose as\na test of it.\n\nSir William Hamilton's theory of the \"quantification of the predicate\"\n(concerning the originality of which in his case there can be no doubt,\nhowever Mr. De Morgan may have also, and independently, originated an\nequivalent doctrine) may be briefly described as follows:--\n\n\"Logically\" (I quote his own words) \"we ought to take into account the\nquantity, always understood in thought, but usually, for manifest\nreasons, elided in its expression, not only of the subject, but also of\nthe predicate of a judgment.\" All A is B, is equivalent to all A is\n_some_ B. No A is B, to No A is _any_ B. Some A is B, is tantamount to\nsome A is _some_ B. Some A is not B, to Some A is _not any_ B. As in\nthese forms of assertion the predicate is exactly coextensive with the\nsubject, they all admit of simple conversion; and by this we obtain two\nadditional forms--Some B is _all_ A, and No B is _some_ A. We may also\nmake the assertion All A is all B, which will be true if the classes A\nand B are exactly coextensive. The last three forms, though conveying\nreal assertions, have no place in the ordinary classification of\nPropositions. All propositions, then, being supposed to be translated\ninto this language, and written each in that one of the preceding forms\nwhich answers to its signification, there emerges a new set of\nsyllogistic rules, materially different from the common ones. A general\nview of the points of difference may be given in the words of Sir W.\nHamilton (_Discussions_, 2nd ed. p. 651):--\n\n\"The revocation of the two terms of a Proposition to their true\nrelation; a proposition being always an _equation_ of its subject and\nits predicate.\n\n\"The consequent reduction of the Conversion of Propositions from three\nspecies to one--that of Simple Conversion.\n\n\"The reduction of all the _General Laws_ of Categorical Syllogisms to a\nsingle Canon.\n\n\"The evolution from that one canon of all the Species and varieties of\nSyllogisms.\n\n\"The abrogation of all the _Special Laws_ of Syllogism.\n\n\"A demonstration of the exclusive possibility of Three syllogistic\nFigures; and (on new grounds) the scientific and final abolition of the\nFourth.\n\n\"A manifestation that Figure is an unessential variation in syllogistic\nform; and the consequent absurdity of Reducing the syllogisms of the\nother figures to the first.\n\n\"An enouncement of _one Organic Principle_ for each Figure.\n\n\"A determination of the true number of the Legitimate Moods; with\n\n\"Their amplification in number (thirty-six);\n\n\"Their numerical equality under all the figures; and\n\n\"Their relative equivalence, or virtual identity, throughout every\nschematic difference.\n\n\"That, in the second and third figures, the extremes holding both the\nsame relation to the middle term, there is not, as in the first, an\nopposition and subordination between a term major and a term minor,\nmutually containing and contained, in the counter wholes of Extension\nand Comprehension.\n\n\"Consequently, in the second and third figures, there is no determinate\nmajor and minor premise, and there are two indifferent conclusions:\nwhereas in the first the premises are determinate, and there is a single\nproximate conclusion.\"\n\nThis doctrine, like that of Mr. De Morgan previously noticed, is a real\naddition to the syllogistic theory; and has moreover this advantage over\nMr. De Morgan's \"numerically definite Syllogism,\" that the forms it\nsupplies are really available as a test of the correctness of\nratiocination; since propositions in the common form may always have\ntheir predicates quantified, and so be made amenable to Sir W.\nHamilton's rules. Considered however as a contribution to the _Science_\nof Logic, that is, to the analysis of the mental processes concerned in\nreasoning, the new doctrine appears to me, I confess, not merely\nsuperfluous, but erroneous; since the form in which it clothes\npropositions does not, like the ordinary form, express what is in the\nmind of the speaker when he enunciates the proposition. I cannot think\nSir William Hamilton right in maintaining that the quantity of the\npredicate is \"always understood in thought.\" It is implied, but is not\npresent to the mind of the person who asserts the proposition. The\nquantification of the predicate, instead of being a means of bringing\nout more clearly the meaning of the proposition, actually leads the mind\nout of the proposition, into another order of ideas. For when we say,\nAll men are mortal, we simply mean to affirm the attribute mortality of\nall men; without thinking at all of the _class_ mortal in the concrete,\nor troubling ourselves about whether it contains any other beings or\nnot. It is only for some artificial purpose that we ever look at the\nproposition in the aspect in which the predicate also is thought of as a\nclass-name, either including the subject only, or the subject and\nsomething more. (See above, p. 104.)\n\nFor a fuller discussion of this subject, see the twenty-second chapter\nof a work already referred to, \"An Examination of Sir William Hamilton's\nPhilosophy.\"\n\n[5] Mr. Herbert Spencer (_Principles of Psychology_, pp. 125-7), though\nhis theory of the syllogism coincides with all that is essential of\nmine, thinks it a logical fallacy to present the two axioms in the text,\nas the regulating principles of syllogism. He charges me with falling\ninto the error pointed out by Archbishop Whately and myself, of\nconfounding exact likeness with literal identity; and maintains, that we\nought not to say that Socrates possesses _the same_ attributes which are\nconnoted by the word Man, but only that he possesses attributes _exactly\nlike_ them: according to which phraseology, Socrates, and the attribute\nmortality, are not two things coexisting with the same thing, as the\naxiom asserts, but two things coexisting with two different things.\n\nThe question between Mr. Spencer and me is merely one of language; for\nneither of us (if I understand Mr. Spencer's opinions rightly) believes\nan attribute to be a real thing, possessed of objective existence; we\nbelieve it to be a particular mode of naming our sensations, or our\nexpectations of sensation, when looked at in their relation to an\nexternal object which excites them. The question raised by Mr. Spencer\ndoes not, therefore, concern the properties of any really existing\nthing, but the comparative appropriateness, for philosophical purposes,\nof two different modes of using a name. Considered in this point of\nview, the phraseology I have employed, which is that commonly used by\nphilosophers, seems to me to be the best. Mr. Spencer is of opinion that\nbecause Socrates and Alcibiades are not the same man, the attribute\nwhich constitutes them men should not be called the same attribute; that\nbecause the humanity of one man and that of another express themselves\nto our senses not by the same individual sensations but by sensations\nexactly alike, humanity ought to be regarded as a different attribute in\nevery different man. But on this showing, the humanity even of any one\nman should be considered as different attributes now and half-an-hour\nhence; for the sensations by which it will then manifest itself to my\norgans will not be a continuation of my present sensations, but a\nrepetition of them; fresh sensations, not identical with, but only\nexactly like the present. If every general conception, instead of being\n\"the One in the Many,\" were considered to be as many different\nconceptions as there are things to which it is applicable, there would\nbe no such thing as general language. A name would have no general\nmeaning if _man_ connoted one thing when predicated of John, and\nanother, though closely resembling, thing when predicated of William.\nAccordingly a recent pamphlet asserts the impossibility of general\nknowledge on this precise ground.\n\nThe meaning of any general name is some outward or inward phenomenon,\nconsisting, in the last resort, of feelings; and these feelings, if\ntheir continuity is for an instant broken, are no longer the same\nfeelings, in the sense of individual identity. What, then, is the common\nsomething which gives a meaning to the general name? Mr. Spencer can\nonly say, it is the similarity of the feelings; and I rejoin, the\nattribute is precisely that similarity. The names of attributes are in\ntheir ultimate analysis names for the resemblances of our sensations (or\nother feelings). Every general name, whether abstract or concrete,\ndenotes or connotes one or more of those resemblances. It will not,\nprobably, be denied, that if a hundred sensations are undistinguishably\nalike, their resemblance ought to be spoken of as one resemblance, and\nnot a hundred resemblances which merely _resemble_ one another. The\nthings compared are many, but the something common to all of them must\nbe conceived as one, just as the name is conceived as one, though\ncorresponding to numerically different sensations of sound each time it\nis pronounced. The general term _man_ does not connote the sensations\nderived once from one man, which, once gone, can no more occur again\nthan the same flash of lightning. It connotes the general type of the\nsensations derived always from all men, and the power (always thought of\nas one) of producing sensations of that type. And the axiom might be\nthus worded: Two _types of sensation_ each of which coexists with a\nthird type, coexist with another; or Two _powers_ each of which coexists\nwith a third power coexist with one another.\n\nMr. Spencer has misunderstood me in another particular. He supposes that\nthe coexistence spoken of in the axiom, of two things with the same\nthird thing, means simultaneousness in time. The coexistence meant is\nthat of being jointly attributes of the same subject. The attribute of\nbeing born without teeth, and the attribute of having thirty-two teeth\nin mature age, are in this sense coexistent, both being attributes of\nman, though _ex vi termini_ never of the same man at the same time.\n\n[6] Supra, p. 128.\n\n[7] _Logic_, p. 239 (9th ed.).\n\n[8] It is hardly necessary to say, that I am not contending for any such\nabsurdity as that we _actually_ \"ought to have known\" and considered the\ncase of every individual man, past, present, and future, before\naffirming that all men are mortal: although this interpretation has\nbeen, strangely enough, put upon the preceding observations. There is no\ndifference between me and Archbishop Whately, or any other defender of\nthe syllogism, on the practical part of the matter; I am only pointing\nout an inconsistency in the logical theory of it, as conceived by almost\nall writers. I do not say that a person who affirmed, before the Duke of\nWellington was born, that all men are mortal, _knew_ that the Duke of\nWellington was mortal; but I do say that he _asserted_ it; and I ask for\nan explanation of the apparent logical fallacy, of adducing in proof of\nthe Duke of Wellington's mortality, a general statement which\npresupposes it. Finding no sufficient resolution of this difficulty in\nany of the writers on Logic, I have attempted to supply one.\n\n[9] The language of ratiocination would, I think, be brought into closer\nagreement with the real nature of the process, if the general\npropositions employed in reasoning, instead of being in the form All men\nare mortal, or Every man is mortal, were expressed in the form Any man\nis mortal. This mode of expression, exhibiting as the type of all\nreasoning from experience \"The men A, B, C, &c. are so and so, therefore\n_any_ man is so and so,\" would much better manifest the true idea--that\ninductive reasoning is always, at bottom, inference from particulars to\nparticulars, and that the whole function of general propositions in\nreasoning, is to vouch for the legitimacy of such inferences.\n\n[10] Review of Quetelet on Probabilities, _Essays_, p. 367.\n\n[11] _Philosophy of Discovery_, p. 289.\n\n[12] _Theory of Reasoning_, ch. iv. to which I may refer for an able\nstatement and enforcement of the grounds of the doctrine.\n\n[13] It is very probable that the doctrine is not new, and that it was,\nas Sir John Herschel thinks, substantially anticipated by Berkeley. But\nI certainly am not aware that it is (as has been affirmed by one of my\nablest and most candid critics) \"among the standing marks of what is\ncalled the empirical philosophy.\"\n\n[14] _Logic_, book iv. ch. i. sect. 1.\n\n[15] See the important chapter on Belief, in Professor Bain's great\ntreatise, _The Emotions and the Will_, pp. 581-4.\n\n[16] A writer in the \"British Quarterly Review\" (August 1846), in a\nreview of this treatise, endeavours to show that there is no _petitio\nprincipii_ in the syllogism, by denying that the proposition, All men\nare mortal, asserts or assumes that Socrates is mortal. In support of\nthis denial, he argues that we may, and in fact do, admit the general\nproposition that all men are mortal, without having particularly\nexamined the case of Socrates, and even without knowing whether the\nindividual so named is a man or something else. But this of course was\nnever denied. That we can and do draw conclusions concerning cases\nspecifically unknown to us, is the datum from which all who discuss this\nsubject must set out. The question is, in what terms the evidence, or\nground, on which we draw these conclusions, may best be\ndesignated--whether it is most correct to say, that the unknown case is\nproved by known cases, or that it is proved by a general proposition\nincluding both sets of cases, the unknown and the known? I contend for\nthe former mode of expression. I hold it an abuse of language to say,\nthat the proof that Socrates is mortal, is that all men are mortal. Turn\nit in what way we will, this seems to me to be asserting that a thing is\nthe proof of itself. Whoever pronounces the words, All men are mortal,\nhas affirmed that Socrates is mortal, though he may never have heard of\nSocrates; for since Socrates, whether known to be so or not, really is a\nman, he is included in the words, All men, and in every assertion of\nwhich they are the subject. If the reviewer does not see that there is a\ndifficulty here, I can only advise him to reconsider the subject until\nhe does: after which he will be a better judge of the success or failure\nof an attempt to remove the difficulty. That he had reflected very\nlittle on the point when he wrote his remarks, is shown by his oversight\nrespecting the _dictum de omni et nullo_. He acknowledges that this\nmaxim as commonly expressed,--\"Whatever is true of a class, is true of\neverything included in the class,\" is a mere identical proposition,\nsince the class _is_ nothing but the things included in it. But he\nthinks this defect would be cured by wording the maxim thus,--\"Whatever\nis true of a class, is true of everything which _can be shown_ to be a\nmember of the class:\" as if a thing could \"be shown\" to be a member of\nthe class without being one. If a class means the sum of all the things\nincluded in the class, the things which can \"be shown\" to be included in\nit are part of the sum, and the _dictum_ is as much an identical\nproposition with respect to them as to the rest. One would almost\nimagine that, in the reviewer's opinion, things are not members of a\nclass until they are called up publicly to take their place in it--that\nso long, in fact, as Socrates is not known to be a man, he _is not_ a\nman, and any assertion which can be made concerning men does not at all\nregard him, nor is affected as to its truth or falsity by anything in\nwhich he is concerned.\n\nThe difference between the reviewer's theory and mine may be thus\nstated. Both admit that when we say, All men are mortal, we make an\nassertion reaching beyond the sphere of our knowledge of individual\ncases; and that when a new individual, Socrates, is brought within the\nfield of our knowledge by means of the minor premise, we learn that we\nhave already made an assertion respecting Socrates without knowing it:\nour own general formula being, to that extent, for the first time\n_interpreted_ to us. But according to the reviewer's theory, the smaller\nassertion is proved by the larger: while I contend, that both assertions\nare proved together, by the same evidence, namely, the grounds of\nexperience on which the general assertion was made, and by which it must\nbe justified.\n\nThe reviewer says, that if the major premise included the conclusion,\n\"we should be able to affirm the conclusion without the intervention of\nthe minor premise; but every one sees that that is impossible.\" A\nsimilar argument is urged by Mr. De Morgan (_Formal Logic_, p. 259):\n\"The whole objection tacitly assumes the superfluity of the minor; that\nis, tacitly assumes we know Socrates[46] to be a man as soon as we know\nhim to be Socrates.\" The objection would be well grounded if the\nassertion that the major premise includes the conclusion, meant that it\nindividually specifies all it includes. As however the only indication\nit gives is a description by marks, we have still to compare any new\nindividual with the marks; and to show that this comparison has been\nmade, is the office of the minor. But since, by supposition, the new\nindividual has the marks, whether we have ascertained him to have them\nor not; if we have affirmed the major premise, we have asserted him to\nbe mortal. Now my position is that this assertion cannot be a necessary\npart of the argument. It cannot be a necessary condition of reasoning\nthat we should begin by making an assertion, which is afterwards to be\nemployed in proving a part of itself. I can conceive only one way out of\nthis difficulty, viz. that what really forms the proof is _the other_\npart of the assertion; the portion of it, the truth of which has been\nascertained previously: and that the unproved part is bound up in one\nformula with the proved part in mere anticipation, and as a memorandum\nof the nature of the conclusions which we are prepared to prove.\n\nWith respect to the minor premise in its formal shape, the minor as it\nstands in the syllogism, predicating of Socrates a definite class name,\nI readily admit that it is no more a necessary part of reasoning than\nthe major. When there is a major, doing its work by means of a class\nname, minors are needed to interpret it: but reasoning can be carried on\nwithout either the one or the other. They are not the conditions of\nreasoning, but a precaution against erroneous reasoning. The only minor\npremise necessary to reasoning in the example under consideration, is,\nSocrates is _like_ A, B, C, and the other individuals who are known to\nhave died. And this is the only universal type of that step in the\nreasoning process which is represented by the minor. Experience,\nhowever, of the uncertainty of this loose mode of inference, teaches the\nexpediency of determining beforehand what _kind_ of likeness to the\ncases observed, is necessary to bring an unobserved case within the same\npredicate; and the answer to this question is the major. Thus the\nsyllogistic major and the syllogistic minor start into existence\ntogether, and are called forth by the same exigency. When we conclude\nfrom personal experience without referring to any record--to any general\ntheorems, either written, or traditional, or mentally registered by\nourselves as conclusions of our own drawing, we do not use, in our\nthoughts, either a major or a minor, such as the syllogism puts into\nwords. When, however, we revise this rough inference from particulars to\nparticulars, and substitute a careful one, the revision consists in\nselecting two syllogistic premises. But this neither alters nor adds to\nthe evidence we had before; it only puts us in a better position for\njudging whether our inference from particulars to particulars is well\ngrounded.\n\n[17] Infra, book iii. ch. ii.\n\n[18] Infra, book iii. ch. iv. \u00a7 3, and elsewhere.\n\n[19] _Mechanical Euclid_, pp. 149 _et seqq._\n\n[20] We might, it is true, insert this property into the definition of\nparallel lines, framing the definition so as to require, both that when\nproduced indefinitely they shall never meet, and also that any straight\nline which intersects one of them shall, if prolonged, meet the other.\nBut by doing this we by no means get rid of the assumption; we are still\nobliged to take for granted the geometrical truth, that all straight\nlines in the same plane, which have the former of these properties, have\nalso the latter. For if it were possible that they should not, that is,\nif any straight lines other than those which are parallel according to\nthe definition, had the property of never meeting although indefinitely\nproduced, the demonstrations of the subsequent portions of the theory of\nparallels could not be maintained.\n\n[21] Some persons find themselves prevented from believing that the\naxiom, Two straight lines cannot inclose a space, could ever become\nknown to us through experience, by a difficulty which may be stated as\nfollows. If the straight lines spoken of are those contemplated in the\ndefinition--lines absolutely without breadth and absolutely\nstraight;--that such are incapable of inclosing a space is not proved by\nexperience, for lines such as these do not present themselves in our\nexperience. If, on the other hand, the lines meant are such straight\nlines as we do meet with in experience, lines straight enough for\npractical purposes, but in reality slightly zigzag, and with some,\nhowever trifling, breadth; as applied to these lines the axiom is not\ntrue, for two of them may, and sometimes do, inclose a small portion of\nspace. In neither case, therefore, does experience prove the axiom.\n\nThose who employ this argument to show that geometrical axioms cannot be\nproved by induction, show themselves unfamiliar with a common and\nperfectly valid mode of inductive proof; proof by approximation. Though\nexperience furnishes us with no lines so unimpeachably straight that two\nof them are incapable of inclosing the smallest space, it presents us\nwith gradations of lines possessing less and less either of breadth or\nof flexure, of which series the straight line of the definition is the\nideal limit. And observation shows that just as much, and as nearly, as\nthe straight lines of experience approximate to having no breadth or\nflexure, so much and so nearly does the space-inclosing power of any two\nof them approach to zero. The inference that if they had no breadth or\nflexure at all, they would inclose no space at all, is a correct\ninductive inference from these facts, conformable to one of the four\nInductive Methods hereinafter characterized, the Method of Concomitant\nVariations; of which the mathematical Doctrine of Limits presents the\nextreme case.\n\n[22] Whewell's _History of Scientific Ideas_, i. 140.\n\n[23] Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it\nunreasonable to contend that we know by experience, that our idea of a\nline exactly resembles a real line. \"It does not appear,\" he says, \"how\nwe can compare our ideas with the realities, since we know the realities\nonly by our ideas.\" We know the realities (I conceive) by our senses.\nDr. Whewell surely does not hold the \"doctrine of perception by means of\nideas,\" which Reid gave himself so much trouble to refute.\n\nIf Dr. Whewell doubts whether we compare our ideas with the\ncorresponding sensations, and assume that they resemble, let me ask on\nwhat evidence do we judge that a portrait of a person not present is\nlike the original. Surely because it is like our idea, or mental image\nof the person, and because our idea is like the man himself.\n\nDr. Whewell also says, that it does not appear why this resemblance of\nideas to the sensations of which they are copies, should be spoken of as\nif it were a peculiarity of one class of ideas, those of space. My reply\nis, that I do not so speak of it. The peculiarity I contend for is only\none of degree. All our ideas of sensation of course resemble the\ncorresponding sensations, but they do so with very different degrees of\nexactness and of reliability. No one, I presume, can recal in\nimagination a colour or an odour with the same distinctness and accuracy\nwith which almost every one can mentally reproduce an image of a\nstraight line or a triangle. To the extent, however, of their\ncapabilities of accuracy, our recollections of colours or of odours may\nserve as subjects of experimentation, as well as those of lines and\nspaces, and may yield conclusions which will be true of their external\nprototypes. A person in whom, either from natural gift or from\ncultivation, the impressions of colour were peculiarly vivid and\ndistinct, if asked which of two blue flowers was of the darkest tinge,\nthough he might never have compared the two, or even looked at them\ntogether, might be able to give a confident answer on the faith of his\ndistinct recollection of the colours; that is, he might examine his\nmental pictures, and find there a property of the outward objects. But\nin hardly any case except that of simple geometrical forms, could this\nbe done by mankind generally, with a degree of assurance equal to that\nwhich is given by a contemplation of the objects themselves. Persons\ndiffer most widely in the precision of their recollection, even of\nforms: one person, when he has looked any one in the face for half a\nminute, can draw an accurate likeness of him from memory; another may\nhave seen him every day for six months, and hardly know whether his nose\nis long or short. But everybody has a perfectly distinct mental image of\na straight line, a circle, or a rectangle. And every one concludes\nconfidently from these mental images to the corresponding outward\nthings. The truth is, that we may, and continually do, study nature in\nour recollections, when the objects themselves are absent; and in the\ncase of geometrical forms we can perfectly, but in most other cases only\nimperfectly, trust our recollections.\n\n[24] _History of Scientific Ideas_, i. 65-67.\n\n[25] Ibid. 60.\n\n[26] _History of Scientific Ideas_, i. 58, 59.\n\n[27] \"If all mankind had spoken one language, we cannot doubt that there\nwould have been a powerful, perhaps a universal, school of philosophers,\nwho would have believed in the inherent connexion between names and\nthings, who would have taken the sound _man_ to be the mode of agitating\nthe air which is essentially communicative of the ideas of reason,\ncookery, bipedality, &c.\"--De Morgan, _Formal Logic_, p. 246.\n\n[28] It would be difficult to name a man more remarkable at once for the\ngreatness and the wide range of his mental accomplishments, than\nLeibnitz. Yet this eminent man gave as a reason for rejecting Newton's\nscheme of the solar system, that God _could not_ make a body revolve\nround a distant centre, unless either by some impelling mechanism, or by\nmiracle:--\"Tout ce qui n'est pas explicable\" says he in a letter to the\nAbb\u00e9 Conti, \"par la nature des cr\u00e9atures, est miraculeux. Il ne suffit\npas de dire: Dieu a fait une telle loi de nature; donc la chose est\nnaturelle. Il faut que la loi soit ex\u00e9cutable par les natures des\ncr\u00e9atures. Si Dieu donnait cette loi, par exemple, \u00e0 un corps libre, de\ntourner \u00e0 l'entour d'un certain centre, _il faudrait ou qu'il y joign\u00eet\nd'autres corps qui par leur impulsion l'obligeassent de rester toujours\ndans son orbite circulaire, ou qu'il m\u00eet un ange \u00e0 ses trousses, ou\nenfin il faudrait qu'il y concour\u00fbt extraordinairement_; car\nnaturellement il s'\u00e9cartera par la tangente.\"--_Works of Leibnitz_, ed.\nDutens, iii. 446.\n\n[29] _Novum Organum Renovatum_, pp. 32, 33.\n\n[30] _History of Scientific Ideas_, i. 264.\n\n[31] _Hist. Sc. Id._, i. 263.\n\n[32] Ibid. 240.\n\n[33] _Hist. Sc. Id._, ii. 25, 26.\n\n[34] _Phil. of Disc._, p. 339.\n\n[35] _Phil. of Disc._, p. 338.\n\n[36] Ib. p. 463.\n\n[37] _Phil. of Disc._, pp. 472, 473.\n\n[38] The _Quarterly Review_ for June 1841, contained an article of great\nability on Dr. Whewell's two great works (since acknowledged and\nreprinted in Sir John Herschel's Essays) which maintains, on the subject\nof axioms, the doctrine advanced in the text, that they are\ngeneralizations from experience, and supports that opinion by a line of\nargument strikingly coinciding with mine. When I state that the whole of\nthe present chapter (except the last four pages, added in the fifth\nedition) was written before I had seen the article, (the greater part,\nindeed, before it was published,) it is not my object to occupy the\nreader's attention with a matter so unimportant as the degree of\noriginality which may or may not belong to any portion of my own\nspeculations, but to obtain for an opinion which is opposed to reigning\ndoctrines, the recommendation derived from a striking concurrence of\nsentiment between two inquirers entirely independent of one another. I\nembrace the opportunity of citing from a writer of the extensive\nacquirements in physical and metaphysical knowledge and the capacity of\nsystematic thought which the article evinces, passages so remarkably in\nunison with my own views as the following:--\n\n\"The truths of geometry are summed up and embodied in its definitions\nand axioms.... Let us turn to the axioms, and what do we find? A string\nof propositions concerning magnitude in the abstract, which are equally\ntrue of space, time, force, number, and every other magnitude\nsusceptible of aggregation and subdivision. Such propositions, where\nthey are not mere definitions, as some of them are, carry their\ninductive origin on the face of their enunciation.... Those which\ndeclare that two straight lines cannot inclose a space, and that two\nstraight lines which cut one another cannot both be parallel to a third,\nare in reality the only ones which express characteristic properties of\nspace, and these it will be worth while to consider more nearly. Now the\nonly clear notion we can form of straightness is uniformity of\ndirection, for space in its ultimate analysis is nothing but an\nassemblage of distances and directions. And (not to dwell on the notion\nof continued contemplation, _i.e._, mental experience, as included in\nthe very idea of uniformity; nor on that of transfer of the\ncontemplating being from point to point, and of experience, during such\ntransfer, of the homogeneity of the interval passed over) we cannot even\npropose the proposition in an intelligible form to any one whose\nexperience ever since he was born has not assured him of the fact. The\nunity of direction, or that we cannot march from a given point by more\nthan one path direct to the same object, is matter of practical\nexperience long before it can by possibility become matter of abstract\nthought. _We cannot attempt mentally to exemplify the conditions of the\nassertion in an imaginary case opposed to it, without violating our\nhabitual recollection of this experience, and defacing our mental\npicture of space as grounded on it._ What but experience, we may ask,\ncan possibly assure us of the homogeneity of the parts of distance,\ntime, force, and measurable aggregates in general, on which the truth of\nthe other axioms depends? As regards the latter axiom, after what has\nbeen said it must be clear that the very same course of remarks equally\napplies to its case, and that its truth is quite as much forced on the\nmind as that of the former by daily and hourly experience, ...\n_including always, be it observed, in our notion of experience, that\nwhich is gained by contemplation of the inward picture which the mind\nforms to itself in any proposed case, or which it arbitrarily selects as\nan example--such picture, in virtue of the extreme simplicity of these\nprimary relations, being called up by the imagination with as much\nvividness and clearness as could be done by any external impression,\nwhich is the only meaning we can attach to the word intuition, as\napplied to such relations_.\"\n\nAnd again, of the axioms of mechanics:--\"As we admit no such\npropositions, other than as truths inductively collected from\nobservation, even in geometry itself, it can hardly be expected that, in\na science of obviously contingent relations, we should acquiesce in a\ncontrary view. Let us take one of these axioms and examine its evidence:\nfor instance, that equal forces perpendicularly applied at the opposite\nends of equal arms of a straight lever will balance each other. What but\nexperience, we may ask, in the first place, can possibly inform us that\na force so applied will have any tendency to turn the lever on its\ncentre at all? or that force can be so transmitted along a rigid line\nperpendicular to its direction, as to act elsewhere in space than along\nits own line of action? Surely this is so far from being self-evident\nthat it has even a paradoxical appearance, which is only to be removed\nby giving our lever thickness, material composition, and molecular\npowers. Again, we conclude, that the two forces, being equal and applied\nunder precisely similar circumstances, must, if they exert any effort at\nall to turn the lever, exert equal and opposite efforts: but what _\u00e0\npriori_ reasoning can possibly assure us that they _do_ act under\nprecisely similar circumstances? that points which differ in place _are_\nsimilarly circumstanced as regards the exertion of force? that universal\nspace may not have relations to universal force--or, at all events, that\nthe organization of the material universe may not be such as to place\nthat portion of space occupied by it in such relations to the forces\nexerted in it, as may invalidate the absolute similarity of\ncircumstances assumed? Or we may argue, what have we to do with the\nnotion of angular movement in the lever at all? The case is one of rest,\nand of quiescent destruction of force by force. Now how is this\ndestruction effected? Assuredly by the counter-pressure which supports\nthe fulcrum. But would not this destruction equally arise, and by the\nsame amount of counter-acting force, if each force simply pressed its\nown half of the lever against the fulcrum? And what can assure us that\nit is not so, except removal of one or other force, and consequent\ntilting of the lever? The other fundamental axiom of statics, that the\npressure on the point of support is the sum of the weights ... is merely\na scientific transformation and more refined mode of stating a coarse\nand obvious result of universal experience, viz. that the weight of a\nrigid body is the same, handle it or suspend it in what position or by\nwhat point we will, and that whatever sustains it sustains its total\nweight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever\nmade a trial for the purpose of showing that the pressure on the support\nis equal to the sum of the weights.' ... But it is precisely because in\nevery action of his life from earliest infancy he has been continually\nmaking the trial, and seeing it made by every other living being about\nhim, that he never dreams of staking its result on one additional\nattempt made with scientific accuracy. This would be as if a man should\nresolve to decide by experiment whether his eyes were useful for the\npurpose of seeing, by hermetically sealing himself up for half an hour\nin a metal case.\"\n\nOn the \"paradox of universal propositions obtained by experience,\" the\nsame writer says: \"If there be necessary and universal truths\nexpressible in propositions of axiomatic simplicity and obviousness, and\nhaving for their subject-matter the elements of all our experience and\nall our knowledge, surely these are the truths which, if experience\nsuggest to us any truths at all, it ought to suggest most readily,\nclearly, and unceasingly. If it were a truth, universal and necessary,\nthat a net is spread over the whole surface of every planetary globe, we\nshould not travel far on our own without getting entangled in its\nmeshes, and making the necessity of some means of extrication an axiom\nof locomotion.... There is, therefore, nothing paradoxical, but the\nreverse, in our being led by observation to a recognition of such\ntruths, as _general_ propositions, coextensive at least with all human\nexperience. That they pervade all the objects of experience, must ensure\ntheir continual suggestion _by_ experience; that they are true, must\nensure that consistency of suggestion, that iteration of uncontradicted\nassertion, which commands implicit assent, and removes all occasion of\nexception; that they are simple, and admit of no misunderstanding, must\nsecure their admission by every mind.\"\n\n\"A truth, necessary and universal, relative to any object of our\nknowledge, must verify itself in every instance where that object is\nbefore our contemplation, and if at the same time it be simple and\nintelligible, its verification must be obvious. _The sentiment of such a\ntruth cannot, therefore, but be present to our minds whenever that\nobject is contemplated, and must therefore make a part of the mental\npicture or idea of that object which we may on any occasion summon\nbefore our imagination.... All propositions, therefore, become not only\nuntrue but inconceivable_, if ... axioms be violated in their\nenunciation.\"\n\nAnother eminent mathematician had previously sanctioned by his authority\nthe doctrine of the origin of geometrical axioms in experience.\n\"Geometry is thus founded likewise on observation; but of a kind so\nfamiliar and obvious, that the primary notions which it furnishes might\nseem intuitive.\"--_Sir John Leslie_, quoted by Sir William Hamilton,\n_Discourses_, &c. p. 272.\n\n[39] _Principles of Psychology._\n\n[40] Mr. Spencer is mistaken in supposing me to claim any peculiar\n\"necessity\" for this axiom as compared with others. I have corrected the\nexpressions which led him into that misapprehension of my meaning.\n\n[41] Mr. Spencer makes a distinction between conceiving myself looking\ninto darkness, and conceiving _that I am_ then and there looking into\ndarkness. To me it seems that this change of the expression to the form\n_I am_, just marks the transition from conception to belief, and that\nthe phrase \"to conceive that _I am_,\" or \"that anything _is_,\" is not\nconsistent with using the word conceive in its rigorous sense.\n\n[42] I have myself accepted the contest, and fought it out on this\nbattleground, in the eleventh chapter of _An Examination of Sir William\nHamilton's Philosophy_.\n\n[43] _Discussions_, &c., 2nd ed. p. 624.\n\n[44] If it be said that the _existence_ of matter is among the things\nproved by the principle of Excluded Middle, that principle must prove\nalso the existence of dragons and hippogriffs, because they must be\neither scaly or not scaly, creeping or not creeping, and so forth.\n\n[45] For further considerations respecting the axioms of Contradiction\nand Excluded Middle, see the twenty-first chapter of _An Examination of\nSir William Hamilton's Philosophy_.\n\n[46] Mr. De Morgan says \"Plato,\" but to prevent confusion I have kept to\nmy own _exemplum_.\n\n\n\n\nBOOK III.\n\nOF INDUCTION.\n\n\n\"According to the doctrine now stated, the highest, or rather the only\nproper object of physics, is to ascertain those established conjunctions\nof successive events, which constitute the order of the universe; to\nrecord the phenomena which it exhibits to our observations, or which it\ndiscloses to our experiments; and to refer these phenomena to their\ngeneral laws.\"--D. STEWART, _Elements of the Philosophy of the Human\nMind_, vol. ii. chap. iv. sect. 1.\n\n\n\n\nCHAPTER I.\n\nPRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.\n\n\n\u00a7 1. The portion of the present inquiry upon which we are now about to\nenter, may be considered as the principal, both from its surpassing in\nintricacy all the other branches, and because it relates to a process\nwhich has been shown in the preceding Book to be that in which the\ninvestigation of nature essentially consists. We have found that all\nInference, consequently all Proof, and all discovery of truths not\nself-evident, consists of inductions, and the interpretation of\ninductions: that all our knowledge, not intuitive, comes to us\nexclusively from that source. What Induction is, therefore, and what\nconditions render it legitimate, cannot but be deemed the main question\nof the science of logic--the question which includes all others. It is,\nhowever, one which professed writers on logic have almost entirely\npassed over. The generalities of the subject have not been altogether\nneglected by metaphysicians; but, for want of sufficient acquaintance\nwith the processes by which science has actually succeeded in\nestablishing general truths, their analysis of the inductive operation,\neven when unexceptionable as to correctness, has not been specific\nenough to be made the foundation of practical rules, which might be for\ninduction itself what the rules of the syllogism are for the\ninterpretation of induction: while those by whom physical science has\nbeen carried to its present state of improvement--and who, to arrive at\na complete theory of the process, needed only to generalize, and adapt\nto all varieties of problems, the methods which they themselves employed\nin their habitual pursuits--never until very lately made any serious\nattempt to philosophize on the subject, nor regarded the mode in which\nthey arrived at their conclusions as deserving of study, independently\nof the conclusions themselves.\n\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\ntrue that (as already shown) the process of indirectly ascertaining\nindividual facts, is as truly inductive as that by which we establish\ngeneral truths. But it is not a different kind of induction; it is a\nform of the very same process: since, on the one hand, generals are but\ncollections of particulars, definite in kind but indefinite in number;\nand on the other hand, whenever the evidence which we derive from\nobservation of known cases justifies us in drawing an inference\nrespecting even one unknown case, we should on the same evidence be\njustified in drawing a similar inference with respect to a whole class\nof cases. The inference either does not hold at all, or it holds in all\ncases of a certain description; in all cases which, in certain definable\nrespects, resemble those we have observed.\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\nwhich general truths are arrived at, is virtually an analysis of all\ninduction whatever. Whether we are inquiring into a scientific principle\nor into an individual fact, and whether we proceed by experiment or by\nratiocination, every step in the train of inferences is essentially\ninductive, and the legitimacy of the induction depends in both cases on\nthe same conditions.\n\nTrue it is that in the case of the practical inquirer, who is\nendeavouring to ascertain facts not for the purposes of science but for\nthose of business, such for instance as the advocate or the judge, the\nchief difficulty is one in which the principles of induction will afford\nhim no assistance. It lies not in making his inductions, but in the\nselection of them; in choosing from among all general propositions\nascertained to be true, those which furnish marks by which he may trace\nwhether the given subject possesses or not the predicate in question. In\narguing a doubtful question of fact before a jury, the general\npropositions or principles to which the advocate appeals are mostly, in\nthemselves, sufficiently trite, and assented to as soon as stated: his\nskill lies in bringing his case under those propositions or principles;\nin calling to mind such of the known or received maxims of probability\nas admit of application to the case in hand, and selecting from among\nthem those best adapted to his object. Success is here dependent on\nnatural or acquired sagacity, aided by knowledge of the particular\nsubject, and of subjects allied with it. Invention, though it can be\ncultivated, cannot be reduced to rule; there is no science which will\nenable a man to bethink himself of that which will suit his purpose.\n\nBut when he _has_ thought of something, science can tell him whether\nthat which he has thought of will suit his purpose or not. The inquirer\nor arguer must be guided by his own knowledge and sagacity in the choice\nof the inductions out of which he will construct his argument. But the\nvalidity of the argument when constructed, depends on principles and\nmust be tried by tests which are the same for all descriptions of\ninquiries, whether the result be to give A an estate, or to enrich\nscience with a new general truth. In the one case and in the other, the\nsenses, or testimony, must decide on the individual facts; the rules of\nthe syllogism will determine whether, those facts being supposed\ncorrect, the case really falls within the formul\u00e6 of the different\ninductions under which it has been successively brought; and finally,\nthe legitimacy of the inductions themselves must be decided by other\nrules, and these it is now our purpose to investigate. If this third\npart of the operation be, in many of the questions of practical life,\nnot the most, but the least arduous portion of it, we have seen that\nthis is also the case in some great departments of the field of science;\nin all those which are principally deductive, and most of all in\nmathematics; where the inductions themselves are few in number, and so\nobvious and elementary that they seem to stand in no need of the\nevidence of experience, while to combine them so as to prove a given\ntheorem or solve a problem, may call for the utmost powers of invention\nand contrivance with which our species is gifted.\n\nIf the identity of the logical processes which prove particular facts\nand those which establish general scientific truths, required any\nadditional confirmation, it would be sufficient to consider that in many\nbranches of science, single facts have to be proved, as well as\nprinciples; facts as completely individual as any that are debated in a\ncourt of justice; but which are proved in the same manner as the other\ntruths of the science, and without disturbing in any degree the\nhomogeneity of its method. A remarkable example of this is afforded by\nastronomy. The individual facts on which that science grounds its most\nimportant deductions, such facts as the magnitudes of the bodies of the\nsolar system, their distances from one another, the figure of the earth,\nand its rotation, are scarcely any of them accessible to our means of\ndirect observation: they are proved indirectly, by the aid of inductions\nfounded on other facts which we can more easily reach. For example, the\ndistance of the moon from the earth was determined by a very circuitous\nprocess. The share which direct observation had in the work consisted in\nascertaining, at one and the same instant, the zenith distances of the\nmoon, as seen from two points very remote from one another on the\nearth's surface. The ascertainment of these angular distances\nascertained their supplements; and since the angle at the earth's centre\nsubtended by the distance between the two places of observation was\ndeducible by spherical trigonometry from the latitude and longitude of\nthose places, the angle at the moon subtended by the same line became\nthe fourth angle of a quadrilateral of which the other three angles were\nknown. The four angles being thus ascertained, and two sides of the\nquadrilateral being radii of the earth; the two remaining sides and the\ndiagonal, or in other words, the moon's distance from the two places of\nobservation and from the centre of the earth, could be ascertained, at\nleast in terms of the earth's radius, from elementary theorems of\ngeometry. At each step in this demonstration we take in a new\ninduction, represented, in the aggregate of its results, by a general\nproposition.\n\nNot only is the process by which an individual astronomical fact was\nthus ascertained, exactly similar to those by which the same science\nestablishes its general truths, but also (as we have shown to be the\ncase in 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\nquantities. And although the moon is almost the only heavenly body the\ndistance of which from the earth can really be thus ascertained, this is\nmerely owing to the accidental circumstances of the other heavenly\nbodies, which render them incapable of affording such data as the\napplication of the theorem requires; for the theorem itself is as true\nof them as it is of the moon.[1]\n\nWe shall fall into no error, then, if in treating of Induction, we\nlimit our attention to the establishment of general propositions. The\nprinciples and rules of Induction as directed to this end, are the\nprinciples and rules of all Induction; and the logic of Science is the\nuniversal Logic, applicable to all inquiries in which man can engage.\n\n\n\n\nCHAPTER II.\n\nOF INDUCTIONS IMPROPERLY SO CALLED.\n\n\n\u00a7 1. Induction, then, is that operation of the mind, by which we infer\nthat what we know to be true in a particular case or cases, will be true\nin all cases which resemble the former in certain assignable respects.\nIn other words, Induction is the process by which we conclude that what\nis true of certain individuals of a class is true of the whole class, or\nthat what is true at certain times will be true in similar circumstances\nat all times.\n\nThis definition excludes from the meaning of the term Induction, various\nlogical operations, to which it is not unusual to apply that name.\n\nInduction, as above defined, is a process of inference; it proceeds from\nthe known to the unknown; and any operation involving no inference, any\nprocess in which what seems the conclusion is no wider than the premises\nfrom which it is drawn, does not fall within the meaning of the term.\nYet in the common books of Logic we find this laid down as the most\nperfect, indeed the only quite perfect, form of induction. In those\nbooks, every process which sets out from a less general and terminates\nin a more general expression,--which admits of being stated in the form,\n\"This and that A are B, therefore every A is B,\"--is called an\ninduction, whether anything be really concluded or not: and the\ninduction is asserted not to be perfect, unless every single individual\nof the class A is included in the antecedent, or premise: that is,\nunless what we affirm of the class has already been ascertained to be\ntrue of every individual in it, so that the nominal conclusion is not\nreally a conclusion, but a mere reassertion of the premises. If we were\nto say, All the planets shine by the sun's light, from observation of\neach separate planet, or All the Apostles were Jews, because this is\ntrue of Peter, Paul, John, and every other apostle,--these, and such as\nthese, would, in the phraseology in question, be called perfect, and the\nonly perfect, Inductions. This, however, is a totally different kind of\ninduction from ours; it is not an inference from facts known to facts\nunknown, but a mere short-hand registration of facts known. The two\nsimulated arguments which we have quoted, are not generalizations; the\npropositions purporting to be conclusions from them, are not really\ngeneral propositions. A general proposition is one in which the\npredicate 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. \"All\nmen are mortal\" 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\nrender it a name not for any and every individual falling under a\ncertain general description, but only for each of a number of\nindividuals designated as such, and as it were counted off individually,\nthe proposition, though it may be general in its language, is no general\nproposition, but merely that number of singular propositions, written in\nan abridged character. The operation may be very useful, as most forms\nof abridged notation are; but it is no part of the investigation of\ntruth, though often bearing an important part in the preparation of the\nmaterials for that investigation.\n\nAs we may sum up a definite number of singular propositions in one\nproposition, which will be apparently, but not really, general, so we\nmay sum up a definite number of general propositions in one proposition,\nwhich will be apparently, but not really, more general. If by a separate\ninduction applied to every distinct species of animals, it has been\nestablished that each possesses a nervous system, and we affirm\nthereupon that all animals have a nervous system; this looks like a\ngeneralization, though as the conclusion merely affirms of all what has\nalready been affirmed of each, it seems to tell us nothing but what we\nknew before. A distinction however must be made. If in concluding that\nall animals have a nervous system, we mean the same thing and no more as\nif we had said \"all known animals,\" the proposition is not general, and\nthe process by which it is arrived at is not induction. But if our\nmeaning is that the observations made of the various species of animals\nhave discovered to us a law of animal nature, and that we are in a\ncondition to say that a nervous system will be found even in animals yet\nundiscovered, this indeed is an induction; but in this case the general\nproposition contains more than the sum of the special propositions from\nwhich it is inferred. The distinction is still more forcibly brought out\nwhen we consider, that if this real generalization be legitimate at all,\nits legitimacy probably does not require that we should have examined\nwithout exception every known species. It is the number and nature of\nthe instances, and not their being the whole of those which happen to be\nknown, that makes them sufficient evidence to prove a general law: while\nthe more limited assertion, which stops at all known animals, cannot be\nmade unless we have rigorously verified it in every species. In like\nmanner (to return to a former example) we might have inferred, not that\nall _the_ planets, but that all _planets_, shine by reflected light: the\nformer is no induction; the latter is an induction, and a bad one, being\ndisproved by the case of double stars--self-luminous bodies which are\nproperly planets, since they revolve round a centre.\n\n\n\u00a7 2. There are several processes used in mathematics which require to be\ndistinguished from Induction, being not unfrequently called by that\nname, and being so far similar to Induction properly so called, that the\npropositions they lead to are really general propositions. For example,\nwhen we have proved with respect to the circle, that a straight line\ncannot meet it in more than two points, and when the same thing has been\nsuccessively proved of the ellipse, the parabola, and the hyperbola, it\nmay be laid down as an universal property of the sections of the cone.\nThe distinction drawn in the two previous examples can have no place\nhere, there being no difference between all _known_ sections of the\ncone and _all_ sections, since a cone demonstrably cannot be intersected\nby a plane except in one of these four lines. It would be difficult,\ntherefore, to refuse to the proposition arrived at, the name of a\ngeneralization, since there is no room for any generalization beyond it.\nBut there is no induction, because there is no inference: the conclusion\nis a mere summing up of what was asserted in the various propositions\nfrom which it is drawn. A case somewhat, though not altogether, similar,\nis the proof of a geometrical theorem by means of a diagram. Whether the\ndiagram be on paper or only in the imagination, the demonstration (as\nformerly observed[2]) does not prove directly the general theorem; it\nproves only that the conclusion, which the theorem asserts generally, is\ntrue of the particular triangle or circle exhibited in the diagram; but\nsince we perceive that in the same way in which we have proved it of\nthat circle, it might also be proved of any other circle, we gather up\ninto one general expression all the singular propositions susceptible of\nbeing thus proved, and embody them in an universal proposition. Having\nshown that the three angles of the triangle ABC are together equal to\ntwo right angles, we conclude that this is true of every other triangle,\nnot because it is true of ABC, but for the same reason which proved it\nto be true of ABC. If this were to be called Induction, an appropriate\nname for it would be, induction by parity of reasoning. But the term\ncannot properly belong to it; the characteristic quality of Induction is\nwanting, since the truth obtained, though really general, is not\nbelieved on the evidence of particular instances. We do not conclude\nthat all triangles have the property because some triangles have, but\nfrom the ulterior demonstrative evidence which was the ground of our\nconviction in the particular instances.\n\nThere are nevertheless, in mathematics, some examples of so-called\nInduction, in which the conclusion does bear the appearance of a\ngeneralization grounded on some of the particular cases included in it.\nA mathematician, when he has calculated a sufficient number of the\nterms of an algebraical or arithmetical series to have ascertained what\nis called the _law_ of the series, does not hesitate to fill up any\nnumber of the succeeding terms without repeating the calculations. But I\napprehend he only does so when it is apparent from _\u00e0 priori_\nconsiderations (which might be exhibited in the form of demonstration)\nthat the mode of formation of the subsequent terms, each from that which\npreceded it, must be similar to the formation of the terms which have\nbeen already calculated. And when the attempt has been hazarded without\nthe sanction of such general considerations, there are instances on\nrecord in which it has led 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\nin which the algebraic formula of each power stands to the exponent of\nthat power, and to the two terms of the binomial. The fact is not\nimprobable: but a mathematician like Newton, who seemed to arrive _per\nsaltum_ at principles and conclusions that ordinary mathematicians only\nreached by a succession of steps, certainly could not have performed the\ncomparison in question without being led by it to the _\u00e0 priori_ ground\nof the law; since any one who understands sufficiently the nature of\nmultiplication to venture upon multiplying several lines of symbols at\none operation, cannot but perceive that in raising a binomial to a\npower, the coefficients must depend on the laws of permutation and\ncombination: and as soon as this is recognised, the theorem is\ndemonstrated. Indeed, when once it was seen that the law prevailed in a\nfew of the lower powers, its identity with the law of permutation would\nat once suggest the considerations which prove it to obtain universally.\nEven, therefore, such cases as these, are but examples of what I have\ncalled Induction by parity of reasoning, that is, not really Induction,\nbecause not involving inference of a general proposition from particular\ninstances.\n\n\n\u00a7 3. There remains a third improper use of the term Induction, which it\nis of real importance to clear up, because the theory of Induction has\nbeen, in no ordinary degree, confused by it, and because the confusion\nis exemplified in the most recent and elaborate treatise on the\ninductive philosophy which exists in our language. The error in question\nis that of confounding a mere description, by general terms, of a set of\nobserved phenomena, with an induction from them.\n\nSuppose that a phenomenon consists of parts, and that these parts are\nonly capable of being observed separately, and as it were piecemeal.\nWhen the observations have been made, there is a convenience (amounting\nfor many purposes to a necessity) in obtaining a representation of the\nphenomenon as a whole, by combining, or as we may say, piecing these\ndetached fragments together. A navigator sailing in the midst of the\nocean discovers land: he cannot at first, or by any one observation,\ndetermine whether it is a continent or an island; but he coasts along\nit, and after a few days finds himself to have sailed completely round\nit: he then pronounces it an island. Now there was no particular time or\nplace of observation at which he could perceive that this land was\nentirely surrounded by water: he ascertained the fact by a succession of\npartial observations, and then selected a general expression which\nsummed up in two or three words the whole of what he so observed. But is\nthere anything of the nature of an induction in this process? Did he\ninfer anything that had not been observed, from something else which\nhad? Certainly not. He had observed the whole of what the proposition\nasserts. That the land in question is an island, is not an inference\nfrom the partial facts which the navigator saw in the course of his\ncircumnavigation; it is the facts themselves; it is a summary of those\nfacts; the description of a complex fact, to which those simpler ones\nare 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's 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\nof the planets, or let us say by the planet Mars (since it was of that\nbody that he first established the two of his three laws which did not\nrequire a comparison of planets). To do this there was no other mode\nthan that of direct observation: and all which observation could do was\nto ascertain a great number of the successive places of the planet; or\nrather, of its apparent places. That the planet occupied successively\nall these positions, or at all events, positions which produced the same\nimpressions on the eye, and that it passed from one of these to another\ninsensibly, and without any apparent breach of continuity; thus much the\nsenses, with the aid of the proper instruments, could ascertain. What\nKepler did more than this, was to find what sort of a curve these\ndifferent points would make, supposing them to be all joined together.\nHe expressed the whole series of the observed places of Mars by what Dr.\nWhewell calls the general conception of an ellipse. This operation was\nfar from being as easy as that of the navigator who expressed the series\nof his observations on successive points of the coast by the general\nconception of an island. But it is the very same sort of operation; and\nif the one is not an induction but a description, this must also be true\nof the other.\n\nThe only real induction concerned in the case, consisted in inferring\nthat because the observed places of Mars were correctly represented by\npoints in an imaginary ellipse, therefore Mars would continue to revolve\nin that same ellipse; and in concluding (before the gap had been filled\nup by further observations) that the positions of the planet during the\ntime which intervened between two observations, must have coincided with\nthe intermediate points of the curve. For these were facts which had not\nbeen directly observed. They were inferences from the observations;\nfacts inferred, as distinguished from facts seen. But these inferences\nwere so far from being a part of Kepler's philosophical operation, that\nthey had been drawn long before he was born. Astronomers had long known\nthat the planets periodically returned to the same places. When this had\nbeen ascertained, there was no induction left for Kepler to make, nor\ndid he make any further induction. He merely applied his new conception\nto the facts inferred, as he did to the facts observed. Knowing already\nthat the planets continued to move in the same paths; when he found that\nan ellipse correctly represented the past path, he knew that it would\nrepresent the future path. In finding a compendious expression for the\none set of facts, he found one for the other: but he found the\nexpression only, not the inference; nor did he (which is the true test\nof a general truth) add anything to the power of prediction already\npossessed.\n\n\n\u00a7 4. The descriptive operation which enables a number of details to be\nsummed up in a single proposition, Dr. Whewell, by an aptly chosen\nexpression, has termed the Colligation of Facts. In most of his\nobservations concerning that mental process I fully agree, and would\ngladly transfer all that portion of his book into my own pages. I only\nthink him mistaken in setting up this kind of operation, which according\nto the old and received meaning of the term, is not induction at all, as\nthe type of induction generally; and laying down, throughout his work,\nas principles 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.\n\"The particular facts,\" says he,[3] \"are not merely brought together,\nbut there is a new element added to the combination by the very act of\nthought by which they are combined.... When the Greeks, after long\nobserving the motions of the planets, saw that these motions might be\nrightly considered as produced by the motion of one wheel revolving in\nthe inside of another wheel, these wheels were creations of their minds,\nadded to the facts which they perceived by sense. And even if the\nwheels were no longer supposed to be material, but were reduced to mere\ngeometrical spheres or circles, they were not the less products of the\nmind alone,--something additional to the facts observed. The same is the\ncase in all other discoveries. The facts are known, but they are\ninsulated and unconnected, till the discoverer supplies from his own\nstore a principle of connexion. The pearls are there, but they will not\nhang together till some one provides the string.\"\n\nLet me first remark that Dr. Whewell, in this passage, blends together,\nindiscriminately, examples of both the processes which I am endeavouring\nto distinguish from one another. When the Greeks abandoned the\nsupposition that the planetary motions were produced by the revolution\nof material wheels, and fell back upon the idea of \"mere geometrical\nspheres or circles,\" there was more in this change of opinion than the\nmere substitution of an ideal curve for a physical one. There was the\nabandonment of a theory, and the replacement of it by a mere\ndescription. No one would think of calling the doctrine of material\nwheels a mere description. That doctrine was an attempt to point out the\nforce by which the planets were acted upon, and compelled to move in\ntheir orbits. But when, by a great step in philosophy, the materiality\nof the wheels was discarded, and the geometrical forms alone retained,\nthe attempt to account for the motions was given up, and what was left\nof the theory was a mere description of the orbits. The assertion that\nthe planets were carried round by wheels revolving in the inside of\nother wheels, gave place to the proposition, that they moved in the same\nlines which would be traced by bodies so carried: which was a mere mode\nof representing the sum of the observed facts; as Kepler's was another\nand a better mode of representing the same observations.\n\nIt is true that for these simply descriptive operations, as well as for\nthe erroneous inductive one, a conception of the mind was required. The\nconception of an ellipse must have presented itself to Kepler's mind,\nbefore he could identify the planetary orbits with it. According to Dr.\nWhewell, the conception was something added to the facts. He expresses\nhimself as if Kepler had put something into the facts by his mode of\nconceiving them. But Kepler did no such thing. The ellipse was in the\nfacts before Kepler recognised it; just as the island was an island\nbefore it had been sailed round. Kepler did not _put_ what he had\nconceived into the facts, but _saw_ it in them. A conception implies,\nand corresponds to, something conceived: and though the conception\nitself is not in the facts, but in our mind, yet if it is to convey any\nknowledge relating to them, it must be a conception _of_ something which\nreally is in the facts, some property which they actually possess, and\nwhich they would manifest to our senses, if our senses were able to take\ncognizance of it. If, for instance, the planet left behind it in space a\nvisible track, and if the observer were in a fixed position at such a\ndistance from the plane of the orbit as would enable him to see the\nwhole of it at once, he would see it to be an ellipse; and if gifted\nwith appropriate instruments and powers of locomotion, he could prove it\nto be such by measuring its different dimensions. Nay, further: if the\ntrack were visible, and he were so placed that he could see all parts of\nit in succession, but not all of them at once, he might be able, by\npiecing together his successive observations, to discover both that it\nwas an ellipse and that the planet moved in it. The case would then\nexactly resemble that of the navigator who discovers the land to be an\nisland by sailing round it. If the path was visible, no one I think\nwould dispute that to identify it with an ellipse is to describe it: and\nI cannot see why any difference should be made by its not being directly\nan object of sense, when every point in it is as exactly ascertained as\nif it were so.\n\nSubject to the indispensable condition which has just been stated, I\ncannot conceive that the part which conceptions have in the operation of\nstudying facts, has ever been overlooked or undervalued. No one ever\ndisputed that in order to reason about anything we must have a\nconception of it; or that when we include a multitude of things under a\ngeneral expression, there is implied in the expression a conception of\nsomething common to those things. But it by no means follows that the\nconception is necessarily pre-existent, or constructed by the mind out\nof its own materials. If the facts are rightly classed under the\nconception, it is because there is in the facts themselves something of\nwhich the conception is itself a copy; and which if we cannot directly\nperceive, it is because of the limited power of our organs, and not\nbecause the thing itself is not there. The conception itself is often\nobtained by abstraction from the very facts which, in Dr. Whewell's\nlanguage, it is afterwards called in to connect. This he himself admits,\nwhen he observes, (which he does on several occasions,) how great a\nservice would be rendered to the science of physiology by the\nphilosopher \"who should establish a precise, tenable, and consistent\nconception of life.\"[4] Such a conception can only be abstracted from\nthe phenomena of life itself; from the very facts which it is put in\nrequisition to connect. In other cases, no doubt, instead of collecting\nthe conception from the very phenomena which we are attempting to\ncolligate, we select it from among those which have been previously\ncollected by abstraction from other facts. In the instance of Kepler's\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\nidentify directly the path of the planet, the conception requisite for\nframing a general description of that path could not be collected by\nabstraction from the observations themselves; the mind had to supply\nhypothetically, from among the conceptions it had obtained from other\nportions of its experience, some one which would correctly represent the\nseries of the observed facts. It had to frame a supposition respecting\nthe general course of the phenomenon, and ask itself, If this be the\ngeneral description, what will the details be? and then compare these\nwith the details actually observed. If they agreed, the hypothesis would\nserve for a description of the phenomenon: if not, it was necessarily\nabandoned, and another tried. It is such a case as this which gives rise\nto the doctrine that the mind, in framing the descriptions, adds\nsomething of its own which 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\nan ellipse, or (to express the meaning in less technical language)\nknowing what an ellipse was, Kepler tried whether the observed places of\nthe planet were consistent with such a path. He found they were so; and\nhe, consequently, asserted as a fact that the planet moved in an\nellipse. But this fact, which Kepler did not add to, but found in, the\nmotions of the planet, namely, that it occupied in succession the\nvarious points in the circumference of a given ellipse, was the very\nfact, the separate parts of which had been separately observed; it was\nthe sum of the different observations.\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 \"conception\" 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\nto Induction itself, and what functions belong to it in that department,\nwill be 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\nwhich minute precision was neither attained nor sought, presented\nnothing inconsistent with the representation of the path of a planet as\nan exact circle, having the earth for its centre. As observations\nincreased in accuracy, and facts were disclosed which were not\nreconcileable with this simple supposition; for the colligation of those\nadditional facts, the supposition was varied; and varied again and again\nas facts became more numerous and precise. The earth was removed from\nthe centre to some other point within the circle; the planet was\nsupposed to revolve in a smaller circle called an epicycle, round an\nimaginary point which revolved in a circle round the earth: in\nproportion as observation elicited fresh facts contradictory to these\nrepresentations, other epicycles and other excentrics were added,\nproducing additional complication; until at last Kepler swept all these\ncircles away, and substituted the conception of an exact ellipse. Even\nthis is found not to represent with complete correctness the accurate\nobservations of the present day, which disclose many slight deviations\nfrom an orbit exactly elliptical. Now Dr. Whewell has remarked that\nthese successive general expressions, though apparently so conflicting,\nwere all correct: they all answered the purpose of colligation; they all\nenabled the mind to represent to itself with facility, and by a\nsimultaneous glance, the whole body of facts at the time ascertained:\neach in its turn served as a correct description of the phenomena, so\nfar as the senses had up to that time taken cognizance of them. If a\nnecessity afterwards arose for discarding one of these general\ndescriptions of the planet's orbit, and framing a different imaginary\nline, by which to express the series of observed positions, it was\nbecause a number of new facts had now been added, which it was necessary\nto combine with the old facts into one general description. But this did\nnot affect the correctness of the former expression, considered as a\ngeneral statement of the only facts which it was intended to represent.\nAnd so true is this, that, as is well remarked by M. Comte, these\nancient generalizations, even the rudest and most imperfect of them,\nthat of uniform movement in a circle, are so far from being entirely\nfalse, that they are even now habitually employed by astronomers when\nonly a rough approximation to correctness is required. \"L'astronomie\nmoderne, en d\u00e9truisant sans retour les hypoth\u00e8ses primitives, envisag\u00e9es\ncomme lois r\u00e9elles du monde, a soigneusement maintenu leur valeur\npositive et permanente, la propri\u00e9t\u00e9 de repr\u00e9senter commod\u00e9ment les\nph\u00e9nom\u00e8nes quand il s'agit d'une premi\u00e8re \u00e9bauche. Nos ressources \u00e0 cet\n\u00e9gard sont m\u00eame bien plus \u00e9tendues, pr\u00e9cis\u00e9ment \u00e0 cause que nous ne nous\nfaisons aucune illusion sur la r\u00e9alit\u00e9 des hypoth\u00e8ses; ce qui nous\npermet d'employer sans scrupule, en chaque cas, celle que nous jugeons\nla plus avantageuse.\"[5]\n\nDr. Whewell's 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\nas they 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\ntheir prediction: meaning by prediction, the determination of the\nconditions under which similar facts may be expected again to occur. To\nthe first of these three operations the name of Induction does not\nproperly belong: to the other two it does. Now, Dr. Whewell's\nobservation is true of the first alone. Considered as a mere\ndescription, the circular theory of the heavenly motions represents\nperfectly well their general features: and by adding epicycles without\nlimit, those motions, even as now known to us, might be expressed with\nany degree of accuracy that might be required. The elliptical theory, as\na mere description, would have a great advantage in point of simplicity,\nand in the consequent facility of conceiving it and reasoning about it;\nbut it would not really be more true than the other. Different\ndescriptions, therefore, may be all true: but not, surely, different\nexplanations. The doctrine that the heavenly bodies moved by a virtue\ninherent in their celestial nature; the doctrine that they were moved by\nimpact, (which led to the hypothesis of vortices as the only impelling\nforce capable of whirling bodies in circles,) and the Newtonian\ndoctrine, that they are moved by the composition of a centripetal with\nan original projectile force; all these are explanations, collected by\nreal induction from supposed parallel cases; and they were all\nsuccessively received by philosophers, as scientific truths on the\nsubject of the heavenly bodies. Can it be said of these, as was said of\nthe different descriptions, that they are all true as far as they go? Is\nit not clear that only one can be true in any degree, and the other two\nmust be altogether false? So much for explanations: let us now compare\ndifferent predictions: the first, that eclipses will occur when one\nplanet or satellite is so situated as to cast its shadow upon another;\nthe second, that they will occur when some great calamity is impending\nover mankind. Do these two doctrines only differ in the degree of their\ntruth, as expressing real facts with unequal degrees of accuracy?\nAssuredly the one is true, and the other absolutely false.[6]\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\ncorrelation, which it is important to conceive correctly. Colligation is\nnot always induction; but induction is always colligation. The assertion\nthat the planets move in ellipses, was but a mode of representing\nobserved facts; it was but a colligation; while the assertion that they\nare drawn, or tend, towards the sun, was the statement of a new fact,\ninferred by induction. But the induction, once made, accomplishes the\npurposes of colligation likewise. It brings the same facts, which Kepler\nhad connected by his conception of an ellipse, under the additional\nconception of bodies acted upon by a central force, and serves therefore\nas a new bond of connexion for those facts; a new principle for their\nclassification.\n\nFurther, the descriptions which are improperly confounded with\ninduction, are nevertheless a necessary preparation for induction; no\nless necessary than correct observation of the facts themselves. Without\nthe previous colligation of detached observations by means of one\ngeneral conception, we could never have obtained any basis for an\ninduction, except in the case of phenomena of very limited compass. We\nshould not be able to affirm any predicates at all, of a subject\nincapable of being observed otherwise than piecemeal: much less could we\nextend those predicates by induction to other similar subjects.\nInduction, therefore, always presupposes, not only that the necessary\nobservations are made with the necessary accuracy, but also that the\nresults of these observations are, so far as practicable, connected\ntogether by general descriptions, enabling the mind to represent to\nitself as wholes whatever phenomena are capable of being so represented.\n\n\n\u00a7 5. Dr. Whewell has replied at some length to the preceding\nobservations, re-stating his opinions, but without (as far as I can\nperceive) adding anything material to his former arguments. Since,\nhowever, mine have not had the good fortune to make any impression upon\nhim, I will subjoin a few remarks, tending to show more clearly in what\nour difference of opinion consists, as well as, in some measure, to\naccount for it.\n\nNearly all the definitions of induction, by writers of authority, make\nit consist in drawing inferences from known cases to unknown; affirming\nof a class, a predicate which has been found true of some cases\nbelonging to the class; concluding, because some things have a certain\nproperty, that other things which resemble them have the same\nproperty--or because a thing has manifested a property at a certain\ntime, that it has and will have that property at other times.\n\nIt will scarcely be contended that Kepler's operation was an Induction\nin this sense of the term. The statement, that Mars moves in an\nelliptical orbit, was no generalization from individual cases to a class\nof cases. Neither was it an extension to all time, of what had been\nfound true at some particular time. The whole amount of generalization\nwhich the case admitted of, was already completed, or might have been\nso. Long before the elliptic theory was thought of, it had been\nascertained that the planets returned periodically to the same apparent\nplaces; the series of these places was, or might have been, completely\ndetermined, and the apparent course of each planet marked out on the\ncelestial globe in an uninterrupted line. Kepler did not extend an\nobserved truth to other cases than those in which it had been observed:\nhe did not widen the _subject_ of the proposition which expressed the\nobserved facts. The alteration he made was in the predicate. Instead of\nsaying, the successive places of Mars are so and so, he summed them up\nin the statement, that the successive places of Mars are points in an\nellipse. It is true, this statement, as Dr. Whewell says, was not the\nsum of the observations _merely_; it was the sum of the observations\n_seen under a new point of view_.[7] But it was not the sum of _more_\nthan the observations, as a real induction is. It took in no cases but\nthose which had been actually observed, or which could have been\ninferred from the observations before the new point of view presented\nitself. There was not that transition from known cases to unknown,\nwhich constitutes Induction in the original and acknowledged meaning of\nthe term.\n\nOld definitions, it is true, cannot prevail against new knowledge: and\nif the Keplerian operation, as a logical process, be really identical\nwith what takes place in acknowledged induction, the definition of\ninduction ought to be so widened as to take it in; since scientific\nlanguage ought to adapt itself to the true relations which subsist\nbetween the things it is employed to designate. Here then it is that I\nam at issue with Dr. Whewell. He does think the operations identical. He\nallows of no logical process in any case of induction, other than what\nthere was in Kepler's case, namely, guessing until a guess is found\nwhich tallies with the facts; and accordingly, as we shall see\nhereafter, he rejects all canons of induction, because it is not by\nmeans of them that we guess. Dr. Whewell's theory of the logic of\nscience would be very perfect if it did not pass over altogether the\nquestion of Proof. But in my apprehension there is such a thing as\nproof, and inductions differ altogether from descriptions in their\nrelation to that element. Induction is proof; it is inferring something\nunobserved from something observed: it requires, therefore, an\nappropriate test of proof; and to provide that test, is the special\npurpose of inductive logic. When, on the contrary, we merely collate\nknown observations, and, in Dr. Whewell's phraseology, connect them by\nmeans of a new conception; if the conception does serve to connect the\nobservations, we have all we want. As the proposition in which it is\nembodied pretends to no other truth than what it may share with many\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\nit may 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's so-called law\nbrought the orbit of Mars into the class ellipse, and by doing so,\nproved all the properties of an ellipse to be true of the orbit: but in\nthis proof Kepler's law supplied the minor premise, and not (as is the\ncase with real Inductions) the major.\n\nDr. Whewell calls nothing Induction where there is not a new mental\nconception introduced, and everything induction where there is. But this\nis to confound two very different things, Invention and Proof. The\nintroduction of a new conception belongs to Invention: and invention may\nbe required in any operation, but is the essence of none. A new\nconception may be introduced for descriptive purposes, and so it may for\ninductive purposes. But it is so far from constituting induction, that\ninduction does not necessarily stand in need of it. Most inductions\nrequire no conception but what was present in every one of the\nparticular instances on which the induction is grounded. That all men\nare mortal is surely an inductive conclusion; yet no new conception is\nintroduced by it. Whoever knows that any man has died, has all the\nconceptions involved in the inductive generalization. But Dr. Whewell\nconsiders the process of invention which consists in framing a new\nconception consistent with the facts, to be not merely a necessary part\nof all induction, but the whole of it.\n\nThe mental operation which extracts from a number of detached\nobservations certain general characters in which the observed phenomena\nresemble one another, or resemble other known facts, is what Bacon,\nLocke, and most subsequent metaphysicians, have understood by the word\nAbstraction. A general expression obtained by abstraction, connecting\nknown facts by means of common characters, but without concluding from\nthem to unknown, may, I think, with strict logical correctness, be\ntermed a Description; nor do I know in what other way things can ever be\ndescribed. My position, however, does not depend on the employment of\nthat particular word; I am quite content to use Dr. Whewell's term\nColligation, or the more general phrases, \"mode of representing, or of\nexpressing, phenomena:\" provided it be clearly seen that the process is\nnot Induction, but something radically different.\n\nWhat more may usefully be said on the subject of Colligation, or of the\ncorrelative expression invented by Dr. Whewell, the Explication of\nConceptions, and generally on the subject of ideas and mental\nrepresentations as connected with the study of facts, will find a more\nappropriate place in the Fourth Book, on the Operations Subsidiary to\nInduction: to which I must refer the reader for the removal of any\ndifficulty which the present discussion may have left.\n\n\n\n\nCHAPTER III.\n\nOF THE GROUND OF INDUCTION.\n\n\n\u00a7 1. Induction properly so called, as distinguished from those mental\noperations, sometimes though improperly designated by the name, which I\nhave attempted in the preceding chapter to characterize, may, then, be\nsummarily defined as Generalization from Experience. It consists in\ninferring from some individual instances in which a phenomenon is\nobserved to occur, that it occurs in all instances of a certain class;\nnamely, in all which _resemble_ the former, in what are regarded as the\nmaterial circumstances.\n\nIn what way the material circumstances are to be distinguished from\nthose which are immaterial, or why some of the circumstances are\nmaterial and others not so, we are not yet ready to point out. We must\nfirst observe, that there is a principle implied in the very statement\nof what Induction is; an assumption with regard to the course of nature\nand the order of the universe; namely, that there are such things in\nnature as parallel cases; that what happens once, will, under a\nsufficient degree of similarity of circumstances, happen again, and not\nonly again, but as often as the same circumstances recur. This, I say,\nis an assumption, involved in every case of induction. And, if we\nconsult the actual course of nature, we find that the assumption is\nwarranted. The universe, so far as known to us, is so constituted, that\nwhatever 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\nuniverse is governed by general laws; and the like. One of the most\nusual of these modes of expression, but also one of the most inadequate,\nis that which has been brought into familiar use by the metaphysicians\nof the school of Reid and Stewart. The disposition of the human mind to\ngeneralize from experience,--a propensity considered by these\nphilosophers as an instinct of our nature,--they usually describe under\nsome such name as \"our intuitive conviction that the future will\nresemble the past.\" Now it has been well pointed out by Mr. Bailey,[8]\nthat (whether the tendency be or not an original and ultimate element of\nour nature), Time, in its modifications of past, present, and future,\nhas no concern either with the belief itself, or with the grounds of it.\nWe believe that fire will burn to-morrow, because it burned to-day and\nyesterday; but we believe, on precisely the same grounds, that it burned\nbefore we were born, and that it burns this very day in Cochin-China. It\nis not from the past to the future, as past and future, that we infer,\nbut from the known to the unknown; from facts observed to facts\nunobserved; from what we have perceived, or been directly conscious of,\nto what has not come within our experience. In this last predicament is\nthe whole region of the future; but also the vastly greater portion of\nthe 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\ngeneral axiom, of Induction. It would yet be a great error to offer this\nlarge generalization 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\ngeneralizations. The obscurer laws of nature were discovered by means\nof it, but the more obvious ones must have been understood and assented\nto as general truths before it was ever heard of. We should never have\nthought of affirming that all phenomena take place according to general\nlaws, if we had not first arrived, in the case of a great multitude of\nphenomena, at some knowledge of the laws themselves; which could be done\nno otherwise than by induction. In what sense, then, can a principle,\nwhich is so far from being our earliest induction, be regarded as our\nwarrant for all the others? In the only sense, in which (as we have\nalready seen) the general propositions which we place at the head of our\nreasonings when we throw them into syllogisms, ever really contribute to\ntheir validity. As Archbishop Whately remarks, every induction is a\nsyllogism with the major premise suppressed; or (as I prefer expressing\nit) every induction may be thrown into the form of a syllogism, by\nsupplying a major premise. If this be actually done, the principle which\nwe are now considering, that of the uniformity of the course of nature,\nwill appear as the ultimate major premise of all inductions, and will,\ntherefore, stand to all inductions in the relation in which, as has been\nshown at so much length, the major proposition of a syllogism always\nstands to the conclusion; not contributing at all to prove it, but being\na necessary condition of its being proved; since no conclusion is\nproved, for which there cannot be found a true major premise.[9]\n\nThe statement, that the uniformity of the course of nature is the\nultimate major premise in all cases of induction, may be thought to\nrequire some explanation. The immediate major premise in every inductive\nargument, it certainly is not. Of that, Archbishop Whately's must be\nheld to be the correct account. The induction, \"John, Peter, &c. are\nmortal, therefore all mankind are mortal,\" may, as he justly says, be\nthrown into a syllogism by prefixing as a major premise (what is at any\nrate a necessary condition of the validity of the argument) namely, that\nwhat is true of John, Peter, &c. is true of all mankind. But how came we\nby this major premise? It is not self-evident; nay, in all cases of\nunwarranted generalization, it is not true. How, then, is it arrived at?\nNecessarily either by induction or ratiocination; and if by induction,\nthe process, like all other inductive arguments, may be thrown into the\nform of a syllogism. This previous syllogism it is, therefore, necessary\nto construct. There is, in the long run, only one possible construction.\nThe real proof that what is true of John, Peter, &c. is true of all\nmankind, can only be, that a different supposition would be inconsistent\nwith the uniformity which we know to exist in the course of nature.\nWhether there would be this inconsistency or not, may be a matter of\nlong and delicate inquiry; but unless there would, we have no sufficient\nground for the major of the inductive syllogism. It hence appears, that\nif we throw the whole course of any inductive argument into a series of\nsyllogisms, we shall arrive by more or fewer steps at an ultimate\nsyllogism, which will have for its major premise the principle, or\naxiom, of the uniformity of the course of nature.[10]\n\nIt was not to be expected that in the case of this axiom, any more than\nof other axioms, there should be unanimity among thinkers with respect\nto the grounds on which it is to be received as true. I have already\nstated that I regard it as itself a generalization from experience.\nOthers hold it to be a principle which, antecedently to any verification\nby experience, we are compelled by the constitution of our thinking\nfaculty to assume as true. Having so recently, and at so much length,\ncombated a similar doctrine as applied to the axioms of mathematics, by\narguments which are in a great measure applicable to the present case, I\nshall defer the more particular discussion of this controverted point in\nregard to the fundamental axiom of induction, until a more advanced\nperiod of our inquiry.[11] At present it is of more importance to\nunderstand thoroughly the import of the axiom itself. For the\nproposition, that the course of nature is uniform, possesses rather the\nbrevity suitable to popular, than the precision requisite in\nphilosophical language: its terms require to be explained, and a\nstricter than their ordinary signification given to them, before the\ntruth of the assertion can be admitted.\n\n\n\u00a7 2. Every person's consciousness assures him that he does not always\nexpect uniformity in the course of events; he does not always believe\nthat the unknown will be similar to the known, that the future will\nresemble the past. Nobody believes that the succession of rain and fine\nweather will be the same in every future year as in the present. Nobody\nexpects to have the same dreams repeated every night. On the contrary,\neverybody mentions it as something extraordinary, if the course of\nnature is constant, and resembles itself, in these particulars. To look\nfor constancy where constancy is not to be expected, as for instance\nthat a day which has once brought good fortune will always be a\nfortunate day, is justly accounted superstition.\n\nThe course of nature, in truth, is not only uniform, it is also\ninfinitely various. Some phenomena are always seen to recur in the very\nsame combinations in which we met with them at first; others seem\naltogether capricious; while some, which we had been accustomed to\nregard as bound down exclusively to a particular set of combinations, we\nunexpectedly find detached from some of the elements with which we had\nhitherto found them conjoined, and united to others of quite a contrary\ndescription. To an inhabitant of Central Africa, fifty years ago, no\nfact probably appeared to rest on more uniform experience than this,\nthat all human beings are black. To Europeans, not many years ago, the\nproposition, All swans are white, appeared an equally unequivocal\ninstance of uniformity in the course of nature. Further experience has\nproved to both that they were mistaken; but they had to wait fifty\ncenturies for this experience. During that long time, mankind believed\nin an uniformity of the course of nature where no such uniformity really\nexisted.\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 \"Inductio per enumerationem simplicem, ubi non\nreperitur instantia contradictoria.\" 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\nis natural to the mind when unaccustomed to scientific methods. The\ntendency, which some call an instinct, and which others account for by\nassociation, to infer the future from the past, the known from the\nunknown, is simply a habit of expecting that what has been found true\nonce or several times, and never yet found false, will be found true\nagain. Whether the instances are few or many, conclusive or\ninconclusive, does not much affect the matter: these are considerations\nwhich occur only on reflection; the unprompted tendency of the mind is\nto generalize its experience, provided this points all in one direction;\nprovided no other experience of a conflicting character comes unsought.\nThe notion of seeking it, of experimenting for it, of _interrogating_\nnature (to use Bacon's expression) is of much later growth. The\nobservation of nature, by uncultivated intellects, is purely passive:\nthey accept the facts which present themselves, without taking the\ntrouble of searching for more: it is a superior mind only which asks\nitself what facts are needed to enable it to come to a safe conclusion,\nand 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\nhave known of them. This assurance, in the great majority of cases, we\ncannot have, or can have only in a very moderate degree. The possibility\nof having it, is the foundation on which we shall see hereafter that\ninduction by simple enumeration may in some remarkable cases amount\npractically to proof.[12] 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\ncarries us but a little way. We are forced to begin with it; we must\noften rely on it provisionally, in the absence of means of more\nsearching investigation. But, for the accurate study of nature, we\nrequire a surer and a more potent 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\nerrors) his writings contain, more or less fully developed, several of\nthe most important principles of the Inductive Method, physical\ninvestigation has now far outgrown the Baconian conception of Induction.\nMoral and political inquiry, indeed, are as yet far behind that\nconception. The current and approved modes of reasoning on these\nsubjects are still of the same vicious description against which Bacon\nprotested; the method almost exclusively employed by those professing to\ntreat such matters inductively, is the very _inductio per enumerationem\nsimplicem_ which he condemns; and the experience which we hear so\nconfidently appealed to by all sects, parties, and interests, is still,\nin his own emphatic words, _mera palpatio_.\n\n\n\u00a7 3. In order to a better understanding of the problem which the\nlogician must solve if he would establish a scientific theory of\nInduction, let us compare a few cases of incorrect inductions with\nothers which are acknowledged to be legitimate. Some, we know, which\nwere believed for centuries to be correct, were nevertheless incorrect.\nThat all swans are white, cannot have been a good induction, since the\nconclusion has turned out erroneous. The experience, however, on which\nthe conclusion rested, was genuine. From the earliest records, the\ntestimony of the inhabitants of the known world was unanimous on the\npoint. The uniform experience, therefore, of the inhabitants of the\nknown world, agreeing in a common result, without one known instance of\ndeviation from that result, is not always sufficient to establish a\ngeneral conclusion.\n\nBut let us now turn to an instance apparently not very dissimilar to\nthis. Mankind were wrong, it seems, in concluding that all swans were\nwhite: are we also wrong, when we conclude that all men's heads grow\nabove their shoulders, and never below, in spite of the conflicting\ntestimony of the naturalist Pliny? As there were black swans, though\ncivilized people had existed for three thousand years on the earth\nwithout meeting with them, may there not also be \"men whose heads do\ngrow beneath their shoulders,\" notwithstanding a rather less perfect\nunanimity of negative testimony from observers? Most persons would\nanswer No; it was more credible that a bird should vary in its colour,\nthan that men should vary in the relative position of their principal\norgans. And there is no doubt that in so saying they would be right: but\nto say why they are right, would be impossible, without entering more\ndeeply than is usually done, into the true 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\nupon it 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\ndoubt to be true even in the region of the fixed stars. When a chemist\nannounces the existence and properties of a newly-discovered substance,\nif we confide in his accuracy, we feel assured that the conclusions he\nhas arrived at will hold universally, though the induction be founded\nbut on a single instance. We do not withhold our assent, waiting for a\nrepetition of the experiment; or if we do, it is from a doubt whether\nthe one experiment was properly made, not whether if properly made it\nwould be conclusive. Here, then, is a general law of nature, inferred\nwithout hesitation from a single instance; an universal proposition from\na singular one. Now mark another case, and contrast it with this. Not\nall the instances which have been observed since the beginning of the\nworld, in support of the general proposition that all crows are black,\nwould be deemed a sufficient presumption of the truth of the\nproposition, to outweigh the testimony of one unexceptionable witness\nwho should affirm that in some region of the earth not fully explored,\nhe had caught and examined 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,\nand has solved the problem of induction.\n\n\n\n\nCHAPTER IV.\n\nOF LAWS OF NATURE.\n\n\n\u00a7 1. In the contemplation of that uniformity in the course of nature,\nwhich is assumed in every inference from experience, one of the first\nobservations that present themselves is, that the uniformity in question\nis not properly uniformity, but uniformities. The general regularity\nresults from the coexistence 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\nwhenever certain circumstances are present, and does not occur when they\nare absent; the like is true of another fact; and so on. From these\nseparate threads of connexion between parts of the great whole which we\nterm nature, a general tissue of connexion unavoidably weaves itself, by\nwhich the whole is held together. If A is always accompanied by D, B by\nE, and C by F, it follows that A B is accompanied by D E, A C by D F, B\nC by E F, and finally A B C by D E F; and thus the general character of\nregularity is produced, which, along with and in the midst of infinite\ndiversity, pervades 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\nfact, compounded of all the separate uniformities which exist in respect\nto single phenomena. These various uniformities, when ascertained by\nwhat is regarded as a sufficient induction, we call in common parlance,\nLaws of Nature. Scientifically speaking, that title is employed in a\nmore restricted sense, to designate the uniformities when reduced to\ntheir most simple expression. Thus in the illustration already employed,\nthere were seven uniformities; all of which, if considered sufficiently\ncertain, would in the more lax application of the term, be called laws\nof nature. But of the seven, three alone are properly distinct and\nindependent: these being presupposed, the others follow of course. The\nthree first, therefore, according to the stricter acceptation, are\ncalled laws of nature; the remainder not; because they are in truth mere\n_cases_ of the three first; virtually included in them; said, therefore,\nto _result_ from them: whoever affirms those three has already affirmed\nall 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\ndirections, and the law that pressure in one direction, not opposed by\nequal pressure in the contrary direction, produces motion, which does\nnot cease until equilibrium is restored. From these three uniformities\nwe should be able to predict another uniformity, namely, the rise of the\nmercury in the Torricellian tube. This, in the stricter use of the\nphrase, is not a law of nature. It is the result of laws of nature. It\nis a _case_ of each and every one of the three laws: and is the only\noccurrence by which they could all be fulfilled. If the mercury were not\nsustained in the barometer, and sustained at such a height that the\ncolumn of mercury were equal in weight to a column of the atmosphere of\nthe same diameter; here would be a case, either of the air not pressing\nupon the surface of the mercury with the force which is called its\nweight, or of the downward pressure on the mercury not being propagated\nequally in an upward direction, or of a body pressed in one direction\nand not in the direction opposite, either not moving in the direction in\nwhich it is pressed, or stopping before it had attained equilibrium. If\nwe knew, therefore, the three simple laws, but had never tried the\nTorricellian experiment, we might _deduce_ its result from those laws.\nThe known weight of the air, combined with the position of the\napparatus, would bring the mercury within the first of the three\ninductions; the first induction would bring it within the second, and\nthe second within the third, in the manner which we characterized in\ntreating of Ratiocination. We should thus come to know the more complex\nuniformity, independently of specific experience, through our knowledge\nof the simpler ones from which it results; though, for reasons which\nwill appear hereafter, _verification_ by specific experience would still\nbe desirable, and might possibly be indispensable.\n\nComplex uniformities which, like this, are mere cases of simpler ones,\nand have, therefore, been virtually affirmed in affirming those, may\nwith propriety be called _laws_, but can scarcely, in the strictness of\nscientific speech, be termed Laws of Nature. It is the custom in\nscience, wherever regularity of any kind can be traced, to call the\ngeneral proposition which expresses the nature of that regularity, a\nlaw; as when, in mathematics, we speak of the law of decrease of the\nsuccessive terms of a converging series. But the expression _law of\nnature_ has generally been employed with a sort of tacit reference to\nthe original sense of the word law, namely, the expression of the will\nof a superior. When, therefore, it appeared that any of the uniformities\nwhich were observed in nature, would result spontaneously from certain\nother uniformities, no separate act of creative will being supposed\nnecessary for the production of the derivative uniformities, these have\nnot usually been spoken of as laws of nature. According to one mode of\nexpression, the question, What are the laws of nature? may be stated\nthus:--What are the fewest and simplest assumptions, which being\ngranted, the whole existing order of nature would result? Another mode\nof stating it would be thus: What are the fewest general propositions\nfrom which all the uniformities which exist in the universe might be\ndeductively 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\nextension of the inductive inference, is already an advance in that\ndirection. When Kepler expressed the regularity which exists in the\nobserved motions of the heavenly bodies, by the three general\npropositions called his laws, he, in so doing, pointed out three simple\nsuppositions which, instead of a much greater number, would suffice to\nconstruct the whole scheme of the heavenly motions, so far as it was\nknown up to that time. A similar and still greater step was made when\nthese laws, which at first did not seem to be included in any more\ngeneral truths, were discovered to be cases of the three laws of motion,\nas obtaining among bodies which mutually tend towards one another with a\ncertain force, and have had a certain instantaneous impulse originally\nimpressed upon them. After this great discovery, Kepler's three\npropositions, though still called laws, would hardly, by any person\naccustomed to use language with precision, be termed laws of nature:\nthat phrase would be reserved for the simpler and more general 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\nof taking 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\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\nan improved form of that which was primitively pursued by the human\nunderstanding, while undirected by science. When mankind first formed\nthe idea of studying phenomena according to a stricter and surer method\nthan that which they had in the first instance spontaneously adopted,\nthey did not, conformably to the well-meant but impracticable precept of\nDescartes, set out from the supposition that nothing had been already\nascertained. Many of the uniformities existing among phenomena are so\nconstant, and so open to observation, as to force themselves upon\ninvoluntary recognition. Some facts are so perpetually and familiarly\naccompanied by certain others, that mankind learnt, as children learn,\nto expect the one where they found the other, long before they knew how\nto put their expectation into words by asserting, in a proposition, the\nexistence of a connexion between those phenomena. No science was needed\nto teach that food nourishes, that water drowns, or quenches thirst,\nthat the sun gives light and heat, that bodies fall to the ground. The\nfirst scientific inquirers assumed these and the like as known truths,\nand set out from them to discover others which were unknown: nor were\nthey wrong in so doing, subject, however, as they afterwards began to\nsee, to an ulterior revision of these spontaneous generalizations\nthemselves, when the progress of knowledge pointed out limits to them,\nor showed their truth to be contingent on some circumstance not\noriginally attended to. It will appear, I think, from the subsequent\npart of our inquiry, that there is no logical fallacy in this mode of\nproceeding; but we may see already that any other mode is rigorously\nimpracticable: since it is impossible to frame any scientific method of\ninduction, or test of the correctness of inductions, unless on the\nhypothesis that some inductions deserving of reliance have been already\nmade.\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\nwhy more credible? So long as neither phenomenon had been actually\nwitnessed, what reason was there for finding the one harder to be\nbelieved than the other? Apparently because there is less constancy in\nthe colours of animals, than in the general structure of their anatomy.\nBut how do we know this? Doubtless, from experience. It appears, then,\nthat we need experience to inform us, in what degree, and in what cases,\nor sort of cases, experience is to be relied on. Experience must be\nconsulted in order to learn from it under what circumstances arguments\nfrom it will be valid. We have no ulterior test to which we subject\nexperience in general; but we make experience its own test. Experience\ntestifies, that among the uniformities which it exhibits or seems to\nexhibit, some are more to be relied on than others; and uniformity,\ntherefore, may be presumed, from any given number of instances, with a\ngreater degree of assurance, in proportion as the case belongs to a\nclass in which the uniformities have hitherto been found more uniform.\n\nThis mode of correcting one generalization by means of another, a\nnarrower generalization by a wider, which common sense suggests and\nadopts in practice, is the real type of scientific Induction. All that\nart can do is but to give accuracy and precision to this process, and\nadapt it to all varieties of cases, without any essential alteration in\nits 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\nprevalent character of the uniformities existing throughout nature. The\nindispensable foundation, therefore, of a scientific formula of\ninduction, must be a survey of the inductions to which mankind have been\nconducted in unscientific practice; with the special purpose of\nascertaining what kinds of uniformities have been found perfectly\ninvariable, pervading all nature, and what are those which have been\nfound to vary with difference of time, place, or other changeable\ncircumstances.\n\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\nthe less strong inductions from stronger ones, it acquires, at once, all\nthe strength 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\nbetter established law in which it is now found to be included. We may\nhave inferred, from historical evidence, that the uncontrolled power of\na monarch, of an aristocracy, or of the majority, will often be abused:\nbut we are entitled to rely on this generalization with much greater\nassurance when it is shown to be a corollary from still better\nestablished facts; the very low degree of elevation of character ever\nyet attained by the average of mankind, and the little efficacy, for the\nmost part, of the modes of education hitherto practised, in maintaining\nthe predominance of reason and conscience over the selfish propensities.\nIt is at the same time obvious that even these more general facts derive\nan accession of evidence from the testimony which history bears to the\neffects of despotism. The strong induction becomes still stronger when a\nweaker one has been bound up with it.\n\nOn the other hand, if an induction conflicts with stronger inductions,\nor with conclusions capable of being correctly deduced from them, then,\nunless on reconsideration it should appear that some of the stronger\ninductions have been expressed with greater universality than their\nevidence warrants, the weaker one must give way. The opinion so long\nprevalent that a comet, or any other unusual appearance in the heavenly\nregions, was the precursor of calamities to mankind, or to those at\nleast who witnessed it; the belief in the veracity of the oracles\nof Delphi or Dodona; the reliance on astrology, or on the\nweather-prophecies in almanacs, were doubtless inductions supposed to be\ngrounded on experience:[13] and faith in such delusions seems quite\ncapable of holding out against a great multitude of failures, provided\nit be nourished by a reasonable number of casual coincidences between\nthe prediction and the event. What has really put an end to these\ninsufficient inductions, is their inconsistency with the stronger\ninductions subsequently obtained by scientific inquiry, respecting the\ncauses on which terrestrial events really depend; and where those\nscientific truths have not yet penetrated, the same or similar delusions\nstill prevail.\n\nIt may be affirmed as a general principle, that all inductions, whether\nstrong or weak, which can be connected by ratiocination, are\nconfirmatory of one another; while any which lead deductively to\nconsequences that are incompatible, become mutually each other's 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\nlevel of certainty of the weakest of those from which it is deduced;\nwhile in general all are more or less increased in certainty. Thus the\nTorricellian experiment, though a mere case of three more general laws,\nnot only strengthened greatly the evidence on which those laws rested,\nbut converted one of them (the weight of the atmosphere) from a doubtful\ngeneralization into a completely established doctrine.\n\nIf, then, a survey of the uniformities which have been ascertained to\nexist in nature, should point out some which, as far as any human\npurpose requires certainty, may be considered 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 inductive inference, that either it must\nbe true, or one of these certain and universal inductions must admit of\nan exception; the former generalization will attain the same certainty,\nand indefeasibleness 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.\n\nOF THE LAW OF UNIVERSAL CAUSATION.\n\n\n\u00a7 1. The phenomena of nature exist in two distinct relations to one\nanother; that of simultaneity, and that of succession. Every phenomenon\nis related, in an uniform manner, to some phenomena that coexist with\nit, and to some that have preceded and will follow it.\n\nOf the uniformities which exist among synchronous phenomena, the most\nimportant, on every account, are the laws of number; and next to them\nthose of space, or, in other words, of extension and figure. The laws of\nnumber are common to synchronous and successive phenomena. That two and\ntwo make four, is equally true whether the second two follow the first\ntwo or accompany them. It is as true of days and years as of feet and\ninches. The laws of extension and figure (in other words, the theorems\nof geometry, from its lowest to its highest branches) are, on the\ncontrary, laws of simultaneous phenomena only. The various parts of\nspace, and of the objects which are said to fill space, coexist; and the\nunvarying laws which are the subject of the science of geometry, are an\nexpression of the mode 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\nlapse of time, any variety of facts or events succeeding one another. If\nall the objects in the universe were unchangeably fixed, and had\nremained in that condition from eternity, the propositions of geometry\nwould still be true of those objects. All things which possess\nextension, or, in other words, which fill space, are subject to\ngeometrical laws. Possessing extension, they possess figure; possessing\nfigure, they must possess some figure in particular, and have all the\nproperties which geometry assigns to that figure. If one body be a\nsphere and another a cylinder, of equal height and diameter, the one\nwill be exactly two-thirds of the other, let the nature and quality of\nthe material be what it will. Again, each body, and each point of a\nbody, must occupy some place or position among other bodies; and the\nposition of two bodies relatively to each other, of whatever nature the\nbodies be, may be unerringly inferred from the position of each of them\nrelatively 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 it renders us unable even to conceive\nany exception to them; and philosophers have been led, though (as I have\nendeavoured to show) erroneously, to consider their evidence as lying\nnot in experience, but in the original constitution of the intellect. If\ntherefore, from the laws of space and number, we were able to deduce\nuniformities of any other description, this would be conclusive evidence\nto us that those other uniformities possessed the same rigorous\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\nis founded every reasonable anticipation of future facts, and whatever\npower we possess of influencing those facts to our advantage. Even the\nlaws of geometry are chiefly of practical importance to us as being a\nportion of the premises from which the order of the succession of\nphenomena may be inferred. Inasmuch as the motion of bodies, the action\nof forces, and the propagation of influences of all sorts, take place in\ncertain lines and over definite spaces, the properties of those lines\nand spaces are an important part of the laws to which those phenomena\nare themselves subject. Again, motions, forces or other influences, and\ntimes, are numerable quantities; and the properties of number are\napplicable to them as to all other things. But though the laws of number\nand space are important elements in the ascertainment of uniformities\nof succession, they can do nothing towards it when taken by themselves.\nThey can only be made instrumental to that purpose when we combine with\nthem additional premises, expressive of uniformities of succession\nalready known. By taking, for instance, as premises these propositions,\nthat bodies acted upon by an instantaneous force move with uniform\nvelocity in straight lines; that bodies acted upon by a continuous force\nmove with accelerated velocity in straight lines; and that bodies acted\nupon by two forces in different directions move in the diagonal of a\nparallelogram, whose sides represent the direction and quantity of those\nforces; we may by combining these truths with propositions relating to\nthe properties of straight lines and of parallelograms, (as that a\ntriangle is half a parallelogram of the same base and altitude,) deduce\nanother important uniformity of succession, viz., that a body moving\nround a centre of force describes areas proportional to the times. But\nunless there had been laws of succession in our premises, there could\nhave been no truths of succession in our conclusions. A similar remark\nmight be extended to every other class of phenomena really peculiar;\nand, had it been attended to, would have prevented many chimerical\nattempts at demonstrations of the indemonstrable, and explanations which\ndo not explain.\n\nIt is not, therefore, enough for us that the laws of space, which are\nonly laws of simultaneous phenomena, and the laws of number, which\nthough true of successive phenomena do not relate to their succession,\npossess the rigorous certainty and universality of which we are in\nsearch. We must endeavour to find some law of succession which has those\nsame attributes, and is therefore fit to be made the foundation of\nprocesses for discovering, and of a test for verifying, all other\nuniformities of succession. This fundamental law must resemble the\ntruths of geometry in their most remarkable peculiarity, that of never\nbeing, in any instance whatever, defeated or suspended by any change of\ncircumstances.\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\nbeing examples of it. This law is the Law of Causation. The truth that\nevery fact 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,\nsince after all it asserts only this: \"it is a law; that every event\ndepends on some law:\" \"it is a law, that there is a law for everything.\"\nWe must not, however, conclude that the generality of the principle is\nmerely verbal; it will be found on inspection to be no vague or\nunmeaning assertion, but a most important and really fundamental truth.\n\n\n\u00a7 2. The notion of Cause being the root of the whole theory of\nInduction, it is indispensable that this idea should, at the very outset\nof our inquiry, be, with the utmost practicable degree of precision,\nfixed and determined. If, indeed, it were necessary for the purpose of\ninductive logic that the strife should be quelled, which has so long\nraged among the different schools of metaphysicians, respecting the\norigin and analysis of our idea of causation; the promulgation, or at\nleast the general reception, of a true theory of induction, might be\nconsidered desperate for a long time to come. But the science of the\nInvestigation of Truth by means of Evidence, is happily independent of\nmany of the controversies which perplex the science of the ultimate\nconstitution of the human mind, and is under no necessity of pushing the\nanalysis of mental phenomena to that extreme limit which alone ought to\nsatisfy 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\nthat sense alone, in which one physical fact is said to be the cause of\nanother. Of the efficient causes of phenomena, or whether any such\ncauses exist at all, I am not called upon to give an opinion. The notion\nof causation is deemed, by the schools of metaphysics most in vogue at\nthe present 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. The only notion of a cause, which the theory of\ninduction requires, is such a notion as can be gained from experience.\nThe Law of Causation, the recognition of which is the main pillar of\ninductive science, is but the familiar truth, that invariability of\nsuccession is found by observation to obtain between every fact in\nnature and some other fact which has preceded it; independently of all\nconsideration respecting the ultimate mode of production of phenomena,\nand of every other question regarding the nature of \"Things in\nthemselves.\"\n\nBetween the phenomena, then, which exist at any instant, and the\nphenomena which exist at the succeeding instant, there is an invariable\norder of succession; and, as we said in speaking of the general\nuniformity of the course of nature, this web is composed of separate\nfibres; this collective order is made up of particular sequences,\nobtaining invariably among the separate parts. To certain facts, certain\nfacts always do, and, as we believe, will continue to, succeed. The\ninvariable antecedent is termed the cause; the invariable consequent,\nthe effect. And the universality of the law of causation consists in\nthis, that every consequent is connected in this manner with some\nparticular antecedent, or set of antecedents. Let the fact be what it\nmay, if it has begun to exist, it was preceded by some fact or facts,\nwith which it is invariably connected. For every event there exists some\ncombination of objects or events, some given concurrence of\ncircumstances, 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\nsuch a one, and that it never occurs without having the phenomenon in\nquestion as its effect or consequence. On the universality of this truth\ndepends the possibility of reducing the inductive process to rules. The\nundoubted assurance we have that there is a law to be found if we only\nknew how to find it, will be seen presently to be the source from which\nthe canons of the Inductive Logic derive their validity.\n\n\n\u00a7 3. It is seldom, if ever, between a consequent and a single\nantecedent, that this invariable sequence subsists. It is usually\nbetween a consequent and the sum of several antecedents; the concurrence\nof all of them being requisite to produce, that is, to be certain of\nbeing followed by, the consequent. In such cases it is very common to\nsingle out one only of the antecedents under the denomination of Cause,\ncalling the others merely Conditions. Thus, if a person eats of a\nparticular dish, and dies in consequence, that is, would not have died\nif he had not eaten of it, people would be apt to say that eating of\nthat dish was the cause of his death. There needs not, however, be any\ninvariable connexion between eating of the dish and death; but there\ncertainly is, among the circumstances which took place, some combination\nor other on which death is invariably consequent: as, for instance, the\nact of eating of the dish, combined with a particular bodily\nconstitution, a particular state of present health, and perhaps even a\ncertain state of the atmosphere; the whole of which circumstances\nperhaps constituted in this particular case the _conditions_ of the\nphenomenon, or, in other words, the set of antecedents which determined\nit, and but for which it would not have happened. The real Cause, is the\nwhole of these antecedents; and we have, philosophically speaking, no\nright to give the name of cause to one of them, exclusively of the\nothers. What, in the case we have supposed, disguises the incorrectness\nof the expression, is this: that the various conditions, except the\nsingle one of eating the food, were not _events_ (that is, instantaneous\nchanges, or successions of instantaneous changes) but _states_,\npossessing more or less of permanency; and might therefore have preceded\nthe effect by an indefinite length of duration, for want of the event\nwhich was requisite to complete the required concurrence of conditions:\nwhile as soon as that event, eating the food, occurs, no other cause is\nwaited for, but the effect begins immediately to take place: and hence\nthe 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\nname of cause to that one condition, the fulfilment of which completes\nthe tale, and brings about the effect without further delay; this\ncondition has really no closer relation to the effect than any of the\nother conditions has. The production of the consequent required that\nthey should all _exist_ immediately previous, though not that they\nshould all _begin_ to exist immediately previous. The statement of the\ncause is incomplete, unless in some shape or other we introduce all the\nconditions. A man takes mercury, goes out of doors, and catches cold. We\nsay, perhaps, that the cause of his taking cold was exposure to the air.\nIt is clear, however, that his having taken mercury may have been a\nnecessary condition of catching cold; and though it might consist with\nusage to say that the cause of his attack was exposure to the air, to be\naccurate we ought to say that the cause was exposure to the air while\nunder the effect of mercury.\n\nIf we do not, when aiming at accuracy, enumerate all the conditions, it\nis only because some of them will in most cases be understood without\nbeing expressed, or because for the purpose in view they may without\ndetriment be overlooked. For example, when we say, the cause of a man's\ndeath was that his foot slipped in climbing a ladder, we omit as a\nthing unnecessary to be stated the circumstance of his weight, though\nquite as indispensable a condition of the effect which took place. When\nwe say that the assent of the crown to a bill makes it law, we mean that\nthe assent, being never given until all the other conditions are\nfulfilled, makes up the sum of the conditions, though no one now regards\nit as the principal one. When the decision of a legislative assembly has\nbeen determined by the casting vote of the chairman, we sometimes say\nthat this one person was the cause of all the effects which resulted\nfrom the enactment. Yet we do not really suppose that his single vote\ncontributed more to the result than that of any other person who voted\nin the affirmative; but, for the purpose we have in view, which is to\ninsist on his individual responsibility, the part which any other person\nhad in the transaction is not material.\n\nIn all these instances the fact which was dignified with the name of\ncause, was the one condition which came last into existence. But it must\nnot be supposed that in the employment of the term this or any other\nrule is always adhered to. Nothing can better show the absence of any\nscientific ground for the distinction between the cause of a phenomenon\nand its conditions, than the capricious manner in which we select from\namong the conditions that which we choose to denominate the cause.\nHowever numerous the conditions may be, there is hardly any of them\nwhich may not, according to the purpose of our immediate discourse,\nobtain that nominal pre-eminence. This will be seen by analysing the\nconditions of some one familiar phenomenon. For example, a stone thrown\ninto water falls to the bottom. What are the conditions of this event?\nIn the first place there must be a stone, and water, and the stone must\nbe thrown into the water; but these suppositions forming part of the\nenunciation of the phenomenon itself, to include them also among the\nconditions would be a vicious tautology; and this class of conditions,\ntherefore, have never received the name of cause from any but the\nAristotelians, by whom they were called the _material_ cause, _causa\nmaterialis_. The next condition is, there must be an earth: and\naccordingly it is often said, that the fall of a stone is caused by the\nearth; or by a power or property of the earth, or a force exerted by the\nearth, all of which are merely roundabout ways of saying that it is\ncaused by the earth; or, lastly, the earth's attraction; which also is\nonly a technical mode of saying that the earth causes the motion, with\nthe additional particularity that the motion is towards the earth, which\nis not a character of the cause, but of the effect. Let us now pass to\nanother condition. It is not enough that the earth should exist; the\nbody must be within that distance from it, in which the earth's\nattraction preponderates over that of any other body. Accordingly we may\nsay, and the expression would be confessedly correct, that the cause of\nthe stone's falling is its being _within the sphere_ of the earth's\nattraction. We proceed to a further condition. The stone is immersed in\nwater: it is therefore a condition of its reaching the ground, that its\nspecific gravity exceed that of the surrounding fluid, or in other words\nthat it surpass in weight an equal volume of water. Accordingly any one\nwould be acknowledged to speak correctly who said, that the cause of the\nstone's going to the bottom is its exceeding in specific gravity the\nfluid in which it is immersed.\n\nThus we see that each and every condition of the phenomenon may be taken\nin its turn, and, with equal propriety in common parlance, but with\nequal impropriety in scientific discourse, may be spoken of as if it\nwere the entire cause. And in practice, that particular condition is\nusually styled the cause, whose share in the matter is superficially the\nmost conspicuous, or whose requisiteness to the production of the effect\nwe happen to be insisting on at the moment. So great is the force of\nthis last consideration, that it sometimes induces us to give the name\nof cause even to one of the negative conditions. We say, for example,\nThe army was surprised because the sentinel was off his post. But since\nthe sentinel's absence was not what created the enemy, or put the\nsoldiers asleep, how did it cause them to be surprised? All that is\nreally meant is, that the event would not have happened if he had been\nat his duty. His being off his post was no producing cause, but the mere\nabsence of a preventing cause: it was simply equivalent to his\nnon-existence. From nothing, from a mere negation, no consequences can\nproceed. All effects are connected, by the law of causation, with some\nset of _positive_ conditions; negative ones, it is true, being almost\nalways required in addition. In other words, every fact or phenomenon\nwhich has a beginning, invariably arises when some certain combination\nof positive facts exists, provided certain other positive facts do not\nexist.\n\nThere is, no doubt, a tendency (which our first example, that of death\nfrom taking a particular food, sufficiently illustrates) to associate\nthe idea of causation with the proximate antecedent _event_, rather than\nwith any of the antecedent _states_, or permanent facts, which may\nhappen also to be conditions of the phenomenon; the reason being that\nthe event not only exists, but begins to exist immediately previous;\nwhile the other conditions may have pre-existed for an indefinite time.\nAnd this tendency shows itself very visibly in the different logical\nfictions which are resorted to, even by men of science, to avoid the\nnecessity of giving the name of cause to anything which had existed for\nan indeterminate length of time before the effect. Thus, rather than say\nthat the earth causes the fall of bodies, they ascribe it to a _force_\nexerted by the earth, or an _attraction_ by the earth, abstractions\nwhich they can represent to themselves as exhausted by each effort, and\ntherefore constituting at each successive instant a fresh fact,\nsimultaneous with, or only immediately preceding, the effect. Inasmuch\nas the coming of the circumstance which completes the assemblage of\nconditions, is a change or event, it thence happens that an event is\nalways the antecedent in closest apparent proximity to the consequent:\nand this may account for the illusion which disposes us to look upon the\nproximate event as standing more peculiarly in the position of a cause\nthan any of the antecedent states. But even this peculiarity, of being\nin closer proximity to the effect than any other of its conditions, is,\nas we have already seen, far from being necessary to the common notion\nof a cause; with which notion, on the contrary, any one of the\nconditions, either positive or negative, is found, on occasion,\ncompletely to accord.[14]\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\nphenomenon, a special enumeration of which would generally be very\nprolix, may be all summed up under one head, namely, the absence of\npreventing or counteracting causes. The convenience of this mode of\nexpression is mainly grounded on the fact, that the effects of any cause\nin counteracting another cause may in most cases be, with strict\nscientific exactness, regarded as a mere extension of its own proper and\nseparate effects. If gravity retards the upward motion of a projectile,\nand deflects it into a parabolic trajectory, it produces, in so doing,\nthe very same kind of effect, and even (as mathematicians know) the\nsame quantity of effect, as it does in its ordinary operation of causing\nthe fall of bodies when simply deprived of their support. If an alkaline\nsolution mixed with an acid destroys its sourness, and prevents it from\nreddening vegetable blues, it is because the specific effect of the\nalkali is to combine with the acid, and form a compound with totally\ndifferent qualities. This property, which causes of all descriptions\npossess, of preventing the effects of other causes by virtue (for the\nmost part) of the same laws according to which they produce their\nown,[15] enables us, by establishing the general axiom that all causes\nare liable to be counteracted in their effects by one another, to\ndispense with the consideration of negative conditions entirely, and\nlimit the notion of cause to the assemblage of the positive conditions\nof the phenomenon: one negative condition invariably understood, and the\nsame in all instances (namely, the absence of counteracting causes)\nbeing sufficient, along with the sum of the positive conditions, to make\nup the whole set of circumstances on which the phenomenon is dependent.\n\n\n\u00a7 4. Among the positive conditions, as we have seen that there are some\nto which, in common parlance, the term cause is more readily and\nfrequently awarded, so there are others to which it is, in ordinary\ncircumstances, refused. In most cases of causation a distinction is\ncommonly drawn between something which acts, and some other thing which\nis acted upon; between an _agent_ and a _patient_. Both of these, it\nwould be universally allowed, are conditions of the phenomenon; but it\nwould be thought absurd to call the latter the cause, that title being\nreserved for the former. The distinction, however, vanishes on\nexamination, or rather is found to be only verbal; arising from an\nincident of mere expression, namely, that the object said to be acted\nupon, and which is considered as the scene in which the effect takes\nplace, is commonly included in the phrase by which the effect is spoken\nof, so that if it were also reckoned as part of the cause, the seeming\nincongruity would arise of its being supposed to cause itself. In the\ninstance which we have already had, of falling bodies, the question was\nthus put: What is the cause which makes a stone fall? and if the answer\nhad been \"the stone itself,\" the expression would have been in apparent\ncontradiction to the meaning of the word cause. The stone, therefore, is\nconceived as the patient, and the earth (or, according to the common and\nmost unphilosophical practice, some occult quality of the earth) is\nrepresented as the agent or cause. But that there is nothing fundamental\nin the distinction may be seen from this, that it is quite possible to\nconceive the stone as causing its own fall, provided the language\nemployed be such as to save the mere verbal incongruity. We might say\nthat the stone moves towards the earth by the properties of the matter\ncomposing it; and according to this mode of presenting the phenomenon,\nthe stone itself might without impropriety be called the agent; though,\nto save the established doctrine of the inactivity of matter, men\nusually prefer here also to ascribe the effect to an occult quality, and\nsay that the cause is not the stone itself, but the _weight_ or\n_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\nassume of speaking of phenomena as _states_ of the various objects which\ntake part in them, (an artifice of which so much use has been made by\nsome philosophers, Brown in particular, for the apparent explanation of\nphenomena,) is simply a sort of logical fiction, useful sometimes as one\namong several modes of expression, but which should never be supposed to\nbe the enunciation of a scientific truth. Even those attributes of an\nobject which might seem with greatest propriety to be called states of\nthe object itself, its sensible qualities, its colour, hardness, shape,\nand the like, are in reality (as no one has pointed out more clearly\nthan Brown himself) phenomena of causation, in which the substance is\ndistinctly the agent, or producing cause, the patient being our own\norgans, and those of other sentient beings. What we call states of\nobjects, are always sequences into which the objects enter, generally as\nantecedents or causes; and things are never more active than in the\nproduction of those phenomena in which they are said to be acted upon.\nThus, in the example of a stone falling to the earth, according to the\ntheory of gravitation the stone is as much an agent as the earth, which\nnot only attracts, but is itself attracted by, the stone. In the case of\na sensation produced in our organs, the laws of our organization, and\neven those of our minds, are as directly operative in determining the\neffect produced, as the laws of the outward object. Though we call\nprussic acid the agent of a person's death, the whole of the vital and\norganic properties of the patient are as actively instrumental as the\npoison, in the chain of effects which so rapidly terminates his sentient\nexistence. In the process of education, we may call the teacher the\nagent, and the scholar only the material acted upon; yet in truth all\nthe facts which pre-existed in the scholar's mind exert either\nco-operating or counteracting agencies in relation to the teacher's\nefforts. It is not light alone which is the agent in vision, but light\ncoupled with the active properties of the eye and brain, and with those\nof the visible object. The distinction between agent and patient is\nmerely verbal: patients are always agents; in a great proportion,\nindeed, of all natural phenomena, they are so to such a degree as to\nreact forcibly on the causes which acted upon them: and even when this\nis not the case, they contribute, in the same manner as any of the other\nconditions, to the production of the effect of which they are vulgarly\ntreated as the mere theatre. All the positive conditions of a phenomenon\nare alike agents, alike active; and in any expression of the cause which\nprofesses to be complete, none of them can with reason be excluded,\nexcept such as have already been implied in the words used for\ndescribing the effect; nor by including even these would there be\nincurred any but a merely verbal impropriety.\n\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\nof the 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 \"the antecedent which\nit invariably follows,\" we do not use this phrase as exactly synonymous\nwith \"the antecedent which it invariably _has_ followed in our past\nexperience.\" Such a mode of conceiving causation would be liable to the\nobjection very plausibly urged by Dr. Reid, namely, that according to\nthis doctrine night must be the cause of day, and day the cause of\nnight; since these phenomena have invariably succeeded one another from\nthe beginning of the world. But it is necessary to our using the word\ncause, that we should believe not only that the antecedent always _has_\nbeen followed by the consequent, but that, as long as the present\nconstitution of things[16] endures, it always _will_ be so. And this\nwould not be true of day and night. We do not believe that night will be\nfollowed by day under all imaginable circumstances, but only that it\nwill be so _provided_ the sun rises above the horizon. If the sun ceased\nto rise, which, for aught we know, may be perfectly compatible with the\ngeneral laws of matter, night would be, or might be, eternal. On the\nother hand, if the sun is above the horizon, his light not extinct, and\nno opaque body between us and him, we believe firmly that unless a\nchange takes place in the properties of matter, this combination of\nantecedents will be followed by the consequent, day; that if the\ncombination of antecedents could be indefinitely prolonged, it would be\nalways day; and that if the same combination had always existed, it\nwould always have been day, quite independently of night as a previous\ncondition. Therefore is it that we do not call night the cause, nor even\na condition, of day. The existence of the sun (or some such luminous\nbody), and there being no opaque medium in a straight line[17] between\nthat body and the part of the earth where we are situated, are the sole\nconditions; and the union of these, without the addition of any\nsuperfluous circumstance, constitutes the cause. This is what writers\nmean when they say that the notion of cause involves the idea of\nnecessity. If there be any meaning which confessedly belongs to the term\nnecessity, it is _unconditionalness_. That which is necessary, that\nwhich _must_ be, means that which will be, whatever supposition we may\nmake in regard to all other things. The succession of day and night\nevidently is not necessary in this sense. It is conditional on the\noccurrence of other antecedents. That which will be followed by a given\nconsequent when, and only when, some third circumstance also exists, is\nnot the cause, even though no case should ever have occurred in which\nthe phenomenon 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\nyet we do not regard as cases of causation, but as conjunctions in some\nsort accidental. Such, to an accurate thinker, is that of day and night.\nThe one might have existed for any length of time, and the other not\nhave followed the sooner for its existence; it follows only if certain\nother antecedents exist; and where those antecedents existed, it would\nfollow in any case. No one, probably, ever called night the cause of\nday; mankind must so soon have arrived at the very obvious\ngeneralization, that the state of general illumination which we call day\nwould follow from the presence of a sufficiently luminous body, whether\ndarkness had preceded or not.\n\nWe may define, therefore, the cause of a phenomenon, to be the\nantecedent, or the concurrence of antecedents, on which it is invariably\nand _unconditionally_ consequent. Or if we adopt the convenient\nmodification of the meaning of the word cause, which confines it to the\nassemblage of positive conditions without the negative, then instead of\n\"unconditionally,\" we must say, \"subject to no other than negative\nconditions.\"\n\nTo some it may appear, that the sequence between night and day being\ninvariable in our experience, we have as much ground in this case as\nexperience can give in any case, for recognising the two phenomena as\ncause and effect; and that to say that more is necessary--to require a\nbelief that the succession is unconditional, or in other words that it\nwould be invariable under all changes of circumstances, is to\nacknowledge in causation an element of belief not derived from\nexperience. The answer to this is, that it is experience itself which\nteaches us that one uniformity of sequence is conditional and another\nunconditional. When we judge that the succession of night and day is a\nderivative sequence, depending on something else, we proceed on grounds\nof experience. It is the evidence of experience which convinces us that\nday could equally exist without being followed by night, and that night\ncould equally exist without being followed by day. To say that these\nbeliefs are \"not generated by our mere observation of sequence,\"[18] is\nto forget that twice in every twenty-four hours, when the sky is clear,\nwe have an _experimentum crucis_ that the cause of day is the sun. We\nhave an experimental knowledge of the sun which justifies us on\nexperimental grounds in concluding, that if the sun were always above\nthe horizon there would be day, though there had been no night, and that\nif the sun were always below the horizon there would be night, though\nthere had been no day. We thus know from experience that the succession\nof night and day is not unconditional. Let me add, that the antecedent\nwhich is only conditionally invariable, is not the invariable\nantecedent. Though a fact may, in experience, have always been followed\nby another fact, yet if the remainder of our experience teaches us that\nit might not always be so followed, or if the experience itself is such\nas leaves room for a possibility that the known cases may not correctly\nrepresent all possible cases, the hitherto invariable antecedent is not\naccounted the cause; but why? Because we are not sure that it _is_ the\ninvariable antecedent.\n\nSuch cases of sequence as that of day and night not only do not\ncontradict the doctrine which resolves causation into invariable\nsequence, but are necessarily implied in that doctrine. It is evident,\nthat from a limited number of unconditional sequences, there will\nresult a much greater number of conditional ones. Certain causes being\ngiven, that is, certain antecedents which are unconditionally followed\nby certain consequents; the mere coexistence of these causes will give\nrise 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\nor succeeding one another in some particular order, which order will be\ninvariable while the causes continue to coexist, but no longer. The\nmotion of the earth in a given orbit round the sun, is a series of\nchanges which follow one another as antecedents and consequents, and\nwill continue to do so while the sun's attraction, and the force with\nwhich the earth tends to advance in a direct line through space,\ncontinue to coexist in the same quantities as at present. But vary\neither of these causes, and this particular succession of motions would\ncease to take place. The series of the earth's motions, therefore,\nthough a case of sequence invariable within the limits of human\nexperience, is not a case of causation. It is not unconditional.\n\nThis distinction between the relations of succession which so far as we\nknow are unconditional, and those relations, whether of succession or of\ncoexistence, which, like the earth's motions, or the succession of day\nand night, depend on the existence or on the coexistence of other\nantecedent facts--corresponds to the great division which Dr. Whewell\nand other writers have made of the field of science, into the\ninvestigation of what they term the Laws of Phenomena, and the\ninvestigation of causes; a phraseology, as I conceive, not\nphilosophically sustainable, inasmuch as the ascertainment of causes,\nsuch causes as the human faculties can ascertain, namely, causes which\nare themselves phenomena, is, therefore, merely the ascertainment of\nother and more universal Laws of Phenomena. And let me here observe,\nthat Dr. Whewell, and in some degree even Sir John Herschel, seem to\nhave misunderstood the meaning of those writers who, like M. Comte,\nlimit the sphere of scientific investigation to Laws of Phenomena, and\nspeak of the inquiry into causes as vain and futile. The causes which M.\nComte designates as inaccessible, are efficient causes. The\ninvestigation of physical, as opposed to efficient, causes (including\nthe study of all the active forces in Nature, considered as facts of\nobservation) is as important a part of M. Comte's conception of science\nas of Dr. Whewell's. His objection to the _word_ cause is a mere matter\nof nomenclature, in which, as a matter of nomenclature, I consider him\nto be entirely wrong. \"Those,\" it is justly remarked by Mr. Bailey,[19]\n\"who, like M. Comte, object to designate _events_ as causes, are\nobjecting without any real ground to a mere but extremely convenient\ngeneralization, to a very useful common name, the employment of which\ninvolves, or needs involve, no particular theory.\" To which it may be\nadded, that by rejecting this form of expression, M. Comte leaves\nhimself without any term for marking a distinction which, however\nincorrectly expressed, is not only real, but is one of the fundamental\ndistinctions in science; indeed it is on this alone, as we shall\nhereafter find, that the possibility rests of framing a rigorous Canon\nof Induction. And as things left without a name are apt to be forgotten,\na Canon of that description is not one of the many benefits which the\nphilosophy of Induction has received from M. Comte's great powers.\n\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--as when we say that fire is the cause of\nwarmth, the sun and moisture the cause of vegetation, and the like?\nSince a cause does not necessarily perish because its effect has been\nproduced, the two things do very generally coexist; and there are some\nappearances, and some common expressions, seeming to imply not only that\ncauses may, but that they must, be contemporaneous with their effects.\n_Cessante caus\u00e2 cessat et effectus_, has been a dogma of the schools:\nthe necessity for the continued existence of the cause in order to the\ncontinuance of the effect, seems to have been once a generally received\ndoctrine. Kepler's numerous attempts to account for the motions of the\nheavenly bodies on mechanical principles, were rendered abortive by his\nalways supposing that the agency which set those bodies in motion must\ncontinue to operate in order to keep up the motion which it at first\nproduced. Yet there were at all times many familiar instances of the\ncontinuance of effects, long after their causes had ceased. A _coup de\nsoleil_ gives a person a brain fever: will the fever go off as soon as\nhe is moved out of the sunshine? A sword is run through his body: must\nthe sword remain in his body in order that he may continue dead? A\nploughshare once made, remains a ploughshare, without any continuance of\nheating and hammering, and even after the man who heated and hammered it\nhas been gathered to his fathers. On the other hand, the pressure which\nforces up the mercury in an exhausted tube must be continued in order to\nsustain it in the tube. This (it may be replied) is because another\nforce is acting without intermission, the force of gravity, which would\nrestore it to its level, unless counterpoised by a force equally\nconstant. But again; a tight bandage causes pain, which pain will\nsometimes 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\nalso necessary for its continuance; though more commonly its continuance\nrequires no condition except negative ones. Most things, once produced,\ncontinue as they are, until something changes or destroys them; but some\nrequire the permanent presence of the agencies which produced them at\nfirst. These may, if we please, be considered as instantaneous\nphenomena, requiring to be renewed at each instant by the cause by which\nthey were at first generated. Accordingly, the illumination of any given\npoint of space has always been looked upon as an instantaneous fact,\nwhich perishes and is perpetually renewed as long as the necessary\nconditions subsist. If we adopt this language we avoid the necessity of\nadmitting that the continuance of the cause is ever required to maintain\nthe effect. We may say, it is not required to maintain, but to\nreproduce, the effect, or else to counteract some force tending to\ndestroy it. And this may be a convenient phraseology. But it is only a\nphraseology. The fact remains, that in some cases (though these are a\nminority) the continuance of the conditions which produced an effect is\nnecessary to the continuance of the effect.\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\nwith much ingenuity by Sir John Herschel in an Essay already\nquoted,[20]) the inquiry is of no consequence for our present purpose.\nThere certainly are cases in which the effect follows without any\ninterval perceptible by our faculties: and when there is an interval, we\ncannot tell by how many intermediate links imperceptible to us that\ninterval may really be filled up. But even granting that an effect may\ncommence simultaneously with its cause, the view I have taken of\ncausation is in no way practically affected. Whether the cause and its\neffect be necessarily successive or not, the beginning of a phenomenon\nis what implies a cause, and causation is the law of the succession of\nphenomena. If these axioms be granted, we can afford, though I see no\nnecessity for doing so, to drop the words antecedent and consequent as\napplied to cause and effect. I have no objection to define a cause, the\nassemblage 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\nwhen we are in doubt, between two coexistent phenomena, which is cause\nand which effect, we rightly deem the question solved if we can\nascertain which of them preceded the other.\n\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\nother words, one and the same phenomenon is seen to be followed by\nseveral sorts of effects quite heterogeneous, but which go on\nsimultaneously one with another; provided, of course, that all other\nconditions requisite for each of them also exist. Thus, the sun produces\nthe celestial motions, it produces daylight, and it produces heat. The\nearth causes the fall of heavy bodies, and it also, in its capacity of a\ngreat magnet, causes the phenomena of the magnetic needle. A crystal of\ngalena causes the sensations of hardness, of weight, of cubical form, of\ngrey colour, and many others between which we can trace no\ninterdependence. The purpose to which the phraseology of Properties and\nPowers is specially adapted, is the expression of this sort of cases.\nWhen the same phenomenon is followed (either subject or not to the\npresence of other conditions) by effects of different and dissimilar\norders, it is usual to say that each different sort of effect is\nproduced by a different property of the cause. Thus we distinguish the\nattractive or gravitative property of the earth, and its magnetic\nproperty: the gravitative, luminiferous, and calorific properties of the\nsun: the colour, shape, weight, and hardness of a crystal. These are\nmere phrases, which explain nothing, and add nothing to our knowledge of\nthe subject; but, considered as abstract names denoting the connexion\nbetween the different effects produced and the object which produces\nthem, they 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\nto be of great importance, that of a Permanent Cause, or original\nnatural agent. There exist in nature a number of permanent causes, which\nhave subsisted ever since the human race has been in existence, and for\nan indefinite and probably an enormous length of time previous. The sun,\nthe earth, and planets, with their various constituents, air, water, and\nother distinguishable substances, whether simple or compound, of which\nnature is made up, are such Permanent Causes. These have existed, and\nthe effects 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\norigin of the Permanent Causes themselves. Why these particular natural\nagents existed originally and no others, or why they are commingled in\nsuch and such proportions, and distributed in such and such a manner\nthroughout space, is a question we cannot answer. More than this: we can\ndiscover nothing regular in the distribution itself; we can reduce it to\nno uniformity, to no law. There are no means by which, from the\ndistribution of these causes or agents in one part of space, we could\nconjecture whether a similar distribution prevails in another. The\ncoexistence, therefore, of Primeval Causes, ranks, to us, among merely\ncasual concurrences: and all those sequences or coexistences among the\neffects of several such causes, which, though invariable while those\ncauses coexist, would, if the coexistence terminated, terminate along\nwith it, we do not class as cases of causation, or laws of nature: we\ncan only calculate on finding these sequences or coexistences where we\nknow by direct evidence, that the natural agents on the properties of\nwhich they ultimately depend, are distributed in the requisite manner.\nThese Permanent Causes are not always objects; they are sometimes\nevents, that is to say, periodical cycles of events, that being the only\nmode in which events can possess the property of permanence. Not only,\nfor instance, is the earth itself a permanent cause, or primitive\nnatural agent, but the earth's rotation is so too: it is a cause which\nhas produced, from the earliest period, (by the aid of other necessary\nconditions,) the succession of day and night, the ebb and flow of the\nsea, and many other effects, while, as we can assign no cause (except\nconjecturally) for the rotation itself, it is entitled to be ranked as a\nprimeval cause. It is, however, only the _origin_ of the rotation which\nis mysterious to us: once begun, its continuance is accounted for by the\nfirst law of motion (that of the permanence of rectilinear motion once\nimpressed) combined with the gravitation of the parts of the earth\ntowards one another.\n\nAll phenomena without exception which begin to exist, that is, all\nexcept the primeval causes, are effects either immediate or remote of\nthose primitive 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\nmore of the phenomena which preceded it; insomuch that it will happen\nagain as often as those phenomena occur again, and as no other\nphenomenon having the character of a counteracting cause shall coexist.\nThese antecedent phenomena, again, were connected in a similar manner\nwith some that preceded them; and so on, until we reach, as the ultimate\nstep attainable by us, either the properties of some one primeval cause,\nor the conjunction of several. The whole of the phenomena of nature were\ntherefore the necessary, or in other words, the unconditional,\nconsequences of some former collocation of the Permanent Causes.\n\nThe state of the whole universe at any instant, we believe to be the\nconsequence of its state at the previous instant; insomuch that one who\nknew all the agents which exist at the present moment, their collocation\nin space, and all their properties, in other words, the laws of their\nagency, could predict the whole subsequent history of the universe, at\nleast unless some new volition of a power capable of controlling the\nuniverse should supervene.[21] And if any particular state of the\nentire universe could ever recur a second time, all subsequent states\nwould return too, and history would, like a circulating decimal of many\nfigures, periodically repeat itself:--\n\n Jam redit et virgo, redeunt Saturnia regna....\n Alter erit tum Tiphys, et altera qu\u00e6 vehat Argo\n Delectos heroas; erunt quoque altera bella,\n Atque iterum ad Trojam magnus mittetur Achilles.\n\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\nfar more 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\n\u00a7 8. Since everything which occurs is determined by laws of causation\nand collocations of the original causes, it follows that the\ncoexistences which are observable among effects cannot be themselves the\nsubject of any similar set of laws, distinct from laws of causation.\nUniformities there are, as well of coexistence as of succession, among\neffects; but these must in all cases be a mere result either of the\nidentity or of the coexistence of their causes: if the causes did not\ncoexist, neither could the effects. And these causes being also effects\nof prior causes, and these of others, until we reach the primeval\ncauses, it follows that (except in the case of effects which can be\ntraced immediately or remotely to one and the same cause) the\ncoexistences of phenomena can in no case be universal, unless the\ncoexistences of the primeval causes to which the effects are ultimately\ntraceable, can be reduced to an universal law: but we have seen that\nthey cannot. There are, accordingly, no original and independent, in\nother words no unconditional, uniformities of coexistence, between\neffects of different causes; if they coexist, it is only because the\ncauses 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\neffects of the same cause; in other words, between different properties\nof the same natural agent. This portion of the Laws of Nature will be\ntreated of in the latter part of the present Book, under the name of the\nSpecific Properties of Kinds.\n\n\n\u00a7 9. It is proper in this place to advert to a rather ancient doctrine\nrespecting causation, which has been revived during the last few years\nin many quarters, and at present gives more signs of life than any other\ntheory of causation at variance with that set forth in the preceding\npages.\n\nAccording to the theory in question, Mind, or, to speak 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\nis affirmed 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, \"of force exerted, of power in\naction, which is necessarily causal, or causative.\" This feeling of\nenergy or force, inherent in an act of will, is knowledge _\u00e0 priori_;\nassurance, prior to experience, that we have the power of causing\neffects. Volition, therefore, it is asserted, is something more than an\nunconditional antecedent; it is a cause, in a different sense from that\nin which physical phenomena are said to cause one another: it is an\nEfficient Cause. From this the transition is easy to the further\ndoctrine, that Volition is the _sole_ Efficient Cause of all phenomena.\n\"It is inconceivable that dead force could continue unsupported for a\nmoment beyond its creation. We cannot even conceive of change or\nphenomena without the energy of a mind.\" \"The word _action_\" itself,\nsays another writer of the same school, \"has no real significance except\nwhen applied to the doings of an intelligent agent. Let any one\nconceive, if he can, of any power, energy, or force, inherent in a lump\nof matter.\" Phenomena may have the semblance of being produced by\nphysical causes, but they are in reality produced, say these writers, by\nthe immediate agency of mind. All things which do not proceed from a\nhuman (or, I suppose, an animal) will, proceed, they say, directly from\ndivine will. The earth is not moved by the combination of a centripetal\nand a projectile force; this is but a mode of speaking, which serves to\nfacilitate our conceptions. It is moved by the direct volition of an\nomnipotent Being, in a path coinciding with that which we deduce from\nthe 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\nphysical or phenomenal causes, belongs as much to Logic as to\nMetaphysics, and is a fit subject for discussion here.\n\nTo my apprehension, a volition is not an efficient, but simply a\nphysical, cause. Our will causes our bodily actions in the same sense,\nand in no other, in which cold causes ice, or a spark causes an\nexplosion of gunpowder. The volition, a state of our mind, is the\nantecedent; the motion of our limbs in conformity to the volition, is\nthe consequent. This sequence I conceive to be not a subject of direct\nconsciousness, in the sense intended by the theory. The antecedent,\nindeed, and the consequent, are subjects of consciousness. But the\nconnexion between them is a subject of experience. I cannot admit that\nour consciousness of the volition contains in itself any _\u00e0 priori_\nknowledge that the muscular motion will follow. If our nerves of motion\nwere paralysed, or our muscles stiff and inflexible, and had been so all\nour lives, I do not see the slightest ground for supposing that we\nshould ever (unless by information from other people) have known\nanything of volition as a physical power, or been conscious of any\ntendency in feelings of our mind to produce motions of our body, or of\nother bodies. I will not undertake to say whether we should in that case\nhave had the physical feeling which I suppose is meant when these\nwriters speak of \"consciousness of effort:\" I see no reason why we\nshould not; since that physical feeling is probably a state of nervous\nsensation beginning and ending in the brain, without involving the\nmotory apparatus: but we certainly should not have designated it by any\nterm equivalent to effort, since effort implies consciously aiming at an\nend, which we should not only in that case have had no reason to do, but\ncould not even have had the idea of doing. If conscious at all of this\npeculiar sensation, we should have been conscious of it, I conceive,\nonly as a kind of uneasiness, accompanying our feelings of desire.\n\nIt is well argued by Sir William Hamilton against the theory in\nquestion, that it \"is refuted by the consideration, that between the\novert fact of corporeal movement of which we are cognisant, and the\ninternal act of mental determination of which we are also cognisant,\nthere intervenes a numerous series of intermediate agencies of which we\nhave no knowledge; and, consequently, that we can have no consciousness\nof any causal connexion between the extreme links of this chain, the\nvolition to move and the limb moving, as this hypothesis asserts. No one\nis immediately conscious, for example, of moving his arm through his\nvolition. Previously to this ultimate movement, muscles, nerves, a\nmultitude of solid and fluid parts, must be set in motion by the will,\nbut of this motion we know, from consciousness, absolutely nothing. A\nperson struck with paralysis is conscious of no inability in his limb to\nfulfil the determinations of his will; and it is only after having\nwilled, and finding that his limbs do not obey his volition, that he\nlearns by this experience, that the external movement does not follow\nthe internal act. But as the paralytic learns after the volition that\nhis limbs do not obey his mind; so it is only after volition that the\nman in health learns, that his limbs do obey the mandates of his\nwill.\"[22]\n\nThose against whom I am contending have never produced, and do not\npretend to produce, any positive evidence[23] that the power of our will\nto move our bodies would be known to us independently of experience.\nWhat they have to say on the subject is, that the production of physical\nevents by a will seems to carry its own explanation with it, while the\naction of matter upon matter seems to require something else to explain\nit; and is even, according to them, \"inconceivable\" on any other\nsupposition than that some will intervenes between the apparent cause\nand its apparent effect. They thus rest their case on an appeal to the\ninherent laws of our conceptive faculty; mistaking, as I apprehend, for\nthe laws of that faculty its acquired habits, grounded on the\nspontaneous tendencies of its uncultured state. The succession between\nthe will to move a limb and the actual motion, is one of the most direct\nand instantaneous of all sequences which come under our observation, and\nis familiar to every moment's experience from our earliest infancy; more\nfamiliar than any succession of events exterior to our bodies, and\nespecially more so than any other case of the apparent origination (as\ndistinguished from the mere communication) of motion. Now, it is the\nnatural tendency of the mind to be always attempting to facilitate its\nconception of unfamiliar facts by assimilating them to others which are\nfamiliar. Accordingly, our voluntary acts, being the most familiar to us\nof all cases of causation, are, in the infancy and early youth of the\nhuman race, spontaneously taken as the type of causation in general, and\nall phenomena are supposed to be directly produced by the will of some\nsentient being. This original Fetichism I shall not characterize in the\nwords of Hume, or of any follower of Hume, but in those of a religious\nmetaphysician, Dr. Reid, in order more effectually to show the unanimity\nwhich exists on the subject among all competent thinkers.\n\n\"When we turn our attention to external objects, and begin to exercise\nour rational faculties about them, we find that there are some motions\nand changes in them which we have power to produce, and that there are\nmany which must have some other cause. Either the objects must have life\nand active power, as we have, or they must be moved or changed by\nsomething that has life and active power, as external objects are moved\nby us.\n\n\"Our first thoughts seem to be, that the objects in which we perceive\nsuch motion have understanding and active power as we have. 'Savages,'\nsays the Abb\u00e9 Raynal, 'wherever they see motion which they cannot\naccount for, there they suppose a soul.' All men may be considered as\nsavages in this respect, until they are capable of instruction, and of\nusing their faculties in a more perfect manner than savages do.\n\n\"The Abb\u00e9 Raynal's observation is sufficiently confirmed, both from\nfact, and from the structure of all languages.\n\n\"Rude nations do really believe sun, moon, and stars, earth, sea, and\nair, fountains, and lakes, to have understanding and active power. To\npay homage to them, and implore their favour, is a kind of idolatry\nnatural to savages.\n\n\"All languages carry in their structure the marks of their being formed\nwhen this belief prevailed. The distinction of verbs and participles\ninto active 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's observation,\nsavages suppose a soul.\n\n\"Thus 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\nby men 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\"There 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\nwe find the same sentiments indicated in the structure of all languages,\nthose sentiments must have been common to the human species when\nlanguages were invented.\n\n\"When 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\ninvites to further discoveries of the same kind.\n\n\"As philosophy advances, life and activity in natural objects retires,\nand leaves them dead and inactive. Instead of moving voluntarily, we\nfind them to be moved necessarily; instead of acting, we find them to be\nacted upon; and Nature appears as one great machine, where one wheel is\nturned by another, that by a third; and how far this necessary\nsuccession may reach, the philosopher does not know.\"[24]\n\nThere is, then, a spontaneous tendency of the intellect to account to\nitself for all cases of causation by assimilating them to the\nintentional acts of voluntary agents like itself. This is the\ninstinctive philosophy of the human mind in its earliest stage, before\nit has become familiar with any other invariable sequences than those\nbetween its own volitions or those of other human beings and their\nvoluntary acts. As the notion of fixed laws of succession among external\nphenomena gradually establishes itself, the propensity to refer all\nphenomena 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\nmaintains its ground in the mind, underneath the growths obtained by\ncultivation, and keeps up a constant resistance to their throwing their\nroots deep into the soil. The theory against which I am contending\nderives its nourishment from that substratum. Its strength does not lie\nin argument, but in its affinity to an obstinate tendency of the infancy\nof the human mind.\n\nThat this tendency, however, is not the result of an inherent mental\nlaw, is proved by superabundant evidence. The history of science, from\nits earliest dawn, shows that mankind have not been unanimous in\nthinking either that the action of matter upon matter was not\nconceivable, or that the action of mind upon matter was. To some\nthinkers, and some schools of thinkers, both in ancient and in modern\ntimes, this last has appeared much more inconceivable than the former.\nSequences entirely physical and material, as soon as they had become\nsufficiently familiar to the human mind, came to be thought perfectly\nnatural, and were regarded not only as needing no explanation\nthemselves, but as being capable of affording it to others, and even of\nserving as the ultimate explanation of things in general.\n\nOne of the ablest recent supporters of the Volitional theory has\nfurnished an explanation, at once historically true and philosophically\nacute, of the failure of the Greek philosophers in physical inquiry, in\nwhich, as I conceive, he unconsciously depicts his own state of mind.\n\"Their stumbling-block was one as to the nature of the evidence they had\nto expect for their conviction.... They had not seized the idea that\nthey must not expect to understand the processes of outward causes, but\nonly their results: and consequently, the whole physical philosophy of\nthe Greeks was an attempt to identify mentally the effect with its\ncause, to feel after some not only necessary but natural connexion,\nwhere they meant by natural that which would _per se_ carry some\npresumption to their own mind.... They wanted to see some _reason_ why\nthe physical antecedent should produce this particular consequent, and\ntheir only attempts were in directions where they could find such\nreasons.\"[25] In other words, they were not content merely to know that\none phenomenon was always followed by another; they thought that they\nhad not attained the true aim of science, unless they could perceive\nsomething in the nature of the one phenomenon from which it might have\nbeen known or presumed _previous to trial_ that it would be followed by\nthe other: just what the writer, who has so clearly pointed out their\nerror, thinks that he perceives in the nature of the phenomenon\nVolition. And to complete the statement of the case, he should have\nadded that these early speculators not only made this their aim, but\nwere quite satisfied with their success in it; not only sought for\ncauses 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\na very different state: they were able to derive from the assimilation\nof physical facts to other physical facts, the kind of mental\nsatisfaction which we connect with the word explanation, and which the\nreviewer would have us think can only be found in referring phenomena to\na will. When Thales and Hippo held that moisture was the universal\ncause, and external element, of which all other things were but the\ninfinitely various sensible manifestations; when Anaximenes predicated\nthe same thing of air, Pythagoras of numbers, and the like, they all\nthought that they had found a real explanation; and were content to rest\nin this explanation as ultimate. The ordinary sequences of the external\nuniverse appeared to them, no less than to their critic, to be\ninconceivable without the supposition of some universal agency to\nconnect the antecedents with the consequents; but they did not think\nthat Volition, exerted by minds, was the only agency which fulfilled\nthis requirement. Moisture, or air, or numbers, carried to their minds a\nprecisely similar impression of making intelligible what was otherwise\ninconceivable, and gave the same full satisfaction to the demands of\ntheir conceptive faculty.\n\nIt was not the Greeks alone, who \"wanted to see some reason why the\nphysical antecedent should produce this particular consequent,\" some\nconnexion \"which would _per se_ carry some presumption to their own\nmind.\" Among modern philosophers, Leibnitz laid it down as a\nself-evident principle that all physical causes without exception must\ncontain in their own nature something which makes it intelligible that\nthey should be able to produce the effects which they do produce. Far\nfrom admitting Volition as the only kind of cause which carried internal\nevidence of its own power, and as the real bond of connexion between\nphysical antecedents and their consequents, he demanded some naturally\nand _per se_ efficient physical antecedent as the bond of connexion\nbetween Volition itself and its effects. He distinctly refused to admit\nthe will of God as a sufficient explanation of anything except miracles;\nand insisted upon finding something that would account _better_ for the\nphenomena of nature than a mere reference to divine volition.[26]\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\nall other 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\nnecessary connexion, no relation _\u00e0 priori_, between a motion and a\nthought. And as the Cartesians, more than any other school of\nphilosophical speculation before or since, made their own minds the\nmeasure of all things, and refused, on principle, to believe that Nature\nhad done what they were unable to see any reason why she must do, they\naffirmed it to be impossible that a material and a mental fact could be\ncauses one of another. They regarded them as mere Occasions on which the\nreal agent, God, thought fit to exert his power as a Cause. When a man\nwills to move his foot, it is not his will that moves it, but God (they\nsaid) moves it on the occasion of his will. God, according to this\nsystem, is the only efficient cause, not _qu\u00e2_ mind, or _qu\u00e2_ endowed\nwith volition, but _qu\u00e2_ omnipotent. This hypothesis was, as I said,\noriginally suggested by the supposed inconceivability of any real mutual\naction between Mind and Matter: but it was afterwards extended to the\naction of Matter upon Matter, for on a nicer examination they found this\ninconceivable too, and therefore, according to their logic, impossible.\nThe _deus ex machin\u00e2_ was ultimately called in to produce a spark on the\noccasion of a flint and steel coming together, or to break an egg on the\noccasion of its falling on 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\nmay seem to explain their being so. But we also see that this demand may\nbe completely satisfied by an agency purely physical, provided it be\nmuch more familiar than that which it is invoked to explain. To Thales\nand Anaximenes, it appeared inconceivable that the antecedents which we\nsee in nature, should produce the consequents; but perfectly natural\nthat water, or air, should produce them. The writers whom I oppose\ndeclare this inconceivable, but can conceive that mind, or volition, is\n_per se_ an efficient cause: while the Cartesians could not conceive\neven that, but peremptorily declared that no mode of production of any\nfact whatever was conceivable, except the direct agency of an omnipotent\nbeing. Thus giving additional proof of what finds new confirmation in\nevery stage of the history of science: that both what persons can, and\nwhat they cannot, conceive, is very much an affair of accident, and\ndepends altogether on their experience, and their habits of thought;\nthat by cultivating the requisite associations of ideas, people may make\nthemselves unable to conceive any given thing; and may make themselves\nable to conceive most things, however inconceivable these may at first\nappear: and the same facts in each person's mental history which\ndetermine what is or is not conceivable to him, determine also which\namong the various sequences in nature will appear to him so natural and\nplausible, as to need no other proof of their existence; to be evident\nby their own light, independent equally of experience and of\nexplanation.\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;\nthey appeal each to his own subjective feelings. One says, the\nsuccession C, B, appears to me more natural, conceivable, and credible\n_per se_, than the succession A, B; you are therefore mistaken in\nthinking that B depends upon A; I am certain, though I can give no other\nevidence of it, that C comes in between A and B, and is the real and\nonly cause of B. The other answers--the successions C, B, and A, B,\nappear to me equally natural and conceivable, or the latter more so than\nthe former: A is quite capable of producing B without any other\nintervention. A third agrees with the first in being unable to conceive\nthat A can produce B, but finds the sequence D, B, still more natural\nthan C, B, or of nearer kin to the subject matter, and prefers his D\ntheory to the C theory. It is plain that there is no universal law\noperating here, except the law that each person's conceptions are\ngoverned and limited by his individual experience and habits of thought.\nWe are warranted in saying of all three, what each of them already\nbelieves of the other two, namely, that they exalt into an original law\nof the human intellect and of outward nature, one particular sequence of\nphenomena, which appears to them more natural and more conceivable than\nother sequences, only because it is more familiar. And from this\njudgment I am unable to except the theory, that Volition is an Efficient\nCause.\n\nI am unwilling to leave the subject without adverting to the additional\nfallacy contained in the corollary from this theory; in the inference\nthat because Volition is an efficient cause, therefore it is the only\ncause, and the direct agent in producing even what is apparently\nproduced by something else. Volitions are not known to produce anything\ndirectly except nervous action, for the will influences even the muscles\nonly through the nerves. Though it were granted, then, that every\nphenomenon has an efficient, and not merely a phenomenal cause, and that\nvolition, in the case of the peculiar phenomena which are known to be\nproduced by it, is that efficient cause; are we therefore to say, with\nthese writers, that since we know of no other efficient cause, and ought\nnot to assume one without evidence, there _is_ no other, and volition is\nthe direct cause of all phenomena? A more outrageous stretch of\ninference could hardly be made. Because among the infinite variety of\nthe phenomena of nature there is one, namely, a particular mode of\naction of certain nerves, which has for its cause, and as we are now\nsupposing for its efficient cause, a state of our mind; and because this\nis the only efficient cause of which we are conscious, being the only\none of which in the nature of the case we _can_ be conscious, since it\nis the only one which exists within ourselves; does this justify us in\nconcluding that all other phenomena must have the same kind of efficient\ncause with that one eminently special, narrow, and peculiarly human or\nanimal, phenomenon? The nearest parallel to this specimen of\ngeneralization is suggested by the recently revived controversy on the\nold subject of Plurality of Worlds, in which the contending parties have\nbeen so conspicuously successful in overthrowing one another. Here also\nwe have experience only of a single case, that of the world in which we\nlive, but that this is inhabited we know absolutely, and without\npossibility of doubt. Now if on this evidence any one were to infer that\nevery heavenly body without exception, sun, planet, satellite, comet,\nfixed star or nebula, is inhabited, and must be so from the inherent\nconstitution of things, his inference would exactly resemble that of the\nwriters who conclude that because volition is the efficient cause of our\nown bodily motions, it must be the efficient cause of everything else in\nthe universe. It is true there are cases in which, with acknowledged\npropriety, we generalize from a single instance to a multitude of\ninstances. But they must be instances which resemble the one known\ninstance, and not such as have no circumstance in common with it except\nthat of being instances. I have, for example, no direct evidence that\nany creature is alive except myself: yet I attribute, with full\nassurance, life and sensation to other human beings and animals. But I\ndo not conclude that all other things are alive merely because I am. I\nascribe to certain other creatures a life like my own, because they\nmanifest it by the same sort of indications by which mine is manifested.\nI find that their phenomena and mine conform to the same laws, and it is\nfor this reason that I believe both to arise from a similar cause.\nAccordingly I do not extend the conclusion beyond the grounds for it.\nEarth, 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\nor of organic nature.\n\n\nNOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.\n\n The author of the Second Burnett Prize Essay (Dr. Tulloch), who\n has employed a considerable number of pages in controverting\n the doctrines of the preceding chapter, has somewhat surprised\n me by denying a fact, which I imagined too well known to\n require proof--that there have been philosophers who found in\n physical explanations of phenomena the same complete mental\n satisfaction which we are told is only given by volitional\n explanation, and others who denied the Volitional Theory on the\n same ground of inconceivability on which it is defended. The\n assertion of the Essayist is countersigned still more\n positively by an able reviewer of the Essay:[27] \"Two\n illustrations,\" says the reviewer, \"are advanced by Mr. Mill:\n the case of Thales and Anaximenes, stated by him to have\n maintained, the one Moisture and the other Air to be the origin\n of all things; and that of Descartes and Leibnitz, whom he\n asserts to have found the action of Mind upon Matter the grand\n inconceivability. In counterstatement as to the first of these\n cases the author shows--what we believe now hardly admits of\n doubt--that the Greek philosophers distinctly recognised as\n beyond and above their primal material source, the [Greek:\n nous], or Divine Intelligence, as the efficient and originating\n Source of all: and as to the second, by proof that it was the\n _mode_, not the _fact_, of that action on matter, which was\n represented as inconceivable.\"\n\n A greater quantity of historical error has seldom been\n comprised in a single sentence. With regard to Thales, the\n assertion that he considered water as a mere material in the\n hands of [Greek: nous] rests on a passage of Cicero _de Natur\u00e2\n Deorum_: and whoever will refer to any of the accurate\n historians of philosophy, will find that they treat this as a\n mere fancy of Cicero, resting on no authority, opposed to all\n the evidence; and make surmises as to the manner in which\n Cicero may have been led into the error. (See Ritter, vol. i.\n p. 211, 2nd ed.; Brandis, vol. i. pp. 118-9, 1st ed.; Preller,\n _Historia Philosophi\u00e6 Gr\u00e6co-Roman\u00e6_, p. 10. \"Schiefe Ansicht,\n durchaus zu verwerfen;\" \"augenscheinlich folgernd statt zu\n berichten;\" \"quibus vera sententia Thaletis plane detorquetur;\"\n are the expressions of these writers.) As for Anaximenes, he,\n even according to Cicero, maintained, not that air was the\n material out of which God made the world, but that the air was\n a god: \"Anaximenes a\u00ebra deum statuit:\" or according to St.\n Augustine, that it was the material out of which the gods were\n made; \"non tamen ab ipsis [Diis] a\u00ebrem factum, sed ipsos ex\n a\u00ebre ortos credidit.\" Those who are not familiar with the\n metaphysical terminology of antiquity, must not be misled by\n finding it stated that Anaximenes attributed [Greek: psych\u00ea]\n (translated _soul_, or _life_) to his universal element, the\n air. The Greek philosophers acknowledged several kinds of\n [Greek: psych\u00ea], the nutritive, the sensitive, and the\n intellective.[28] Even the moderns with admitted correctness\n attribute life to plants. As far as we can make out the meaning\n of Anaximenes, he made choice of Air as the universal agent, on\n the ground that it is perpetually in motion, without any\n apparent cause external to itself: so that he conceived it as\n exercising spontaneous force, and as the principle of life and\n activity in all things, men and gods inclusive. If this be not\n representing it as the Efficient Cause, the dispute altogether\n has no meaning.\n\n If either Anaximenes, or Thales, or any of their cotemporaries,\n had held the doctrine that [Greek: nous] was the Efficient\n Cause, that doctrine could not have been reputed, as it was\n throughout antiquity, to have originated with Anaxagoras. The\n testimony of Aristotle, in the first book of his Metaphysics,\n is perfectly decisive with respect to these early speculations.\n After enumerating four kinds of causes, or rather four\n different meanings of the word Cause, viz. the Essence of a\n thing, the Matter of it, the Origin of Motion (Efficient\n Cause), and the End or Final Cause, he proceeds to say, that\n most of the early philosophers recognised only the second kind\n of Cause, the Matter of a thing, [Greek: tas en hyl\u00eas eidei\n monas \u00f4\u00eath\u00easan archas einai pant\u00f4n]. As his first example he\n specifies Thales, whom he describes as taking the lead in this\n view of the subject, [Greek: ho t\u00eas toiaut\u00eas arch\u00eagos\n philosophias], and goes on to Hippon, Anaximenes, Diogenes (of\n Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.\n Anaxagoras, however, (he proceeds to say,) taught a different\n doctrine, as we know, and it is _alleged_ that Hermotimus of\n Clazomen\u00e6 taught it before him. Anaxagoras represented, that\n even if these various theories of the universal material were\n true, there would be need of some other cause to account for\n the transformations of the material, since the material cannot\n originate its own changes: [Greek: ou gar d\u00ea to ge hypokeimenon\n auto poiei metaballein heauto; leg\u00f4 d' oion oute to xylon oute\n ho chalkos aitios tou metaballein hekateron aut\u00f4n, oude poiei\n to men xylon klin\u00ean ho de chalkos andrianta, all' heteron ti\n t\u00eas metabol\u00eas aition], viz., the other kind of cause [Greek:\n hothen h\u00ea arch\u00ea t\u00eas kin\u00ease\u00f4s]--an Efficient Cause. Aristotle\n expresses great approbation of this doctrine (which he says\n made its author appear the only sober man among persons raving,\n [Greek: oion n\u00eaph\u00f4n ephan\u00ea par' eik\u00ea legontas tous proteron]);\n but while describing the influence which it exercised over\n subsequent speculation, he remarks that the philosophers\n against whom this, as he thinks, insuperable difficulty was\n urged, had not felt it to be any difficulty: [Greek: ouden\n edyscheranan en heautois]. It is surely unnecessary to say more\n in proof of the matter of fact which Dr. Tulloch and his\n reviewer deny.\n\n Having pointed out what he thinks the error of these early\n speculators in not recognising the need of an efficient cause,\n Aristotle goes on to mention two other efficient causes to\n which they might have had recourse, instead of intelligence:\n [Greek: tych\u00ea], chance, and [Greek: to automaton], spontaneity.\n He indeed puts these aside as not sufficiently worthy causes\n for the order in the universe, [Greek: oud' au t\u00f4 automat\u00f4 kai\n t\u00ea tych\u00ea tosouton epitrepsai pragma kal\u00f4s eichen]: but he does\n not reject them as incapable of producing any effect, but only\n as incapable of producing _that_ effect. He himself recognises\n [Greek: tych\u00ea] and [Greek: to automaton] as co-ordinate agents\n with Mind in producing the phenomena of the universe; the\n department allotted to them being composed of all the classes\n of phenomena which are not supposed to follow any uniform law.\n By thus including Chance among efficient causes, Aristotle fell\n into an error which philosophy has now outgrown, but which is\n by no means so alien to the spirit even of modern speculation\n as it may at first sight appear. Up to quite a recent period\n philosophers went on ascribing, and many of them have not yet\n ceased to ascribe, a real existence to the results of\n abstraction. Chance could make out as good a title to that\n dignity as many other of the mind's abstract creations: it had\n had a name given to it, and why should it not be a reality? As\n for [Greek: to automaton], it is recognised even yet as one of\n the modes of origination of phenomena, by all those thinkers\n who maintain what is called the Freedom of the Will. The same\n self-determining power which that doctrine attributes to\n volitions, was supposed by the ancients to be possessed also by\n some other natural phenomena: a circumstance which throws\n considerable light on more than one of the supposed invincible\n necessities of belief. I have introduced it here, because this\n belief of Aristotle, or rather of the Greek philosophers\n generally, is as fatal as the doctrines of Thales and the Ionic\n school, to the theory that the human mind is compelled by its\n constitution to conceive volition as the origin of all force,\n and the efficient cause of all phenomena.[29]\n\n With regard to the modern philosophers (Leibnitz and the\n Cartesians) whom I had cited as having maintained that the\n action of mind upon matter, so far from being the only\n conceivable origin of material phenomena, is itself\n inconceivable; the attempt to rebut this argument by asserting\n that the mode, not the fact, of the action of mind on matter\n was represented as inconceivable, is an abuse of the privilege\n of writing confidently about authors without reading them: for\n any knowledge whatever of Leibnitz would have taught those who\n thus speak of him, that the inconceivability of the mode, and\n the impossibility of the thing, were in his mind convertible\n expressions. What was his famous Principle of the Sufficient\n Reason, the very corner stone of his philosophy, from which the\n Preestablished Harmony, the doctrine of Monads, and all the\n opinions most characteristic of Leibnitz, were corollaries? It\n was, that nothing exists, the existence of which is not capable\n of being proved and explained _\u00e0 priori_; the proof and\n explanation in the case of contingent facts being derived from\n the nature of their causes; which could not be the causes\n unless there was something in their nature showing them to be\n capable of producing those particular effects. And this\n \"something\" which accounts for the production of physical\n effects, he was able to find in many physical causes, but could\n not find it in any finite minds, which therefore he\n unhesitatingly asserted to be incapable of producing any\n physical effects whatever. \"On ne saurait concevoir,\" he says,\n \"une action r\u00e9ciproque de la mati\u00e8re et de l'intelligence l'une\n sur l'autre,\" and there is therefore (he contends) no choice\n but between the Occasional Causes of the Cartesians, and his\n own Preestablished Harmony, according to which there is no more\n connexion between our volitions and our muscular actions than\n there is between two clocks which are wound up to strike at the\n same instant. But he felt no similar difficulty as to physical\n causes: and throughout his speculations, as in the passage I\n have already cited respecting gravitation, he distinctly\n refuses to consider as part of the order of nature any fact\n which is not explicable from the nature of its physical cause.\n\n With regard to the Cartesians (not Descartes; I did not make\n that mistake, though the reviewer of Dr. Tulloch's Essay\n attributes it to me) I take a passage almost at random from\n Malebranche, who is the best known of the Cartesians, and,\n though not the inventor of the system of Occasional Causes, is\n its principal expositor. In Part 2, chap. 3, of his Sixth Book,\n having first said that matter cannot have the power of moving\n itself, he proceeds to argue that neither can mind have the\n power of moving it. \"Quand on examine l'id\u00e9e que l'on a de tous\n les esprits finis, on ne voit point de liaison n\u00e9cessaire entre\n leur volont\u00e9 et le mouvement de quelque corps que ce soit, on\n voit au contraire qu'il n'y en a point, et qu'il n'y en peut\n avoir;\" (there is nothing in the idea of finite mind which can\n account for its causing the motion of a body;) \"on doit aussi\n conclure, si on veut raisonner selon ses lumi\u00e8res, qu'il n'y a\n aucun esprit cr\u00e9\u00e9 qui puisse remuer quelque corps que ce soit\n comme cause v\u00e9ritable ou principale, de m\u00eame que l'on a dit\n qu'aucun corps ne se pouvait remuer soi-m\u00eame:\" thus the idea of\n Mind is according to him as incompatible as the idea of Matter\n with the exercise of active force. But when, he continues, we\n consider not a created but a Divine Mind, the case is altered;\n for the idea of a Divine Mind includes omnipotence; and the\n idea of omnipotence does contain the idea of being able to move\n bodies. Thus it is the nature of omnipotence which renders the\n motion of bodies even by the divine mind credible or\n conceivable, while, so far as depended on the mere nature of\n mind, it would have been inconceivable and incredible. If\n Malebranche had not believed in an omnipotent being, he would\n have held all action of mind on body to be a demonstrated\n impossibility.[30]\n\n A doctrine more precisely the reverse of the Volitional theory\n of causation cannot well be imagined. The volitional theory is,\n that we know by intuition or by direct experience the action of\n our own mental volitions on matter; that we may hence infer all\n other action upon matter to be that of volition, and might thus\n know, without any other evidence, that matter is under the\n government of a divine mind. Leibnitz and the Cartesians, on\n the contrary, maintain that our volitions do not and cannot act\n upon matter, and that it is only the existence of an\n all-governing Being, and that Being omnipotent, which can\n account for the sequence between our volitions and our bodily\n actions. When we consider that each of these two theories,\n which, as theories of causation, stand at the opposite extremes\n of possible divergence from one another, invokes not only as\n its evidence, but as its sole evidence, the absolute\n inconceivability of any theory but itself, we are enabled to\n measure the worth of this kind of evidence; and when we find\n the Volitional theory entirely built upon the assertion that by\n our mental constitution we are compelled to recognise our\n volitions as efficient causes, and then find other thinkers\n maintaining that we know that they are not, and cannot be such\n causes, and cannot conceive them to be so, I think we have a\n right to say, that this supposed law of our mental constitution\n does not exist.\n\n Dr. Tulloch (pp. 45-7) thinks it a sufficient answer to this,\n that Leibnitz and the Cartesians were Theists, and believed the\n will of God to be an efficient cause. Doubtless they did, and\n the Cartesians even believed, though Leibnitz did not, that it\n is the only such cause. Dr. Tulloch mistakes the nature of the\n question. I was not writing on Theism, as Dr. Tulloch is, but\n against a particular theory of causation, which if it be\n unfounded, can give no effective support to Theism or to\n anything else. I found it asserted that volition is the only\n efficient cause, on the ground that no other efficient cause is\n conceivable. To this assertion I oppose the instances of\n Leibnitz and of the Cartesians, who affirmed with equal\n positiveness that volition as an efficient cause is itself not\n conceivable, and that omnipotence, which renders all things\n conceivable, can alone take away the impossibility. This I\n thought, and think, a conclusive answer to the argument on\n which this theory of causation avowedly depends. But I\n certainly did not imagine that Theism was bound up with that\n theory; nor expected to be charged with denying Leibnitz and\n the Cartesians to be Theists because I denied that they held\n the theory.\n\n\n\n\nCHAPTER VI.\n\nON THE COMPOSITION OF CAUSES.\n\n\n\u00a7 1. To complete the general notion of causation on which the rules of\nexperimental inquiry into the laws of nature must be founded, one\ndistinction still remains to be pointed out: a distinction so radical,\nand of so much importance, as to require a chapter to itself.\n\nThe preceding discussions have rendered us familiar with the case in\nwhich several agents, or causes, concur as conditions to the production\nof an effect: a case, in truth, almost universal, there being very few\neffects to the production of which no more than one agent contributes.\nSuppose, then, that two different agents, operating jointly, are\nfollowed, under a certain set of collateral conditions, by a given\neffect. If either of these agents, instead of being joined with the\nother, had operated alone, under the same set of conditions in all other\nrespects, some effect would probably have followed; which would have\nbeen different from the joint effect of the two, and more or less\ndissimilar to it. Now, if we happen to know what would be the effect of\neach cause when acting separately from the other, we are often able to\narrive deductively, or _\u00e0 priori_, at a correct prediction of what will\narise from their conjunct agency. To enable us to do this, it is only\nnecessary that the same law which expresses the effect of each cause\nacting by itself, shall also correctly express the part due to that\ncause, of the effect which follows from the two together. This condition\nis realized in the extensive and important class of phenomena commonly\ncalled mechanical, namely the phenomena of the communication of motion\n(or of pressure, which is tendency to motion) from one body to another.\nIn this important class of cases of causation, one cause never, properly\nspeaking, defeats or frustrates another; both have their full effect.\nIf a body is propelled in two directions by two forces, one tending to\ndrive it to the north and the other to the east, it is caused to move in\na given time exactly as far in both directions as the two forces would\nseparately have carried it; and is left precisely where it would have\narrived if it had been acted upon first by one of the two forces, and\nafterwards by the other. This law of nature is called, in dynamics, the\nprinciple of the Composition of Forces: and in imitation of that\nwell-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\nseparate effects.\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 blue 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\ncan compute 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\nin combination 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 organized\nbodies; and in which those extraordinary new uniformities arise, which\nare called the laws of life. All organized bodies are composed of parts\nsimilar to those composing inorganic nature, and which have even\nthemselves existed in an inorganic state; but the phenomena of life,\nwhich result from the juxtaposition of those parts in a certain manner,\nbear no analogy to any of the effects which would be produced by the\naction of the component substances considered as mere physical agents.\nTo whatever degree we might imagine our knowledge of the properties of\nthe several ingredients of a living body to be extended and perfected,\nit is certain that no mere summing up of the separate actions of those\nelements will ever amount to the action of the living body itself. The\ntongue, for instance, is, like all other parts of the animal frame,\ncomposed of gelatine, fibrin, and other products of the chemistry of\ndigestion, but from no knowledge of the properties of those substances\ncould we ever predict that it could taste, unless gelatine or fibrin\ncould themselves taste; for no elementary fact can be in the conclusion,\nwhich was not in the premises.\n\nThere are thus two different modes of the conjunct action of causes;\nfrom which arise two modes of conflict, or mutual interference, between\nlaws of nature. Suppose, at a given point of time and space, two or more\ncauses, which, if they acted separately, would produce effects contrary,\nor at least conflicting with each other; one of them tending to undo,\nwholly or partially, what the other tends to do. Thus, the expansive\nforce of the gases generated by the ignition of gunpowder tends to\nproject a bullet towards the sky, while its gravity tends to make it\nfall to the ground. A stream running into a reservoir at one end tends\nto fill it higher and higher, while a drain at the other extremity tends\nto empty it. Now, in such cases as these, even if the two causes which\nare in joint action exactly annul one another, still the laws of both\nare fulfilled; the effect is the same as if the drain had been open for\nhalf an hour first,[31] and the stream had flowed in for as long\nafterwards. Each agent produced the same amount of effect as if it had\nacted separately, though the contrary effect which was taking place\nduring the same time obliterated it as fast as it was produced. Here\nthen are two causes, producing by their joint operation an effect which\nat first seems quite dissimilar to those which they produce separately,\nbut which on examination proves to be really the sum of those separate\neffects. It will be noticed that we here enlarge the idea of the sum of\ntwo effects, so as to include what is commonly called their difference,\nbut which is in reality the result of the addition of opposites; a\nconception to which mankind are indebted for that admirable extension of\nthe algebraical calculus, which has so vastly increased its powers as an\ninstrument of discovery, by introducing into its reasonings (with the\nsign of subtraction prefixed, and under the name of Negative Quantities)\nevery description whatever of positive phenomena, provided they are of\nsuch a quality in reference to those previously introduced, that to add\nthe one is equivalent to subtracting an equal quantity of the other.\n\nThere is, then, one mode of the mutual interference of laws of nature,\nin which, even when the concurrent causes annihilate each other's\neffects, each exerts its full efficacy according to its own law, its law\nas a separate agent. But in the other description of cases, the agencies\nwhich are brought together cease entirely, and a totally different set\nof phenomena arise: as in the experiment of two liquids which, when\nmixed in certain proportions, instantly become, not a larger amount of\nliquid, but a solid mass.\n\n\n\u00a7 2. This difference between the case in which the joint effect of\ncauses is the sum of their separate effects, and the case in which it\nis heterogeneous 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\ndo not, as to some of their phenomena, obey the principle of the\nComposition of Causes; none that have not some laws which are rigidly\nfulfilled in every combination into which the objects enter. The weight\nof a body, for instance, is a property which it retains in all the\ncombinations in which it is placed. The weight of a chemical compound,\nor of an organized body, is equal to the sum of the weights of the\nelements which compose it. The weight either of the elements or of the\ncompound will vary, if they be carried farther from their centre of\nattraction, or brought nearer to it; but whatever affects the one\naffects the other. They always remain precisely equal. So again, the\ncomponent parts of a vegetable or animal substance do not lose their\nmechanical and chemical properties as separate agents, when, by a\npeculiar mode of juxtaposition, they, as an aggregate whole, acquire\nphysiological or vital properties in addition. Those bodies continue, as\nbefore, to obey mechanical and chemical laws, in so far as the operation\nof those laws is not counteracted by the new laws which govern them as\norganized beings. When, in short, a concurrence of causes takes place\nwhich calls into action new laws bearing no analogy to any that we can\ntrace in the separate operation of the causes, the new laws, while they\nsupersede one portion of the previous laws, may coexist with another\nportion, and may even compound the effect of those previous laws with\ntheir own.\n\nAgain, laws which were themselves generated in the second mode, may\ngenerate others in the first. Though there are laws which, like those of\nchemistry and physiology, owe their existence to a breach of the\nprinciple of Composition of Causes, it does not follow that these\npeculiar, or as they might be termed, _heteropathic_ laws, are not\ncapable of composition with one another. The causes which by one\ncombination have had their laws altered, may carry their new laws with\nthem unaltered into their ulterior combinations. And hence there is no\nreason to despair of ultimately raising chemistry and physiology to the\ncondition of deductive sciences; for though it is impossible to deduce\nall chemical and physiological truths from the laws or properties of\nsimple substances or elementary agents, they may possibly be deducible\nfrom laws which commence when these elementary agents are brought\ntogether into some moderate number of not very complex combinations. The\nLaws of Life will never be deducible from the mere laws of the\ningredients, but the prodigiously complex Facts of Life may all be\ndeducible from comparatively simple laws of life; which laws (depending\nindeed on combinations, but on comparatively simple combinations, of\nantecedents) may, in more complex circumstances, be strictly compounded\nwith one another, and with the physical and chemical laws of the\ningredients. The details of the vital phenomena, even now, afford\ninnumerable 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\nthe more complex. This will be found equally true in the phenomena of\nmind; and even in social and political phenomena, the results of the\nlaws of mind. It is in the case of chemical phenomena that the least\nprogress has yet been made in bringing the special laws under general\nones from which they may be deduced; but there are even in chemistry\nmany circumstances to encourage the hope that such general laws will\nhereafter be discovered. The different actions of a chemical compound\nwill never, undoubtedly, be found to be the sums of the actions of its\nseparate elements; but there may exist, between the properties of the\ncompound and those of its elements, some constant relation, which, if\ndiscoverable by a sufficient induction, would enable us to foresee the\nsort of compound which will result from a new combination before we have\nactually tried it, and to judge of what sort of elements some new\nsubstance is compounded before we have analysed it. The law of definite\nproportions, first discovered in its full generality by Dalton, is a\ncomplete solution of this problem in one, though but a secondary aspect,\nthat of quantity: and in respect to quality, we have already some\npartial generalizations sufficient to indicate the possibility of\nultimately proceeding farther. We can predicate some common properties\nof the kind of compounds which result from the combination, in each of\nthe small number of possible proportions, of any acid whatever with any\nbase. We have also the curious law, discovered by Berthollet, that two\nsoluble salts mutually decompose one another whenever the new\ncombinations which result produce an insoluble compound, or one less\nsoluble than the two former. Another uniformity is that called the law\nof isomorphism; the identity of the crystalline forms of substances\nwhich possess in common certain peculiarities of chemical composition.\nThus it appears that even heteropathic laws, such laws of combined\nagency as are not compounded of the laws of the separate agencies, are\nyet, at least in some cases, derived from them according to a fixed\nprinciple. There may, therefore, be laws of the generation of laws from\nothers dissimilar to them; and in chemistry, these undiscovered laws of\nthe dependence of the properties of the compound on the properties of\nits elements, may, together with the laws of the elements themselves,\nfurnish the premises by which the science is perhaps destined one day to\nbe rendered deductive.\n\nIt would seem, therefore, that there is no class of phenomena in which\nthe Composition of Causes does not obtain: that as a general rule,\ncauses in combination produce exactly the same effects as when acting\nsingly: but that this rule, though general, is not universal: that in\nsome instances, at some particular points in the transition from\nseparate to united action, the laws change, and an entirely new set of\neffects are either added to, or take the place of, those which arise\nfrom the separate agency of the same causes: the laws of these new\neffects being again susceptible of composition, to an indefinite extent,\nlike the laws which they superseded.\n\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\nsometimes made of this principle in reasonings respecting the laws of\nnature, though it is incumbered with many difficulties and apparent\nexceptions, which much ingenuity has been expended in showing not to be\nreal ones. This proposition, in so far as it is true, enters as a\nparticular case into the general principle of the Composition of Causes;\nthe causes compounded being, in this instance, homogeneous; in which\ncase, if in any, their joint effect might be expected to be identical\nwith the sum of their separate effects. If a force equal to one hundred\nweight will raise a certain body along an inclined plane, a force equal\nto two hundred weight will raise two bodies exactly similar, and thus\nthe effect is proportional to the cause. But does not a force equal to\ntwo hundred weight actually contain in itself two forces each equal to\none hundred weight, which, if employed apart, would separately raise the\ntwo bodies in question? The fact, therefore, that when exerted jointly\nthey raise both bodies at once, results from the Composition of Causes,\nand is a mere instance of the general fact that mechanical forces are\nsubject to the law of Composition. And so in every other case which can\nbe supposed. For the doctrine of the proportionality of effects to their\ncauses cannot of course be applicable to cases in which the augmentation\nof the cause alters the _kind_ of effect; that is, in which the surplus\nquantity superadded to the cause does not become compounded with it, but\nthe two together generate an altogether new phenomenon. Suppose that the\napplication of a certain quantity of heat to a body merely increases its\nbulk, that a double quantity melts it, and a triple quantity decomposes\nit: these three effects being heterogeneous, no ratio, whether\ncorresponding or not to that of the quantities of heat applied, can be\nestablished between them. Thus the supposed axiom of the proportionality\nof effects to their causes fails at the precise point where the\nprinciple of the Composition of Causes also fails; viz., where the\nconcurrence of causes is such as to determine a change in the properties\nof the body generally, and render it subject to new laws, more or less\ndissimilar to those to which it conformed in its previous state. The\nrecognition, therefore, of any such law of proportionality, is\nsuperseded by the more comprehensive principle, in which as much of it\nas 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,\nthemselves laws of causation, or consequences resulting from, and\ncorollaries capable of being deduced from, such laws. If we could\ndetermine what causes are correctly assigned to what effects, and what\neffects to what causes, we should be virtually acquainted with the whole\ncourse of nature. All those uniformities which are mere results of\ncausation, might then be explained and accounted for; and every\nindividual fact or event might be predicted, provided we had the\nrequisite data, that is, the requisite knowledge of the circumstances\nwhich, in the particular instance, preceded it.\n\nTo ascertain, therefore, what are the laws of causation which exist in\nnature; to determine the effect of every cause, and the causes of all\neffects,--is the main business of Induction; and to point out how this\nis done is the chief object of Inductive Logic.\n\n\n\n\nCHAPTER VII.\n\nOF 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\nbe found somewhere among the facts which immediately preceded the\noccurrence, may be taken for certain. The whole of the present facts are\nthe infallible result of all past facts, and more immediately of all the\nfacts which existed at the moment previous. Here, then, is a great\nsequence, which we know to be uniform. If the whole prior state of the\nentire universe could again recur, it would again be followed by the\npresent state. The question is, how to resolve this complex uniformity\ninto the simpler uniformities which compose it, and assign to each\nportion of the vast antecedent the portion of the consequent which is\nattendant 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\na merely 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\nis invariably attendant. To determine that point, we must endeavour to\neffect a separation of the facts from one another, not in our minds\nonly, but in nature. The mental analysis, however, must take place\nfirst. And every one knows that in the mode of performing it, one\nintellect differs immensely from another. It is the essence of the act\nof observing; for the observer is not he who merely sees the thing which\nis before his eyes, but he who sees what parts that thing is composed\nof. To do this well is a rare talent. One person, from inattention, or\nattending only in the wrong place, overlooks half of what he sees:\nanother sets down much more than he sees, confounding it with what he\nimagines, or with what he infers; another takes note of the _kind_ of\nall the circumstances, but being inexpert in estimating their degree,\nleaves the quantity of each vague and uncertain; another sees indeed the\nwhole, but makes such an awkward division of it into parts, throwing\nthings into one mass which require to be separated, and separating\nothers which might more conveniently be considered as one, that the\nresult is much the same, sometimes even worse, than if no analysis had\nbeen attempted at all. It would be possible to point out what qualities\nof mind, and modes of mental culture, fit a person for being a good\nobserver: that, however, is a question not of Logic, but of the Theory\nof Education, in the most enlarged sense of the term. There is not\nproperly an Art of Observing. There may be rules for observing. But\nthese, like rules for inventing, are properly instructions for the\npreparation of one's own mind; for putting it into the state in which it\nwill be most fitted to observe, or most likely to invent. They are,\ntherefore, 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\nlimbs, not 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\nstate of the whole universe at any particular moment is impossible, but\nwould also be useless. In making chemical experiments, we do not think\nit necessary 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\nthe heavenly bodies, it might have been unphilosophical to omit\nascertaining the precise condition of those bodies at the moment of the\nexperiment. As to the degree of minuteness of the mental subdivision; if\nwe were obliged to break down what we observe into its very simplest\nelements, that is, literally into single facts, it would be difficult to\nsay where we should find them: we can hardly ever affirm that our\ndivisions of any kind have reached the ultimate unit. But this too is\nfortunately unnecessary. The only object of the mental separation is to\nsuggest the requisite physical separation, so that we may either\naccomplish it ourselves, or seek for it in nature; and we have done\nenough when we have carried the subdivision as far as the point at which\nwe are able to see what observations or experiments we require. It is\nonly essential, at whatever point our mental decomposition of facts may\nfor the present have stopped, that we should hold ourselves ready and\nable to carry it farther as occasion requires, and should not allow the\nfreedom of our discriminating faculty to be imprisoned by the swathes\nand bands of ordinary classification; as was the case with all early\nspeculative inquirers, not excepting the Greeks, to whom it seldom\noccurred that what was called by one abstract name might, in reality, be\nseveral phenomena, or that there was a possibility of decomposing the\nfacts of the universe into any elements but those which ordinary\nlanguage already recognised.\n\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\nand many consequents. If those antecedents could not be severed from\none another except in thought, or if those consequents never were found\napart, it would be impossible for us to distinguish (_\u00e0 posteriori_ at\nleast) the real laws, or to assign to any cause its effect, or to any\neffect its cause. To do so, we must be able to meet with some of the\nantecedents apart from the rest, and observe what follows from them; or\nsome of the consequents, and observe by what they are preceded. We must,\nin short, follow the Baconian rule of _varying the circumstances_. This\nis, indeed, only the first rule of physical inquiry, and not, as some\nhave thought, the 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\nmode in which it is obtained: its employment for the purposes of\ninduction depends on the same principles in the one case and in the\nother; as the uses of money are the same whether it is inherited or\nacquired. There is, in short, no difference in kind, no real logical\ndistinction, between the two processes of investigation. There are,\nhowever, practical distinctions to which it is of considerable\nimportance to advert.\n\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\nthe circumstances than nature spontaneously offers, but also, in\nthousands of cases, to produce the precise _sort_ of variation which we\nare in want of for discovering the law of the phenomenon; a service\nwhich nature, being constructed on a quite different scheme from that of\nfacilitating our studies, is seldom so friendly as to bestow upon us.\nFor example, in order to ascertain what principle in the atmosphere\nenables it to sustain life, the variation we require is that a living\nanimal should be immersed in each component element of the atmosphere\nseparately. But nature does not supply either oxygen or azote in a\nseparate state. We are indebted to artificial experiment for our\nknowledge that it is the former, and not the latter, which supports\nrespiration; and for our knowledge of the very existence of the two\ningredients.\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's 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\nover spontaneous instances,--of our own experiments over even the same\nexperiments when made by nature,--which 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\nwere, home with us, and observe it in the midst of circumstances with\nwhich in all other respects we are accurately acquainted. If we desire\nto know what are the effects of the cause A, and are able to produce A\nby means at our disposal, we can generally determine at our own\ndiscretion, so far as is compatible with the nature of the phenomenon A,\nthe whole of the circumstances which shall be present along with it: and\nthus, knowing exactly the simultaneous state of everything else which is\nwithin the reach of A's influence, we have only to observe what\nalteration is made in that state by the presence of A.\n\nFor example, by the electric machine we can produce in the midst of\nknown circumstances, the phenomena which nature exhibits on a grander\nscale in the form of lightning and thunder. Now let any one consider\nwhat amount of knowledge of the effects and laws of electric agency\nmankind could have obtained from the mere observation of thunder-storms,\nand compare it with that which they have gained, and may expect to gain,\nfrom electrical and galvanic experiments. This example is the more\nstriking, now that we have reason to believe that electric action is of\nall natural phenomena (except heat) the most pervading and universal,\nwhich, therefore, it might antecedently have been supposed could stand\nleast in need of artificial means of production to enable it to be\nstudied; while the fact is so much the contrary, that without the\nelectric machine, the Leyden jar, and the voltaic battery, we probably\nshould never have suspected the existence of electricity as one of the\ngreat agents in nature; the few electric phenomena we should have known\nof would have continued to be regarded either as supernatural, or as a\nsort of anomalies and eccentricities in the 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\nwe think best calculated to bring the laws of the phenomenon into a\nclear light. By introducing one well-defined circumstance after another\ninto the experiment, we obtain assurance of the manner in which the\nphenomenon behaves under an indefinite variety of possible\ncircumstances. Thus, chemists, after having obtained some\nnewly-discovered substance in a pure state, (that is, having made sure\nthat there is nothing present which can interfere with and modify its\nagency,) introduce various other substances, one by one, to ascertain\nwhether it will combine with them, or decompose them, and with what\nresult; and also apply heat, or electricity, or pressure, to discover\nwhat will happen to the substance under each of these 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\nit, the task before us is very different. Instead of being able to\nchoose what the concomitant circumstances shall be, we now have to\ndiscover what they are; which, when we go beyond the simplest and most\naccessible cases, it is next to impossible to do, with any precision and\ncompleteness. Let us take, as an exemplification of a phenomenon which\nwe have no means of fabricating artificially, a human mind. Nature\nproduces many; but the consequence of our not being able to produce\nthem by art is, that in every instance in which we see a human mind\ndeveloping itself, or acting upon other things, we see it surrounded and\nobscured by an indefinite multitude of unascertainable circumstances,\nrendering the use of the common experimental methods almost delusive. We\nmay conceive to what extent this is true, if we consider, among other\nthings, that whenever nature produces a human mind, she produces, in\nclose connexion with it, a body; that is, a vast complication of\nphysical facts, in no two cases perhaps exactly similar, and most of\nwhich (except the mere structure, which we can examine in a sort of\ncoarse way after it has ceased to act), are radically out of the reach\nof our means of exploration. If, instead of a human mind, we suppose the\nsubject of investigation to be a human society or State, all the same\ndifficulties recur in a greatly augmented degree.\n\nWe have thus already come within sight of a conclusion, which the\nprogress of the inquiry will, I think, bring before us with the clearest\nevidence: namely, that in the sciences which deal with phenomena in\nwhich artificial experiments are impossible (as in the case of\nastronomy), or in which they have a very limited range (as in mental\nphilosophy, social science, and even physiology), induction from direct\nexperience is practised at a disadvantage in most cases equivalent to\nimpracticability: from which it follows that the methods of those\nsciences, in order to accomplish anything worthy of attainment, must be\nto a great extent, if not principally, deductive. This is already known\nto be the case with the first of the sciences we have mentioned,\nastronomy; that it is not generally recognised as true of the others, is\nprobably one of the reasons why they are not in a more advanced state.\n\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\ndirect exploration of phenomena, there is another branch in which the\nadvantage is 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\nthe road which leads from the one point to the other: we may either\ninquire into the effects of a given cause, or into the causes of a given\neffect. The fact that light blackens chloride of silver might have been\ndiscovered either by experiments on light, trying what effect it would\nproduce on various substances, or by observing that portions of the\nchloride had repeatedly become black, and inquiring into the\ncircumstances. The effect of the urali poison might have become known\neither by administering it to animals, or by examining how it happened\nthat the wounds which the Indians of Guiana inflict with their arrows\nprove so uniformly mortal. Now it is manifest from the mere statement of\nthe examples, without any theoretical discussion, that artificial\nexperimentation is applicable only to the former of these modes of\ninvestigation. We can take a cause, and try what it will produce: but we\ncannot take an effect, and try what it will be produced by. We can only\nwatch till we see it produced, or are enabled to produce 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.\nIf, on the contrary, the conditions on which a phenomenon depends are\nobscure, but the phenomenon itself familiar, we must commence our\ninquiry from the effect. If we are struck with the fact that chloride of\nsilver has been blackened, and have no suspicion of the cause, we have\nno resource but to compare instances in which the fact has chanced to\noccur, until by that comparison we discover that in all those instances\nthe substances had been exposed to light. If we knew nothing of the\nIndian arrows but their fatal effect, accident alone could turn our\nattention to experiments on the urali; in the regular course of\ninvestigation, we could only inquire, or try to observe, what had been\ndone 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\nto the consequents, not the antecedents, we are necessarily destitute of\nthe resource of artificial experimentation. We cannot, at our choice,\nobtain consequents, as we can antecedents, under any set of\ncircumstances compatible with their nature. There are no means of\nproducing effects but through their causes, and by the supposition the\ncauses of the effect in question are not known to us. We have therefore\nno expedient but to study it where it offers itself spontaneously. If\nnature happens to present us with instances sufficiently varied in their\ncircumstances, and if we are able to discover, either among the\nproximate antecedents or among some other order of antecedents,\nsomething which is always found when the effect is found, however\nvarious the circumstances, and never found when it is not; we may\ndiscover, by mere observation without experiment, a real uniformity in\nnature.\n\nBut though this is certainly the most favourable case for sciences of\npure observation, as contrasted with those in which artificial\nexperiments are possible, there is in reality no case which more\nstrikingly illustrates the inherent imperfection of direct induction\nwhen not founded on experimentation. Suppose that, by a comparison of\ncases of the effect, we have found an antecedent which appears to be,\nand perhaps is, invariably connected with it: we have not yet proved\nthat antecedent to be the cause, until we have reversed the process, and\nproduced the effect by means of that antecedent. If we can produce the\nantecedent artificially, and if, when we do so, the effect follows, the\ninduction is complete; that antecedent is the cause of that\nconsequent.[32] But we have then added the evidence of experiment to\nthat of simple observation. Until we had done so, we had only proved\n_invariable_ antecedence within the limits of experience, but not\n_unconditional_ antecedence, or causation. Until it had been shown by\nthe actual production of the antecedent under known circumstances, and\nthe occurrence thereupon of the consequent, that the antecedent was\nreally the condition on which it depended; the uniformity of succession\nwhich was proved to exist between them might, for aught we knew, be\n(like the succession of day and night) not a case of causation at all;\nboth antecedent and consequent might be successive stages of the effect\nof an ulterior cause. Observation, in short, without experiment\n(supposing no aid from deduction) can ascertain sequences and\ncoexistences, but cannot prove causation.\n\nIn order to see these remarks verified by the actual state of the\nsciences, we have only to think of the condition of natural history. In\nzoology, for example, there is an immense number of uniformities\nascertained, some of coexistence, others of succession, to many of\nwhich, notwithstanding considerable variations of the attendant\ncircumstances, we know not any exception: but the antecedents, for the\nmost part, are such as we cannot artificially produce; or if we can, it\nis only by setting in motion the exact process by which nature produces\nthem; and this being to us a mysterious process, of which the main\ncircumstances are not only unknown but unobservable, we do not succeed\nin obtaining the antecedents under known circumstances. What is the\nresult? That on this vast subject, which affords so much and such varied\nscope for observation, we have made most scanty progress in ascertaining\nany laws of causation. We know not with certainty, in the case of most\nof the phenomena that we find conjoined, which is the condition of the\nother; which is cause, and which effect, or whether either of them is\nso, or they are not rather conjunct effects of causes yet to be\ndiscovered, complex results 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\nand sciences of experimentation, and the extreme disadvantage under\nwhich directly inductive inquiry is necessarily carried on in the\nformer, were the best preparation for discussing the methods of direct\ninduction; a preparation rendering superfluous much that must otherwise\nhave been introduced, with some inconvenience, into the heart of that\ndiscussion. To the consideration of these methods we now proceed.\n\n\n\n\nCHAPTER VIII.\n\nOF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.\n\n\n\u00a7 1. The simplest and most obvious modes of singling out from among the\ncircumstances which precede or follow a phenomenon, those with which it\nis really connected by an invariable law, are two in number. One is, by\ncomparing together different instances in which the phenomenon occurs.\nThe other is, by comparing instances in which the phenomenon does occur,\nwith instances in other respects similar in which it does not. These two\nmethods may be respectively denominated, the Method of Agreement, and\nthe Method of Difference.\n\nIn illustrating these methods, it will be necessary to bear in mind the\ntwofold character of inquiries into the laws of phenomena; which may be\neither inquiries into the cause of a given effect, or into the effects\nor properties of a given cause. We shall consider the methods in their\napplication to either order of investigation, and shall draw our\nexamples equally from both.\n\nWe shall denote antecedents by the large letters of the alphabet, and\nthe consequents corresponding to them by the small. Let A, then, be an\nagent or cause, and let the object of our inquiry be to ascertain what\nare the effects of this cause. If we can either find, or produce, the\nagent A in such varieties of circumstances, that the different cases\nhave no circumstance in common except A; then whatever effect we find to\nbe produced in all our trials, is indicated as the effect of A. Suppose,\nfor example, that A is tried along with B and C, and that the effect is\n_a b c_; and suppose that A is next tried with D and E, but without B\nand C, 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\nfirst. Whatever is really the effect of A must have been produced in\nboth instances; now this condition is fulfilled by no circumstance\nexcept _a_. The phenomenon _a_ cannot have been the effect of B or C,\nsince it was produced where they were not; nor of D or E, since it was\nproduced where they were not. Therefore it is the effect of A.\n\nFor example, let the antecedent A be the contact of an alkaline\nsubstance and an oil. This combination being tried under several\nvarieties of circumstances, resembling each other in nothing else, the\nresults agree in the production of a greasy and detersive or saponaceous\nsubstance: it is therefore concluded that the combination of an oil and\nan alkali causes the production of a soap. It is thus we inquire, by the\nMethod of Agreement, 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\nof which we know not the origin, and try to find its mode of production\nby producing it: if we succeeded in such a random trial it could only be\nby accident. But if we can observe _a_ in two different combinations, _a\nb 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\ncausation. B and C, we may say, cannot be causes of _a_, since on its\nsecond occurrence they were not present; nor are D and E, for they were\nnot present on its first occurrence. A, alone of the five circumstances,\nwas found 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\nhave no other point of agreement; and we find them to have one, and as\nfar as we can observe, only one, antecedent in common: the deposition of\na solid matter from a liquid state, either a state of fusion or of\nsolution. We conclude, therefore, that the solidification of a\nsubstance from a liquid state is an invariable antecedent of its\ncrystallization.\n\nIn this example we may go farther, and say, it is not only the\ninvariable antecedent but the cause; or at least the proximate event\nwhich completes the cause. For in this case we are able, after detecting\nthe antecedent A, to produce it artificially, and by finding that _a_\nfollows it, verify the result of our induction. The importance of thus\nreversing the proof was strikingly manifested when by keeping a phial of\nwater charged with siliceous particles undisturbed for years, a chemist\n(I believe Dr. Wollaston) succeeded in obtaining crystals of quartz: and\nin the equally interesting experiment in which Sir James Hall produced\nartificial marble, by the cooling of its materials from fusion under\nimmense pressure: two admirable examples of the light which may be\nthrown upon the most secret processes of nature by well-contrived\ninterrogation 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\ncertain of having ascertained all the invariable antecedents, we might\nbe sure that the unconditional invariable antecedent, or cause, must be\nfound somewhere 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\nto what was really the operating circumstance in the means they\nemployed, namely, the pressure of the atmosphere on the open surface of\nthe water. It is, however, much easier to analyse completely a set of\narrangements made by ourselves, than the whole complex mass of the\nagencies which nature happens to be exerting at the moment of the\nproduction of a given phenomenon. We may overlook some of the material\ncircumstances in an experiment with an electrical machine; but we shall,\nat the worst, be better acquainted with them than with those of a\nthunder-storm.\n\nThe mode of discovering and proving laws of nature, which we have now\nexamined, proceeds on the following axiom: Whatever circumstances can be\nexcluded, without prejudice to the phenomenon, or can be absent\nnotwithstanding its presence, is not connected with it in the way of\ncausation. The casual circumstances being thus eliminated, if only one\nremains, that one is the cause which we are in search of: if more than\none, they either are, or contain among them, the cause; and so, _mutatis\nmutandis_, of the effect. As this method proceeds by comparing different\ninstances to ascertain in what they agree, I have termed it the Method\nof Agreement: and we may adopt as its regulating principle the following\ncanon:--\n\nFIRST CANON.\n\n_If two or more instances of the phenomenon under investigation have\nonly one 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\nalmost immediately return, we proceed to a still more potent instrument\nof the investigation of nature, the Method of Difference.\n\n\n\u00a7 2. In the Method of Agreement, we endeavoured to obtain instances\nwhich agreed in the given circumstance but differed in every other: in\nthe present method we require, on the contrary, two instances resembling\none another in every other respect, but differing in the presence or\nabsence of the phenomenon we wish to study. If our object be to discover\nthe effects 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\nabsent. If the effect of A B C is _a b c_, and the effect of B C, _b c_,\nit is evident that the effect of A is _a_. So again, if we begin at the\nother end, and desire to investigate the cause of an effect _a_, we must\nselect an instance, as _a b c_, in which the effect occurs, and in which\nthe antecedents were A B C, and we must look out for another instance in\nwhich the remaining circumstances, _b c_, occur without _a_. If the\nantecedents, in that instance, are B C, we know that the cause of _a_\nmust be A: either A alone, or A in conjunction with some of the other\ncircumstances present.\n\nIt is scarcely necessary to give examples of a logical process to which\nwe owe almost all the inductive conclusions we draw in daily life. When\na man is shot through the heart, it is by this method we know that it\nwas the gun-shot which killed him: for he was in the fulness of life\nimmediately before, 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\nof a particular one, is the effect of that one. Instead of comparing\ndifferent instances of a phenomenon, to discover in what they agree,\nthis method compares an instance of its occurrence with an instance of\nits non-occurrence, to discover in what they differ. The canon which is\nthe regulating principle of the Method of Difference may be expressed as\nfollows:\n\nSECOND CANON.\n\n_If an instance in which the phenomenon under investigation occurs, and\nan instance in which it does not occur, have every circumstance in\ncommon save one, that one occurring only in the former; the circumstance\nin which alone the two instances differ, is the effect, or the cause, or\nan indispensable part of the cause, of the phenomenon._\n\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\nare methods of _elimination_. This term (employed in the theory of\nequations to denote the process by which one after another of the\nelements of a question is excluded, and the solution made to depend on\nthe relation between the remaining elements only) is well suited to\nexpress the operation, analogous to this, which has been understood\nsince the time of Bacon to be the foundation of experimental inquiry:\nnamely, the successive exclusion of the various circumstances which are\nfound to accompany a phenomenon in a given instance, in order to\nascertain what are those among them which can be absent consistently\nwith the existence of the phenomenon. The Method of Agreement stands on\nthe ground that whatever can be eliminated, is not connected with the\nphenomenon by any law. The Method of Difference has for its foundation,\nthat whatever cannot be eliminated, is connected with the phenomenon by\na 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,\nthat the nature of the combinations which it requires is much more\nstrictly defined than in the Method of Agreement. The two instances\nwhich are to be compared with one another must be exactly similar, in\nall circumstances except the one which we are attempting to investigate:\nthey must be in the relation of A B C and B C, or of _a b c_ and _b c_.\nIt is true that this similarity of circumstances needs not extend to\nsuch as are already known to be immaterial to the result. And in the\ncase of most phenomena we learn at once, from the commonest experience,\nthat most of the coexistent phenomena of the universe may be either\npresent or absent without affecting the given phenomenon; or, if\npresent, are present indifferently when the phenomenon does not happen\nand when it does. Still, even limiting the identity which is required\nbetween the two instances, A B C and B C, to such circumstances as are\nnot already known to be indifferent; it is very seldom that nature\naffords two instances, of which we can be assured that they stand in\nthis precise relation to one another. In the spontaneous operations of\nnature there is generally such complication and such obscurity, they are\nmostly either on so overwhelmingly large or on so inaccessibly minute a\nscale, we are so ignorant of a great part of the facts which really take\nplace, and even those of which we are not ignorant are so multitudinous,\nand therefore so seldom exactly alike in any two cases, that a\nspontaneous experiment, of the kind required by the Method of\nDifference, is commonly not to be found. When, on the contrary, we\nobtain a phenomenon by an artificial experiment, a pair of instances\nsuch as the method requires is obtained almost as a matter of course,\nprovided the process does not last a long time. A certain state of\nsurrounding circumstances existed before we commenced the experiment;\nthis is B C. We then introduce A; say, for instance, by merely bringing\nan object from another part of the room, before there has been time for\nany change in the other elements. It is, in short (as M. Comte\nobserves), the very nature of an experiment, to introduce into the\npre-existing state of circumstances a change perfectly definite. We\nchoose a previous state of things with which we are well acquainted, so\nthat no unforeseen alteration in that state is likely to pass\nunobserved; and into this we introduce, as rapidly as possible, the\nphenomenon which we wish to study; so that in general we are entitled to\nfeel complete assurance that the pre-existing state, and the state which\nwe have produced, differ in nothing except the presence or absence of\nthat phenomenon. If a bird is taken from a cage, and instantly plunged\ninto carbonic acid gas, the experimentalist may be fully assured (at all\nevents after one or two repetitions) that no circumstance capable of\ncausing suffocation had supervened in the interim, except the change\nfrom immersion in the atmosphere to immersion in carbonic acid gas.\nThere is one doubt, indeed, which may remain in some cases of this\ndescription; the effect may have been produced not by the change, but by\nthe means employed to produce the change. The possibility, however, of\nthis last supposition generally admits of being conclusively tested by\nother experiments. It thus appears that in the study of the various\nkinds of phenomena which we can, by our voluntary agency, modify or\ncontrol, 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\ninstances whatever, in which nature presents us with a phenomenon, may\nbe examined for the purposes of this method; and if all such instances\nagree in anything, a conclusion of considerable value is already\nattained. We can seldom, indeed, be sure that the one point of agreement\nis the only one; but this ignorance does not, as in the Method of\nDifference, vitiate the conclusion; the certainty of the result, as far\nas it goes, is not affected. We have ascertained one invariable\nantecedent or consequent, however many other invariable antecedents or\nconsequents may still remain unascertained. If A B C, A D E, A F G, are\nall equally followed by _a_, then _a_ is an invariable consequent of A.\nIf _a b c_, _a d e_, _a f g_, all number A among their antecedents, then\nA is connected as an antecedent, by some invariable law, with _a_. But\nto determine whether this invariable antecedent is a cause, or this\ninvariable consequent an effect, we must be able, in addition, to\nproduce the one by means of the other; or, at least, to obtain that\nwhich alone constitutes our assurance of having produced anything,\nnamely, an instance in which the effect, _a_, has come into existence,\nwith no other change in the pre-existing circumstances than the addition\nof A. And this, if we can do it, is an application of the Method of\nDifference, not of the Method of Agreement.\n\nIt thus appears to be by the Method of Difference alone that we can\never, in the way of direct experience, arrive with certainty at causes.\nThe Method of Agreement leads only to laws of phenomena (as some writers\ncall them, but improperly, since laws of causation are also laws of\nphenomena): that is, to uniformities, which either are not laws of\ncausation, or in which the question of causation must for the present\nremain undecided. The Method of Agreement is chiefly to be resorted to,\nas a means of suggesting applications of the Method of Difference (as in\nthe last example the comparison of A B C, A D E, A F G, suggested that A\nwas the antecedent on which to try the experiment whether it could\nproduce _a_); or as an inferior resource, in case the Method of\nDifference is impracticable; which, as we before showed, generally\narises from the impossibility of artificially producing the phenomena.\nAnd hence it is that the Method of Agreement, though applicable in\nprinciple to either case, is more emphatically the method of\ninvestigation on those subjects where artificial experimentation is\nimpossible: because on those it is, generally, our only resource of a\ndirectly inductive nature; while, in the phenomena which we can produce\nat pleasure, the Method of Difference generally affords a more\nefficacious process, which will ascertain causes as well as mere laws.\n\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 a\ncombination of antecedents, which we have no power of separating from\neach other, and exhibiting apart. For instance, suppose the subject of\ninquiry to be the cause of the double refraction of light. We can\nproduce this phenomenon at pleasure, by employing any one of the many\nsubstances which are known to refract light in that peculiar manner. But\nif, taking one of those substances, as Iceland spar for example, we wish\nto determine on which of the properties of Iceland spar this remarkable\nphenomenon depends, we can make no use, for that purpose, of the Method\nof Difference; 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\nthey agree in the circumstance of being crystalline substances; and\nthough the converse does not hold, though all crystalline substances\nhave not the property of double refraction, it was concluded, with\nreason, that there is a real connexion between these two properties;\nthat either crystalline structure, or the cause which gives rise to that\nstructure, is one of the conditions 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\nnot possible to obtain the precise pair of instances which our second\ncanon requires--instances agreeing in every antecedent except A, or in\nevery consequent except _a_; we may yet be able, by a double employment\nof the Method of Agreement, to discover in what the instances which\ncontain A or _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)\nno other circumstance, the Method of Agreement, so far, bears testimony\nto a connexion 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,\nto leave out A, and observe whether by doing so, _a_ is prevented. Now\nsupposing (what is often the case) that we are not able to try this\ndecisive experiment; yet, provided we can by any means discover what\nwould be its result if we could try it, the advantage will be the same.\nSuppose, then, that as we previously examined a variety of instances in\nwhich _a_ occurred, and found them to agree in containing A, so we now\nobserve a variety of instances in which _a_ does not occur, and find\nthem agree in not containing A; which establishes, by the Method of\nAgreement, the same connexion between the absence of A and the absence\nof _a_, which was before established between their presence. As, then,\nit had been shown that whenever A is present _a_ is present, so it being\nnow shown that when A is taken away _a_ is removed along with it, we\nhave by the one proposition A B C, _a b c_, by the other B C, _b c_,\nthe positive and negative instances which the Method of Difference\nrequires.\n\nThis method may be called the Indirect Method of Difference, or the\nJoint Method of Agreement and Difference; and consists in a double\nemployment of the Method of Agreement, each proof being independent of\nthe other, and corroborating it. But it is not equivalent to a proof by\nthe direct Method of Difference. For the requisitions of the Method of\nDifference are not satisfied, unless we can be quite sure either that\nthe instances affirmative of _a_ agree in no antecedent whatever but A,\nor that the instances negative of _a_ agree in nothing but the negation\nof A. Now if it were possible, which it never is, to have this\nassurance, we should not need the joint method; for either of the two\nsets of instances separately would then be sufficient to prove\ncausation. This indirect method, therefore, can only be regarded as a\ngreat extension and improvement of the Method of Agreement, but not as\nparticipating in the more cogent nature of the Method of Difference. The\nfollowing may be stated as its canon:--\n\nTHIRD CANON.\n\n_If two or more instances in which the phenomenon occurs have only one\ncircumstance in common, while two or more instances in which it does not\noccur have nothing in common save the absence of that circumstance; the\ncircumstance in which alone the two sets of instances differ, is the\neffect, or the cause, or an indispensable part of the cause, of the\nphenomenon._\n\nWe shall presently see that the Joint Method of Agreement and Difference\nconstitutes, in another respect not yet adverted to, an improvement upon\nthe common Method of Agreement, namely, in being unaffected by a\ncharacteristic imperfection of that method, the nature of which still\nremains to be pointed out. But as we 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 a statement of two other methods, which will\ncomplete the enumeration of the means which mankind possess for\nexploring the laws of nature by specific observation and experience.\n\n\n\u00a7 5. The first of these has been aptly denominated the Method of\nResidues. Its principle is very simple. Subducting from any given\nphenomenon all the portions which, by virtue of preceding inductions,\ncan be assigned to known causes, the remainder will be the effect of the\nantecedents which had been overlooked, or of which the effect was as yet\nan unknown quantity.\n\nSuppose, as before, that we have the antecedents A B C, followed by the\nconsequents _a b c_, and that by previous inductions (founded, we will\nsuppose, on the Method of Difference) we have ascertained the causes of\nsome of these effects, or the effects of some of these causes; and are\nthence apprised that the effect of A is _a_, and that the effect of B is\n_b_. Subtracting the sum of these effects from the total phenomenon,\nthere remains _c_, which now, without any fresh experiments, we may know\nto be 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\nc_, could have been compared with a single instance A B, _a b_, we\nshould have proved C to be the cause of _c_, by the common process of\nthe Method of Difference. In the present case, however, instead of a\nsingle instance A B, we have had to study separately the causes A and B,\nand to infer from the effects which they produce separately, what effect\nthey must produce in the case A B C where they act together. Of the two\ninstances, therefore, which the Method of Difference requires,--the one\npositive, the other negative,--the negative one, or that in which the\ngiven phenomenon is absent, is not the direct result of observation and\nexperiment, but has been arrived at by deduction. As one of the forms of\nthe Method of Difference, the Method of Residues partakes of its\nrigorous certainty, provided the previous inductions, those which gave\nthe effects of A and B, were obtained by the same infallible method, and\nprovided 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\nis not complete unless we can obtain C artificially and try it\nseparately, or unless its agency, when once suggested, can be accounted\nfor, and proved deductively 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:--\n\nFOURTH CANON.\n\n_Subduct from any phenomenon such part as is known by previous\ninductions to be the effect of certain antecedents, and the residue of\nthe phenomenon is the effect of the remaining antecedents._\n\n\n\u00a7 6. There remains a class of laws which it is impracticable to\nascertain by any of the three methods which I have attempted to\ncharacterize; namely, the laws of those Permanent Causes, or\nindestructible natural agents, which it is impossible either to exclude\nor to isolate; which we can neither hinder from being present, nor\ncontrive that they shall be present alone. It would appear at first\nsight that we could by no means separate the effects of these agents\nfrom the effects of those other phenomena with which they cannot be\nprevented from coexisting. In respect, indeed, to most of the permanent\ncauses, no such difficulty exists; since though we cannot eliminate\nthem as coexisting facts, we can eliminate them as influencing agents,\nby simply trying our experiment in a local situation beyond the limits\nof their influence. The pendulum, for example, has its oscillations\ndisturbed by the vicinity of a mountain: we remove the pendulum to a\nsufficient distance from the mountain, and the disturbance ceases: from\nthese data we can determine by the Method of Difference, the amount of\neffect due to the mountain; and beyond a certain distance everything\ngoes on precisely as it would do if the mountain exercised no influence\nwhatever, which, accordingly, we, with sufficient reason, conclude to be\nthe 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\nmountain, but it cannot be removed from the influence of the earth: we\ncannot take away the earth from the pendulum, nor the pendulum from the\nearth, to ascertain whether it would continue to vibrate if the action\nwhich the earth exerts upon it were withdrawn. On what evidence, then,\ndo we ascribe its vibrations to the earth's influence? Not on any\nsanctioned by the Method of Difference; for one of the two instances,\nthe negative instance, is wanting. Nor by the Method of Agreement; for\nthough all pendulums agree in this, that during their oscillations the\nearth is always present, why may we not as well ascribe the phenomenon\nto the sun, which is equally a coexistent fact in all the experiments?\nIt is evident that to establish even so simple a fact of causation as\nthis, there was required some method over and above those which we have\nyet examined.\n\nAs another example, let us take the phenomenon Heat. Independently of\nall hypothesis as to the real nature of the agency so called, this fact\nis certain, that we are unable to exhaust any body of the whole of its\nheat. It is equally certain, that no one ever perceived heat not\nemanating from a body. Being unable, then, to separate Body and Heat, we\ncannot effect such a variation of circumstances as the foregoing three\nmethods require; we cannot ascertain, by those methods, what portion of\nthe phenomena exhibited by any body is due to the heat contained in it.\nIf we could observe a body with its heat, and the same body entirely\ndivested of heat, the Method of Difference would show the effect due to\nthe heat, apart from that due to the body. If we could observe heat\nunder circumstances agreeing in nothing but heat, and therefore not\ncharacterized also by the presence of a body, we could ascertain the\neffects of heat, from an instance of heat with a body and an instance of\nheat without a body, by the Method of Agreement; or we could determine\nby the Method of Difference what effect was due to the body, when the\nremainder which was due to the heat would be given by the Method of\nResidues. But we can do none of these things; and without them the\napplication of any of the three methods to the solution of this problem\nwould be illusory. It would be idle, for instance, to attempt to\nascertain the effect of heat by subtracting from the phenomena exhibited\nby a body, all that is due to its other properties; for as we have never\nbeen able to observe any bodies without a portion of heat in them,\neffects due to that heat might form a part of the very results, which we\nwere affecting to subtract in order that the effect of heat might be\nshown 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\nheat as a cause. But we have still a resource. Though we cannot exclude\nan antecedent altogether, we may be able to produce, or nature may\nproduce for us, some modification in it. By a modification is here\nmeant, a change in it, not amounting to its total removal. If some\nmodification in the antecedent A is always followed by a change in the\nconsequent _a_, the other consequents _b_ and _c_ remaining the same; or\n_vice vers\u00e2_, if every change in _a_ is found to have been preceded by\nsome modification in A, none being observable in any of the other\nantecedents; we may safely conclude that _a_ is, wholly or in part, an\neffect traceable to A, or at least in some way connected with it through\ncausation. For example, in the case of heat, though we cannot expel it\naltogether from any body, we can modify it in quantity, we can increase\nor diminish it; and doing so, we find by the various methods of\nexperimentation or observation already treated of, that such increase or\ndiminution of heat is followed by expansion or contraction of the body.\nIn this manner we arrive at the conclusion, otherwise unattainable by\nus, that one of the effects of heat is to enlarge the dimensions of\nbodies; or what is the same thing in other words, to widen the distances\nbetween their particles.\n\nA change in a thing, not amounting to its total removal, that is, a\nchange which leaves it still the same thing it was, must be a change\neither in its quantity, or in some of its variable relations to other\nthings, of which variable relations the principal is its position in\nspace. In the previous example, the modification which was produced in\nthe antecedent was an alteration in its quantity. Let us now suppose the\nquestion to be, what influence the moon exerts on the surface of the\nearth. We cannot try an experiment in the absence of the moon, so as to\nobserve what terrestrial phenomena her annihilation would put an end to;\nbut when we find that all the variations in the _position_ of the moon\nare followed by corresponding variations in the time and place of high\nwater, the place being always either the part of the earth which is\nnearest to, or that which is most remote from, the moon, we have ample\nevidence that the moon is, wholly or partially, the cause which\ndetermines the tides. It very commonly happens, as it does in this\ninstance, that the variations of an effect are correspondent, or\nanalogous, to those of its cause; as the moon moves farther towards the\neast, the high water point does the same: but this is not an\nindispensable condition; as may be seen in the same example, for along\nwith that high water point there is at the same instant another high\nwater point diametrically opposite to it, and which, therefore, of\nnecessity, moves towards the west, as the moon, followed by the nearer\nof the tide waves, advances towards the east: and yet both these motions\nare equally effects of the moon's 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's 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.\nIn every twenty-four hours, by the earth's rotation, the line drawn from\nthe body at right angles to the earth coincides successively with all\nthe radii 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's position, the line in which bodies tend to fall\ncontinues to be directed towards it: which proves that terrestrial\ngravity is directed to the earth, and not, as was once fancied by some,\nto a fixed point of space.\n\nThe method by which these results were obtained, may be termed the\nMethod of Concomitant Variations: it is regulated by the following\ncanon:--\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\ncause and the other effect. The same thing may, and indeed must happen,\nsupposing them to be two different effects of a common cause: and by\nthis method 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\nascertain whether we can produce the one set of variations by means of\nthe other. In the case of heat, for example, by increasing the\ntemperature of a body we increase its bulk, but by increasing its bulk\nwe do not increase its temperature; on the contrary, (as in the\nrarefaction of air under the receiver of an air-pump,) we generally\ndiminish it: therefore heat is not an effect, but a cause, of increase\nof bulk. If we cannot ourselves produce the variations, we must\nendeavour, though it is an attempt which is seldom successful, to find\nthem produced by nature in some case in which the pre-existing\ncircumstances 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,\nthe same precautions must be used as in any other case of the\ndetermination of an invariable sequence. We must endeavour to retain all\nthe other antecedents unchanged, while that particular one is subjected\nto the requisite 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\nassumes a 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_,\nany variation in the quantity or in the various relations of A, is\nuniformly followed by a variation in the quantity or relations of _a_.\nTo take a familiar instance, that of gravitation. The sun causes a\ncertain tendency to motion in the earth; here we have cause and effect;\nbut that tendency is _towards_ the sun, and therefore varies in\ndirection as the sun varies in the relation of position; and moreover\nthe tendency varies in intensity, in a certain numerical correspondence\nto the sun's distance from the earth, that is, according to another\nrelation of the sun. Thus we see that there is not only an invariable\nconnexion between the sun and the earth's gravitation, but that two of\nthe relations of the sun, its position with respect to the earth and its\ndistance from the earth, are invariably connected as antecedents with\nthe quantity and direction of the earth's gravitation. The cause of the\nearth's gravitating at all, is simply the sun; but the cause of its\ngravitating with a given intensity and in a given direction, is the\nexistence of the sun in a given direction and at a given distance. It is\nnot strange that a modified cause, which is in truth a different cause,\nshould produce a different effect.\n\nAlthough it is for the most part true that a modification of the cause\nis followed 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\nof which is evident; for if the thing itself had no influence on the\neffect, neither could the modifications of the thing have any influence.\nIf the stars have no power over the fortunes of mankind, it is implied\nin the very terms, that the conjunctions or oppositions of different\nstars can have 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\ncases; it may often usefully follow after the Method of Difference, to\ngive additional precision to a solution which that has found. When by\nthe Method of Difference it has first been ascertained that a certain\nobject produces a certain effect, the Method of Concomitant Variations\nmay be usefully called in, to determine according to what law the\nquantity or the different relations of the effect follow those of the\ncause.\n\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\nof quantity. Of such variations we may in general affirm with safety,\nthat they 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\nof causation; cases of the opposite description, in which causes change\ntheir properties on being conjoined with one another, being, on the\ncontrary, special and exceptional. Suppose, then, that when A changes\nin quantity, _a_ also changes in quantity, and in such a manner that we\ncan trace the numerical relation which the changes of the one bear to\nsuch changes of the other as take place within our limits of\nobservation. We may then, with certain precautions, safely conclude that\nthe same numerical relation will hold beyond those limits. If, for\ninstance, we find that when A is double, _a_ is double; that when A is\ntreble or quadruple, _a_ is treble or quadruple; we may conclude that if\nA were a half or a third, _a_ would be a half or a third, and finally,\nthat if A were annihilated, _a_ would be annihilated, and that _a_ is\nwholly the effect of A, or wholly the effect of the same cause with A.\nAnd so with any other numerical relation according to which A and _a_\nwould vanish simultaneously; as for instance, if _a_ were proportional\nto the square of A. If, on the other hand, _a_ is not wholly the effect\nof A, but yet varies when A varies, it is probably a mathematical\nfunction not of A alone, but of A and something else: its changes, for\nexample, may be such as would occur if part of it remained constant, or\nvaried on some other principle, and the remainder varied in some\nnumerical relation to the variations of A. In that case, when A\ndiminishes, _a_ will be seen to approach not towards zero, but towards\nsome other limit: and when the series of variations is such as to\nindicate what that limit is, if constant, or the law of its variation if\nvariable, the limit will exactly measure how much of _a_ is the effect\nof some other and independent cause, and the remainder will be the\neffect of A (or of the cause of A).\n\nThese conclusions, however, must not be drawn without certain\nprecautions. In the first place, the possibility of drawing them at all,\nmanifestly supposes that we are acquainted not only with the variations,\nbut with the absolute quantities both of A and _a_. If we do not know\nthe total quantities, we cannot, of course, determine the real numerical\nrelation according to which those quantities vary. It is therefore an\nerror to conclude, as some have concluded, that because increase of heat\nexpands bodies, that is, increases the distance between their particles,\ntherefore the distance is wholly the effect of heat, and that if we\ncould entirely exhaust the body of its heat, the particles would be in\ncomplete contact. This is no more than a guess, and of the most\nhazardous sort, not a legitimate induction: for since we neither know\nhow much heat there is in any body, nor what is the real distance\nbetween any two of its particles, we cannot judge whether the\ncontraction of the distance does or does not follow the diminution of\nthe quantity of heat according to such a numerical relation that the two\nquantities 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\nin open opposition to first appearances; all terrestrial objects, when\nin motion, gradually abate their velocity and at last stop; which\naccordingly the ancients, with their _inductio per enumerationem\nsimplicem_, imagined to be the law. Every moving body, however,\nencounters various obstacles, as friction, the resistance of the\natmosphere, &c., which we know by daily experience to be causes capable\nof destroying motion. It was suggested that the whole of the retardation\nmight be owing to these causes. How was this inquired into? If the\nobstacles could have been entirely removed, the case would have been\namenable to the Method of Difference. They could not be removed, they\ncould only be diminished, and the case, therefore, admitted only of the\nMethod of Concomitant Variations. This accordingly being employed, it\nwas found that every diminution of the obstacles diminished the\nretardation of the motion: and inasmuch as in this case (unlike the case\nof heat) the total quantities both of the antecedent and of the\nconsequent were known; it was practicable to estimate, with an approach\nto accuracy, both the amount of the retardation and the amount of the\nretarding 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\ncause was. The simple oscillation of a weight suspended from a fixed\npoint, and moved a little out of the perpendicular, which in ordinary\ncircumstances lasts but a few minutes, was prolonged in Borda's\nexperiments to more than thirty hours, by diminishing as much as\npossible the friction at the point of suspension, and by making the body\noscillate in a space exhausted as nearly as possible of its air. There\ncould therefore be no hesitation in assigning the whole of the\nretardation of motion to the influence of the obstacles; and since,\nafter subducting this retardation from the total phenomenon, the\nremainder was an uniform velocity, the result was the proposition known\nas the first law of motion.\n\nThere is also another characteristic uncertainty affecting the inference\nthat the law of variation which the quantities observe within our limits\nof observation, will hold beyond those limits. There is of course, in\nthe first 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\ncircumstances we are able to observe. This is an element of uncertainty\nwhich enters largely into all our predictions of effects; but it is not\npeculiarly applicable to the Method of Concomitant Variations. The\nuncertainty, however, of which I am about to speak, is characteristic of\nthat method; especially in the cases in which the extreme limits of our\nobservation are very narrow, in comparison with the possible variations\nin the quantities of the phenomena. Any one who has the slightest\nacquaintance with mathematics, is aware that very different laws of\nvariation may produce numerical results which differ but slightly from\none another within narrow limits; and it is often only when the absolute\namounts of variation are considerable, that the difference between the\nresults given by one law and by another becomes appreciable. When,\ntherefore, such variations in the quantity of the antecedents as we have\nthe means of observing, are small in comparison with the total\nquantities, there is much danger lest we should mistake the numerical\nlaw, and be led to miscalculate the variations which would take place\nbeyond the limits; a miscalculation which would vitiate any conclusion\nrespecting the dependence of the effect upon the cause, that could be\nfounded on those variations. Examples are not wanting of such mistakes.\n\"The formul\u00e6,\" says Sir John Herschel,[33] \"which have been empirically\ndeduced for the elasticity of steam, (till very recently,) and those for\nthe resistance of fluids, and other similar subjects,\" when relied on\nbeyond the limits of the observations from which they were deduced,\n\"have almost invariably failed to support the theoretical structures\nwhich have been erected on them.\"\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\nor smaller than those which we have had the means of observing, cannot\nbe considered to rest on a complete induction. All that in such a case\ncan be regarded as proved on the subject of causation is, that there is\nsome connexion between the two phenomena; that A, or something which can\ninfluence A, must be _one_ of the causes which collectively determine\n_a_. We may, however, feel assured that the relation which we have\nobserved to exist between the variations of A and _a_, will hold true in\nall cases which fall between the same extreme limits; that is, wherever\nthe utmost increase or diminution in which the result has been found by\nobservation to coincide with the law, is not exceeded.\n\nThe four methods which it has now been attempted to describe, are the\nonly possible modes of experimental inquiry--of direct induction _\u00e0\nposteriori_, as distinguished from deduction: at least, I know not, nor\nam able to imagine, any others. And even of these, the Method of\nResidues, as we have seen, is not independent of deduction; though, as\nit also requires specific experience, it may, without impropriety, be\nincluded among methods 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\nis expedient to illustrate the use of the methods, by suitable examples\ndrawn from actual physical investigations. These, accordingly, will form\nthe subject of the succeeding chapter.\n\n\n\n\nCHAPTER IX.\n\nMISCELLANEOUS EXAMPLES OF THE FOUR METHODS.\n\n\n\u00a7 1. I shall select, as a first example, an interesting speculation of\none of the most eminent of theoretical chemists, Baron Liebig. The\nobject in view, is to ascertain the immediate cause of the death\nproduced by metallic poisons.\n\nArsenious acid, and the salts of lead, bismuth, copper, and mercury, if\nintroduced into the animal organism, except in the smallest doses,\ndestroy life. These facts have long been known, as insulated truths of\nthe lowest order of generalization; but it was reserved for Liebig, by\nan apt employment of the first two of our methods of experimental\ninquiry, to connect these truths together by a higher induction,\npointing out what property, common to all these deleterious substances,\nis the really operating 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\ntendency to 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\nto destroy life, eschars are produced, that is, certain superficial\nportions of the tissues are destroyed, which are afterwards thrown off\nby the reparative 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\naction of the poisons are in a state of life, in others only in a state\nof organization, in others not even in that. And what is the result\nwhich follows in all the cases? The conversion of the animal substance\n(by combination with the poison) into a chemical compound, held together\nby so powerful a force as to resist the subsequent action of the\nordinary causes of decomposition. Now, organic life (the necessary\ncondition of sensitive life) consisting in a continual state of\ndecomposition and recomposition of the different organs and tissues;\nwhatever incapacitates them for this decomposition destroys life. And\nthus the proximate cause of the death produced by this description of\npoisons, is ascertained, as far as the Method of Agreement can ascertain\nit.\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\nwhich constitute life,) and the consequent is death, either of the whole\norganism, or of some portion of it; let us compare with these cases\nother cases, as much resembling them as possible, but in which that\neffect is not produced. And, first, \"many insoluble basic salts of\narsenious acid are known not to be poisonous. The substance called\nalkargen, discovered by Bunsen, which contains a very large quantity of\narsenic, and approaches very closely in composition to the organic\narsenious compounds found in the body, has not the slightest injurious\naction upon the organism.\" Now when these substances are brought into\ncontact with the tissues in any way, they do not combine with them; they\ndo not arrest their progress to decomposition. As far, therefore, as\nthese instances go, it appears that when the effect is absent, it is by\nreason of the absence of that antecedent which we had already good\nground for considering as the proximate 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\nwith the poisonous substances in every property, except the particular\none, of entering into a difficultly decomposable compound with the\nanimal tissues. To render the method strictly applicable, we need an\ninstance, not of a different substance, but of one of the very same\nsubstances, in circumstances which would prevent it from forming, with\nthe tissues, the sort of compound in question; and then, if death does\nnot follow, our case is made out. Now such instances are afforded by the\nantidotes to these poisons. For example, in case of poisoning by\narsenious acid, if hydrated peroxide of iron is administered, the\ndestructive agency is instantly checked. Now this peroxide is known to\ncombine with the acid, and form a compound, which, being insoluble,\ncannot act at all on animal tissues. So, again, sugar is a well-known\nantidote to poisoning by salts of copper; and sugar reduces those salts\neither into metallic copper, or into the red suboxide, neither of which\nenters into combination with animal matter. The disease called painter's\ncolic, so common in manufactories of white lead, is unknown where the\nworkmen are accustomed to take, as a preservative, sulphuric acid\nlemonade (a solution of sugar rendered acid by sulphuric acid). Now\ndiluted sulphuric acid has the property of decomposing all compounds of\nlead with organic matter, or of preventing them from being formed.\n\nThere is another class of instances, of the nature required by the\nMethod of Difference, which seem at first sight to conflict with the\ntheory. Soluble salts of silver, such for instance as the nitrate, have\nthe same stiffening antiseptic effect on decomposing animal substances\nas corrosive sublimate and the most deadly metallic poisons; and when\napplied to the external parts of the body, the nitrate is a powerful\ncaustic; depriving those parts of all active vitality, and causing them\nto be thrown off by the neighbouring living structures, in the form of\nan eschar. The nitrate and the other salts of silver ought, then, it\nwould seem, if the theory be correct, to be poisonous; yet they may be\nadministered internally with perfect impunity. From this apparent\nexception arises the strongest confirmation which the theory has yet\nreceived. Nitrate of silver, in spite of its chemical properties, does\nnot poison when introduced into the stomach; but in the stomach, as in\nall animal liquids, there is common salt; and in the stomach there is\nalso free muriatic acid. These substances operate as natural antidotes,\ncombining with the nitrate, and if its quantity is not too great,\nimmediately converting it into chloride of silver; a substance very\nslightly soluble, and therefore incapable of combining with the tissues,\nalthough to the extent of its solubility it has a medicinal influence,\nthough an entirely different class of organic actions.\n\nThe preceding instances have afforded an induction of a high order of\nconclusiveness, illustrative of the two simplest of our four methods;\nthough not rising to the maximum of certainty which the Method of\nDifference, in its most perfect exemplification, is capable of\naffording. For (let us not forget) the positive instance and the\nnegative one which the rigour of that method requires, ought to differ\nonly in the presence or absence of one single circumstance. Now, in the\npreceding argument, they differ in the presence or absence not of a\nsingle _circumstance_, but of a single _substance_: and as every\nsubstance has innumerable properties, there is no knowing what number of\nreal differences are involved in what is nominally and apparently only\none difference. It is conceivable that the antidote, the peroxide of\niron for example, may counteract the poison through some other of its\nproperties than that of forming an insoluble compound with it; and if\nso, the theory would fall to the ground, so far as it is supported by\nthat instance. This source of uncertainty, which is a serious hindrance\nto all extensive generalizations in chemistry, is however reduced in the\npresent case to almost the lowest degree possible, when we find that\nnot only one substance, but many substances, possess the capacity of\nacting as antidotes to metallic poisons, and that all these agree in the\nproperty of forming insoluble compounds with the poisons, while they\ncannot be ascertained to agree in any other property whatsoever. We have\nthus, in favour of the theory, all the evidence which can be obtained by\nwhat we termed the Indirect Method of Difference, or the Joint Method of\nAgreement and Difference; the evidence of which, though it never can\namount to that of the Method of Difference properly so called, may\napproach indefinitely near to it.\n\n\n\u00a7 2. Let the object be[34] to ascertain the law of what is termed\n_induced_ electricity; to find under what conditions any electrified\nbody, whether positively or negatively electrified, gives rise to a\ncontrary electric state in some other body adjacent to it.\n\nThe most familiar exemplification of the phenomenon to be investigated\nis the following. Around the prime conductors of an electrical machine,\nthe atmosphere to some distance, or any conducting surface suspended in\nthat atmosphere, is found to be in an electric condition opposite to\nthat of the prime conductor itself. Near and around the positive prime\nconductor there is negative electricity, and near and around the\nnegative prime conductor there is positive electricity. When pith balls\nare brought near to either of the conductors, they become electrified\nwith the opposite electricity to it; either receiving a share from the\nalready electrified atmosphere by conduction, or acted upon by the\ndirect inductive influence of the conductor itself: they are then\nattracted by the conductor to which they are in opposition; or, if\nwithdrawn in their electrified state, they will be attracted by any\nother oppositely charged body. In like manner the hand, if brought near\nenough to the conductor, receives or gives an electric discharge; now we\nhave no evidence that a charged conductor can be suddenly discharged\nunless by the approach of a body oppositely electrified. In the case,\ntherefore, of the electric machine, it appears that the accumulation of\nelectricity in an insulated conductor is always accompanied by the\nexcitement of the contrary electricity in the surrounding atmosphere,\nand in every conductor placed near the former conductor. It does not\nseem possible, in this case, to produce one electricity by itself.\n\nLet us now examine all the other instances which we can obtain,\nresembling this instance in the given consequent, namely, the evolution\nof an opposite electricity in the neighbourhood of an electrified body.\nAs one remarkable instance we have the Leyden jar; and after the\nsplendid experiments of Faraday in complete and final establishment of\nthe substantial identity of magnetism and electricity, we may cite the\nmagnet, both the natural and the electro-magnet, in neither of which it\nis possible to produce one kind of electricity by itself, or to charge\none pole without charging an opposite pole with the contrary electricity\nat the 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\nwhich a body can become charged with electricity; and in all of them\nthere is found, as a concomitant or consequent, the excitement of the\nopposite electric state in some other body or bodies. It seems to follow\nthat the two facts are invariably connected, and that the excitement of\nelectricity in any body has for one of its necessary conditions the\npossibility of a simultaneous excitement of the opposite electricity in\nsome neighbouring body.\n\nAs the two contrary electricities can only be produced together, so\nthey can only cease together. This may be shown by an application of the\nMethod of Difference to the example of the Leyden jar. It needs scarcely\nbe here remarked that in the Leyden jar, electricity can be accumulated\nand retained 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\nis charged negatively, and it was by virtue of this fact that the Leyden\njar served 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\nquantity be allowed to pass from the negative side: if one coating be\nperfectly insulated, the charge is safe. The dissipation of one must\nproceed _pari passu_ 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\nmachine, the neighbouring body which is to be oppositely electrified is\nthe surrounding 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\nimposes a corresponding limit to the capacity of the conductor for being\ncharged. As the capacity of the neighbouring body for supporting the\nopposition increases, a higher charge becomes possible: and to this\nappears to be owing the great superiority of the Leyden jar.\n\nA further and most decisive confirmation by the Method of Difference,\nis to be found in one of Faraday's 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\nknow whether, as the prime conductor develops opposite electricity upon\na conductor in its vicinity, so a voltaic current running along a wire\nwould induce an opposite current upon another wire laid parallel to it\nat a short distance. Now this case is similar to the cases previously\nexamined, in every circumstance except the one to which we have ascribed\nthe effect. We found in the former instances that whenever electricity\nof one kind was excited in one body, electricity of the opposite kind\nmust be excited in a neighbouring body. But in Faraday's experiment this\nindispensable opposition exists within the wire itself. From the nature\nof a voltaic charge, the two opposite currents necessary to the\nexistence of each other are both accommodated in one wire; and there is\nno need of another wire placed beside it to contain one of them, in the\nsame way as the Leyden jar must have a positive and a negative surface.\nThe exciting cause can and does produce all the effect which its laws\nrequire, independently of any electric excitement of a neighbouring\nbody. Now the result of the experiment with the second wire was, that no\nopposite current was produced. There was an instantaneous effect at the\nclosing and breaking of the voltaic circuit; electric inductions\nappeared when the two wires were moved to and from one another; but\nthese are phenomena of a different class. There was no induced\nelectricity in the sense in which this is predicated of the Leyden jar;\nthere was no sustained current running up the one wire while an opposite\ncurrent ran down the neighbouring wire; and this alone would have been a\ntrue 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\nMethod of Difference, that neither of the two kinds of electricity can\nbe excited without an equal excitement of the other and opposite kind:\nthat both are effects of the same cause; that the possibility of the one\nis a condition of the possibility of the other, and the quantity of the\none an impassable limit to the quantity of the other. A scientific\nresult of considerable interest in itself, and illustrating those three\nmethods in a manner both characteristic and easily intelligible.[35]\n\n\n\u00a7 3. Our third example shall be extracted from Sir John Herschel's\n_Discourse on the Study of Natural Philosophy_, a work replete with\nhappily-selected exemplifications of inductive processes from almost\nevery department of physical science, and in which alone, of all books\nwhich I have met with, the four methods of induction are distinctly\nrecognised, though not so clearly characterized and defined, nor their\ncorrelation so fully shown, as has appeared to me desirable. The present\nexample is described by Sir John Herschel as \"one of the most beautiful\nspecimens\" which can be cited \"of inductive experimental inquiry lying\nwithin a moderate compass;\" the theory of dew, first promulgated by the\nlate Dr. Wells, and now universally adopted by scientific authorities.\nThe passages in inverted commas are extracted verbatim from the\nDiscourse.[36]\n\n\"Suppose _dew_ were the phenomenon proposed, whose cause we would know.\nIn the first place\" we must determine precisely what we mean by dew:\nwhat the fact really is, whose cause we desire to investigate. \"We must\nseparate dew from rain, and the moisture of fogs, and limit the\napplication of the term to what is really meant, which is the\nspontaneous appearance of moisture on substances exposed in the open air\nwhen no rain or _visible_ wet is falling.\" This answers to a preliminary\noperation which will be characterized in the ensuing book, treating of\noperations subsidiary to induction.[37]\n\n\"Now, here we have analogous phenomena in the moisture which bedews a\ncold metal or stone when we breathe upon it; that which appears on a\nglass of water fresh from the well in hot weather; that which appears on\nthe inside of windows when sudden rain or hail chills the external air;\nthat which runs down our walls when, after a long frost, a warm moist\nthaw comes on.\" Comparing these cases, we find that they all contain the\nphenomenon which was proposed as the subject of investigation. Now \"all\nthese instances agree in one point, the coldness of the object dewed, in\ncomparison with the air in contact with it.\" But there still remains the\nmost important case of all, that of nocturnal dew: does the same\ncircumstance exist in this case? \"Is it a fact that the object dewed is\ncolder than the air? Certainly not, one would at first be inclined to\nsay; for what is to _make_ it so? But ... the experiment is easy: we\nhave only to lay a thermometer in contact with the dewed substance, and\nhang one at a little distance above it, out of reach of its influence.\nThe experiment has been therefore made, the question has been asked, and\nthe answer has been invariably in the affirmative. Whenever an object\ncontracts dew, it _is_ colder than the air.\"\n\nHere then is a complete application of the Method of Agreement,\nestablishing the fact of an invariable connexion between the deposition\nof dew on a surface, and the coldness of that surface compared with the\nexternal air. But which of these is cause, and which effect? or are they\nboth effects of something else? On this subject the Method of Agreement\ncan afford us no light: we must call in a more potent method. \"We must\ncollect more facts, or, which comes to the same thing, vary the\ncircumstances; since every instance in which the circumstances differ is\na fresh fact: and especially, we must note the contrary or negative\ncases, _i.e._ where no dew is produced:\" a comparison between instances\nof dew and instances of no dew, being the condition necessary to bring\nthe Method of Difference into play.\n\n\"Now, first, no dew is produced on the surface of polished metals, but\nit _is_ very copiously on glass, both exposed with their faces upwards,\nand in some cases the under side of a horizontal plate of glass is also\ndewed.\" 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\nthe canon 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\nother substances on which dew is deposited, have only one quality in\ncommon, and that polished metals and the other substances on which dew\nis not deposited have also nothing in common but the one circumstance,\nof not having the one quality which the others have; the requisitions of\nthe Method 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\"In 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,\nby exposing polished surfaces of various kinds. This done, a _scale of\nintensity_ becomes obvious. Those polished substances are found to be\nmost strongly dewed which conduct heat worst; while those which conduct\nwell, resist dew most effectually.\" The complication increases; here is\nthe Method of Concomitant Variations called to our assistance; and no\nother method was practicable on this occasion; for the quality of\nconducting heat could not be excluded, since all substances conduct heat\nin some degree. The conclusion obtained is, that _c\u00e6teris paribus_ the\ndeposition of dew is in some proportion to the power which the body\npossesses of resisting the passage of heat; and that this, therefore,\n(or something connected with this,) must be at least one of the causes\nwhich assist in producing the deposition of dew on the surface.\n\n\"But if we expose rough surfaces instead of polished, we sometimes find\nthis law interfered with. Thus, roughened iron, especially if painted\nover or blackened, becomes dewed sooner than varnished paper; the kind\nof _surface_, therefore, has a great influence. Expose, then, the _same_\nmaterial in very diversified states as to surface,\" (that is, employ the\nMethod of Difference to ascertain concomitance of variations,) \"and\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.\" 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\nheat in some degree or other. The conclusion obtained by this new\napplication of the method is, that _c\u00e6teris paribus_ the deposition of\ndew is also in some proportion to the power of radiating heat; and that\nthe quality of doing this abundantly (or some cause on which that\nquality depends) is another of the causes which promote the deposition\nof dew on the substance.\n\n\"Again, the influence ascertained to exist of _substance_ and _surface_\nleads us to consider that of _texture_: and here, again, we are\npresented on trial with remarkable differences, and with a third scale\nof intensity, pointing out substances of a close firm texture, such as\nstones, metals, &c., as unfavourable, but those of a loose one, as\ncloth, velvet, wool, eider-down, cotton, &c., as eminently favourable to\nthe contraction of dew.\" The Method of Concomitant Variations is here,\nfor the third time, had recourse to; and, as before, from necessity,\nsince the texture of no substance is absolutely firm or absolutely\nloose. Looseness of texture, therefore, or something which is the cause\nof that quality, is another circumstance which promotes the deposition\nof dew; but this third cause resolves itself into the first, viz. the\nquality of resisting the passage of heat: for substances of loose\ntexture \"are precisely those which are best adapted for clothing, or for\nimpeding the free passage of heat from the skin into the air, so as to\nallow their outer surfaces to be very cold, while they remain warm\nwithin;\" and this last is, therefore, an induction (from fresh\ninstances) simply _corroborative_ of a former induction.\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,\nin this only, that they either radiate heat rapidly or conduct it\nslowly: qualities between which there is no other circumstance of\nagreement, than that by virtue of either, the body tends to lose heat\nfrom the surface more rapidly than it can be restored from within. The\ninstances, on the contrary, in which no dew, or but a small quantity of\nit, is formed, and which are also extremely various, agree (as far as we\ncan observe) in nothing except in _not_ having this same property. We\nseem, therefore, to have detected the characteristic difference between\nthe substances on which dew is produced, and those on which it is not\nproduced. And thus have been realized the requisitions of what we have\ntermed the Indirect Method of Difference, or the Joint Method of\nAgreement and Difference. The example afforded of this indirect method,\nand of the manner in which the data are prepared for it by the Methods\nof Agreement and of Concomitant Variations, is the most important of all\nthe illustrations of induction afforded by this interesting speculation.\n\nWe might now consider the question, on what the deposition of dew\ndepends, to be completely solved, if we could be quite sure that the\nsubstances on which dew is produced differ from those on which it is\nnot, in _nothing_ but in the property of losing heat from the surface\nfaster than the loss can be repaired from within. And though we never\ncan have that complete certainty, this is not of so much importance as\nmight at first be supposed; for we have, at all events, ascertained\nthat even if there be any other quality hitherto unobserved which is\npresent in all the substances which contract dew, and absent in those\nwhich do not, this other property must be one which, in all that great\nnumber of substances, is present or absent exactly where the property of\nbeing a better radiator than conductor is present or absent; an extent\nof coincidence which affords a strong presumption of a community of\ncause, and a consequent invariable coexistence between the two\nproperties; so that the property of being a better radiator than\nconductor, if not itself the cause, almost certainly always accompanies\nthe cause, and, for purposes of prediction, no error is likely to be\ncommitted by treating it as if it were really such.\n\nReverting now to an earlier stage of the inquiry, let us remember that\nwe had 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,\nin every such instance, the substance is one which, by its own\nproperties or laws, would, if exposed in the night, become colder than\nthe surrounding air. The coldness therefore being accounted for\nindependently of the dew, while it is proved that there is a connexion\nbetween the two, it must be the dew which depends on the coldness; or in\nother words, the coldness 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\nair or any other gas; and though we have not yet come to the Deductive\nMethod, we will not omit what is necessary to render this speculation\ncomplete. It is known by direct experiment that only a limited quantity\nof water can remain suspended in the state of vapour at each degree of\ntemperature, and that this maximum grows less and less as the\ntemperature diminishes. From this it follows, deductively, that if there\nis already as much vapour suspended as the air will contain at its\nexisting temperature, any lowering of that temperature will cause a\nportion of the vapour to be condensed, and become water. But, again, we\nknow deductively, from the laws of heat, that the contact of the air\nwith a body colder than itself, will necessarily lower the temperature\nof the stratum of air immediately applied to its surface; and will\ntherefore cause it to part with a portion of its water, which\naccordingly will, by the ordinary laws of gravitation or cohesion,\nattach itself to the surface of the body, thereby constituting dew. This\ndeductive proof, it will have been seen, has the advantage of at once\nproving causation as well as coexistence; and it has the additional\nadvantage that it also accounts for the exceptions to the occurrence of\nthe phenomenon, the cases in which, although the body is colder than the\nair, yet no dew is deposited; by showing that this will necessarily be\nthe case when the air is so under-supplied with aqueous vapour,\ncomparatively to its temperature, that even when somewhat cooled by the\ncontact of the colder body, it can still continue to hold in suspension\nall the vapour which was previously suspended in it: thus in a very dry\nsummer there are no dews, in a very dry winter no hoar frost. Here,\ntherefore, is an additional condition of the production of dew, which\nthe methods we previously made use of failed to detect, and which might\nhave remained still undetected, if recourse had not been had to the plan\nof 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,\naccording to the canon of the Method of Difference. We can, by cooling\nthe surface of any body, find in all cases some temperature, (more or\nless inferior to that of the surrounding air, according to its\nhygrometric condition,) at which dew will begin to be deposited. Here,\ntoo, therefore, the causation is directly proved. We can, it is true,\naccomplish this only on a small scale; but we have ample reason to\nconclude that the same operation, if conducted in Nature's great\nlaboratory, 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\nwhich nature 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\neffect so rapidly that there is not time for any other material change\nin the pre-existing circumstances. \"It is observed that dew is never\ncopiously deposited in situations much screened from the open sky, and\nnot at all in a cloudy night; but _if the clouds withdraw even for a few\nminutes, and leave a clear opening, a deposition of dew presently\nbegins_, and goes on increasing.... Dew formed in clear intervals will\noften even evaporate again when the sky becomes thickly overcast.\" The\nproof, therefore, is complete, that the presence or absence of an\nuninterrupted communication with the sky causes the deposition or\nnon-deposition of dew. Now, since a clear sky is nothing but the absence\nof clouds, and it is a known property of clouds, as of all other bodies\nbetween which and any given object nothing intervenes but an elastic\nfluid, that they tend to raise or keep up the superficial temperature of\nthe object by radiating heat to it, we see at once that the\ndisappearance of clouds will cause the surface to cool; so that Nature,\nin this case, produces a change in the antecedent by definite and known\nmeans, and the consequent follows accordingly: a natural experiment\nwhich satisfies the requisitions of the Method of Difference.[38]\n\nThe accumulated proof of which the Theory of Dew has been found\nsusceptible, is a striking instance of the fulness of assurance which\nthe inductive evidence of laws of causation may attain, in cases in\nwhich the invariable sequence is by no means obvious to a superficial\nview.\n\n\n\u00a7 4. The admirable physiological investigations of Dr. Brown-S\u00e9quard\nafford brilliant examples of the application of the Inductive Methods to\na class of inquiries in which, for reasons which will presently be\ngiven, direct induction takes place under peculiar difficulties and\ndisadvantages. As one of the most apt instances I select his speculation\n(in the Proceedings of the Royal Society for May 16, 1861) on the\nrelations between muscular irritability, cadaveric rigidity, and\nputrefaction.\n\nThe law which Dr. Brown-S\u00e9quard's investigation tends to establish, is\nthe following:--\"The greater the degree of muscular irritability at the\ntime of death, the later the cadaveric rigidity sets in, and the longer\nit lasts, and the later also putrefaction appears, and the slower it\nprogresses.\" One would say at first sight that the method here required\nmust be that of Concomitant Variations. But this is a delusive\nappearance, arising from the circumstance that the conclusion to be\ntested is itself a fact of concomitant variation. For the establishment\nof that fact any of the Methods may be put in requisition, and it will\nbe found that the fourth Method, though really employed, has only a\nsubordinate place in this particular investigation.\n\nThe evidences by which Dr. Brown-S\u00e9quard establishes the law may be\nenumerated as follows:--\n\n1st. Paralysed muscles have greater irritability than healthy muscles.\nNow, paralysed muscles are later in assuming the cadaveric rigidity than\nhealthy muscles, the rigidity lasts longer, and putrefaction sets in\nlater and proceeds more slowly.\n\nBoth these propositions had to be proved by experiment; and for the\nexperiments which prove them, science is also indebted to Dr.\nBrown-S\u00e9quard. The former of the two--that paralysed muscles have\ngreater irritability than healthy muscles--he ascertained in various\nways, but most decisively by \"comparing the duration of irritability in\na paralysed muscle and in the corresponding healthy one of the opposite\nside, while they are both submitted to the same excitation.\" He \"often\nfound in experimenting in that way, that the paralysed muscle remained\nirritable twice, three times, or even four times as long as the healthy\none.\" This is a case of induction by the Method of Difference. The two\nlimbs, being those of the same animal, were presumed to differ in no\ncircumstance material to the case except the paralysis, to the presence\nand absence of which, therefore, the difference in the muscular\nirritability was to be attributed. This assumption of complete\nresemblance in all material circumstances save one, evidently could not\nbe safely made in any one pair of experiments, because the two legs of\nany given animal might be accidentally in very different pathological\nconditions; but if, besides taking pains to avoid any such difference,\nthe experiment was repeated sufficiently often in different animals to\nexclude the supposition that any abnormal circumstance could be present\nin them all, the conditions of the Method of Difference were adequately\nsecured.\n\nIn the same manner in which Dr. Brown-S\u00e9quard proved that paralysed\nmuscles have greater irritability, he also proved the correlative\nproposition respecting cadaveric rigidity and putrefaction. Having, by\nsection of the roots of the sciatic nerve, and again of a lateral half\nof the spinal cord, produced paralysis in one hind leg of an animal\nwhile the other remained healthy, he found that not only did muscular\nirritability last much longer in the paralysed limb, but rigidity set in\nlater and ended later, and putrefaction began later and was less rapid\nthan on the healthy side. This is a common case of the Method of\nDifference, requiring no comment. A further and very important\ncorroboration was obtained by the same method. When the animal was\nkilled, not shortly after the section of the nerve, but a month later,\nthe effect was reversed; rigidity set in sooner, and lasted a shorter\ntime, than in the healthy muscles. But after this lapse of time, the\nparalysed muscles, having been kept by the paralysis in a state of rest,\nhad lost a great part of their irritability, and instead of more, had\nbecome less irritable than those on the healthy side. This gives the A B\nC, a b c, and B C, b c, of the Method of Difference. One antecedent,\nincreased irritability, being changed, and the other circumstances being\nthe same, the consequence did not follow; and moreover, when a new\nantecedent, contrary to the first, was supplied, it was followed by a\ncontrary consequent. This instance is attended with the special\nadvantage, of proving that the retardation and prolongation of the\nrigidity do not depend directly on the paralysis, since that was the\nsame in both the instances; but specifically on one effect of the\nparalysis, namely, the increased irritability; since they ceased when it\nceased, and were reversed when it was reversed.\n\n2ndly. Diminution of the temperature of muscles before death increases\ntheir irritability. But diminution of their temperature also retards\ncadaveric rigidity and putrefaction.\n\nBoth these truths were first made known by Dr. Brown-S\u00e9quard himself,\nthrough experiments which conclude according to the Method of\nDifference. There is nothing in the nature of the process requiring\nspecific analysis.\n\n3rdly. Muscular exercise, prolonged to exhaustion, diminishes the\nmuscular irritability. This is a well-known truth, dependent on the most\ngeneral laws of muscular action, and proved by experiments under the\nMethod of Difference, constantly repeated. Now it has been shown by\nobservation that overdriven cattle, if killed before recovery from their\nfatigue, become rigid and putrefy in a surprisingly short time. A\nsimilar fact has been observed in the case of animals hunted to death;\ncocks killed during or shortly after a fight; and soldiers slain in the\nfield of battle. These various cases agree in no circumstance, directly\nconnected with the muscles, except that these have just been subjected\nto exhausting exercise. Under the canon, therefore, of the Method of\nAgreement, it may be inferred that there is a connexion between the two\nfacts. The Method of Agreement, indeed, as has been shown, is not\ncompetent to prove causation. The present case, however, is already\nknown to be a case of causation, it being certain that the state of the\nbody after death must somehow depend upon its state at the time of\ndeath. We are therefore warranted in concluding that the single\ncircumstance in which all the instances agree, is the part of the\nantecedent which is the cause of that particular consequent.\n\n4thly. In proportion as the nutrition of muscles is in a good state,\ntheir irritability is high. This fact also rests on the general evidence\nof the laws of physiology, grounded on many familiar applications of the\nMethod of Difference. Now, in the case of those who die from accident or\nviolence, with their muscles in a good state of nutrition, the muscular\nirritability continues long after death, rigidity sets in late, and\npersists long without the putrefactive change. On the contrary, in cases\nof disease in which nutrition has been diminished for a long time before\ndeath, all these effects are reversed. These are the conditions of the\nJoint Method of Agreement and Difference. The cases of retarded and long\ncontinued rigidity here in question, agree only in being preceded by a\nhigh state of nutrition of the muscles; the cases of rapid and brief\nrigidity agree only in being preceded by a low state of muscular\nnutrition; a connexion is therefore inductively proved between the\ndegree of the nutrition, and the slowness and prolongation of the\nrigidity.\n\n5thly. Convulsions, like exhausting exercise, but in a still greater\ndegree, diminish the muscular irritability. Now, when death follows\nviolent and prolonged convulsions, as in tetanus, hydrophobia, some\ncases of cholera, and certain poisons, rigidity sets in very rapidly,\nand after a very brief duration, gives place to putrefaction. This is\nanother example of the Method of Agreement, of the same character with\nNo. 3.\n\n6thly. The series of instances which we shall take last, is of a more\ncomplex character, and requires a more minute analysis.\n\nIt has long been observed that in some cases of death by lightning,\ncadaveric rigidity either does not take place at all, or is of such\nextremely brief duration as to escape notice, and that in these cases\nputrefaction is very rapid. In other cases, however, the usual cadaveric\nrigidity appears. There must be some difference in the cause, to account\nfor this difference in the effect. Now \"death by lightning may be the\nresult of, 1st, a syncope by fright, or in consequence of a direct or\nreflex influence of lightning on the par vagum; 2ndly, hemorrhage in or\naround the brain, or in the lungs, the pericardium, &c.; 3rdly,\nconcussion, or some other alteration in the brain;\" none of which\nphenomena have any known property capable of accounting for the\nsuppression, or almost suppression, of the cadaveric rigidity. But the\ncause of death may also be that the lightning produces \"a violent\nconvulsion of every muscle in the body,\" of which, if of sufficient\nintensity, the known effect would be that \"muscular irritability ceases\nalmost at once.\" If Dr. Brown-S\u00e9quard's generalization is a true law,\nthese will be the very cases in which rigidity is so much abridged as to\nescape notice; and the cases in which, on the contrary, rigidity takes\nplace as usual, will be those in which the stroke of lightning operates\nin some of the other modes which have been enumerated. How, then, is\nthis brought to the test? By experiments not on lightning, which cannot\nbe commanded at pleasure, but on the same natural agency in a manageable\nform, that of artificial galvanism. Dr. Brown-S\u00e9quard galvanized the\nentire bodies of animals immediately after death. Galvanism cannot\noperate in any of the modes in which the stroke of lightning may have\noperated, except the single one of producing muscular convulsions. If,\ntherefore, after the bodies have been galvanized, the duration of\nrigidity is much shortened and putrefaction much accelerated, it is\nreasonable to ascribe the same effects when produced by lightning, to\nthe property which galvanism shares with lightning, and not to those\nwhich it does not. Now this Dr. Brown-S\u00e9quard found to be the fact. The\ngalvanic experiment was tried with charges of very various degrees of\nstrength; and the more powerful the charge, the shorter was found to be\nthe duration of rigidity, and the more speedy and rapid the\nputrefaction. In the experiment in which the charge was strongest, and\nthe muscular irritability most promptly destroyed, the rigidity only\nlasted fifteen minutes. On the principle, therefore, of the Method of\nConcomitant Variations, it maybe inferred that the duration of the\nrigidity depends on the degree of the irritability; and that if the\ncharge had been as much stronger than Dr. Brown-S\u00e9quard's strongest, as\na stroke of lightning must be stronger than any electric shock which we\ncan produce artificially, the rigidity would have been shortened in a\ncorresponding ratio, and might have disappeared altogether. This\nconclusion having been arrived at, the case of an electric shock,\nwhether natural or artificial, becomes an instance in addition to all\nthose already ascertained, of correspondence between the irritability of\nthe muscle and the duration of rigidity.\n\nAll these instances are summed up in the following statement:--\"That\nwhen the degree of muscular irritability at the time of death is\nconsiderable, either in consequence of a good state of nutrition, as in\npersons who die in full health from an accidental cause, or in\nconsequence of rest, as in cases of paralysis, or on account of the\ninfluence of cold, cadaveric rigidity in all these cases sets in late\nand lasts long, and putrefaction appears late, and progresses slowly:\"\nbut \"that when the degree of muscular irritability at the time of death\nis slight, either in consequence of a bad state of nutrition, or of\nexhaustion from over-exertion, or from convulsions caused by disease or\npoison, cadaveric rigidity sets in and ceases soon, and putrefaction\nappears and progresses quickly.\" These facts present, in all their\ncompleteness, the conditions of the Joint Method of Agreement and\nDifference. Early and brief rigidity takes place in cases which agree\nonly in the circumstance of a low state of muscular irritability.\nRigidity begins late and lasts long in cases which agree only in the\ncontrary circumstance, of a muscular irritability high and unusually\nprolonged. It follows that there is a connexion through causation\nbetween the degree of muscular irritability after death, and the\ntardiness and prolongation of the cadaveric rigidity. This\ninvestigation places in a strong light the value and efficacy of the\nJoint Method. For, as we have already seen, the defect of that Method\nis, that like the Method of Agreement, of which it is only an improved\nform, it cannot prove causation. But in the present case (as in one of\nthe steps in the argument which led up to it) causation is already\nproved; since there could never be any doubt that the rigidity\naltogether, and the putrefaction which follows it, are caused by the\nfact of death: the observations and experiments on which this rests are\ntoo familiar to need analysis, and fall under the Method of Difference.\nIt being, therefore, beyond doubt that the aggregate antecedent, the\ndeath, is the actual cause of the whole train of consequents, whatever\nof the circumstances attending the death can be shown to be followed in\nall its variations by variations in the effect under investigation, must\nbe the particular feature of the fact of death on which that effect\ndepends. The degree of muscular irritability at the time of death\nfulfils this condition. The only point that could be brought into\nquestion, would be whether the effect depended on the irritability\nitself, or on something which always accompanied the irritability: and\nthis doubt is set at rest by establishing, as the instances do, that by\nwhatever cause the high or low irritability is produced, the effect\nequally follows; and cannot, therefore, depend upon the causes of\nirritability, nor upon the other effects of those causes, which are as\nvarious as the causes themselves; but upon the irritability, solely.\n\n\n\u00a7 5. The last two examples will have conveyed to any one by whom they\nhave been duly followed, so clear a conception of the use and practical\nmanagement of three of the four methods of experimental inquiry, as to\nsupersede the necessity of any further exemplification of them. The\nremaining method, that of Residues, not having found a place in any of\nthe preceding investigations, I shall quote from Sir John Herschel some\nexamples of that method, with the remarks by which they are introduced.\n\n\"It 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\nconstantly appearing in the form of phenomena altogether new, and\nleading to the most important conclusions.\n\n\"For 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\nand planets is the sole and sufficient cause of all the phenomena of its\norbitual motion; but when the effect of this cause is strictly\ncalculated and subducted from the observed motion, there is found to\nremain behind a _residual phenomenon_, which would never have been\notherwise ascertained to exist, which is a small anticipation of the\ntime of its reappearance, or a diminution of its periodic time, which\ncannot be accounted for by gravity, and whose cause is therefore to be\ninquired into. Such an anticipation would be caused by the resistance of\na medium disseminated through the celestial regions; and as there are\nother good reasons for believing this to be a _vera causa_,\" (an\nactually existing antecedent,) \"it has therefore been ascribed to such a\nresistance.[39]\n\n\"M. Arago, having suspended a magnetic needle by a silk thread, and set\nit in vibration, observed, that it came much sooner to a state of rest\nwhen suspended over a plate of copper, than when no such plate was\nbeneath it. Now, in both cases there were two _ver\u00e6 caus\u00e6_\" (antecedents\nknown to exist) \"why it _should_ come at length to rest, viz. the\nresistance of the air, which opposes, and at length destroys, all\nmotions performed in it; and the want of perfect mobility in the silk\nthread. But the effect of these causes being exactly known by the\nobservation made in the absence of the copper, and being thus allowed\nfor and subducted, a residual phenomenon appeared, in the fact that a\nretarding influence was exerted by the copper itself; and this fact,\nonce ascertained, speedily led to the knowledge of an entirely new and\nunexpected class of relations.\" This example belongs, however, not to\nthe Method of Residues but to the Method of Difference, the law being\nascertained by a direct comparison of the results of two experiments,\nwhich differed in nothing but the presence or absence of the plate of\ncopper. To have made it exemplify the Method of Residues, the effect of\nthe resistance of the air and that of the rigidity of the silk should\nhave been calculated _\u00e0 priori_, from the laws obtained by separate and\nforegone experiments.\n\n\"Unexpected 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\nto the 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\nmode of propagation, from which its velocity in the air could be\nprecisely calculated. The calculations were performed; but, when\ncompared with fact, though the agreement was quite sufficient to show\nthe general correctness of the cause and mode of propagation assigned,\nyet the _whole_ velocity could not be shown to arise from this theory.\nThere was still a residual velocity to be accounted for, which placed\ndynamical philosophers for a long time in great dilemma. At length\nLaplace struck on the happy idea, that this might arise from the _heat_\ndeveloped in the act of that condensation which necessarily takes place\nat every vibration by which sound is conveyed. The matter was subjected\nto exact calculation, and the result was at once the complete\nexplanation of the residual phenomenon, and a striking confirmation of\nthe general law of the development of heat by compression, under\ncircumstances beyond artificial imitation.\"\n\n\"Many 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\nlurking places of new chemical ingredients: witness iodine, brome,\nselenium, and the new metals accompanying platina in the experiments of\nWollaston and Tennant. It was a happy thought of Glauber to examine what\neverybody else threw away.\"[40]\n\n\"Almost all the greatest discoveries in Astronomy,\" says the same\nauthor,[41] \"have resulted from the consideration of residual phenomena\nof a quantitative or numerical kind.... It was thus that the grand\ndiscovery of the precession of the equinoxes resulted as a residual\nphenomenon, from the imperfect explanation of the return of the seasons\nby the return of the sun to the same apparent place among the fixed\nstars. Thus, also, aberration and nutation resulted as residual\nphenomena from that portion of the changes of the apparent places of the\nfixed stars which was left unaccounted for by precession. And thus again\nthe apparent proper motions of the stars are the observed residues of\ntheir apparent movements outstanding and unaccounted for by strict\ncalculation of the effects of precession, nutation, and aberration. The\nnearest approach which human theories can make to perfection is to\ndiminish this residue, this _caput mortuum_ of observation, as it may be\nconsidered, as much as practicable, and, if possible, to reduce it to\nnothing, either by showing that something has been neglected in our\nestimation of known causes, or by reasoning upon it as a new fact, and\non the principle of the inductive philosophy ascending from the effect\nto its cause or causes.\"\n\nThe disturbing effects mutually produced by the earth and planets upon\neach other's motions were first brought to light as residual phenomena,\nby the difference which appeared between the observed places of those\nbodies, and the places calculated on a consideration solely of their\ngravitation towards the sun. It was this which determined astronomers\nto consider the law of gravitation as obtaining between all bodies\nwhatever, and therefore between all particles of matter; their first\ntendency having been to regard it as a force acting only between each\nplanet or satellite and the central body to whose system it belonged.\nAgain, the catastrophists, in geology, be their opinion right or wrong,\nsupport it on the plea, that after the effect of all causes now in\noperation has been allowed for, there remains in the existing\nconstitution of the earth a large residue of facts, proving the\nexistence at former periods either of other forces, or of the same\nforces in a much greater degree of intensity. To add one more example:\nthose who assert, what no one has shown any real ground for believing,\nthat there is in one human individual, one sex, or one race of mankind\nover 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\ntraced by 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\ndoctrine.\n\nThe spirit of the Method of Residues being, it is hoped, sufficiently\nintelligible from these examples, and the other three methods having\nalready been so fully exemplified, we may here close our exposition of\nthe four methods, considered as employed in the investigation of the\nsimpler and more elementary order of the combinations of phenomena.\n\n\n\u00a7 6. Dr. Whewell has expressed a very unfavourable opinion of the\nutility of the Four Methods, as well as of the aptness of the examples\nby which I have attempted to illustrate them. His words are these:--[42]\n\n\"Upon these methods, the obvious thing to remark is, that they take for\ngranted the very thing which is most difficult to discover, the\nreduction of the phenomena to formul\u00e6 such as are here presented to us.\nWhen we have any set of complex facts offered to us; for instance, those\nwhich were offered in the cases of discovery which I have\nmentioned,--the facts of the planetary paths, of falling bodies, of\nrefracted rays, of cosmical motions, of chemical analysis; and when, in\nany of these cases, we would discover the law of nature which governs\nthem, or, if any one chooses so to term it, the feature in which all the\ncases agree, where are we to look for our A, B, C, and _a_, _b_, _c_?\nNature does not present to us the cases in this form; and how are we to\nreduce them to this form? You say, _when_ we find the combination of A B\nC with _a b c_ and A B D with _a b d_, then we may draw our inference.\nGranted; but when and where are we to find such combinations? Even now\nthat the discoveries are made, who will point out to us what are the A,\nB, C, and _a_, _b_, _c_ elements of the cases which have just been\nenumerated? Who will tell us which of the methods of inquiry those\nhistorically real and successful inquiries exemplify? Who will carry\nthese formul\u00e6 through the history of the sciences, as they have really\ngrown up; and show us that these four methods have been operative in\ntheir formation; or that any light is thrown upon the steps of their\nprogress by reference to these formul\u00e6?\"\n\nHe adds that, in this work, the methods have not been applied \"to a\nlarge body of conspicuous and undoubted examples of discovery, extending\nalong the whole history of science;\" which ought to have been done in\norder that the methods might be shown to possess the \"advantage\" (which\nhe claims as belonging to his own) of being those \"by which all great\ndiscoveries in science have really been made.\"--(p. 277.)\n\nThere is a striking similarity between the objections here made against\nCanons of Induction, and what was alleged, in the last century, by as\nable men as Dr. Whewell, against the acknowledged Canon of\nRatiocination. Those who protested against the Aristotelian Logic said\nof the Syllogism, what Dr. Whewell says of the Inductive Methods, that\nit \"takes for granted the very thing which is most difficult to\ndiscover, the reduction of the argument to formul\u00e6 such as are here\npresented to us.\" The grand difficulty, they said, is to obtain your\nsyllogism, not to judge of its correctness when obtained. On the matter\nof fact, both they and Dr. Whewell are right. The greatest difficulty in\nboth cases is first that of obtaining the evidence, and next, of\nreducing it to the form which tests its conclusiveness. But if we try to\nreduce it without knowing _to what_, we are not likely to make much\nprogress. It is a more difficult thing to solve a geometrical problem,\nthan to judge whether a proposed solution is correct: but if people were\nnot able to judge of the solution when found, they would have little\nchance of finding it. And it cannot be pretended that to judge of an\ninduction when found, is perfectly easy, is a thing for which aids and\ninstruments are superfluous; for erroneous inductions, false inferences\nfrom experience, are quite as common, on some subjects much commoner,\nthan true ones. The business of Inductive Logic is to provide rules and\nmodels (such as the Syllogism and its rules are for ratiocination) to\nwhich if inductive arguments conform, those arguments are conclusive,\nand not otherwise. This is what the Four Methods profess to be, and what\nI believe they are universally considered to be by experimental\nphilosophers, who had practised all of them long before any one sought\nto reduce the practice to theory.\n\nThe assailants of the Syllogism had also anticipated Dr. Whewell in the\nother branch of his argument. They said that no discoveries were ever\nmade by syllogism; and Dr. Whewell says, or seems to say, that none were\never made by the four Methods of Induction. To the former objectors,\nArchbishop Whately very pertinently answered, that their argument, if\ngood at all, was good against the reasoning process altogether; for\nwhatever cannot be reduced to syllogism, is not reasoning. And Dr.\nWhewell's argument, if good at all, is good against all inferences from\nexperience. In saying that no discoveries were ever made by the four\nMethods, he affirms that none were ever made by observation and\nexperiment; for assuredly if any were, it was by processes reducible to\none or other of those methods.\n\nThis difference between us accounts for the dissatisfaction which my\nexamples give him; for I did not select them with a view to satisfy any\none who required to be convinced that observation and experiment are\nmodes of acquiring knowledge: I confess that in the choice of them I\nthought only of illustration, and of facilitating the _conception_ of\nthe Methods by concrete instances. If it had been my object to justify\nthe processes themselves as means of investigation, there would have\nbeen no need to look far off, or make use of recondite or complicated\ninstances. As a specimen of a truth ascertained by the Method of\nAgreement, I might have chosen the proposition \"Dogs bark.\" This dog,\nand that dog, and the other dog, answer to A B C, A D E, A F G. The\ncircumstance of being a dog, answers to A. Barking answers to _a_. As a\ntruth made known by the Method of Difference, \"Fire burns\" might have\nsufficed. Before I touch the fire I am not burnt; this is B C; I touch\nit, and am burnt; this is A B C, _a_ B C.\n\nSuch familiar experimental processes are not regarded as inductions by\nDr. Whewell; but they are perfectly homogeneous with those by which,\neven on his own showing, the pyramid of science is supplied with its\nbase. In vain he attempts to escape from this conclusion by laying the\nmost arbitrary restrictions on the choice of examples admissible as\ninstances of Induction: they must neither be such as are still matter of\ndiscussion (p. 265), nor must any of them be drawn from mental and\nsocial subjects (p. 269), nor from ordinary observation and practical\nlife (pp. 241-247). They must be taken exclusively from the\ngeneralizations by which scientific thinkers have ascended to great and\ncomprehensive laws of natural phenomena. Now it is seldom possible, in\nthese complicated inquiries, to go much beyond the initial steps,\nwithout calling in the instrument of Deduction, and the temporary aid of\nhypotheses; as I myself, in common with Dr. Whewell, have maintained\nagainst the purely empirical school. Since therefore such cases could\nnot conveniently be selected to illustrate the principles of mere\nobservation and experiment, Dr. Whewell is misled by their absence into\nrepresenting the Experimental Methods as serving no purpose in\nscientific investigation; forgetting that if those methods had not\nsupplied the first generalizations, there would have been no materials\nfor his own conception of Induction to work upon.\n\nHis challenge, however, to point out which of the four methods are\nexemplified in certain important cases of scientific inquiry, is easily\nanswered. \"The planetary paths,\" as far as they are a case of induction\nat all,[43] fall under the Method of Agreement. The law of \"falling\nbodies,\" namely that they describe spaces proportional to the squares of\nthe times, was historically a deduction from the first law of motion;\nbut the experiments by which it was verified, and by which it might have\nbeen discovered, were examples of the Method of Agreement; and the\napparent variation from the true law, caused by the resistance of the\nair, was cleared up by experiments _in vacuo_, constituting an\napplication of the Method of Difference. The law of \"refracted rays\"\n(the constancy of the ratio between the sines of incidence and of\nrefraction for each refracting substance) was ascertained by direct\nmeasurement, and therefore by the Method of Agreement. The \"cosmical\nmotions\" were determined by highly complex processes of thought, in\nwhich Deduction was predominant, but the Methods of Agreement and of\nConcomitant Variations had a large part in establishing the empirical\nlaws. Every case without exception of \"chemical analysis\" constitutes a\nwell-marked example of the Method of Difference. To any one acquainted\nwith the subjects--to Dr. Whewell himself, there would not be the\nsmallest difficulty in setting out \"the A B C and _a b c_ elements\" of\nthese cases.\n\nIf discoveries are ever made by observation and experiment without\nDeduction, the four methods are methods of discovery: but even if they\nwere not methods of discovery, it would not be the less true that they\nare the sole methods of Proof; and in that character, even the results\nof deduction are amenable to them. The great generalizations which begin\nas Hypotheses, must end by being proved, and are in reality (as will be\nshown hereafter) proved, by the Four Methods. Now it is with Proof, as\nsuch, that Logic is principally concerned. This distinction has indeed\nno chance of finding favour with Dr. Whewell; for it is the peculiarity\nof his system, not to recognise, in cases of Induction, any necessity\nfor proof. If, after assuming an hypothesis and carefully collating it\nwith facts, nothing is brought to light inconsistent with it, that is,\nif experience does not _disprove_ it, he is content: at least until a\nsimpler hypothesis, equally consistent with experience, presents itself.\nIf this be Induction, doubtless there is no necessity for the four\nmethods. But to suppose that it is so, appears to me a radical\nmisconception of the nature of the evidence of physical truths.\n\nSo real and practical is the need of a test for induction, similar to\nthe syllogistic test of ratiocination, that inferences which bid\ndefiance to the most elementary notions of inductive logic are put forth\nwithout misgiving by persons eminent in physical science, as soon as\nthey are off the ground on which they are conversant with the facts, and\nnot reduced to judge only by the arguments; and as for educated persons\nin general, it may be doubted if they are better judges of a good or a\nbad induction than they were before Bacon wrote. The improvement in the\nresults of thinking has seldom extended to the processes; or has\nreached, if any process, that of investigation only, not that of proof.\nA knowledge of many laws of nature has doubtless been arrived at, by\nframing hypotheses and finding that the facts corresponded to them; and\nmany errors have been got rid of by coming to a knowledge of facts which\nwere inconsistent with them, but not by discovering that the mode of\nthought which led to the errors was itself faulty, and might have been\nknown to be such independently of the facts which disproved the\nspecific conclusion. Hence it is, that while the thoughts of mankind\nhave on many subjects worked themselves practically right, the thinking\npower remains as weak as ever: and on all subjects on which the facts\nwhich would check the result are not accessible, as in what relates to\nthe invisible world, and even, as has been seen lately, to the visible\nworld of the planetary regions, men of the greatest scientific\nacquirements argue as pitiably as the merest ignoramus. For though they\nhave made many sound inductions, they have not learnt from them (and Dr.\nWhewell thinks there is no necessity that they should learn) the\nprinciples of inductive _evidence_.\n\n\n\n\nCHAPTER X.\n\nOF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS.\n\n\n\u00a7 1. In the preceding exposition of the four methods of observation and\nexperiment, by which we contrive to distinguish among a mass of\ncoexistent phenomena the particular effect due to a given cause, or the\nparticular cause which gave birth to a given effect; it has been\nnecessary to suppose, in the first instance, for the sake of\nsimplification, that this analytical operation is encumbered by no other\ndifficulties than what are essentially inherent in its nature; and to\nrepresent to ourselves, therefore, every effect, on the one hand as\nconnected exclusively with a single cause, and on the other hand as\nincapable of being mixed and confounded with any other coexistent\neffect. We have regarded _a b c d e_, the aggregate of the phenomena\nexisting at any moment, as consisting of dissimilar facts, _a_, _b_,\n_c_, _d_, and _e_, for each of which one, and only one, cause needs be\nsought; the difficulty being only that of singling out this one cause\nfrom the multitude of antecedent circumstances, A, B, C, D, and E. The\ncause indeed may not be simple; it may consist of an assemblage of\nconditions; but we have supposed that there was only one possible\nassemblage of conditions, from which the given effect could result.\n\nIf such were the fact, it would be comparatively an easy task to\ninvestigate the laws of nature. But the supposition does not hold, in\neither of its parts. In the first place, it is not true that the same\nphenomenon is always produced by the same cause: the effect _a_ may\nsometimes arise from A, sometimes from B. And, secondly, the effects of\ndifferent causes are often not dissimilar, but homogeneous, and marked\nout by no assignable boundaries from one another: A and B may produce\nnot _a_ and _b_, but different portions of an effect _a_. The obscurity\nand difficulty of the investigation of the laws of phenomena is\nsingularly increased by the necessity of adverting to these two\ncircumstances; Intermixture of Effects, and Plurality of Causes. To the\nlatter, being the simpler of the two considerations, we shall first\ndirect 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\nmay produce motion: many causes may produce some kinds of sensation:\nmany causes may produce death. A given effect may really be produced by\na certain cause, and yet be perfectly capable of being produced without\nit.\n\n\n\u00a7 2. One of the principal consequences of this fact of Plurality of\nCauses is, to render the first of the inductive methods, that of\nAgreement, uncertain. To illustrate that method, we supposed two\ninstances, A B C followed by _a b c_, and A D E followed by _a d e_.\nFrom these instances it might apparently be concluded that A is an\ninvariable antecedent of _a_, and even that it is the unconditional\ninvariable antecedent, or cause, if we could be sure that there is no\nother antecedent common to the two cases. That this difficulty may not\nstand in the way, let us suppose the two cases positively ascertained to\nhave no antecedent in common except A. The moment, however, that we let\nin the possibility of a plurality of causes, the conclusion fails. For\nit involves a tacit supposition, that _a_ must have been produced in\nboth instances by the same cause. If there can possibly have been two\ncauses, those two may, for example, be C and E: the one may have been\nthe cause of _a_ in the former of the instances, the other in the\nlatter, A having no influence in either case.\n\nSuppose, for example, that two great artists, or great philosophers,\nthat two extremely selfish, or extremely generous characters, were\ncompared together as to the circumstances of their education and\nhistory, and the two cases were found to agree only in one circumstance:\nwould it follow that this one circumstance was the cause of the quality\nwhich characterized both those individuals? Not at all; for the causes\nwhich may produce any type of character are innumerable; and the two\npersons might equally have agreed in their character, though there had\nbeen no manner of resemblance 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\ninstance at least, A was either the cause of _a_, or an indispensable\nportion of its cause, even though the cause which produces it in other\ninstances may be altogether different. Plurality of Causes, therefore,\nnot only does not diminish the reliance due to the Method of Difference,\nbut does not even render a greater number of observations or experiments\nnecessary: two instances, the one positive and the other negative, are\nstill sufficient for the most complete and rigorous induction. Not so,\nhowever, with the Method of Agreement. The conclusions which that\nyields, when the number of instances compared is small, are of no real\nvalue, except as, in the character of suggestions, they may lead either\nto experiments bringing them to the test of the Method of Difference, or\nto reasonings which may explain 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\nD E, though these instances have no antecedent in common except A, yet\nas the effect may possibly have been produced in the two cases by\ndifferent causes, the result is at most only a slight probability in\nfavour of A; there may be causation, but it is almost equally probable\nthat there was only a coincidence. But the oftener we repeat the\nobservation, varying the circumstances, the more we advance towards a\nsolution of this doubt. For if we try A F G, A H K, &c., all unlike one\nanother except in containing the circumstance A, and if we find the\neffect _a_ entering into the result in all these cases, we must suppose\none of two things, either that it is caused by A, or that it has as many\ndifferent causes as there are instances. With each addition, therefore,\nto the number of instances, the presumption is strengthened in favour of\nA. The inquirer, of course, will not neglect, if an opportunity present\nitself, to exclude A from some one of these combinations, from A H K for\ninstance, and by trying H K separately, appeal to the Method of\nDifference in aid of the Method of Agreement. By the Method of\nDifference alone can it be ascertained that A is the cause of _a_; but\nthat it is either the cause, or another effect of the same cause, may be\nplaced beyond any reasonable doubt by the Method of Agreement, provided\nthe instances are very numerous, as well as sufficiently various.\n\nAfter how great a multiplication, then, of varied instances, all\nagreeing in no other antecedent except A, is the supposition of a\nplurality of causes sufficiently rebutted, and the conclusion that _a_\nis connected with A divested of the characteristic imperfection, and\nreduced to a virtual certainty? This is a question which we cannot be\nexempted from answering: but the consideration of it belongs to what is\ncalled the Theory of Probability, which will form the subject of a\nchapter hereafter. It is seen, however, at once, that the conclusion\ndoes amount to a practical certainty after a sufficient number of\ninstances, and that the method, therefore, is not radically vitiated by\nthe characteristic imperfection. The result of these considerations is\nonly, in the first place, to point out a new source of inferiority in\nthe Method of Agreement as compared with other modes of investigation,\nand new reasons for never resting contented with the results obtained by\nit, without attempting to confirm them either by the Method of\nDifference, or by connecting them deductively with some law or laws\nalready ascertained by that superior method. And, in the second place,\nwe learn from this the true theory of the value of mere _number_ of\ninstances in inductive inquiry. The Plurality of Causes is the only\nreason 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\nproportioned to the mere _mass_ of the experience on which they appear\nto rest; not considering that by the addition of instances to instances,\nall of the same kind, that is, differing from one another only in points\nalready recognised as immaterial, nothing whatever is added to the\nevidence of the conclusion. A single instance eliminating some\nantecedent which existed in all the other cases, is of more value than\nthe greatest multitude of instances which are reckoned by their number\nalone. It is necessary, no doubt, to assure ourselves, by repetition of\nthe observation or experiment, that no error has been committed\nconcerning the individual facts observed; and until we have assured\nourselves of this, instead of varying the circumstances, we cannot too\nscrupulously repeat the same experiment or observation without any\nchange. But when once this assurance has been obtained, the\nmultiplication of instances which do not exclude any more circumstances\nis entirely useless, provided there have been already enough to exclude\nthe supposition of Plurality of Causes.\n\nIt is of importance to remark, that the peculiar modification of the\nMethod of Agreement, which, as partaking in some degree of the nature of\nthe Method of Difference, I have called the Joint Method of Agreement\nand Difference, is not affected by the characteristic imperfection now\npointed out. For, in the joint method, it is supposed not only that the\ninstances in which _a_ is, agree only in containing A, but also that the\ninstances in which _a_ is not, agree only in not containing A. Now, if\nthis be so, A must be not only the cause of _a_, but the only possible\ncause: for if there were another, as for example B, then in the\ninstances in which _a_ is not, B must have been absent as well as A, and\nit would not be true that these instances agree _only_ in not containing\nA. This, therefore, constitutes an immense advantage of the joint\nmethod over the simple Method of Agreement. It may seem, indeed, that\nthe advantage does not belong so much to the joint method, as to one of\nits two premises, (if they may be so called,) the negative premise. The\nMethod of Agreement, when applied to negative instances, or those in\nwhich a phenomenon does _not_ take place, is certainly free from the\ncharacteristic imperfection which affects it in the affirmative case.\nThe negative premise, it might therefore be supposed, could be worked as\na simple case of the Method of Agreement, without requiring an\naffirmative premise to be joined with it. But though this is true in\nprinciple, it is generally altogether impossible to work the Method of\nAgreement by negative instances without positive ones: it is so much\nmore difficult to exhaust the field of negation than that of\naffirmation. For instance, let the question be, what is the cause of the\ntransparency of bodies; with what prospect of success could we set\nourselves to inquire directly in what the multifarious substances which\nare _not_ transparent, agree? But we might hope much sooner to seize\nsome point of resemblance among the comparatively few and definite\nspecies of objects which _are_ transparent; and this being attained, we\nshould quite naturally be put upon examining whether the _absence_ of\nthis one circumstance be not precisely the point in which all opaque\nsubstances 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\nthe Method of Difference properly so called, it proceeds by ascertaining\nhow and in what the cases where the phenomenon is present, differ from\nthose in which it is absent) is, after the Direct Method of Difference,\nthe most powerful of the remaining instruments of inductive\ninvestigation; and in the sciences which depend on pure observation,\nwith little or no aid from experiment, this method, so well exemplified\nin the speculation on the cause of dew, is the primary resource, so far\nas direct appeals to experience are concerned.\n\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\na case actually occurring in nature, and which, as often as it does\noccur, our 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\nfor detecting 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\nit, another that percussion, another that electricity, another that\nchemical action is such a source. Or (secondly) the plurality may come\nto light in the course of collating a number of instances, when we\nattempt to find some circumstance in which they all agree, and fail in\ndoing so. We find it impossible to trace, in all the cases in which the\neffect is met with, any common circumstance. We find that we can\neliminate _all_ the antecedents; that no one of them is present in all\nthe instances, no one of them indispensable to the effect. On closer\nscrutiny, however, it appears that though no one is always present, one\nor other of several always is. If, on further analysis, we can detect in\nthese any common element, we may be able to ascend from them to some one\ncause which is the really operative circumstance in them all. Thus it is\nnow thought that in the production of heat by friction, percussion,\nchemical action, &c., the ultimate source is one and the same. But if\n(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\nEffects, and the interference of causes with one another: a case\nconstituting the principal part of the complication and difficulty of\nthe study of nature; and with which the four only possible methods of\ndirectly inductive investigation by observation and experiment, are for\nthe most part, as will appear presently, quite unequal to cope. The\ninstrument of Deduction alone is adequate to unravel the complexities\nproceeding from this source; and the four methods have little more in\ntheir power than to supply premises for, and a verification of, our\ndeductions.\n\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\ndifferent forces in mechanics, the separate effects of all the causes\ncontinue to be produced, but are compounded with one another, and\ndisappear in one total. In the other, illustrated by the case of\nchemical action, the separate effects cease entirely, and are succeeded\nby phenomena altogether different, and governed by different laws.\n\nOf these cases the former is by far the more frequent, and this case it\nis which, for the most part, eludes the grasp of our experimental\nmethods. The other and exceptional case is essentially amenable to them.\nWhen the laws of the original agents cease entirely, and a phenomenon\nmakes its appearance, which, with reference to those laws, is quite\nheterogeneous; when, for example, two gaseous substances, hydrogen and\noxygen, on being brought together, throw off their peculiar properties,\nand produce the substance called water; in such cases the new fact may\nbe subjected to experimental inquiry, like any other phenomenon; and the\nelements which are said to compose it may be considered as the mere\nagents of its production; the conditions on which it depends, the facts\nwhich make up its 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.\nIn the first place, the origin and actual production of the phenomenon\nare most frequently inaccessible to our observation. If we could not\nhave learned the composition of water until we found instances in which\nit was actually produced from oxygen and hydrogen, we should have been\nforced to wait until the casual thought struck some one of passing an\nelectric spark through a mixture of the two gases, or inserting a\nlighted taper into it, merely to try what would happen. Besides, many\nsubstances, though they can be analysed, cannot by any known artificial\nmeans be recompounded. Further, even if we could have ascertained, by\nthe Method of Agreement, that oxygen and hydrogen were both present when\nwater is produced, no experimentation on oxygen and hydrogen separately,\nno knowledge of their laws, could have enabled us deductively to infer\nthat they would produce water. We require a specific experiment on the\ntwo 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\nthe gradual progress of experimentation on the different combinations of\nwhich the producing agents are susceptible; if it were not for a\npeculiarity belonging to effects of this description, that they often,\nunder some particular combination of circumstances, reproduce their\ncauses. If water results from the juxtaposition of hydrogen and oxygen\nwhenever this can be made sufficiently close and intimate, so, on the\nother hand, if water itself be placed in certain situations, hydrogen\nand oxygen are reproduced from it: an abrupt termination is put to the\nnew laws, and the agents reappear separately with their own properties\nas at first. What is called chemical analysis is the process of\nsearching for the causes of a phenomenon among its effects, or rather\namong the effects produced by the action of some other causes upon it.\n\nLavoisier, by heating mercury to a high temperature in a close vessel\ncontaining air, found that the mercury increased in weight, and became\nwhat was then called red precipitate, while the air, on being examined\nafter the experiment, proved to have lost weight, and to have become\nincapable of supporting life or combustion. When red precipitate was\nexposed to a still greater heat, it became mercury again, and gave off a\ngas which did support life and flame. Thus the agents which by their\ncombination produced red precipitate, namely the mercury and the gas,\nreappear as effects resulting from that precipitate when acted upon by\nheat. So, if we decompose water by means of iron filings, we produce two\neffects, rust and hydrogen: now rust is already known by experiments\nupon the component substances, to be an effect of the union of iron and\noxygen: the iron we ourselves supplied, but the oxygen must have been\nproduced from the water. The result therefore is that water has\ndisappeared, and hydrogen and oxygen have appeared in its stead: or in\nother words, the original laws of these gaseous agents, which had been\nsuspended by the superinduction of the new laws called the properties of\nwater, have again started into existence, and the causes of water are\nfound among its effects.\n\nWhere two phenomena, between the laws or properties of which considered\nin themselves no connexion can be traced, are thus reciprocally cause\nand effect, each capable in its turn of being produced from the other,\nand each, when it produces the other, ceasing itself to exist (as water\nis produced from oxygen and hydrogen, and oxygen and hydrogen are\nreproduced from water); this causation of the two phenomena by one\nanother, each being generated by the other's destruction, is properly\ntransformation. The idea of chemical composition is an idea of\ntransformation, but of a transformation which is incomplete; since we\nconsider the oxygen and hydrogen to be present in the water _as_ oxygen\nand hydrogen, and capable of being discovered in it if our senses were\nsufficiently keen: a supposition (for it is no more) grounded solely on\nthe fact, that the weight of the water is the sum of the separate\nweights of the two ingredients. If there had not been this exception to\nthe entire disappearance, in the compound, of the laws of the separate\ningredients; if the combined agents had not, in this one particular of\nweight, preserved their own laws, and produced a joint result equal to\nthe sum of their separate results; we should never, probably, have had\nthe notion now implied by the words chemical composition: and, in the\nfacts of water produced from hydrogen and oxygen, and hydrogen and\noxygen produced from water, as the transformation would have been\ncomplete, we should have seen only a transformation.\n\nThe very promising generalization now commonly known as the Conservation\nor Persistence of Force, bears a close resemblance to what the\nconception of chemical composition would become, if divested of the one\ncircumstance which now distinguishes it from simple transformation. It\nhas long been known that heat is capable of producing electricity, and\nelectricity heat; that mechanical motion in numerous cases produces and\nis produced by them both; and so of all other physical forces. It has of\nlate become the general belief of scientific inquirers that mechanical\nforce, electricity, magnetism, heat, light, and chemical action (to\nwhich has subsequently been added vital action) are not so much causes\nof one another as convertible into one another; and they are now\ngenerally spoken of as forms of one and the same force, varying only in\nits manifestations. This doctrine may be admitted, without by any means\nimplying that Force is a real entity, a Thing in itself, distinct from\nall its phenomenal manifestations to our organs. Supposing the doctrine\ntrue, the several kinds of phenomena which it identifies in respect of\ntheir origin would nevertheless remain different facts; facts which\nwould be causes of one another--reciprocally causes and effects, which\nis the first element in the form of causation properly called\ntransformation. What the doctrine contains more than this, is, that in\neach of these cases of reciprocal causation, the causes are reproduced\nwithout alteration in quantity. This is what takes place in the\ntransformations of matter: when water has been converted into hydrogen\nand oxygen, these can be reconverted into precisely the same quantity of\nwater from which they were produced. To establish a corresponding law in\nregard to Force, it has to be proved that heat is capable of being\nconverted into electricity, electricity into chemical action, chemical\naction into mechanical force, and mechanical force back again into the\nexact quantity of heat which was originally expended; and so through\nall the interchanges. Were this proved, it would establish what\nconstitutes transformation, as distinguished from the simple fact of\nreciprocal causation. The fact in issue is simply the quantitative\nequivalence of all these natural agencies; whereby a given quantity of\nany one is convertible into, and interchangeable with, a given, and\nalways the same, quantity of any other: this, no less, but also no more.\nIt cannot yet be said that the law has been fully proved of any case,\nexcept that of interchange between heat and mechanical motion. It does\nseem to be ascertained, not only that these two are convertible into\neach other, but that after any number of conversions the original\nquantities reappear without addition or diminution, like the original\nquantities of hydrogen and oxygen after passing through the condition of\nwater. If the same thing comes to be proved true of all the other\nforces, in relation to these two and to one another, the law of\nConservation will be established; and it will be a legitimate mode of\nexpressing the fact, to speak of Force, as we already speak of Matter,\nas indestructible. But Force will not the less remain, to the\nphilosopher, a mere abstraction of the mind. All that will have been\nproved is, that in the phenomena of Nature, nothing actually ceases\nwithout generating a calculable, and always the same, quantity of some\nother natural phenomenon, which again, when it ceases, will in its turn\neither generate a calculable, and always the same, quantity of some\nthird phenomenon, or reproduce the original quantity of the first.\n\nIn these cases, where the heteropathic effect (as we called it in a\nformer chapter)[44] is but a transformation of its cause, or in other\nwords, where the effect and its cause are reciprocally such, and\nmutually convertible into each other; the problem of finding the cause\nresolves itself into the far easier one of finding an effect, which is\nthe kind of inquiry that admits of being prosecuted by direct\nexperiment. But there are other cases of heteropathic effects to which\nthis mode of investigation is not applicable. Take, for instance, the\nheteropathic laws of mind; that portion of the phenomena of our mental\nnature which are analogous to chemical rather than to dynamical\nphenomena; as when a complex passion is formed by the coalition of\nseveral elementary impulses, or a complex emotion by several simple\npleasures or pains, of which it is the result without being the\naggregate, or in any respect homogeneous with them. The product, in\nthese cases, is generated by its various factors; but the factors cannot\nbe reproduced from the product; just as a youth can grow into an old\nman, but an old man cannot grow into a youth. We cannot ascertain from\nwhat simple feelings any of our complex states of mind are generated, as\nwe ascertain the ingredients of a chemical compound, by making it, in\nits turn, generate them. We can only, therefore, discover these laws by\nthe slow process of studying the simple feelings themselves, and\nascertaining synthetically, by experimenting on the various combinations\nof which they are susceptible, what they, by their mutual action upon\none another, are capable of generating.\n\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\nto the 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\nof surrounding phenomena. It admits therefore of being easily brought\nunder the canons of Induction, provided instances can be obtained such\nas those canons require: and the non-occurrence of such instances, or\nthe want of means to produce them artificially, is the real and only\ndifficulty in such investigations; a difficulty not logical, but in some\nsort physical. It is otherwise with cases of what, in a preceding\nchapter, has been denominated the Composition of Causes. There, the\neffects of the separate causes do not terminate and give place to\nothers, thereby ceasing to form any part of the phenomenon to be\ninvestigated; on the contrary, they still take place, but are\nintermingled with, and disguised by, the homogeneous and closely allied\neffects of other causes. They are no longer _a_, _b_, _c_, _d_, _e_,\nexisting side by side, and continuing to be separately discernible; they\nare + _a_, - _a_, 1/2 _b_, - _b_, 2 _b_, &c., some of which cancel one\nanother, while many others do not appear distinguishably, but merge in\none sum: forming altogether a result, between which and the causes\nwhereby it was produced there is often an insurmountable difficulty in\ntracing by observation any fixed relation whatever.\n\nThe general idea of the Composition of Causes has been seen to be, that\nthough two or more laws interfere with one another, and apparently\nfrustrate or modify one another's operation, yet in reality all are\nfulfilled, the collective effect being the exact sum of the effects of\nthe causes taken separately. A familiar instance is that of a body kept\nin equilibrium by two equal and contrary forces. One of the forces if\nacting alone would carry the body in a given time a certain distance to\nthe west, the other if acting alone would carry it exactly as far\ntowards the east; and the result is the same as if it had been first\ncarried to the west as far as the one force would carry it, and then\nback towards the east as far as the other would carry it, that is,\nprecisely the same distance; being ultimately left where it was found at\nfirst.\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\nin which it really is entirely fulfilled, do not, at first sight, appear\nto be cases of its operation at all. It is so in the example just\nadduced: a force, in mechanics, means neither more nor less than a cause\nof motion, yet the sum of the effects of two causes of motion may be\nrest. Again, a body solicited by two forces in directions making an\nangle with one another, moves in the diagonal; and it seems a paradox to\nsay that motion in the diagonal is the sum of two motions in two other\nlines. Motion, however, is but change of place, and at every instant the\nbody is in the exact place it would have been in if the forces had acted\nduring alternate instants instead of acting in the same instant; (saving\nthat if we suppose two forces to act successively which are in truth\nsimultaneous, we must of course allow them double the time.) It is\nevident, therefore, that each force has had, during each instant, all\nthe effect which belonged to it; and that the modifying influence which\none of two concurrent causes is said to exercise with respect to the\nother, may be considered as exerted not over the action of the cause\nitself, but over the effect after it is completed. For all purposes of\npredicting, calculating, or explaining their joint result, causes which\ncompound their effects may be treated as if they produced simultaneously\neach of them its own effect, and all these effects coexisted visibly.\n\nSince the laws of causes are as really fulfilled when the causes are\nsaid to be counteracted by opposing causes, as when they are left to\ntheir own undisturbed action, we must be cautious not to express the\nlaws in such terms as would render the assertion of their being\nfulfilled in those cases a contradiction. If, for instance, it were\nstated as a law of nature that a body to which a force is applied moves\nin the direction of the force, with a velocity proportioned to the force\ndirectly, and to its own mass inversely; when in point of fact some\nbodies to which a force is applied do not move at all, and those which\ndo move (at least in the region of our earth) are, from the very first,\nretarded by the action of gravity and other resisting forces, and at\nlast stopped altogether; it is clear that the general proposition,\nthough it would be true under a certain hypothesis, would not express\nthe facts as they actually occur. To accommodate the expression of the\nlaw to the real phenomena, we must say, not that the object moves, but\nthat it _tends_ to move, in the direction and with the velocity\nspecified. We might, indeed, guard our expression in a different mode,\nby saying that the body moves in that manner unless prevented, or except\nin so far as prevented, by some counteracting cause. But the body does\nnot only move in that manner unless counteracted; it _tends_ to move in\nthat manner even when counteracted; it still exerts, in the original\ndirection, the same energy of movement as if its first impulse had been\nundisturbed, and produces, by that energy, an exactly equivalent\nquantity of effect. This is true even when the force leaves the body as\nit found it, in a state of absolute rest; as when we attempt to raise a\nbody of three tons weight with a force equal to one ton. For if, while\nwe are applying this force, wind or water or any other agent supplies an\nadditional force just exceeding two tons, the body will be raised; thus\nproving that the force we applied exerted its full effect, by\nneutralizing an equivalent portion of the weight which it was\ninsufficient altogether to overcome. And if while we are exerting this\nforce of one ton upon the object in a direction contrary to that of\ngravity, it be put into a scale and weighed, it will be found to have\nlost a ton of its weight, or in other words, to press downwards with a\nforce only equal to the difference of the two forces.\n\nThese facts are correctly indicated by the expression _tendency_. All\nlaws of 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\nsimilar improvement in terminology would be very salutary in many other\nbranches of 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\nrough generalizations suggested by common observation usually have\nexceptions; but principles of science, or in other words, laws of\ncausation, have not. \"What is thought to be an exception to a\nprinciple,\" (to quote words used on a different occasion,) \"is always\nsome other and distinct principle cutting into the former; some other\nforce which impinges[45] against the first force, and deflects it from\nits direction. There are not a law and an exception to that law, the law\nacting in ninety-nine cases, and the exception in one. There are two\nlaws, each possibly acting in the whole hundred cases, and bringing\nabout a common effect by their conjunct operation. If the force which,\nbeing the less conspicuous of the two, is called the _disturbing_ force,\nprevails sufficiently over the other force in some one case, to\nconstitute that case what is commonly called an exception, the same\ndisturbing force probably acts as a modifying cause in many other cases\nwhich no one will call exceptions.\n\n\"Thus 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\nballoon an exception to that pretended law of nature. But the real law\nis, that all heavy bodies _tend_ to fall; and to this there is no\nexception, not even the sun and moon; for even they, as every astronomer\nknows, tend towards the earth, with a force exactly equal to that with\nwhich the earth tends towards them. The resistance of the atmosphere\nmight, in the particular case of the balloon, from a misapprehension of\nwhat the law of gravitation is, be said to _prevail over_ the law; but\nits disturbing effect is quite as real in every other case, since though\nit does not prevent, it retards the fall of all bodies whatever. The\nrule, and the so-called exception, do not divide the cases between them;\neach of them is a comprehensive rule extending to all cases. To call one\nof these concurrent principles an exception to the other, is\nsuperficial, and contrary to the correct principles of nomenclature and\narrangement. An effect of precisely the same kind, and arising from the\nsame cause, ought not to be placed in two different categories, merely\nas there does or does not exist another cause preponderating over\nit.\"[46]\n\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;\nhow we are enabled to trace each effect to the concurrence of causes in\nwhich it originated, and ascertain the conditions of its recurrence--the\ncircumstances in which it may be expected again to occur. The conditions\nof a phenomenon which arises from a composition of causes, may be\ninvestigated either deductively or experimentally.\n\nThe case, it is evident, is naturally susceptible of the deductive mode\nof investigation. The law of an effect of this description is a result\nof the laws of the separate causes on the combination of which it\ndepends, and is therefore in itself capable of being deduced from these\nlaws. This is called the method _\u00e0 priori_. The other, or _\u00e0 posteriori_\nmethod, professes to proceed according to the canons of experimental\ninquiry. Considering the whole assemblage of concurrent causes which\nproduced the phenomenon, as one single cause, it attempts to ascertain\nthe cause in the ordinary manner, by a comparison of instances. This\nsecond method subdivides itself into two different varieties. If it\nmerely collates instances of the effect, it is a method of pure\nobservation. If it operates upon the causes, and tries different\ncombinations of them, in hopes of ultimately hitting the precise\ncombination which will produce the given total effect, it is a method of\nexperiment.\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 \"clothe them in\ncircumstances.\" 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\nhealth and disease in the human body; or (for greater simplicity) the\nconditions of recovery from a given disease; and in order to narrow the\nquestion still more, let it be limited, in the first instance, to this\none inquiry: Is, or is not some particular medicament (mercury, for\ninstance) a remedy for the given disease.\n\nNow, the deductive method would set out from known properties of\nmercury, and known laws of the human body, and by reasoning from these,\nwould attempt to discover whether mercury will act upon the body when in\nthe morbid condition supposed, in such a manner as to restore health.\nThe experimental method would simply administer mercury in as many cases\nas possible, noting the age, sex, temperament, and other peculiarities\nof bodily constitution, the particular form or variety of the disease,\nthe particular stage of its progress, &c., remarking in which of these\ncases it produced a salutary effect, and with what circumstances it was\non those occasions combined. The method of simple observation would\ncompare instances of recovery, to find whether they agreed in having\nbeen preceded by the administration of mercury; or would compare\ninstances of recovery with instances of failure, to find cases which,\nagreeing in all other respects, differed only in the fact that mercury\nhad been administered, or that it had not.\n\n\n\u00a7 7. That the last of these three modes of investigation is applicable\nto the case, no one has ever seriously contended. No conclusions of\nvalue on a subject of such intricacy, ever were obtained in that way.\nThe utmost that could result would be a vague general impression for or\nagainst the efficacy of mercury, of no avail for guidance unless\nconfirmed by one of the other two methods. Not that the results, which\nthis method strives to obtain, would not be of the utmost possible value\nif they could be obtained. If all the cases of recovery which presented\nthemselves, in an examination extending to a great number of instances,\nwere cases in which mercury had been administered, we might generalize\nwith confidence from this experience, and should have obtained a\nconclusion of real value. But no such basis for generalization can we,\nin a case of this description, hope to obtain. The reason is that which\nwe have spoken of as constituting the characteristic imperfection of the\nMethod of Agreement; Plurality of Causes. Supposing even that mercury\ndoes tend to cure the disease, so many other causes, both natural and\nartificial, also tend to cure it, that there are sure to be abundant\ninstances of recovery in which mercury has not been administered:\nunless, indeed, the practice be to administer it in all cases; on which\nsupposition it will equally be found in the cases of failure.\n\nWhen an effect results from the union of many causes, the share which\neach has in the determination of the effect cannot in general be great:\nand the effect is not likely, even in its presence or absence, still\nless in its variations, to follow, even approximately, any one of the\ncauses. Recovery from a disease is an event to which, in every case,\nmany influences must concur. Mercury may be one such influence; but from\nthe very fact that there are many other such, it will necessarily happen\nthat although 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\nbeing sufficiently powerful without it. Neither, therefore, will the\ninstances of recovery agree in the administration of mercury, nor will\nthe instances of failure agree in its non-administration. It is much if,\nby multiplied and accurate returns from hospitals and the like, we can\ncollect that there are rather more recoveries and rather fewer failures\nwhen mercury is administered than when it is not; a result of very\nsecondary value even as a guide to practice, and almost worthless as a\ncontribution to the theory of the subject.\n\n\n\u00a7 8. The inapplicability of the method of simple observation to\nascertain the conditions of effects dependent on many concurring\ncauses, being thus recognised; we shall next inquire whether any greater\nbenefit can be expected from the other branch of the _\u00e0 posteriori_\nmethod, that which proceeds by directly trying different combinations of\ncauses, either artificially produced or found in nature, and taking\nnotice what is their effect: as, for example, by actually trying the\neffect of mercury, in as many different circumstances as possible. This\nmethod differs from the one which we have just examined, in turning our\nattention directly to the causes or agents, instead of turning it to the\neffect, recovery from the disease. And since, as a general rule, the\neffects of causes are far more accessible to our study than the causes\nof effects, it is natural to think that this method has a much better\nchance of proving successful than the former.\n\nThe method now under consideration is called the Empirical Method; and\nin order to estimate it fairly, we must suppose it to be completely, not\nincompletely, empirical. We must exclude from it everything which\npartakes of the nature not of an experimental but of a deductive\noperation. If for instance we try experiments with mercury upon a person\nin health, in order to ascertain the general laws of its action upon the\nhuman body, and then reason from these laws to determine how it will act\nupon persons affected with a particular disease, this may be a really\neffectual method, but this is deduction. The experimental method does\nnot derive the law of a complex case from the simpler laws which\nconspire to produce it, but makes its experiments directly upon the\ncomplex case. We must make entire abstraction of all knowledge of the\nsimpler tendencies, the _modi operandi_ of mercury in detail. Our\nexperimentation must aim at obtaining a direct answer to the specific\nquestion, Does or does not mercury tend to cure the particular disease?\n\nLet us see, therefore, how far the case admits of the observance of\nthose rules of experimentation, which it is found necessary to observe\nin other cases. When we devise an experiment to ascertain the effect of\na given agent, there are certain precautions which we never, if we can\nhelp it, omit. In the first place, we introduce the agent into the midst\nof a set of circumstances which we have exactly ascertained. It needs\nhardly be remarked how far this condition is from being realized in any\ncase connected with the phenomena of life; how far we are from knowing\nwhat are all the circumstances which pre-exist in any instance in which\nmercury is administered to a living being. This difficulty, however,\nthough insuperable in most cases, may not be so in all; there are\nsometimes concurrences of many causes, in which we yet know accurately\nwhat the causes are. Moreover, the difficulty may be attenuated by\nsufficient multiplication of experiments, in circumstances rendering it\nimprobable that any of the unknown causes should exist in them all. But\nwhen we have got clear of this obstacle, we encounter another still more\nserious. In other cases, when we intend to try an experiment, we do not\nreckon it enough that there be no circumstance in the case the presence\nof which is unknown to us. We require also that none of the\ncircumstances which we do know, shall have effects susceptible of being\nconfounded with those of the agent whose properties we wish to study. We\ntake the utmost pains to exclude all causes capable of composition with\nthe given cause; or if forced to let in any such causes, we take care to\nmake them such that we can compute and allow for their influence, so\nthat the effect of the given cause may, after the subduction of those\nother effects, be apparent as a residual 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\nfrom knowing whether it has any effect or not. Unless we already knew\nwhat and how much is owing to every other circumstance, (that is, unless\nwe suppose the very problem solved which we are considering the means of\nsolving,) we cannot tell that those other circumstances may not have\nproduced the whole of the effect, independently or even in spite of the\nmercury. The Method of Difference, in the ordinary mode of its use,\nnamely by comparing the state of things following the experiment with\nthe state which preceded it, is thus, in the case of intermixture of\neffects, entirely unavailing; because other causes than that whose\neffect we are seeking to determine, have been operating during the\ntransition. As for the other mode of employing the Method of Difference,\nnamely by comparing, not the same case at two different periods, but\ndifferent cases, this in the present instance is quite chimerical. In\nphenomena so complicated it is questionable if two cases, similar in all\nrespects but one, ever occurred; and were they to occur, we could not\npossibly know that they were so exactly 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\ncertain cause is _very often_ followed by a certain effect. For, in one\nof these conjunct effects, the portion which is determined by any one of\nthe influencing agents, is generally, as we before remarked, but small;\nand it must be a more potent cause than most, if even the tendency which\nit really exerts is not thwarted by other tendencies in nearly as many\ncases as it is fulfilled.\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\npolitics and history. There, Plurality of Causes exists in almost\nboundless excess, and effects are, for the most part, inextricably\ninterwoven with one another. To add to the embarrassment, most of the\ninquiries in political science relate to the production of effects of a\nmost comprehensive description, such as the public wealth, public\nsecurity, public morality, and the like: results liable to be affected\ndirectly or indirectly either in _plus_ or in _minus_ by nearly every\nfact which exists, or event which occurs, in human society. The vulgar\nnotion, that the safe methods on political subjects are those of\nBaconian induction--that the true guide is not general reasoning, but\nspecific experience--will one day be quoted as among the most\nunequivocal marks of a low state of the speculative faculties in any\nage in which it is accredited. Nothing can be more ludicrous than the\nsort of parodies on experimental reasoning which one is accustomed to\nmeet with, not in popular discussion only, but in grave treatises, when\nthe affairs of nations are the theme. \"How,\" it is asked, \"can an\ninstitution be bad, when the country has prospered under it?\" \"How can\nsuch or such causes have contributed to the prosperity of one country,\nwhen another has prospered without them?\" Whoever makes use of an\nargument of this kind, not intending to deceive, should be sent back to\nlearn the elements of some one of the more easy physical sciences. Such\nreasoners ignore the fact of Plurality of Causes in the very case which\naffords the most signal example of it. So little could be concluded, in\nsuch a case, from any possible collation of individual instances, that\neven the impossibility, in social phenomena, of making artificial\nexperiments, a circumstance otherwise so prejudicial to directly\ninductive inquiry, hardly affords, in this case, additional reason of\nregret. For even if we could try experiments upon a nation or upon the\nhuman race, with as little scruple as M. Magendie tried them on dogs and\nrabbits, we should never succeed in making two instances identical in\nevery respect except the presence or absence of some one definite\ncircumstance. The nearest approach to an experiment in the philosophical\nsense, which takes place in politics, is the introduction of a new\noperative element into national affairs by some special and assignable\nmeasure of government, such as the enactment or repeal of a particular\nlaw. But where there are so many influences at work, it requires some\ntime for the influence of any new cause upon national phenomena to\nbecome apparent; and as the causes operating in so extensive a sphere\nare not only infinitely numerous, but in a state of perpetual\nalteration, it is always certain that before the effect of the new cause\nbecomes conspicuous enough to be a subject of induction, so many of the\nother influencing circumstances will have changed as to vitiate the\nexperiment.\n\nTwo, therefore, of the three possible methods for the study of phenomena\nresulting from the composition of many causes, being, from the very\nnature of the case, inefficient and illusory, there remains only the\nthird,--that which considers the causes separately, and infers the\neffect from the balance of the different tendencies which produce it: in\nshort, the deductive, or _\u00e0 priori_ method. The more particular\nconsideration of this intellectual process requires a chapter to itself.\n\n\n\n\nCHAPTER XI.\n\nOF THE DEDUCTIVE METHOD.\n\n\n\u00a7 1. The mode of investigation which, from the proved inapplicability of\ndirect methods of observation and experiment, remains to us as the main\nsource of the knowledge we possess or can acquire respecting the\nconditions, and laws of recurrence, of the more complex phenomena, is\ncalled, in its most general expression, the Deductive Method; and\nconsists of three operations: the first, one of direct induction; the\nsecond, of ratiocination; the third, of verification.\n\nI call the first step in the process an inductive operation, because\nthere must be a direct induction as the basis of the whole; though in\nmany particular investigations the place of the induction may be\nsupplied by a prior deduction; but the premises of this prior deduction\nmust have been derived from induction.\n\nThe problem of the Deductive Method is, to find the law of an effect,\nfrom the laws of the different tendencies of which it is the joint\nresult. The first requisite, therefore, is to know the laws of those\ntendencies; the law of each of the concurrent causes: and this supposes\na previous process of observation or experiment upon each cause\nseparately; or else a previous deduction, which also must depend for its\nultimate premises on observation or experiment. Thus, if the subject be\nsocial or historical phenomena, the premises of the Deductive Method\nmust be the laws of the causes which determine that class of phenomena;\nand those causes are human actions, together with the general outward\ncircumstances under the influence of which mankind are placed, and which\nconstitute man's position on the earth. The Deductive Method, applied to\nsocial phenomena, must begin, therefore, by investigating, or must\nsuppose to have been already investigated, the laws of human action,\nand those properties of outward things by which the actions of human\nbeings in society are determined. Some of these general truths will\nnaturally be obtained by observation and experiment, others by\ndeduction: the more complex laws of human action, for example, may be\ndeduced from the simpler ones; but the simple or elementary laws will\nalways, and necessarily, have been obtained by a directly inductive\nprocess.\n\nTo ascertain, then, the laws of each separate cause which takes a share\nin producing the effect, is the first desideratum of the Deductive\nMethod. To know what the causes are, which must be subjected to this\nprocess of study, may or may not be difficult. In the case last\nmentioned, this first condition is of easy fulfilment. That social\nphenomena depend on the acts and mental impressions of human beings,\nnever could have been a matter of any doubt, however imperfectly it may\nhave been known either by what laws those impressions and actions are\ngoverned, or to what social consequences their laws naturally lead.\nNeither, again, after physical science had attained a certain\ndevelopment, could there be any real doubt where to look for the laws on\nwhich the phenomena of life depend, since they must be the mechanical\nand chemical laws of the solid and fluid substances composing the\norganized body and the medium in which it subsists, together with the\npeculiar vital laws of the different tissues constituting the organic\nstructure. In other cases, really far more simple than these, it was\nmuch 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\nwhich experience had proved concerning the heavenly motions, and led to\npredictions which it always verified, mankind never knew that those\n_were_ the causes. But whether we are able to put the question before,\nor not until after, we have become capable of answering it, in either\ncase it must be answered; the laws of the different causes must be\nascertained, before we can proceed to deduce from them the conditions of\nthe effect.\n\nThe mode of ascertaining those laws neither is, nor can be, any other\nthan the fourfold method of experimental inquiry, already discussed. A\nfew remarks on the application of that method to cases of the\nComposition of Causes, 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\nthe tendency is not, in the ordinary sense of the word, counteracted,\nbut only modified, by having its effects compounded with the effects\narising from some other tendency or tendencies, we are still in an\nunfavourable position for tracing, by means of such cases, the law of\nthe tendency itself. It would have been scarcely possible to discover\nthe law that every body in motion tends to continue moving in a straight\nline, by an induction from instances in which the motion is deflected\ninto a curve, by being compounded with the effect of an accelerating\nforce. Notwithstanding the resources afforded in this description of\ncases by the Method of Concomitant Variations, the principles of a\njudicious experimentation prescribe that the law of each of the\ntendencies should be studied, if possible, in cases in which that\ntendency operates alone, or in combination with no agencies but those of\nwhich the effect can, from previous knowledge, be calculated and allowed\nfor.\n\nAccordingly, in the cases, unfortunately very numerous and important, in\nwhich the causes do not suffer themselves to be separated and observed\napart, there is much difficulty in laying down with due certainty the\ninductive foundation necessary to support the deductive method. This\ndifficulty is most of all conspicuous in the case of physiological\nphenomena; it being seldom possible to separate the different agencies\nwhich collectively compose an organized body, without destroying the\nvery phenomena which it is our object to investigate:\n\n --following life, in creatures we dissect,\n We lose it, in the moment we detect.\n\nAnd for this reason I am inclined to the opinion, that physiology\n(greatly and rapidly progressive as it now is) is embarrassed by\ngreater natural difficulties, and is probably susceptible of a less\ndegree of ultimate perfection, than even the social science; inasmuch as\nit is possible to study the laws and operations of one human mind apart\nfrom other minds, much less imperfectly than we can study the laws of\none organ or tissue of the human body apart from the other organs or\ntissues.\n\nIt has been judiciously remarked that pathological facts, or, to speak\nin common language, diseases in their different forms and degrees,\nafford in the case of physiological investigation the most valuable\nequivalent to experimentation properly so called; inasmuch as they often\nexhibit to us a definite disturbance in some one organ or organic\nfunction, the remaining organs and functions being, in the first\ninstance at least, unaffected. It is true that from the perpetual\nactions and reactions which are going on among all parts of the organic\neconomy, there can be no prolonged disturbance in any one function\nwithout ultimately involving many of the others; and when once it has\ndone so, the experiment for the most part loses its scientific value.\nAll depends on observing the early stages of the derangement; which,\nunfortunately, are of necessity the least marked. If, however, the\norgans and functions not disturbed in the first instance, become\naffected in a fixed order of succession, some light is thereby thrown\nupon 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\nnecessary that we should know that the original derangement _was_ local.\nIf it was what is termed constitutional, that is, if we do not know in\nwhat part of the animal economy it took its rise, or the precise nature\nof the disturbance which took place in that part, we are unable to\ndetermine which of the various derangements was cause and which effect;\nwhich of them were produced by one another, and which by the direct,\nthough perhaps tardy, action of the original cause.\n\nBesides natural pathological facts, we can produce pathological facts\nartificially; we can try experiments, even in the popular sense of the\nterm, by subjecting the living being to some external agent, such as the\nmercury of our former example, or the section of a nerve to ascertain\nthe functions of different parts of the nervous system. As this\nexperimentation is not intended to obtain a direct solution of any\npractical question, but to discover general laws, from which afterwards\nthe conditions of any particular effect may be obtained by deduction;\nthe best cases to select are those of which the circumstances can be\nbest ascertained: and such are generally not those in which there is any\npractical object in view. The experiments are best tried, not in a state\nof disease, which is essentially a changeable state, but in the\ncondition of health, comparatively a fixed state. In the one, unusual\nagencies are at work, the results of which we have no means of\npredicting; in the other, the course of the accustomed physiological\nphenomena would, it may generally be presumed, remain undisturbed, were\nit 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 incumbered 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\nit not in our power to make trial of them in a state of actual\nseparation. The insufficiency of these resources is so glaring, that no\none can be surprised at the backward state of the science of physiology;\nin which indeed our knowledge of causes is so imperfect, that we can\nneither explain, nor could without specific experience have predicted,\nmany of the facts which are certified to us by the most ordinary\nobservation. Fortunately, we are much better informed as to the\nempirical laws of the phenomena, that is, the uniformities respecting\nwhich we cannot yet decide whether they are cases of causation, or mere\nresults of it. Not only has the order in which the facts of organization\nand life successively manifest themselves, from the first germ of\nexistence to death, been found to be uniform, and very accurately\nascertainable; but, by a great application of the Method of Concomitant\nVariations to the entire facts of comparative anatomy and physiology,\nthe characteristic organic structure corresponding to each class of\nfunctions has been determined with considerable precision. Whether these\norganic conditions are the whole of the conditions, and in many cases\nwhether they are conditions at all, or mere collateral effects of some\ncommon cause, we are quite ignorant: nor are we ever likely to know,\nunless we could construct an organized body, and try whether it would\nlive.\n\nUnder such disadvantages do we, in cases of this description, attempt\nthe initial, or inductive step, in the application of the Deductive\nMethod to complex phenomena. But such, fortunately, is not the common\ncase. In general, the laws of the causes on which the effect depends may\nbe obtained by an induction from comparatively simple instances, or, at\nthe worst, by deduction from the laws of simpler causes, so obtained. By\nsimple instances are meant, of course, those in which the action of each\ncause was not intermixed or interfered with, or not to any great extent,\nby other causes whose laws were unknown. And only when the induction\nwhich furnished the premises to the Deductive method rested on such\ninstances, has the application of such a method to the ascertainment of\nthe laws of a complex effect, been attended with brilliant results.\n\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\nterm; and very often involves processes of calculation in the narrowest\nsense. It is a ratiocination; and when our knowledge of the causes is so\nperfect, as to extend to the exact numerical laws which they observe in\nproducing their effects, the ratiocination may reckon among its premises\nthe theorems of the science of number, in the whole immense extent of\nthat science. Not only are the most advanced truths of mathematics often\nrequired to enable us to compute an effect, the numerical law of which\nwe already know; but, even by the aid of those most advanced truths, we\ncan go but a little way. In so simple a case as the common problem of\nthree bodies gravitating towards one another, with a force directly as\ntheir mass and inversely as the square of the distance, all the\nresources of the calculus have not hitherto sufficed to obtain any\ngeneral solution but an approximate one. In a case a little more\ncomplex, but still one of the simplest which arise in practice, that of\nthe motion of a projectile, the causes which affect the velocity and\nrange (for example) of a cannon-ball may be all known and estimated; the\nforce of the gunpowder, the angle of elevation, the density of the air,\nthe strength and direction of the wind; but it is one of the most\ndifficult 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\npremises, where the effects take place in space, and involve motion and\nextension, as in mechanics, optics, acoustics, astronomy. But when the\ncomplication increases, and the effects are under the influence of so\nmany and such shifting causes as to give no room either for fixed\nnumbers, or for straight lines and regular curves, (as in the case of\nphysiological, to say nothing of mental and social phenomena,) the laws\nof number and extension are applicable, if at all, only on that large\nscale on which precision of details becomes unimportant. Although these\nlaws play a conspicuous part in the most striking examples of the\ninvestigation of nature by the Deductive Method, as for example in the\nNewtonian theory of the celestial motions, they are by no means an\nindispensable part of every such process. All that is essential in it is\nreasoning from a general law to a particular case, that is, determining\nby means of the particular circumstances of that case, what result is\nrequired in that instance to fulfil the law. Thus in the Torricellian\nexperiment, if the fact that air has weight had been previously known,\nit would have been easy, without any numerical data, to deduce from the\ngeneral law of equilibrium, that the mercury would stand in the tube at\nsuch a height that the column of mercury would exactly balance a column\nof the atmosphere of equal diameter; because, otherwise, equilibrium\nwould not exist.\n\nBy such ratiocinations from the separate laws of the causes, we may, to\na certain extent, succeed in answering either of the following\nquestions: Given a certain combination of causes, what effect will\nfollow? and, What combination of causes, if it existed, would produce a\ngiven effect? In the one case, we determine the effect to be expected in\nany complex circumstances of which the different elements are known: in\nthe other case we learn, according to what law--under what antecedent\nconditions--a given complex effect will occur.\n\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\nforce against 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_ we\nhave taken all these into our reckoning? How many must we not generally\nbe ignorant of? Among those which we know, how probable that some have\nbeen overlooked; and, even were all included, how vain the pretence of\nsumming up the effects of many causes, unless we know accurately the\nnumerical law of each,--a condition in most cases not to be fulfilled;\nand even when fulfilled, to make the calculation transcends, in any but\nvery simple cases, the utmost power of mathematical science with all its\nmost modern improvements.\n\nThese objections have real weight, and would be altogether unanswerable,\nif there were no test by which, when we employ the Deductive Method, we\nmight judge whether an error of any of the above descriptions had been\ncommitted or not. Such a test however there is: and its application\nforms, under the name of Verification, the third essential component\npart of the Deductive Method; without which all the results it can give\nhave little other value than that of conjecture. To warrant reliance on\nthe general conclusions arrived at by deduction, these conclusions must\nbe found, on careful comparison, to accord with the results of direct\nobservation wherever it can be had. If, when we have experience to\ncompare with them, this experience confirms them, we may safely trust to\nthem in other cases of which our specific experience is yet to come. But\nif our deductions have led to the conclusion that from a particular\ncombination of causes a given effect would result, then in all known\ncases where that combination can be shown to have existed, and where the\neffect has not followed, we must be able to show (or at least to make a\nprobable surmise) what frustrated it: if we cannot, the theory is\nimperfect, and not yet to be relied upon. Nor is the verification\ncomplete, unless some of the cases in which the theory is borne out by\nthe observed result, are of at least equal complexity with any other\ncases in which its application could be called for.\n\nIf direct observation and collation of instances have furnished us with\nany empirical laws of the effect (whether true in all observed cases, or\nonly true for the most part), the most effectual verification of which\nthe theory could be susceptible would be, that it led deductively to\nthose empirical laws; that the uniformities, whether complete or\nincomplete, which were observed to exist among the phenomena, were\naccounted for by the laws of the causes--were such as could not but\nexist if those be really the causes by which the phenomena are produced.\nThus it was very reasonably deemed an essential requisite of any true\ntheory of the causes of the celestial motions, that it should lead by\ndeduction to Kepler's laws: which, accordingly, the Newtonian theory\ndid.\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\ninstances, conformably to the Method of Agreement: as well as (it must\nbe added) that the phenomena themselves should be described, in the most\ncomprehensive as well as accurate manner possible; by collecting from\nthe observation of parts, the simplest possible correct expressions for\nthe corresponding wholes: as when the series of the observed places of a\nplanet was first expressed by a circle, then by a system of epicycles,\nand subsequently by an ellipse.\n\nIt is worth remarking, that complex instances which would have been of\nno use for the discovery of the simple laws into which we ultimately\nanalyse their phenomena, nevertheless, when they have served to verify\nthe analysis, become additional evidence of the laws themselves.\nAlthough we could not have got at the law from complex cases, still when\nthe law, got at otherwise, is found to be in accordance with the result\nof a complex case, that case becomes a new experiment on the law, and\nhelps to confirm what it did not assist to discover. It is a new trial\nof the principle in a different set of circumstances; and occasionally\nserves to eliminate some circumstance not previously excluded, and the\nexclusion of which might require an experiment impossible to be\nexecuted. This was strikingly conspicuous in the example formerly\nquoted, in which the difference between the observed and the calculated\nvelocity of sound was ascertained to result from the heat extricated by\nthe condensation which takes place in each sonorous vibration. This was\na trial, in new circumstances, of the law of the development of heat by\ncompression; and it added materially to the proof of the universality of\nthat law. Accordingly any law of nature is deemed to have gained in\npoint of certainty, by being found to explain some complex case which\nhad not previously been thought of in connexion with it; and this indeed\nis a consideration to which it is the habit of scientific inquirers to\nattach rather too much value than too little.\n\nTo the Deductive Method, thus characterized in its three constituent\nparts, Induction, Ratiocination, and Verification, the human mind is\nindebted for its most conspicuous triumphs in the investigation of\nnature. To it we owe all the theories by which vast and complicated\nphenomena are embraced under a few simple laws, which, considered as the\nlaws of those great phenomena, could never have been detected by their\ndirect study. We may form some conception of what the method has done\nfor us, from the case of the celestial motions; one of the simplest\namong the greater instances of the Composition of Causes, since (except\nin a few cases not of primary importance) each of the heavenly bodies\nmay be considered, without material inaccuracy, to be never at one time\ninfluenced by the attraction of more than two bodies, the sun and one\nother planet or satellite; making, with the reaction of the body itself,\nand the force generated by the body's own motion and acting in the\ndirection of the tangent, only four different agents on the concurrence\nof which the motions of that body depend; a much smaller number, no\ndoubt, than that by which any other of the great phenomena of nature is\ndetermined or modified. Yet how could we ever have ascertained the\ncombination of forces on which the motions of the earth and planets are\ndependent, 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,\nin a degree so rare among the effects of a concurrence of causes; and\nalthough the periodical recurrence of exactly the same effect, affords\npositive proof that all the combinations of causes which occur at all,\nrecur periodically; we should not have known what the causes were, if\nthe existence of agencies precisely similar on our own earth had not,\nfortunately, brought the causes themselves within the reach of\nexperimentation under simple circumstances. As we shall have occasion to\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\nnot to prove laws of phenomena, but to explain them.\n\n\n\n\nCHAPTER XII.\n\nOF THE EXPLANATION OF LAWS OF NATURE.\n\n\n\u00a7 1. The deductive operation by which we derive the law of an effect\nfrom the laws of the causes, the concurrence of which gives rise to it,\nmay be undertaken either for the purpose of discovering the law, or of\nexplaining a law already discovered. The word _explanation_ occurs so\ncontinually and holds so important a place in philosophy, that a little\ntime spent in fixing 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\nproduction is an instance. Thus, a conflagration is explained, when it\nis proved to have arisen from a spark falling into the midst of a heap\nof combustibles. And in a similar manner, a law or uniformity in nature\nis said to be explained, when another law or laws are pointed out, of\nwhich that law itself is but a case, and from which it could be deduced.\n\n\n\u00a7 2. There are three distinguishable sets of circumstances in which a\nlaw of causation may be explained from, or, as it also is often\nexpressed, resolved into, other laws.\n\nThe first is the case already so fully considered; an intermixture of\nlaws, producing a joint effect equal to the sum of the effects of the\ncauses taken separately. The law of the complex effect is explained, by\nbeing resolved into the separate laws of the causes which contribute to\nit. Thus, the law of the motion of a planet is resolved into the law of\nthe acquired force, which tends to produce 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 coexistence. The one is as essential an\ningredient as the other; whether the object be to discover the law of\nthe effect, or only to explain it. To deduce the laws of the heavenly\nmotions, we require not only to know the law of a rectilineal and that\nof a gravitative force, but the existence of both these forces in the\ncelestial regions, and even their relative amount. The complex laws of\ncausation are thus resolved into two distinct kinds of elements: the\none, simpler laws of causation, the other (in the aptly selected\nexpression of Dr. Chalmers) collocations; the collocations consisting in\nthe existence of certain agents or powers, in certain circumstances of\nplace and time. We shall hereafter have occasion to return to this\ndistinction, and to dwell on it at such length as dispenses with the\nnecessity of further insisting on it here. The first mode, then, of the\nexplanation of Laws of Causation, is when the law of an effect is\nresolved into the various tendencies of which it is the result, together\nwith the laws of those tendencies.\n\n\n\u00a7 3. A second case is when, between what seemed the cause and what was\nsupposed to be its effect, further observation detects an intermediate\nlink; a fact caused by the antecedent, and in its turn causing the\nconsequent; so that the cause at first assigned is but the remote cause,\noperating through the intermediate phenomenon. A seemed the cause of C,\nbut it subsequently appeared that A was only the cause of B, and that it\nis B which was the cause of C. For example: mankind were aware that the\nact of touching an outward object caused a sensation. It was\nsubsequently discovered, that after we have touched the object, and\nbefore we experience the sensation, some change takes place in a kind of\nthread called a nerve, which extends from our outward organs to the\nbrain. Touching the object, therefore, is only the remote cause of our\nsensation; that is, not the cause, properly speaking, but the cause of\nthe cause;--the real cause of the sensation is the change in the state\nof the nerve. Future experience may not only give us more knowledge than\nwe now have of the particular nature of this change, but may also\ninterpolate another link: between the contact (for example) of the\nobject with our outward organs, and the production of the change of\nstate in the nerve, there may take place some electric phenomenon; or\nsome phenomenon of a nature not resembling the effects of any known\nagency. Hitherto, however, no such intermediate link has been\ndiscovered; and the touch of the object must be considered,\nprovisionally, as the proximate cause of the affection of the nerve. The\nsequence, therefore, of a sensation of touch on contact with an object,\nis ascertained not to be an ultimate law; it is resolved, as the phrase\nis, into two other laws,--the law, that contact with an object produces\nan affection of the nerve; and the law, that an affection of the nerve\nproduces sensation.\n\nTo take another example: the more powerful acids corrode or blacken\norganic compounds. This is a case of causation, but of remote causation;\nand is said to be explained when it is shown that there is an\nintermediate link, namely, the separation of some of the chemical\nelements of the organic structure from the rest, and their entering into\ncombination with the acid. The acid causes this separation of the\nelements, and the separation of the elements causes the disorganization,\nand often the charring of the structure. So, again, chlorine extracts\ncolouring matters, (whence its efficacy in bleaching,) and purifies the\nair from infection. This law is resolved into the two following laws.\nChlorine has a powerful affinity for bases of all kinds, particularly\nmetallic bases and hydrogen. Such bases are essential elements of\ncolouring matters and contagious compounds: which substances, therefore,\nare decomposed and destroyed by chlorine.\n\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\nthe non-fulfilment of some negative condition: the tendency, therefore,\nof B to produce C may be defeated. Now the law that A produces B, is\nequally fulfilled whether B is followed by C or not; but the law that A\nproduces C by means of B, is of course only fulfilled when B is really\nfollowed by C, and is therefore less general than the law that A\nproduces B. It is also less general than the law that B produces C. For\nB may have other causes besides A; and as A produces C only by means of\nB, while B produces C whether it has itself been produced by A or by\nanything else, the second law embraces a greater number of instances,\ncovers as it were a greater space of ground, than the first.\n\nThus, in our former example, the law that the contact of an object\ncauses a change in the state of the nerve, is more general than the law\nthat contact with an object causes sensation, since, for aught we know,\nthe change in the nerve may equally take place when, from a\ncounteracting cause, as for instance, strong mental excitement, the\nsensation does not follow; as in a battle, where wounds are sometimes\nreceived without any consciousness of receiving them. And again, the law\nthat change in the state of a nerve produces sensation, is more general\nthan the law that contact with an object produces sensation; since the\nsensation equally follows the change in the nerve when not produced by\ncontact with an object, but by some other cause; as in the well-known\ncase, when a person who has lost a limb, feels the same sensation which\nhe has been accustomed to 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\nis, but (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\ndepend on an intervening phenomenon, then, however constant and\ninvariable the sequence of A and C has hitherto been found,\npossibilities arise of its failure, exceeding those which can affect\neither of the more immediate sequences, A, B, and B, C. The tendency of\nA to produce C may be defeated by whatever is capable of defeating\neither the tendency of A to produce B, or the tendency of B to produce\nC; it is therefore twice as liable to failure as either of those more\nelementary tendencies; and the generalization that A is always followed\nby C, is twice as likely to be found erroneous. And so of the converse\ngeneralization, that C is always preceded and caused by A; which will be\nerroneous not only if there should happen to be a second immediate mode\nof production of C itself, but moreover if there be a second mode of\nproduction of B, the immediate antecedent 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\nfor. As soon as we know that B intervenes between A and C, we also know\nthat if there be cases in which the sequence of A and C does not hold,\nthese are most likely to be found by studying the effects or the\nconditions of the phenomenon B.\n\nIt appears, then, that in the second of the three modes in which a law\nmay be resolved into other laws, the latter are more general, that is,\nextend to more cases, and are also less likely to require limitation\nfrom subsequent experience, than the law which they serve to explain.\nThey are more nearly unconditional; they are defeated by fewer\ncontingencies; they are a nearer approach to the universal truth of\nnature. The same observations are still more evidently true with regard\nto the first of the three modes of resolution. When the law of an effect\nof combined causes is resolved into the separate laws of the causes, the\nnature of the case implies that the law of the effect is less general\nthan the law of any of the causes, since it only holds when they are\ncombined; while the law of any one of the causes holds good both then,\nand also when that cause acts apart from the rest. It is also manifest\nthat the complex law is liable to be oftener unfulfilled than any one\nof the simpler laws of which it is the result, since every contingency\nwhich defeats any of the laws prevents so much of the effect as depends\non it, and thereby defeats the complex law. The mere rusting, for\nexample, of some small part of a great machine, often suffices entirely\nto prevent the effect which ought to result from the joint action of all\nthe parts. The law of the effect of a combination of causes is always\nsubject to the whole of the negative conditions which attach to the\naction of all the causes severally.\n\nThere is another and an equally strong reason why the law of a complex\neffect must be less general than the laws of the causes which conspire\nto produce 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,\ngives rise to an elliptical motion; but if the ratio of the two forces\nto each other were slightly altered, it is demonstrated that the motion\nproduced would be in a circle, or a parabola, or an hyperbola: and it is\nthought that in the case of some comets one of these is probably the\nfact. Yet the law of the parabolic motion would be resolvable into the\nvery same simple laws into which that of the elliptical motion is\nresolved, namely, the law of the permanence of rectilineal motion, and\nthe law of gravitation. If, therefore, in the course of ages, some\ncircumstance were to manifest itself which, without defeating the law of\neither of those forces, should merely alter their proportion to one\nanother, (such as the shock of some solid body, or even the accumulating\neffect of the resistance of the medium in which astronomers have been\nled to surmise that the motions of the heavenly bodies take place,) the\nelliptical motion might be changed into a motion in some other conic\nsection; and the complex law, that the planetary motions take place in\nellipses, would be deprived of its universality, though the discovery\nwould not at all detract from the universality of the simpler laws into\nwhich that complex law is resolved. The law, in short, of each of the\nconcurrent causes remains the same, however their collocations may vary;\nbut the law of their joint effect varies with every difference in the\ncollocations. There needs no more to show how much more general the\nelementary laws must be, than any of the complex laws which are derived\nfrom them.\n\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\ngathering up of several laws into one more general law which includes\nthem all. The most splendid example of this operation was when\nterrestrial gravity and the central force of the solar system were\nbrought together under the general law of gravitation. It had been\nproved antecedently that the earth and the other planets tend to the\nsun; and it had been known from the earliest times that terrestrial\nbodies tend towards the earth. These were similar phenomena; and to\nenable them both to be subsumed under one law, it was only necessary to\nprove that, as the effects were similar in quality, so also they, as to\nquantity, conform to the same rules. This was first shown to be true of\nthe moon, which agreed with terrestrial objects not only in tending to a\ncentre, but in the fact that this centre was the earth. The tendency of\nthe moon towards the earth being ascertained to vary as the inverse\nsquare of the distance, it was deduced from this, by direct calculation,\nthat if the moon were as near to the earth as terrestrial objects are,\nand the acquired force in the direction of the tangent were suspended,\nthe moon would fall towards the earth through exactly as many feet in a\nsecond as those objects do by virtue of their weight. Hence the\ninference was irresistible, that the moon also tends to the earth by\nvirtue of its weight: and that the two phenomena, the tendency of the\nmoon to the earth and the tendency of terrestrial objects to the earth,\nbeing not only similar in quality, but, when in the same circumstances,\nidentical in quantity, are cases of one and the same law of causation.\nBut the tendency of the moon to the earth, and the tendency of the earth\nand planets to the sun, were already known to be cases of the same law\nof causation: and thus the law of all these tendencies, and the law of\nterrestrial gravity, were recognised as identical, and were subsumed\nunder one general law, that of gravitation.\n\nIn a similar manner, the laws of magnetic phenomena have more recently\nbeen subsumed under known laws of electricity. It is thus that the most\ngeneral laws of nature are usually arrived at: we mount to them by\nsuccessive steps. For, to arrive by correct induction at laws which hold\nunder such an immense variety of circumstances, laws so general as to be\nindependent of any varieties of space or time which we are able to\nobserve, requires for the most part many distinct sets of experiments or\nobservations, conducted at different times and by different people. One\npart of the law is first ascertained, afterwards another part: one set\nof observations teaches us that the law holds good under some\nconditions, another that it holds good under other conditions, by\ncombining which observations we find that it holds good under conditions\nmuch more general, or even universally. The general law, in this case,\nis literally the sum of all the partial ones; it is the recognition of\nthe same sequence in different sets of instances; and may, in fact, be\nregarded as merely one step in the process of elimination. That tendency\nof bodies towards one another, which we now call gravity, had at first\nbeen observed only on the earth's surface, where it manifested itself\nonly as a tendency of all bodies towards the earth, and might,\ntherefore, be ascribed to a peculiar property of the earth itself: one\nof the circumstances, namely, the proximity of the earth, had not been\neliminated. To eliminate this circumstance required a fresh set of\ninstances in other parts of the universe: these we could not ourselves\ncreate; and though nature had created them for us, we were placed in\nvery unfavourable circumstances for observing them. To make these\nobservations, fell naturally to the lot of a different set of persons\nfrom those who studied terrestrial phenomena; and had, indeed, been a\nmatter of great interest at a time when the idea of explaining celestial\nfacts by terrestrial laws was looked upon as the confounding of an\nindefeasible distinction. When, however, the celestial motions were\naccurately ascertained, and the deductive processes performed, from\nwhich it appeared that their laws and those of terrestrial gravity\ncorresponded, those celestial observations became a set of instances\nwhich exactly eliminated the circumstance of proximity to the earth; and\nproved that in the original case, that of terrestrial objects, it was\nnot the earth, as such, that caused the motion or the pressure, but the\ncircumstance common to that case with the celestial instances, namely,\nthe presence of some great body within certain limits of distance.\n\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\nof the causes, together with the fact of their combination. Secondly,\nwhen the 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\ntwo or more; in the third, two or more are resolved into one: when,\nafter the law has been shown to hold good in several different classes\nof cases, we decide that what is true in each of these classes of cases,\nis true under some more general supposition, consisting of what all\nthose classes of cases have in common. We may here remark that this last\noperation involves none of the uncertainties attendant on induction by\nthe Method of Agreement, since we need not suppose the result to be\nextended by way of inference to any new class of cases, different from\nthose by the comparison 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 extended to, and others besides. In the first two modes they\nare also resolved into laws more certain, in other words, more\nuniversally true than themselves; they are, in fact, proved not to be\nthemselves laws of nature, the character of which is to be universally\ntrue, but _results_ of laws of nature, which may be only true\nconditionally, and for the most part. No difference of this sort exists\nin the third case; since here the partial laws are, in fact, the very\nsame law as the general one, and any exception to them would be an\nexception 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\ndemonstratively from the laws into which they are resolved. As already\nremarked, the same deductive process which proves a law or fact of\ncausation if unknown, serves 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\na mystery which has become familiar, and has grown to _seem_ not\nmysterious, for one which is still strange. And this is the meaning of\nexplanation, in common parlance. But the process with which we are here\nconcerned often does the very contrary: it resolves a phenomenon with\nwhich we are familiar, into one of which we previously knew little or\nnothing; as when the common fact of the fall of heavy bodies was\nresolved into the tendency of all particles of matter towards one\nanother. It must be kept constantly in view, therefore, that in science,\nthose who speak of explaining any phenomenon mean (or should mean)\npointing out not some more familiar, but merely some more general,\nphenomenon, of which it is a partial exemplification; or some laws of\ncausation which produce it by their joint or successive action, and from\nwhich, therefore, its conditions may be determined deductively. Every\nsuch operation brings us a step nearer towards answering the question\nwhich was stated in a previous chapter as comprehending the whole\nproblem of the investigation of nature, viz. What are the fewest\nassumptions, which being granted, the order of nature as it exists\nwould be the result? What are the fewest general propositions from which\nall the uniformities existing in nature could be deduced?\n\nThe laws, thus explained or resolved, are sometimes said to be\n_accounted for_; but the expression is incorrect, if taken to mean\nanything more than what has been already stated. In minds not habituated\nto accurate thinking, there is often a confused notion that the general\nlaws are the _causes_ of the partial ones; that the law of general\ngravitation, for example, causes the phenomenon of the fall of bodies to\nthe earth. But to assert this, would be a misuse of the word cause:\nterrestrial gravity is not an effect of general gravitation, but a\n_case_ of it; that is, one kind of the particular instances in which\nthat general law obtains. To account for a law of nature means, and can\nmean, nothing more than to assign other laws more general, together with\ncollocations, which laws and collocations being supposed, the partial\nlaw follows without any additional supposition.\n\n\n\n\nCHAPTER XIII.\n\nMISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.\n\n\n\u00a7 1. The most striking example which the history of science presents, of\nthe explanation of laws of causation and other uniformities of sequence\namong special phenomena, by resolving them into laws of greater\nsimplicity and generality, is the great Newtonian generalization:\nrespecting which typical instance so much having already been said, it\nis sufficient to call attention to the great number and variety of the\nspecial observed uniformities which are in this case accounted for,\neither as particular cases or as consequences of one very simple law of\nuniversal nature. The simple fact of a tendency of every particle of\nmatter towards every other particle, varying inversely as the square of\nthe distance, explains the fall of bodies to the earth, the revolutions\nof the planets and satellites, the motions (so far as known) of comets,\nand all the various regularities which have been observed in these\nspecial phenomena; such as the elliptical orbits, and the variations\nfrom exact ellipses; the relation between the solar distances of the\nplanets and the duration of their revolutions; the precession of the\nequinoxes; the tides, and a vast number of minor astronomical truths.\n\nMention has also been made in the preceding chapter of the explanation\nof the phenomena of magnetism from laws of electricity; the special laws\nof magnetic agency having been affiliated by deduction to observed laws\nof electric action, in which they have ever since been considered to be\nincluded as special cases. An example not so complete in itself, but\neven more fertile in consequences, having been the starting point of the\nreally scientific study of physiology, is the affiliation, commenced by\nBichat, and carried on by subsequent biologists, of the properties of\nthe bodily organs, to the elementary properties of the tissues into\nwhich they are anatomically decomposed.\n\nAnother striking instance is afforded by Dalton's generalization,\ncommonly known as the atomic theory. It had been known from the very\ncommencement of accurate chemical observation, that any two bodies\ncombine chemically with one another in only a certain number of\nproportions; but those proportions were in each case expressed by a\npercentage--so many parts (by weight) of each ingredient, in 100 of the\ncompound; (say 35 and a fraction of one element, 64 and a fraction of\nthe other): in which mode of statement no relation was perceived between\nthe proportion in which a given element combines with one substance, and\nthat in which it combines with others. The great step made by Dalton\nconsisted in perceiving, that a unit of weight might be established for\neach substance, such that by supposing the substance to enter into all\nits combinations in the ratio either of that unit, or of some low\nmultiple of that unit, all the different proportions, previously\nexpressed by percentages, were found to result. Thus 1 being assumed as\nthe unit of hydrogen, if 8 were then taken as that of oxygen, the\ncombination of one unit of hydrogen with one unit of oxygen would\nproduce the exact proportion of weight between the two substances which\nis known to exist in water; the combination of one unit of hydrogen with\ntwo units of oxygen would produce the proportion which exists in the\nother compound of the same two elements, called peroxide of hydrogen;\nand the combinations of hydrogen and of oxygen with all other\nsubstances, would correspond with the supposition that those elements\nenter into combination by single units, or twos, or threes, of the\nnumbers assigned to them, 1 and 8, and the other substances by ones or\ntwos or threes of other determinate numbers proper to each. The result\nis that a table of the equivalent numbers, or, as they are called,\natomic weights, of all the elementary substances, comprises in itself,\nand scientifically explains, all the proportions in which any substance,\nelementary or compound, is found capable of entering into chemical\ncombination with any other substance whatever.\n\n\n\u00a7 2. Some interesting cases of the explanation of old uniformities by\nnewly ascertained laws are afforded by the researches of Professor\nGraham. That eminent chemist was the first who drew attention to the\ndistinction which may be made of all substances into two classes, termed\nby him crystalloids and colloids; or rather, of all states of matter\ninto the crystalloid and the colloidal states, for many substances are\ncapable of existing in either. When in the colloidal state, their\nsensible properties are very different from those of the same substance\nwhen crystallized, or when in a state easily susceptible of\ncrystallization. Colloid substances pass with extreme difficulty and\nslowness into the crystalline state, and are extremely inert in all the\nordinary chemical relations. Substances in the colloid state are almost\nalways, when combined with water, more or less viscous or gelatinous.\nThe most prominent examples of the state are certain animal and\nvegetable substances, particularly gelatine, albumen, starch, the gums,\ncaramel, tannin, and some others. Among substances not of organic\norigin, the most notable instances are hydrated silicic acid, and\nhydrated alumina, with other metallic peroxides of the aluminous class.\n\nNow it is found, that while colloidal substances are easily penetrated\nby water, and by the solutions of crystalloid substances, they are very\nlittle penetrable by one another: which enabled Professor Graham to\nintroduce a highly effective process (termed dialysis) for separating\nthe crystalloid substances contained in any liquid mixture, by passing\nthem through a thin septum of colloidal matter, which does not suffer\nanything colloidal to pass, or suffers it only in very minute quantity.\nThis property of colloids enabled Mr. Graham to account for a number of\nspecial results of observation, not previously explained.\n\nFor instance, \"while soluble crystalloids are always highly sapid,\nsoluble colloids are singularly insipid,\" as might be expected; for, as\nthe sentient extremities of the nerves of the palate \"are probably\nprotected by a colloidal membrane,\" impermeable to other colloids, a\ncolloid, when tasted, probably never reaches those nerves. Again, \"it\nhas been observed that vegetable gum is not digested in the stomach; the\ncoats of that organ dialyse the soluble food, absorbing crystalloids,\nand rejecting all colloids.\" One of the mysterious processes\naccompanying digestion, the secretion of free muriatic acid by the coats\nof the stomach, obtains a probable hypothetical explanation through the\nsame law. Finally, much light is thrown upon the observed phenomena of\nosmose (the passage of fluids outward and inward through animal\nmembranes) by the fact that the membranes are colloidal. In consequence,\nthe water and saline solutions contained in the animal body pass easily\nand rapidly through the membranes, while the substances directly\napplicable to nutrition, which are mostly colloidal, are detained by\nthem.[47]\n\nThe property which salt possesses of preserving animal substances from\nputrefaction is resolved by Liebig into two more general laws, the\nstrong attraction of salt for water, and the necessity of the presence\nof water as a condition of putrefaction. The intermediate phenomenon\nwhich is interpolated between the remote cause and the effect, can here\nbe not merely inferred but seen; for it is a familiar fact, that flesh\nupon which salt 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\ndried and kept in a dry atmosphere does not putrefy; as we see in the\ncase of dried provisions, and human bodies in very dry climates. A\ndeductive explanation of this same law results from Liebig's\nspeculations. The putrefaction of animal and other azotised bodies is a\nchemical process, by which they are gradually dissipated in a gaseous\nform, chiefly in that of carbonic acid and ammonia; now to convert the\ncarbon of the animal substance into carbonic acid requires oxygen, and\nto convert the azote into ammonia requires hydrogen, which are the\nelements of water. The extreme rapidity of the putrefaction of azotised\nsubstances, compared with the gradual decay of non-azotised bodies (such\nas wood and the like) by the action of oxygen alone, he explains from\nthe general law that substances are much more easily decomposed by the\naction of two different affinities upon two of their elements, than by\nthe action of only one.\n\n\n\u00a7 3. Among the many important properties of the nervous system, which\nhave either been first discovered or strikingly illustrated by Dr.\nBrown-S\u00e9quard, I select the reflex influence of the nervous system on\nnutrition and secretion. By reflex nervous action is meant, action which\none part of the nervous system exerts over another part, without any\nintermediate action on the brain, and consequently without\nconsciousness; or which, if it does pass through the brain, at least\nproduces its effects independently of the will. There are many\nexperiments which prove that irritation of a nerve in one part of the\nbody may in this manner excite powerful action in another part; for\nexample, food injected into the stomach through a divided oesophagus,\nnevertheless produces secretion of saliva; warm water injected into the\nbowels, and various other irritations of the lower intestines, have been\nfound to excite secretion of the gastric juice, and so forth. The\nreality of the power being thus proved, its agency explains a great\nvariety of apparently anomalous phenomena; of which I select the\nfollowing from Dr. Brown-S\u00e9quard's _Lectures on the Nervous System_.\n\nThe production of tears by irritation of the eye, or of the mucous\nmembrane of the nose:\n\nThe secretions of the eye and nose increased by exposure of other parts\nof the body to cold:\n\nInflammation of the eye, especially when of traumatic origin, very\nfrequently excites a similar affection in the other eye, which may be\ncured by section of the intervening nerve:\n\nLoss of sight sometimes produced by neuralgia; and has been known to be\nat once cured by the extirpation (for instance) of a carious tooth:\n\nEven cataract has been produced in a healthy eye by cataract in the\nother eye, or by neuralgia, or by a wound of the frontal nerve:\n\nThe well-known phenomenon of a sudden stoppage of the heart's action,\nand consequent death, produced by irritation of some of the nervous\nextremities: _e.g._, by drinking very cold water; or by a blow on the\nabdomen, or other sudden excitation of the abdominal sympathetic nerve;\nthough this nerve may be irritated to any extent without stopping the\nheart's action, if a section be made of the communicating nerves:\n\nThe extraordinary effects produced on the internal organs by an\nextensive burn on the surface of the body; consisting in violent\ninflammation of the tissues of the abdomen, chest, or head: which, when\ndeath ensues from this kind of injury, is one of the most frequent\ncauses of it:\n\nParalysis and an\u00e6sthesia of one part of the body from neuralgia in\nanother part; and muscular atrophy from neuralgia, even when there is no\nparalysis:\n\nTetanus produced by the lesion of a nerve; Dr. Brown-S\u00e9quard thinks it\nhighly probable that hydrophobia is a phenomenon of a similar nature:\n\nMorbid changes in the nutrition of the brain and spinal cord,\nmanifesting themselves by epilepsy, chorea, hysteria, and other\ndiseases, occasioned by lesion of some of the nervous extremities in\nremote places, as by worms, calculi, tumours, carious bones, and in some\ncases even by very slight irritations of the skin.\n\n\n\u00a7 4. From the foregoing and similar instances, we may see the\nimportance, when a law of nature previously unknown has been brought to\nlight, or when new light has been thrown upon a known law by experiment,\nof examining all cases which present the conditions necessary for\nbringing that law into action; a process fertile in demonstrations of\nspecial laws previously unsuspected, and explanations of others already\nempirically 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\nhe found to hold not only of small magnets, but of that great magnet,\nthe earth. The law being thus established experimentally, that\nelectricity is evolved, by a magnet, and a conductor moving at right\nangles to the direction of its poles, we may now look out for fresh\ninstances in which these conditions meet. Wherever a conductor moves or\nrevolves at right angles to the direction of the earth's magnetic poles,\nthere we may expect an evolution of electricity. In the northern\nregions, where the polar direction is nearly perpendicular to the\nhorizon, all horizontal motions of conductors will produce electricity;\nhorizontal wheels, for example, made of metal; likewise all running\nstreams will evolve a current of electricity, which will circulate round\nthem; and the air thus charged with electricity may be one of the causes\nof the Aurora Borealis. In the equatorial regions, on the contrary,\nupright wheels placed parallel to the equator will originate a voltaic\ncircuit, and waterfalls will naturally become electric.\n\nFor a second example; it has been proved, chiefly by the researches of\nProfessor Graham, that gases have a strong tendency to permeate animal\nmembranes, and diffuse themselves through the spaces which such\nmembranes inclose, notwithstanding the presence of other gases in those\nspaces. 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\nhuman or animal body, when surrounded with any gas not already contained\nwithin the body, absorbs it rapidly; such, for instance, as the gases of\nputrefying matters: which helps to explain malaria. 2nd. The carbonic\nacid gas of effervescing drinks, evolved in the stomach, permeates its\nmembranes, and rapidly spreads through the system. 3rd. Alcohol taken\ninto the stomach passes into vapour and spreads through the system with\ngreat rapidity; (which, combined with the high combustibility of\nalcohol, or in other words its ready combination with oxygen, may\nperhaps help to explain the bodily warmth immediately consequent on\ndrinking spirituous liquors.) 4th. In any state of the body in which\npeculiar gases are formed within it, these will rapidly exhale through\nall parts of the body; and hence the rapidity with which, in certain\nstates of disease, the surrounding atmosphere becomes tainted. 5th. The\nputrefaction of the interior parts of a carcase will proceed as rapidly\nas that of the exterior, from the ready passage outwards of the gaseous\nproducts. 6th. The exchange of oxygen and carbonic acid in the lungs is\nnot prevented, but rather promoted, by the intervention of the membrane\nof the lungs and the coats of the blood-vessels between the blood and\nthe 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\n\u00a7 5. The following is a deduction which confirms, by explaining, the old\nbut not undisputed empirical generalization, that soda powders weaken\nthe human system. These powders, consisting of a mixture of tartaric\nacid with bicarbonate of soda, from which the carbonic acid is set free,\nmust pass into the stomach as tartrate of soda. Now, neutral tartrates,\ncitrates, and acetates of the alkalis are found, in their passage\nthrough the system, to be changed into carbonates; and to convert a\ntartrate into a carbonate requires an additional quantity of oxygen, the\nabstraction of which must lessen the oxygen destined for assimilation\nwith the blood, on the quantity of which the vigorous action of the\nhuman system partly depends.\n\nThe instances of new theories agreeing with and explaining old\nempiricisms, are innumerable. All the just remarks made by experienced\npersons on human character and conduct, are so many special laws, which\nthe general laws of the human mind explain and resolve. The empirical\ngeneralizations on which the operations of the arts have usually been\nfounded, are continually justified and confirmed on the one hand, or\ncorrected and improved on the other, by the discovery of the simpler\nscientific laws on which the efficacy of those operations depends. The\neffects of the rotation of crops, of the various manures, and other\nprocesses of improved agriculture, have been for the first time resolved\nin our own day into known laws of chemical and organic action, by Davy,\nLiebig, and others. The processes of the medical art are even now mostly\nempirical: their efficacy is concluded, in each instance, from a special\nand most precarious experimental generalization: but as science advances\nin discovering the simple laws of chemistry and physiology, progress is\nmade in ascertaining the intermediate links in the series of phenomena,\nand the more general laws on which they depend; and thus, while the old\nprocesses are either exploded, or their efficacy, in so far as real,\nexplained, better processes, founded on the knowledge of proximate\ncauses, are continually suggested and brought into use.[48] Many even of\nthe truths of geometry were generalizations from experience before they\nwere deduced from first principles. The quadrature of the cycloid is\nsaid to have been first effected by measurement, or rather by weighing a\ncycloidal card, and comparing its weight with that of a piece of similar\ncard of known dimensions.\n\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\nexperimental law, grounded on the Method of Difference. By deduction\nfrom this law, many of the more special laws which experience shows to\nexist among particular mental phenomena may be demonstrated and\nexplained:--the ease and rapidity, for instance, with which thoughts\nconnected with our passions or our more cherished interests are excited,\nand the firm hold which the facts relating to them have on our memory;\nthe vivid recollection we retain of minute circumstances which\naccompanied any object or event that deeply interested us, and of the\ntimes and places in which we have been very happy or very miserable; the\nhorror with which we view the accidental instrument of any occurrence\nwhich shocked us, or the locality where it took place, and the pleasure\nwe derive from any memorial of past enjoyment; all these effects being\nproportional to the sensibility of the individual mind, and to the\nconsequent intensity of the pain or pleasure from which the association\noriginated. It has been suggested by the able writer of a biographical\nsketch of Dr. Priestley in a monthly periodical,[49] that the same\nelementary law of our mental constitution, suitably followed out, would\nexplain a variety of mental phenomena previously inexplicable, and in\nparticular some of the fundamental diversities of human character and\ngenius. Associations being of two sorts, either between synchronous, or\nbetween successive impressions; and the influence of the law which\nrenders associations stronger in proportion to the pleasurable or\npainful character of the impressions, being felt with peculiar force in\nthe synchronous class of associations; it is remarked by the writer\nreferred to, that in minds of strong organic sensibility synchronous\nassociations will be likely to predominate, producing a tendency to\nconceive things in pictures and in the concrete, richly clothed in\nattributes and circumstances, a mental habit which is commonly called\nImagination, and is one of the peculiarities of the painter and the\npoet; while persons of more moderate susceptibility to pleasure and pain\nwill have a tendency to associate facts chiefly in the order of their\nsuccession, and such persons, if they possess mental superiority, will\naddict themselves to history or science rather than to creative art.\nThis interesting speculation the author of the present work has\nendeavoured, on another occasion, to pursue farther, and to examine how\nfar it will avail towards explaining the peculiarities of the poetical\ntemperament.[50] It is at least an example which may serve, instead of\nmany others, to show the extensive scope which exists for deductive\ninvestigation in the important and hitherto so imperfect Science of\nMind.\n\n\n\u00a7 7. The copiousness with which the discovery and explanation of special\nlaws of phenomena by deduction from simpler and more general ones has\nhere been exemplified, was prompted by a desire to characterize clearly,\nand place in its due position of importance, the Deductive Method;\nwhich, in the present state of knowledge, is destined henceforth\nirrevocably to predominate in the course of scientific investigation. A\nrevolution is peaceably and progressively effecting itself in\nphilosophy, the reverse of that to which Bacon has attached his name.\nThat great man changed the method of the sciences from deductive to\nexperimental, and it is now rapidly reverting from experimental to\ndeductive. But the deductions which Bacon abolished were from premises\nhastily snatched up, or arbitrarily assumed. The principles were neither\nestablished by legitimate canons of experimental inquiry, nor the\nresults tested by that indispensable element of a rational Deductive\nMethod, verification by specific experience. Between the primitive\nmethod of Deduction and that which I have attempted to characterize,\nthere is all the difference which exists between the Aristotelian\nphysics 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\nNewtonian theory), will be found, in all, or even in most cases, among\ntruths now known and admitted. We may rest assured, that many of the\nmost general laws of nature are as yet entirely unthought of; and that\nmany others, destined hereafter to assume the same character, are known,\nif at all, only as laws or properties of some limited class of\nphenomena; just as electricity, now recognised as one of the most\nuniversal of natural agencies, was once known only as a curious property\nwhich certain substances acquired by friction, of first attracting and\nthen repelling light bodies. If the theories of heat, cohesion,\ncrystallization, and chemical action, are destined, as there can be\nlittle doubt that they are, to become deductive, the truths which will\nthen be regarded as the _principia_ of those sciences would probably, if\nnow announced, appear quite as novel[51] as the law of gravitation\nappeared to the cotemporaries of Newton; possibly even more so, since\nNewton's law, after all, was but an extension of the law of weight--that\nis, of a generalization familiar from of old, and which already\ncomprehended a not inconsiderable body of natural phenomena. The general\nlaws of a similarly commanding character, which we still look forward to\nthe discovery of, may not always find so much of their foundations\nalready laid.\n\nThese general truths will doubtless make their first appearance in the\ncharacter of hypotheses; not proved, nor even admitting of proof, in\nthe first instance, but assumed as premises for the purpose of deducing\nfrom them the known laws of concrete phenomena. But this, though their\ninitial, cannot be their final state. To entitle an hypothesis to be\nreceived as one of the truths of nature, and not as a mere technical\nhelp to the human faculties, it must be capable of being tested by the\ncanons of legitimate induction, and must actually have been submitted to\nthat test. When this shall have been done, and done successfully,\npremises will have been obtained from which all the other propositions\nof the science will thenceforth be presented as conclusions, and the\nscience will, by means of a new and unexpected Induction, be rendered\nDeductive.\n\nFOOTNOTES:\n\n[1] Dr. Whewell thinks it improper to apply the term Induction to any\noperation not terminating in the establishment of a general truth.\nInduction, he says (_Philosophy of Discovery_, p. 245), \"is not the same\nthing as experience and observation. Induction is experience or\nobservation _consciously_ looked at in a _general_ form. This\nconsciousness and generality are necessary parts of that knowledge which\nis science.\" And he objects (p. 241) to the mode in which the word\nInduction is employed in this work, as an undue extension of that term\n\"not only to the cases in which the general induction is consciously\napplied to a particular instance, but to the cases in which the\nparticular instance is dealt with by means of experience in that rude\nsense in which experience can be asserted of brutes, and in which of\ncourse we can in no way imagine that the law is possessed or understood\nas a general proposition.\" This use of the term he deems a \"confusion of\nknowledge with practical tendencies.\"\n\nI disclaim, as strongly as Dr. Whewell can do, the application of such\nterms as induction, inference, or reasoning, to operations performed by\nmere instinct, that is, from an animal impulse, without the exertion of\nany intelligence. But I perceive no ground for confining the use of\nthose terms to cases in which the inference is drawn in the forms and\nwith the precautions required by scientific propriety. To the idea of\nScience, an express recognition and distinct apprehension of general\nlaws as such, is essential: but nine-tenths of the conclusions drawn\nfrom experience in the course of practical life, are drawn without any\nsuch recognition: they are direct inferences from known cases, to a case\nsupposed to be similar. I have endeavoured to show that this is not only\nas legitimate an operation, but substantially the same operation, as\nthat of ascending from known cases to a general proposition; except that\nthe latter process has one great security for correctness which the\nformer does not possess. In Science, the inference must necessarily pass\nthrough the intermediate stage of a general proposition, because Science\nwants its conclusions for record, and not for instantaneous use. But the\ninferences drawn for the guidance of practical affairs, by persons who\nwould often be quite incapable of expressing in unexceptionable terms\nthe corresponding generalizations, may and frequently do exhibit\nintellectual powers quite equal to any which have ever been displayed in\nScience: and if these inferences are not inductive, what are they? The\nlimitation imposed on the term by Dr. Whewell seems perfectly arbitrary;\nneither justified by any fundamental distinction between what he\nincludes and what he desires to exclude, nor sanctioned by usage, at\nleast from the time of Reid and Stewart, the principal legislators (as\nfar as the English language is concerned) of modern metaphysical\nterminology.\n\n[2] Supra, p. 214.\n\n[3] _Novum Organum Renovatum_, pp. 72, 73.\n\n[4] _Novum Organum Renovatum_, p. 32.\n\n[5] _Cours de Philosophie Positive_, vol. ii. p. 202.\n\n[6] Dr. Whewell, in his reply, contests the distinction here drawn, and\nmaintains, that not only different descriptions, but different\nexplanations of a phenomenon, may all be true. Of the three theories\nrespecting the motions of the heavenly bodies, he says (_Philosophy of\nDiscovery_, p. 231): \"Undoubtedly all these explanations may be true and\nconsistent with each other, and would be so if each had been followed\nout so as to show in what manner it could be made consistent with the\nfacts. And this was, in reality, in a great measure done. The doctrine\nthat the heavenly bodies were moved by vortices was successfully\nmodified, so that it came to coincide in its results with the doctrine\nof an inverse-quadratic centripetal force.... When this point was\nreached, the vortex was merely a machinery, well or ill devised, for\nproducing such a centripetal force, and therefore did not contradict the\ndoctrine of a centripetal force. Newton himself does not appear to have\nbeen averse to explaining gravity by impulse. So little is it true that\nif one theory be true the other must be false. The attempt to explain\ngravity by the impulse of streams of particles flowing through the\nuniverse in all directions, which I have mentioned in the _Philosophy_,\nis so far from being inconsistent with the Newtonian theory, that it is\nfounded entirely upon it. And even with regard to the doctrine, that the\nheavenly bodies move by an inherent virtue; if this doctrine had been\nmaintained in any such way that it was brought to agree with the facts,\nthe inherent virtue must have had its laws determined; and then it would\nhave been found that the virtue had a reference to the central body; and\nso, the 'inherent virtue' must have coincided in its effect with the\nNewtonian force; and then, the two explanations would agree, except so\nfar as the word 'inherent' was concerned. And if such a part of an\nearlier theory as this word _inherent_ indicates, is found to be\nuntenable, it is of course rejected in the transition to later and more\nexact theories, in Inductions of this kind, as well as in what Mr. Mill\ncalls Descriptions. There is, therefore, still no validity discoverable\nin the distinction which Mr. Mill attempts to draw between descriptions\nlike Kepler's law of elliptical orbits, and other examples of\ninduction.\"\n\nIf the doctrine of vortices had meant, not that vortices existed, but\nonly that the planets moved _in the same manner_ as if they had been\nwhirled by vortices; if the hypothesis had been merely a mode of\nrepresenting the facts, not an attempt to account for them; if, in\nshort, it had been only a Description; it would, no doubt, have been\nreconcileable with the Newtonian theory. The vortices, however, were not\na mere aid to conceiving the motions of the planets, but a supposed\nphysical agent, actively impelling them; a material fact, which might be\ntrue or not true, but could not be both true and not true. According to\nDescartes' theory it was true, according to Newton's it was not true.\nDr. Whewell probably means that since the phrases, centripetal and\nprojectile force, do not declare the nature but only the direction of\nthe forces, the Newtonian theory does not absolutely contradict any\nhypothesis which may be framed respecting the mode of their production.\nThe Newtonian theory, regarded as a mere _description_ of the planetary\nmotions, does not; but the Newtonian theory as an _explanation_ of them\ndoes. For in what does the explanation consist? In ascribing those\nmotions to a general law which obtains between all particles of matter,\nand in identifying this with the law by which bodies fall to the ground.\nIf the planets are kept in their orbits by a force which draws the\nparticles composing them towards every other particle of matter in the\nsolar system, they are not kept in those orbits by the impulsive force\nof certain streams of matter which whirl them round. The one explanation\nabsolutely excludes the other. Either the planets are not moved by\nvortices, or they do not move by a law common to all matter. It is\nimpossible that both opinions can be true. As well might it be said that\nthere is no contradiction between the assertions, that a man died\nbecause somebody killed him, and that he died a natural death.\n\nSo, again, the theory that the planets move by a virtue inherent in\ntheir celestial nature, is incompatible with either of the two others:\neither that of their being moved by vortices, or that which regards them\nas moving by a property which they have in common with the earth and all\nterrestrial bodies. Dr. Whewell says that the theory of an inherent\nvirtue agrees with Newton's when the word inherent is left out, which of\ncourse it would be (he says) if \"found to be untenable.\" But leave that\nout, and where is the theory? The word inherent _is_ the theory. When\nthat is omitted, there remains nothing except that the heavenly bodies\nmove by \"a virtue,\" _i.e._ by a power of some sort; or by virtue of\ntheir celestial nature, which directly contradicts the doctrine that\nterrestrial bodies fall by the same law.\n\nIf Dr. Whewell is not yet satisfied, any other subject will serve\nequally well to test his doctrine. He will hardly say that there is no\ncontradiction between the emission theory and the undulatory theory of\nlight; or that there can be both one and two electricities; or that the\nhypothesis of the production of the higher organic forms by development\nfrom the lower, and the supposition of separate and successive acts of\ncreation, are quite reconcileable; or that the theory that volcanoes are\nfed from a central fire, and the doctrines which ascribe them to\nchemical action at a comparatively small depth below the earth's\nsurface, are consistent with one another, and all true as far as they\ngo.\n\nIf different explanations of the same fact cannot both be true, still\nless, surely, can different predictions. Dr. Whewell quarrels (on what\nground it is not necessary here to consider) with the example I had\nchosen on this point, and thinks an objection to an illustration a\nsufficient answer to a theory. Examples not liable to his objection are\neasily found, if the proposition that conflicting predictions cannot\nboth be true, can be made clearer by any examples. Suppose the\nphenomenon to be a newly-discovered comet, and that one astronomer\npredicts its return once in every 300 years--another once in every 400:\ncan they both be right? When Columbus predicted that by sailing\nconstantly westward he should in time return to the point from which he\nset out, while others asserted that he could never do so except by\nturning back, were both he and his opponents true prophets? Were the\npredictions which foretold the wonders of railways and steamships, and\nthose which averred that the Atlantic could never be crossed by steam\nnavigation, nor a railway train propelled ten miles an hour, both (in\nDr. Whewell's words) \"true, and consistent with one another\"?\n\nDr. Whewell sees no distinction between holding contradictory opinions\non a question of fact, and merely employing different analogies to\nfacilitate the conception of the same fact. The case of different\nInductions belongs to the former class, that of different Descriptions\nto the latter.\n\n[7] _Phil. of Discov._ p. 256.\n\n[8] _Essays on the Pursuit of Truth._\n\n[9] In the first edition a note was appended at this place, containing\nsome criticism on Archbishop Whately's mode of conceiving the relation\nbetween Syllogism and Induction. In a subsequent issue of his _Logic_,\nthe Archbishop made a reply to the criticism, which induced me to cancel\npart of the note, incorporating the remainder in the text. In a still\nlater edition, the Archbishop observes in a tone of something like\ndisapprobation, that the objections, \"doubtless from their being fully\nanswered and found untenable, were silently suppressed,\" and that hence\nhe might appear to some of his readers to be combating a shadow. On this\nlatter point, the Archbishop need give himself no uneasiness. His\nreaders, I make bold to say, will fully credit his mere affirmation that\nthe objections have actually been made.\n\nBut as he seems to think that what he terms the suppression of the\nobjections ought not to have been made \"silently,\" I now break that\nsilence, and state exactly what it is that I suppressed, and why. I\nsuppressed that alone which might be regarded as personal criticism on\nthe Archbishop. I had imputed to him the having omitted to ask himself a\nparticular question. I found that he had asked himself the question, and\ncould give it an answer consistent with his own theory. I had also,\nwithin the compass of a parenthesis, hazarded some remarks on certain\ngeneral characteristics of Archbishop Whately as a philosopher. These\nremarks, though their tone, I hope, was neither disrespectful nor\narrogant, I felt, on reconsideration, that I was hardly entitled to\nmake; least of all, when the instance which I had regarded as an\nillustration of them, failed, as I now saw, to bear them out. The real\nmatter at the bottom of the whole dispute, the different view we take of\nthe function of the major premise, remains exactly where it was; and so\nfar was I from thinking that my opinion had been \"fully answered\" and\nwas \"untenable,\" that in the same edition in which I cancelled the note,\nI not only enforced the opinion by further arguments, but answered\n(though without naming him) those of the Archbishop.\n\nFor not having made this statement before, I do not think it needful to\napologize. It would be attaching very great importance to one's smallest\nsayings, to think a formal retractation requisite every time that one\ncommits an error. Nor is Archbishop Whately's well-earned fame of so\ntender a quality as to require, that in withdrawing a slight criticism\non him I should have been bound to offer a public _amende_ for having\nmade it.\n\n[10] But though it is a condition of the validity of every induction\nthat there be uniformity in the course of nature, it is not a necessary\ncondition that the uniformity should pervade all nature. It is enough\nthat it pervades the particular class of phenomena to which the\ninduction relates. An induction concerning the motions of the planets,\nor the properties of the magnet, would not be vitiated though we were to\nsuppose that wind and weather are the sport of chance, provided it be\nassumed that astronomical and magnetic phenomena are under the dominion\nof general laws. Otherwise the early experience of mankind would have\nrested on a very weak foundation; for in the infancy of science it could\nnot be known that _all_ phenomena are regular in their course.\n\nNeither would it be correct to say that every induction by which we\ninfer any truth, implies the general fact of uniformity _as foreknown_,\neven in reference to the kind of phenomena concerned. It implies,\n_either_ that this general fact is already known, _or_ that we may now\nknow it: as the conclusion, the Duke of Wellington is mortal, drawn from\nthe instances A, B, and C, implies either that we have already concluded\nall men to be mortal, or that we are now entitled to do so from the same\nevidence. A vast amount of confusion and paralogism respecting the\ngrounds of Induction would be dispelled by keeping in view these simple\nconsiderations.\n\n[11] Infra, chap. xxi.\n\n[12] Infra, chap. xxi. xxii.\n\n[13] Dr. Whewell (_Phil. of Discov._ p. 246) will not allow these and\nsimilar erroneous judgments to be called inductions; inasmuch as such\nsuperstitious fancies \"were not collected from the facts by seeking a\nlaw of their occurrence, but were suggested by an imagination of the\nanger of superior powers, shown by such deviations from the ordinary\ncourse of nature.\" I conceive the question to be, not in what manner\nthese notions were at first suggested, but by what evidence they have,\nfrom time to time, been supposed to be substantiated. If the believers\nin these erroneous opinions had been put on their defence, they would\nhave referred to experience: to the comet which preceded the\nassassination of Julius C\u00e6sar, or to oracles and other prophecies known\nto have been fulfilled. It is by such appeals to facts that all\nanalogous superstitions, even in our day, attempt to justify themselves;\nthe supposed evidence of experience is necessary to their hold on the\nmind. I quite admit that the influence of such coincidences would not be\nwhat it is, if strength were not lent to it by an antecedent\npresumption; but this is not peculiar to such cases; preconceived\nnotions of probability form part of the explanation of many other cases\nof belief on insufficient evidence. The _\u00e0 priori_ prejudice does not\nprevent the erroneous opinion from being sincerely regarded as a\nlegitimate conclusion from experience; though it improperly predisposes\nthe mind to that interpretation of experience.\n\nThus much in defence of the sort of examples objected to. But it would\nbe easy to produce instances, equally adapted to the purpose, and in\nwhich no antecedent prejudice is at all concerned. \"For many ages,\" says\nArchbishop Whately, \"all farmers and gardeners were firmly\nconvinced--and convinced of their knowing it by experience--that the\ncrops would never turn out good unless the seed were sown during the\nincrease of the moon.\" This was induction, but bad induction: just as a\nvicious syllogism is reasoning, but bad reasoning.\n\n[14] The assertion, that any and every one of the conditions of a\nphenomenon may be and is, on some occasions and for some purposes,\nspoken of as the cause, has been disputed by an intelligent reviewer of\nthis work in the _Prospective Review_ (the predecessor of the justly\nesteemed _National Review_), who maintains that \"we always apply the\nword cause rather to that element in the antecedents which exercises\n_force_, and which would _tend_ at all times to produce the same or a\nsimilar effect to that which, under certain conditions, it would\nactually produce.\" And he says, that \"every one would feel\" the\nexpression, that the cause of a surprise was the sentinel's being off\nhis post, to be incorrect; but that the \"allurement or force which\n_drew_ him off his post, might be so called, because in doing so it\nremoved a resisting power which would have prevented the surprise.\" I\ncannot think that it would be wrong to say, that the event took place\nbecause the sentinel was absent, and yet right to say that it took place\nbecause he was bribed to be absent. Since the only direct effect of the\nbribe was his absence, the bribe could be called the remote cause of the\nsurprise, only on the supposition that the absence was the proximate\ncause; nor does it seem to me that any one (who had not a theory to\nsupport) would use the one expression and reject the other.\n\nThe reviewer observes, that when a person dies of poison, his possession\nof bodily organs is a necessary condition, but that no one would ever\nspeak of it as the cause. I admit the fact; but I believe the reason to\nbe, that the occasion could never arise for so speaking of it; for when\nin the inaccuracy of common discourse we are led to speak of some one\ncondition of a phenomenon as its cause, the condition so spoken of is\nalways one which it is at least possible that the hearer may require to\nbe informed of. The possession of bodily organs is a known condition,\nand to give that as the answer, when asked the cause of a person's\ndeath, would not supply the information sought. Once conceive that a\ndoubt could exist as to his having bodily organs, or that he were to be\ncompared with some being who had them not, and cases may be imagined in\nwhich it might be said that his possession of them was the cause of his\ndeath. If Faust and Mephistopheles together took poison, it might be\nsaid that Faust died because he was a human being, and had a body, while\nMephistopheles survived because he was a spirit.\n\nIt is for the same reason that no one (as the reviewer remarks) \"calls\nthe cause of a leap, the muscles or sinews of the body, though they are\nnecessary conditions; nor the cause of a self-sacrifice, the knowledge\nwhich was necessary for it; nor the cause of writing a book, that a man\nhas time for it, which is a necessary condition.\" These conditions\n(besides that they are antecedent _states_, and not proximate antecedent\n_events_, and are therefore never the conditions in closest apparent\nproximity to the effect) are all of them so obviously implied, that it\nis hardly possible there should exist that necessity for insisting on\nthem, which alone gives occasion for speaking of a single condition as\nif it were the cause. Wherever this necessity exists in regard to some\none condition, and does not exist in regard to any other, I conceive\nthat it is consistent with usage, when scientific accuracy is not aimed\nat, to apply the name cause to that one condition. If the only condition\nwhich can be supposed to be unknown is a negative condition, the\nnegative condition may be spoken of as the cause. It might be said that\na person died for want of medical advice: though this would not be\nlikely to be said, unless the person was already understood to be ill,\nand in order to indicate that this negative circumstance was what made\nthe illness fatal, and not the weakness of his constitution, or the\noriginal virulence of the disease. It might be said that a person was\ndrowned because he could not swim; the positive condition, namely, that\nhe fell into the water, being already implied in the word drowned. And\nhere let me remark, that his falling into the water is in this case the\nonly positive condition: all the conditions not expressly or virtually\nincluded in this (as that he could not swim, that nobody helped him, and\nso forth) are negative. Yet, if it were simply said that the cause of a\nman's death was falling into the water, there would be quite as great a\nsense of impropriety in the expression, as there would be if it were\nsaid that the cause was his inability to swim; because, though the one\ncondition is positive and the other negative, it would be felt that\nneither of them was sufficient, without the other, to produce death.\n\nWith regard to the assertion that nothing is termed the cause, except\nthe element which exerts active force; I wave the question as to the\nmeaning of active force, and accepting the phrase in its popular sense,\nI revert to a former example, and I ask, would it be more agreeable to\ncustom to say that a man fell because his foot slipped in climbing a\nladder, or that he fell because of his weight? for his weight, and not\nthe motion of his foot, was the active force which determined his fall.\nIf a person walking out in a frosty day, stumbled and fell, it might be\nsaid that he stumbled because the ground was slippery, or because he was\nnot sufficiently careful; but few people, I suppose, would say, that he\nstumbled because he walked. Yet the only active force concerned was that\nwhich he exerted in walking: the others were mere negative conditions;\nbut they happened to be the only ones which there could be any necessity\nto state; for he walked, most likely, in exactly his usual manner, and\nthe negative conditions made all the difference. Again, if a person were\nasked why the army of Xerxes defeated that of Leonidas, he would\nprobably say, because they were a thousand times the number; but I do\nnot think he would say, it was because they fought, though that was the\nelement of active force. To borrow another example, used by Mr. Grove\nand by Mr. Baden Powell, the opening of floodgates is said to be the\ncause of the flow of water; yet the active force is exerted by the water\nitself, and opening the floodgates merely supplies a negative condition.\nThe reviewer adds, \"there are some conditions absolutely passive, and\nyet absolutely necessary to physical phenomena, viz. the relations of\nspace and time; and to these no one ever applies the word cause without\nbeing immediately arrested by those who hear him.\" Even from this\nstatement I am compelled to dissent. Few persons would feel it\nincongruous to say (for example) that a secret became known because it\nwas spoken of when A. B. was within hearing; which is a condition of\nspace: or that the cause why one of two particular trees is taller than\nthe other, is that it has been longer planted; which is a condition of\ntime.\n\n[15] There are a few exceptions; for there are some properties of\nobjects which seem to be purely preventive; as the property of opaque\nbodies, by which they intercept the passage of light. This, as far as we\nare able to understand it, appears an instance not of one cause\ncounteracting another by the same law whereby it produces its own\neffects, but of an agency which manifests itself in no other way than in\ndefeating the effects of another agency. If we knew on what other\nrelations to light, or on what peculiarities of structure, opacity\ndepends, we might find that this is only an apparent, not a real,\nexception to the general proposition in the text. In any case it needs\nnot affect the practical application. The formula which includes all the\nnegative conditions of an effect in the single one of the absence of\ncounteracting causes, is not violated by such cases as this; though, if\nall counteracting agencies were of this description, there would be no\npurpose served by employing the formula, since we should still have to\nenumerate specially the negative conditions of each phenomenon, instead\nof regarding them as implicitly contained in the positive laws of the\nvarious other agencies in nature.\n\n[16] I mean by this expression, the ultimate laws of nature (whatever\nthey may be) as distinguished from the derivative laws and from the\ncollocations. The diurnal revolution of the earth (for example) is not a\npart of the constitution of things, because nothing can be so called\nwhich might possibly be terminated or altered by natural causes.\n\n[17] I use the words \"straight line\" for brevity and simplicity. In\nreality the line in question is not exactly straight, for, from the\neffect of refraction, we actually see the sun for a short interval\nduring which the opaque mass of the earth is interposed in a direct line\nbetween the sun and our eyes; thus realizing, though but to a limited\nextent, the coveted desideratum of seeing round a corner.\n\n[18] _Second Burnett Prize Essay_, by Principal Tulloch, p. 25.\n\n[19] _Letters on the Philosophy of the Human Mind_, First Series, p.\n219.\n\n[20] _Essays_, pp. 206-208.\n\n[21] To the universality which mankind are agreed in ascribing to the\nLaw of Causation, there is one claim of exception, one disputed case,\nthat of the Human Will; the determinations of which, a large class of\nmetaphysicians are not willing to regard as following the causes called\nmotives, according to as strict laws as those which they suppose to\nexist in the world of mere matter. This controverted point will undergo\na special examination when we come to treat particularly of the Logic of\nthe Moral Sciences (Book vi. ch. 2). In the mean time I may remark that\nthese metaphysicians, who, it must be observed, ground the main part of\ntheir objection on the supposed repugnance of the doctrine in question\nto our consciousness, seem to me to mistake the fact which consciousness\ntestifies against. What is really in contradiction to consciousness,\nthey would, I think, on strict self-examination, find to be, the\napplication to human actions and volitions of the ideas involved in the\ncommon use of the term Necessity; which I agree with them in objecting\nto. But if they would consider that by saying that a person's actions\n_necessarily_ follow from his character, all that is really meant (for\nno more is meant in any case whatever of causation) is that he\ninvariably _does_ act in conformity to his character, and that any one\nwho thoroughly knew his character would certainly predict how he would\nact in any supposable case; they probably would not find this doctrine\neither contrary to their experience or revolting to their feelings. And\nno more than this is contended for by any one but an Asiatic fatalist.\n\n[22] _Lectures on Metaphysics_, vol. ii. Lect. xxxix. pp. 391-2.\n\nI regret that I cannot invoke the authority of Sir William Hamilton in\nfavour of my own opinions on Causation, as I can against the particular\ntheory which I am now combating. But that acute thinker has a theory of\nCausation peculiar to himself, which has never yet, as far as I know,\nbeen analytically examined, but which, I venture to think, admits of as\ncomplete refutation as any one of the false or insufficient\npsychological theories which strew the ground in such numbers under his\npotent metaphysical scythe. (Since examined and controverted in the\nsixteenth chapter of _An Examination of Sir William Hamilton's\nPhilosophy_).\n\n[23] Unless we are to consider as such the following statement, by one\nof the writers quoted in the text: \"In the case of mental exertion, the\nresult to be accomplished is preconsidered or meditated, and is\ntherefore known _\u00e0 priori_, or before experience.\"--(Bowen's _Lowell\nLectures on the Application of Metaphysical and Ethical Science to the\nEvidence of Religion_, Boston, 1849.) This is merely saying that when we\nwill a thing we have an idea of it. But to have an idea of what we wish\nto happen, does not imply a prophetic knowledge that it will happen.\nPerhaps it will be said that the _first time_ we exerted our will, when\nwe had of course no experience of any of the powers residing in us, we\nnevertheless must already have known that we possessed them, since we\ncannot will that which we do not believe to be in our power. But the\nimpossibility is perhaps in the words only, and not in the facts; for we\nmay _desire_ what we do not know to be in our power; and finding by\nexperience that our bodies move according to our _desire_, we may then,\nand only then, pass into the more complicated mental state which is\ntermed will.\n\nAfter all, even if we had an instinctive knowledge that our actions\nwould follow our will, this, as Brown remarks, would prove nothing as to\nthe nature of Causation. Our knowing, previous to experience, that an\nantecedent will be followed by a certain consequent, would not prove the\nrelation between them to be anything more than antecedence and\nconsequence.\n\n[24] Reid's _Essays on the Active Powers_, Essay iv. ch. 3.\n\n[25] _Prospective Review_ for February 1850.\n\n[26] Vide supra, p. 270, note.\n\n[27] _Westminster Review_ for October 1855.\n\n[28] See the whole doctrine in Aristotle _de Anim\u00e2_: where the [Greek:\nthreptik\u00ea psych\u00ea] is treated as exactly equivalent to [Greek: threptik\u00ea\ndynamis].\n\n[29] It deserves notice that the parts of nature, which Aristotle\nregards as presenting evidence of design, are the Uniformities: the\nphenomena in so far as reducible to law. [Greek: Tych\u00ea] and [Greek: to\nautomaton] satisfy him as explanations of the variable element in\nphenomena, but their occurring according to a fixed rule can only, to\nhis conceptions, be accounted for by an Intelligent Will. The common, or\nwhat may be called the instinctive, religious interpretation of nature,\nis the reverse of this. The events in which men spontaneously see the\nhand of a supernatural being, are those which cannot, as they think, be\nreduced to a physical law. What they can distinctly connect with\nphysical causes, and especially what they can predict, though of course\nascribed to an Author of Nature if they already recognise such an\nauthor, might be conceived, they think, to arise from a blind fatality,\nand in any case do not appear to them to bear so obviously the mark of a\ndivine will. And this distinction has been countenanced by eminent\nwriters on Natural Theology, in particular by Dr. Chalmers: who thinks\nthat though design is present everywhere, the irresistible evidence of\nit is to be found not in the _laws_ of nature but in the collocations,\n_i.e._ in the part of nature in which it is impossible to trace any law.\nA few properties of dead matter might, he thinks, conceivably account\nfor the regular and invariable succession of effects and causes; but\nthat the different kinds of matter have been so placed as to promote\nbeneficent ends, is what he regards as the proof of a Divine Providence.\nMr. Baden Powell, in his Essay entitled \"Philosophy of Creation,\" has\nreturned to the point of view of Aristotle and the ancients, and\nvigorously reasserts the doctrine that the indication of design in the\nuniverse is not special adaptations, but Uniformity and Law, these being\nthe evidences of mind, and not what appears to us to be a provision for\nour uses. While I decline to express any opinion here on this _vexata\nqu\u00e6stio_, I ought not to mention Mr. Powell's volume without the\nacknowledgment due to the philosophic spirit which pervades generally\nthe three Essays composing it, forming in the case of one of them (the\n\"Unity of Worlds\") an honourable contrast with the other dissertations,\nso far as they have come under my notice, which have appeared on either\nside of that controversy.\n\n[30] In the words of Fontenelle, another celebrated Cartesian, \"les\nphilosophes aussi bien que le peuple avaient cru que l'\u00e2me et le corps\nagissaient r\u00e9ellement et physiquement l'un sur l'autre. Descartes vint,\nqui prouva que leur nature ne permettait point cette sorte de\ncommunication v\u00e9ritable, et qu'ils n'en pouvaient avoir qu'une\napparente, dont Dieu \u00e9tait le M\u00e9diateur.\"--_Oeuvres de Fontenelle_,\ned. 1767, tom. v. p. 534.\n\n[31] I omit, for simplicity, to take into account the effect, in this\nlatter case, of the diminution of pressure, in diminishing the flow of\nwater through the drain; which evidently in no way affects the truth or\napplicability of the principle, since when the two causes act\nsimultaneously the conditions of that diminution of pressure do not\narise.\n\n[32] Unless, indeed, the consequent was generated not by the antecedent,\nbut by the means employed to produce the antecedent. As, however, these\nmeans are under our power, there is so far a probability that they are\nalso sufficiently within our knowledge, to enable us to judge whether\nthat could be the case or not.\n\n[33] _Discourse on the Study of Natural Philosophy_, p. 179.\n\n[34] For this speculation, as for many other of my scientific\nillustrations, I am indebted to Professor Bain, of Aberdeen, who has\nsince, in his profound treatises entitled \"The Senses and the\nIntellect,\" and \"The Emotions and the Will,\" carried the analytic\ninvestigation of the mental phenomena according to the methods of\nphysical science, to the most advanced point which it has yet reached,\nand has worthily inscribed his name among the successive constructors of\nan edifice to which Hartley, Brown, and James Mill had each contributed\ntheir part.\n\n[35] This view of the necessary coexistence of opposite excitements\ninvolves a great extension of the original doctrine of two\nelectricities. The early theorists assumed that, when amber was rubbed,\nthe amber was made positive and the rubber negative to the same degree;\nbut it never occurred to them to suppose that the existence of the amber\ncharge was dependent on an opposite charge in the bodies with which the\namber was contiguous, while the existence of the negative charge on the\nrubber was equally dependent on a contrary state of the surfaces that\nmight accidentally be confronted with it; that, in fact, in a case of\nelectrical excitement by friction, four charges were the minimum that\ncould exist. But this double electrical action is essentially implied in\nthe explanation now universally adopted in regard to the phenomena of\nthe common electric machine.\n\n[36] Pp. 159-162.\n\n[37] Infra, book iv. ch. ii. On Abstraction.\n\n[38] I must, however, remark, that this example, which seems to militate\nagainst the assertion we made of the comparative inapplicability of the\nMethod of Difference to cases of pure observation, is really one of\nthose exceptions which, according to a proverbial expression, prove the\ngeneral rule. For in this case, in which Nature, in her experiment,\nseems to have imitated the type of the experiments made by man, she has\nonly succeeded in producing the likeness of man's most imperfect\nexperiments; namely, those in which, though he succeeds in producing the\nphenomenon, he does so by employing complex means, which he is unable\nperfectly to analyse, and can form therefore no sufficient judgment what\nportion of the effects may be due, not to the supposed cause, but to\nsome unknown agency of the means by which that cause was produced. In\nthe natural experiment which we are speaking of, the means used was the\nclearing off a canopy of clouds; and we certainly do not know\nsufficiently in what this process consists, or on what it depends, to be\ncertain _\u00e0 priori_ that it might not operate upon the deposition of dew\nindependently of any thermometric effect at the earth's surface. Even,\ntherefore, in a case so favourable as this to Nature's experimental\ntalents, her experiment is of little value except in corroboration of a\nconclusion already attained through other means.\n\n[39] In his subsequent work, _Outlines of Astronomy_ (\u00a7 570), Sir John\nHerschel suggests another possible explanation of the acceleration of\nthe revolution of a comet.\n\n[40] Discourse, pp. 156-8, and 171.\n\n[41] _Outlines of Astronomy_, \u00a7 856.\n\n[42] _Philosophy of Discovery_, pp. 263, 264.\n\n[43] See, on this point, the second chapter of the present Book.\n\n[44] Ante, ch. vii. \u00a7 1.\n\n[45] It seems hardly necessary to say that the word _impinge_, as a\ngeneral term to express collision of forces, is here used by a figure of\nspeech, and not as expressive of any theory respecting the nature of\nforce.\n\n[46] _Essays on some Unsettled Questions of Political Economy_, Essay V.\n\n[47] _Vide_ Memoir by Thomas Graham, F.R.S., Master of the Mint, \"On\nLiquid Diffusion Applied to Analysis,\" in the _Philosophical\nTransactions_ for 1862, reprinted in the _Journal of the Chemical\nSociety_, and also separately as a pamphlet.\n\n[48] It was an old generalization in surgery, that tight bandaging had a\ntendency to prevent or dissipate local inflammation. This sequence,\nbeing, in the progress of physiological knowledge, resolved into more\ngeneral laws, led to the important surgical invention made by Dr.\nArnott, the treatment of local inflammation and tumours by means of an\nequable pressure, produced by a bladder partially filled with air. The\npressure, by keeping back the blood from the part, prevents the\ninflammation, or the tumour, from being nourished: in the case of\ninflammation, it removes the stimulus, which the organ is unfit to\nreceive; in the case of tumours, by keeping back the nutritive fluid, it\ncauses the absorption of matter to exceed the supply, and the diseased\nmass is gradually absorbed and disappears.\n\n[49] Since acknowledged and reprinted in Mr. Martineau's _Miscellanies_.\n\n[50] _Dissertations and Discussions_, vol. i., fourth paper.\n\n[51] Written before the rise of the new views respecting the relation of\nheat to mechanical force; but confirmed rather than contradicted by\nthem.\n\n\nEND OF VOL. I.\n\n\n\n\n LONDON:\n SAVILL, EDWARDS AND CO., PRINTERS, CHANDOS STREET,\n COVENT GARDEN.\n\n\n\n\nTranscriber's Notes\n\n\nSpelling irregularities where there was no obviously preferred version\nwere left as is. Variants include: \"alkalies\" and \"alkalis;\" \"apprise\"\nand \"apprize;\" \"coexistent\" and \"co-existent\" (along with derivatives);\n\"coextensive\" and \"co-extensive;\" \"e. g.\" and \"e.g.\"; \"encumbered\" and\n\"incumbered;\" \"formul\u00e6\" and \"formulas;\" \"i. e.\" and \"i.e.\"; \"nonentity\"\nand \"non-entity;\" \"recal\" and \"recall\" (and derivatives); \"rectilinear\"\nand \"rectilineal;\" \"stopt\" and \"stopped.\"\n\nChanged \"3\" to \"4\" on page xiii: \"4. --and from descriptions.\"\n\nInserted missing page number, \"167,\" for Chapter VIII, section 7 on page\nxiii.\n\nMoved the semi-colon inside the quotation marks in the footnote on page\n14: \"the Science of the Formal Laws of Thought;\".\n\nChanged \"sub-divisions\" to \"subdivisions\" on page 59: \"three\nsubdivisions.\"\n\nChanged \"pre-supposed\" to \"presupposed\" on page 75: \"they are\npresupposed.\"\n\nIn the footnote to page 122, changed the Greek character upsilon with\ndasia and oxia to upsilon with psili and oxia, making the\ntransliteration \"deuterai ousiai.\"\n\nChanged \"he\" to \"be\" on page 189: \"to which it may be reduced.\"\n\nChanged \"cb.\" to \"ch.\" in footnote on page 227: \"Theory of Reasoning,\nch. iv.\"\n\nChanged \"reconcilable\" to \"reconcileable\" on page 240: \"not easily\nreconcileable.\"\n\nPreserved the hyphen in \"counter-acting\" on page 280. Usually this is\nspelled without the hyphen, but this instance is in a quotation.\n\nMoved parenthesis that was after \"to\" to before it on page 321: \"(to\nreturn to a former example).\"\n\nPut \"i.e.\" in italics on page 335: \"_i.e._ by a power of some sort.\"\n\nChanged \"paralyzed\" to \"paralysed\" on page 389: \"nerves of motion were\nparalysed.\"\n\nThe footnote from page 396 refers to the footnote on page 270. There is\nno such footnote. The intent may be to refer to the footnote on page\n268. However, the text was not changed.\n\nAdded the dropped \"w\" in \"which\" on page 420: \"which the progress of the\ninquiry.\"\n\nChanged \"developes\" to \"develops\" on page 456: \"the prime conductor\ndevelops.\"\n\nRemoved the additional period at the end of the footnote on page 457:\n\"Pp. 159-162.\"\n\nAdded the dropped \"l\" to \"essential\" on page 515: \"an essential\nrequisite.\"\n\nRemoved extra opening quotation mark before \"gum\" on page 532:\n\"vegetable gum is not digested.\"\n\nIn the Latin-1 text version, the oe-ligature was replaced by the two\ncharacters, \"oe\" (or \"Oe\" when capitalized).\n\n\n\n\n\n
","title":"A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. I","tradition":"philosophy-ethics","translated_text":null,"word_count":203110}