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 INDUCTIVE LOGIC 
 
 INDUCTIVF L.OGIC 
 
 FOWLER 
 
Hontion 
 MACMILLAN AND CO. 
 
 PUBLISHERS TO THE UNIVERSITY OF 
 
 0xfotO 
 
THE ELEMENTS 
 
 OF 
 
 INDUCTIVE LOGIC 
 
 DESIGNED MAINLY 
 FOR THE USE OF STUDENTS IN THE UNIVERSITIES 
 
 'BY 
 
 THOMAS FOWLER, M.A. 
 
 Professor of Logic in the Umversity of Oxford 
 Fellow of Lincoln College 
 
 THIED BDITIOlrt^ // 
 
 CORRECTED ^idkpVISJ^P ^^ 
 
 
 •/ / 
 
 AT THE CLARENDON PRESS \ J^ 
 
 MDCCCLXXVI 
 
 \^All rights reserved^ 
 
BY THE SAME AUTHOR, 
 
 THE ELEMENTS OF DEDUCTIVE LOGIC. 
 
 Sixth Edition, fwith a Collection of Examplei. 
 Oxford : Clarendon Press. Ext. fcap. 8vo, cloth, 3s. 6d. 
 
PREFACE TO THE FIRST EDITION. 
 
 The object of the following work is to serve as an 
 introduction to that branch of scientific method which 
 is known as Induction. It is designed mainly for the 
 use of those who have not time or opportunity to con- 
 sult larger works, or who require some preliminary 
 knowledge before they can profitably enter upon the 
 study of them. , 
 
 To the works of Mr. Mill, Dr. Whewell, and Sir John 
 Herschel, the Author must,\once for all, express his obli- 
 gations. *He has, however,' if he may be allowed to 
 repeat the language already employed in the Preface 
 to his Manual of Deductive Logic ^ ' endeavoured, on all 
 disputed points, to reason out his own conclusions, feel- 
 ing assured that no manual, however elementary, can be 
 of real service to the student, unless it express what may 
 be called the '' reasoned opinions '' of its author.' 
 
 The analysis of Induction presents far more difficulties 
 than that of Deduction, and requires to be illustrated 
 
VI PREFACE TO THE FIRST EDITION. 
 
 by far more numerous and intricate examples. But, 
 on the other hand, it is more interesting both to the 
 teacher and to the student; and, being a comparatively 
 recent study, is less hampered by conventionalities of 
 treatment. Since the time of Bacon, it has always, with 
 more or less of success, claimed a place in liberal 
 education, and many, to whom the technical terms and 
 subtle distinctions of the older logic are justly repulsive, 
 have experienced a peculiar delight in attempting to 
 discover and test the grounds on which the results of 
 modern science mainly rest. 
 
 The study of Deductive Logic can be of little service 
 unless it be supplemented by, at least, some knowledge 
 of the principles of Induction, which supplies its pre- 
 misses. Many of the objections directed against the 
 study of Logic are due to the narrow conceptions which 
 are entertained of its province, and might be easily met 
 by showing that the study, when we include both its 
 parts, has a much wider range than is popularly assigned 
 to it. 
 
 Though the present work is mainly intended for stu- 
 dents in the Universities, it is hoped that it will be found 
 to present some interest for the general reader, and that 
 it may be useful to students of medicine and the physical 
 
PREFACE TO THE FIRST EDITION. Vll 
 
 sciences, as well as to some of the more advanced 
 scholars in our Public Schools. 
 
 The number of scientific examples adduced throughout 
 the work renders it necessary, perhaps, that the Author 
 should state emphatically that the work is intended as an 
 introduction, not to science, but to scientific method. Its 
 object is not to give a rdsumd of the sciences, physical 
 or social, a task to which the Author would be wholly 
 incompetent, but to show the grounds on which our 
 scientific knowledge rests, the methods by which it has 
 been built up, and the defects from which it must be 
 free. Notwithstanding its frequent incursions into the 
 domain of science, the purport of the work must be 
 regarded as strictly logical. 
 
 The examples have, as a rule, been selected from the 
 physical rather than the social sciences, as being usually 
 less open to dispute, and lying within a smaller compass. 
 Wherever it has been possible, they have been given in 
 the exact words of the author from whom they are taken. 
 
 Some of the more complicated cases of inductive 
 reasoning, such as those which deal with Progressive 
 Causes or Intermixture of Eff'ects, have, if alluded to 
 at all, been only briefly noticed. Any detailed exami- 
 nation of these more intricate questions seemed to lie 
 
Vlll PREFACE TO THE FIRST EDITION, 
 
 without the scope of the treatise. The student who has 
 leisure to pursue the subject will find ample information 
 in the pages of Mr. Mill's Logic. 
 
 It only remains for the Author to express his grateful 
 acknowledgments to those who have assisted him in the 
 execution of the work. These are, in the first place, due 
 to Dr. Liddell, Dean of Christ Church, through whose 
 hands the sheets have passed, and who, in addition to 
 revising the proofs, has, from time to time, offered many 
 very valuable suggestions. They are due also, in no 
 small degree, to Sir John Herschel and Professor Bar- 
 tholomew Price, who most kindly undertook to revise 
 the scientific examples ; to Professors Rolleston and 
 Clifton, who have frequently allowed the Author to con- 
 sult them on questions connected with the subjects of 
 their respective chairs, and to the Rev. G. W. Kitchin, 
 the Organising Secretary of the Clarendon Press Series. 
 The Author must, however, be regarded as alone re- 
 sponsible for any errors which may occur either in the 
 theoretical portion of the work or in the examples. 
 
 Lincoln College, 
 Oct. 30, 1869. 
 
PREFACE TO THE SECOND EDITION. 
 
 Some misprints, and some inaccuracies or ambigui- 
 ties of expression, which occurred in the former edition, 
 have been corrected in the present one. A few altera- 
 tions also have been made which cannot, perhaps, be 
 referred to either of these heads, and one or two 
 examples have been added. 
 
 The discussion of the questions raised by some of 
 the Author's reviewers (as, for instance, in the Scotsman, 
 the Saturday Review, and the Academy) would occupy 
 more space than could be conveniently devoted to 
 them in a work which is intended to be mainly edu- 
 cational. The Author, therefore, feels, at least for the 
 present, compelled to waive their consideration. When, 
 however, any adverse criticism has seemed to him to 
 be justified, he has either modified the passage criti- 
 cised, or has attempted to re-state it in such a manner 
 as to prevent future misunderstanding. 
 
 The Author has here, as in his recent edition of the 
 
X PREFACE TO THE SECOND EDITION. 
 
 Deductive Logic, to thank Professor Park, of Belfast, 
 for several suggestions, some of which he has gladly 
 adopted. He can only regret that the plan and object 
 of the work prevent him from availing himself of them 
 to as full an extent as he could otherwise have desired. 
 
 Lincoln College, 
 Sept, 25, 1871. 
 
PREFACE TO THE THIRD EDITION. 
 
 Since the publication of my second edition, there has 
 appeared an important work on Scientific Method, entitled 
 * The Principles of Science,' by Professor Stanley Jevons, 
 of Owens College, Manchester. To this I have made 
 occasional references in the foot-notes to my present 
 edition. ' But, as I differ entirely from Professor Jevons 
 on the fundamental question of the validity of our induc- 
 tive inferences, I think it desirable to offer a few remarks 
 on this point in the present place, rather than to intro- 
 duce controversial matter into the body of the work. 
 
 Mr. Jevbns over and over again asserts the uncertainty, 
 or the mere probability, of all inductive inferences. Thus, 
 for instance, in his chapter on the Philosophy of Induc- 
 tive Inference, he says : — * I have no objection to use 
 the words cause and causation, provided they are never 
 allowed to lead us to imagine that our knowledge of 
 nature can attain to certainty V And again: *We can 
 never recur too often to the truth that our knowledge of 
 
 ^ Vol. i. p. 260. 
 
Xll PREFACE TO THE THIRD EDITION, 
 
 the laws and future events of the external world is only 
 probable ^/ Once more : * By induction we gain no 
 certain knowledge ; but by observation, and the inverse 
 use of deductive reasoning, we estimate the probability 
 that an event which has occurred was preceded by con- 
 ditions of specified character, or that such conditions will 
 be followed by the event ^/ 
 
 At the same time, I am quite unable to reconcile with 
 these passages other passages, such as those in which 
 Mr. Jevons says : ' We know that a penny thrown into 
 the air will certainly fall upon a flat side, so that either 
 the head or tail will be uppermost *,' or, ^ I can be certain 
 that nitric acid will not dissolve gold, provided I know 
 that the substances employed really correspond to those 
 on which I tried the experiment previously ^/ 
 
 But, waiving the question of inconsistency, I maintain 
 as against Mr. Jevons that many of our inductive infer- 
 ences have all the certainty of which human knowledge 
 is capable. Is the law of gravitation one whit less certain 
 than the conclusion of the 47th Proposition of the First 
 Book of Euclid ? Or is the proposition that animal and 
 
 2 Vol. i. p. 271. 3 i^^ p^ 257. 
 
 * Id. p. 228. Mr. Jevons, however, curiously enough is not certain about 
 the truth of the Law of Gravitation. See below. ^ Id. p. 270. 
 
PREFACE TO THE THIRD EDITION, XIU 
 
 vegetable life cannot exist without moisture one whit less 
 certain than the truths of the multiplication table ? Both 
 these physical generalisations are established by the 
 Method of Difference, and, as acfual Laws of Nature, 
 admit, I conceive, of no doubt. But it may be asked 
 if they will always continue to be Laws of Nature ? 
 I reply that, unless the constitution of the Universe shall 
 be changed to an extent which I cannot now even con- 
 ceive, they will so continue, and that no reasonable man 
 has any practical doubt as to their continuance. And 
 why ? Because they are confirmed by the whole of our 
 own experiences, which in both these cases is of enormous 
 extent and variety, by the experience of our ancestors, 
 and by all that we can ascertain of the past history of 
 nature, while their reversal would involve the reversal of 
 almost all the other laws with which we are acquainted. 
 Still, it must be confessed that all our inferences from 
 the present to the future are, in one sense, hypothetical, 
 the hypothesis being that the circumstances on which 
 the laws themselves depend will continue to be the same 
 as now, that is, in the present case, that the constitution 
 of nature, in its most general features, will remain un- 
 changed ; or, to put it in still another form, that the same 
 causes will continue to produce the same effects. What 
 
XIV PREFACE TO THE THIRD EDITION. 
 
 would happen if this expectation were ever frustrated, it 
 is absolutely impossible for us to say, so completely is it 
 assumed in all our plans and reasonings. 
 
 We may say, then, that there are many inductions as 
 to the adual constitution of nature which we may accept 
 with certainty, while, with respect even to the distant 
 future, we may accept them with equal certainty, on the 
 hypothesis that the general course of nature will not be 
 radically changed. And if the general course of nature 
 were changed, might not the change affect our faculties 
 as well as the objects of our knowledge ; and, in that 
 case, are we certain that we should still regard things 
 that are equal to the same thing as equal to one another, 
 or assume that a thing cannot both be and not be in the 
 same place at the same time ? There is, in fact, no limit 
 to the possibility of scepticism with regard to the per- 
 sistency either of the laws of external nature or of the 
 laws of mind. But all our reasonings depend on the 
 hypothesis that the most general laws of matter and the 
 most general laws of mind will continue to be what they 
 are, and of the truth of this hypothesis no reasonable 
 man entertains any practical doubt ^ 
 
 ^ Thus Mr. Jevons, who, when he begins to theorise, has doubts as 
 to the truth of the law of gravitation, has no doubt, when he throws a 
 penny up into the air, that it will fall on a flat side. 
 
PREFACE TO THE THIRD EDITION, XV 
 
 There is, then, I contend, no special uncertainty 
 attaching to the truths arrived at by induction. They 
 are, indeed, Uke all other truths, relative to the present 
 constitution of nature and the present constitution of 
 the human mind, but this is a limitation to which all 
 our knowledge aUke is subject, and which it is vain for 
 us to attempt to transcend. Syllogistic reasoning implies 
 a particular constitution of the mind, as much as inductive 
 reasoning implies a particular constitution of nature. 
 Both mind and nature might, of course, be radically 
 changed by an omnipotent power, but what the con- 
 sequences of that change might be it is utterly impossible 
 for us to say. 
 
 The uniformity of nature, the trustworthiness of our 
 own faculties — these are the ultimate generalisations which ■ 
 lie at the root of all our beliefs, and are the conditions of 
 all our reasonings. It is, of course, always possible to 
 insinuate doubts as to either, but, however curious and 
 entertaining such doubts may be, they have no practical 
 influence even 6n those who originate them. Even Mr. 
 Jevons himself, we have seen, when not under the 
 dominion of his theory, speaks of some of the results 
 of induction as certain, and we can hardly conceive 
 men of science commonly speaking of the most firmly 
 
XVi PREFACE TO THE THIRD EDITION, 
 
 established generalisations of mechanics, optics, or chem- 
 istry, simply as conclusions possessing a high degree of 
 probability. 
 
 Still, Mr. Jevons, appearing not in the character of 
 a physicist, but of a logician, tells us that ' the law of 
 gravitation itself is only probably true ^/ It would be 
 interesting to learn what is the exact amount of this 
 'probability,' or, if it be meant that we can only be 
 certain that the force of gravity is acting here and now, 
 it would be an interesting enquiry to ascertain what is the 
 exact value of the * probability' that it is at this moment 
 acting in Manchester as well as in Oxford, or that it will 
 be acting at this time to-morrow as well as to-day. 
 
 But, if the conclusions of Induction are thus un- 
 certain, where, according to Mr. Jevons, are we to find 
 certainty ? ' Certainty belongs only to the deductive 
 process and to the teachings of direct intuition ^.' Does 
 it then belong to the conclusions of deduction? Ap- 
 parently not, for, at the very beginning of the work^ 
 we are told that 'in its ultimate origin or foundation, 
 all knowledge is inductive,' and Mr. Jevons is, of course, 
 too practised a logician to suppose that the conclusion 
 
 ^ p. 300. « p. 309. ^ p. 14. 
 
PREFACE TO THE THIRD EDITION, XVll 
 
 can be more certain than the premisses. The conclu- 
 sions of geometry, therefore, partake of the same * un- 
 certainty' as the results of the physical sciences, and 
 the region of 'certainty' is confined to our direct in- 
 tuitions and to the rules of syllogism (supposing, that 
 is, a difference to be intended between the 'deduc- 
 tive process' and deductive results). We venture 
 to suggest that this small residuum of ' certainty ' would 
 soon yield to solvents as powerful as those which Mr. 
 Jevons has applied to the results of induction (and 
 apparently also of deduction) ; and that, therefore, its 
 inherent 'uncertainty' is no special characteristic of 
 that method, but one which it shares with all our so- 
 called knowledge. 
 
 The fact is that in all reasoning, whether inductive 
 or deductive, we make, and must make, assumptions 
 which may theoretically be questioned, but of the truth 
 of which no man, in practice, entertains the slightest 
 doubt. Thus, in syllogistic reasoning, we assume at 
 every step the trustworthiness of memory; we assume, 
 moreover, the validity of the premisses, which, as Mr. 
 Jevons acknowledges, must ultimately be guaranteed 
 either by induction or direct observation ; lastly, we 
 assume the validity of the primary axioms of reasoning, 
 
XVlll PREFACE TO THE THIRD EDITION. 
 
 which, according to different theories, are either ob- 
 tained by induction or assumed to be necessary laws 
 of the human mind. In this sense, all reasoning and 
 all science is hypothetical, and the assumption of the 
 Uniformity of Nature does not render inductive reasoning 
 hypothetical in any special sense of the term. For, if 
 the Laws of the Uniformity of Nature and of Universal 
 Causation admit of exceptions or are liable to ultimate 
 frustration, so, for aught we know, may the axioms 
 of syllogistic reasoning or the inductions by which we 
 have established the trustworthiness of our faculties. 
 And, if the conceptions of uniformity and causation 
 be purely relative to man, so, for aught we know, may 
 be the so-called laws of thought themselves ^^. Induction 
 would only be hypothetical in a special sense, if we 
 had any reasonable ground for doubting the truth of 
 the hypotheses" on which it rests. 
 
 ^'^ According to the view of the nature and ultimate origin of human 
 knowledge, accepted both by Mr. Jevons and myself, it is, in fact, no 
 paradox but a mere truism to say that the fundamental axioms of 
 reasoning are themselves only particular uniformities of nature, arrived 
 at by the same evidence and depending for their justification on the 
 same grounds as those ultimate generalisations on causation to which 
 we give the special names of the Law of Universal Causation and 
 the Law of the Uniformity of Nature. 
 
 " I need hardly say that I am not here using the word * hypothesis * in 
 the sense of an unverified assumption. Reasoning, both inductive and 
 
PREFACE TO THE THIRD EDITION, xix 
 
 But, as *in its ultimate origin or foundation, all 
 knowledge ' (including, of course, that of the laws which 
 govern the syllogistic process itself) 'is inductive,' Pro- 
 fessor Jevons must either employ the word * certain ' 
 in a variety of senses, or he must be prepared with 
 the philosophers of the New Academy to maintain the 
 uncertainty of all knowledge whatsoever. 
 
 Such, as it appears to me, are the inconsistences 
 and paradoxes into which a very able writer has been 
 led by a tendency to over-refinement, and, still more 
 perhaps, by a desire to apply the ideas and formulae 
 of mathematics to the explanation of logical problems. 
 
 I must further express my dissidence from Mr. Jevons' 
 statement that all inductive inference is preceded by 
 hypotheses ^^, from his theory that Induction is simply 
 the Inverse Method of Deduction, and, above all, from 
 what appears to me to be the exceedingly misleading 
 
 deductive, is found on analysis to depend, in the last resort, on certain 
 assumptions or hypotheses, but then the truth of these assumptions or 
 hypotheses is guaranteed by the whole experience of the human race, 
 past and present, and beyond this guarantee we conceive that there is no 
 other attainable. In other words, all truth is relative to our faculties of 
 knowing, and this condition it is in vain for us to attempt to transcend. 
 ^^ See chap, i, pp. ii, 12, of this work, 
 
 b 2 
 
XX PREFACE TO THE THIRD EDITION. 
 
 parallel drawn between Nature and a ballot-box. 
 * Events/ says Mr. Jevons, *come out like balls from 
 the vast ballot-box of Nature ^^/ Now the balls were 
 placed in the ballot-box by human hands; the number 
 and character of them may have been due merely to 
 caprice or chance; moreover, they are all isolated en- 
 tities having no connection with each other. Would 
 it be possible to find a stronger contrast to the works 
 of nature? If natural phenomena did indeed admit 
 only of the same kind of study as the drawing of 
 balls from a ballot-box, Mr. Jevons' conception of In- 
 duction would undoubtedly be the true one, and we 
 should agree with him that *no finite number of par- 
 ticular verifications of a supposed law will render that 
 law certain.' But, just because we believe that the 
 operations of Nature are conducted with an uniformity 
 for which we seek in vain amongst the contrivances 
 of men, do we regard ourselves as capable, in many 
 cases, of predicting the one class of events with 
 certainty, while the other affords only matter for more 
 or less probable conjecture. 
 
 Intimately connected with Mr. Jevons' depreciation 
 of the value of the inductive inference is his statement 
 " Vol. i. p. 275. 
 
PREFACE TO THE THIRD EDITION. xxi 
 
 that Induction is simply the inverse method of De- 
 duction. If Induction simply consists in framing hypo- 
 theses, deducing consequences from the hypotheses, and 
 then comparing these consequences with individual facts 
 for the purpose of verifying them by specific ex- 
 perience ^^ I grant that the procedure must, in most 
 cases, be very untrustworthy. In my first Appended 
 Note to my Section on Hypothesis, I have examined 
 this account of Induction, which is virtually identical 
 with that of Dr. Whewell. In opposition to it, I main- 
 tain the following theses, which are explained and 
 defended in the course of my work: i. That our in- 
 ductions are not always preceded by hypotheses (and 
 it might be added that even where they are, the hypo- 
 thesis itself must rest originally on some basis of 
 fact, that is to say, on some induction or other, 
 however imperfect; for a hypothesis must always be 
 suggested by something of which we have had ex- 
 perience); 2. That the mere verification of our hypo- 
 theses by specific experience is not sufficient to 
 constitute a valid induction, unless the instances con- 
 form to the requirements of one of the inductive 
 methods, or (as in the case of the fundamental laws of 
 " Vol. i. pp. 307, 308. 
 
XXll PREFACE TO THE THIRD EDITION, 
 
 inductive reasoning) be coextensive with the whole 
 experience of mankind. Induction, I maintain, may 
 or may not employ hypothesis, but what is essential 
 to it is the inference from the particular to the general, 
 from the known to the unknown, and the nature of 
 this inference it is impossible to represent adequately 
 by reference to the forms of deduction. 
 
 Mr. Jevons' statement that 'induction is really the 
 reverse process of deduction ' I am wholly unable to 
 reconcile with the following statements which occur in 
 the very same page^^: 'In its ultimate origin or founda- 
 tion all knowledge is inductive,' and 'only when we 
 possess such knowledge, in the form of general propo- 
 sitions and natural laws, can we usefully apply the 
 reverse process of deduction to ascertain the exact in- 
 formation required at any moment.' When we compare 
 these statements, the circle seems complete. A precedes 
 B, and B precedes A. A depends for its validity on B, 
 and B depends for its validity on A. No wonder that 
 human reasoning affords us no ' certain ' results ! 
 
 In offering these criticisms on some fundamental 
 points of difference between Mr. Jevons and myself, 
 
 '5 Vol. i. p. 14. 
 
PREFACE TO THE THIRD EDITION. XXlll 
 
 I am far from denying the utility of many portions 
 of his work, especially the chapters on the Methods 
 of Measurement and on Hypothesis. 
 
 In the present Edition of this work, I have occa- 
 sionally availed myself of the 'Inductive Logic' of 
 Mr. Bain, a work which, though it does not, in my 
 opinion, supersede Mr. Mill's Logic, supplies on some 
 points a valuable complement to it. 
 
 In this, as in the last edition, I have to acknowledge 
 the kindness of Professor Park of Belfast, whose cor- 
 rections and suggestions have enabled me to make 
 both my works more accurate and serviceable than 
 they would otherwise have been. 
 
 Lincoln College, 
 Feb. 24, 1876. 
 
 *5^* It may be useful to the reader to be informed 
 that the new matter introduced in the present edition 
 occurs chiefly on pp. 7-9, 53, 218, 219 (Uniformities 
 of Coexistence), pp. 200-202 (the Historical Method), 
 
xxiv PREFACE TO THE THIRD EDITION. 
 
 pp. 217, 218 (the distinction between Inductio per 
 Enumerationem Simplicem and the Method of Agree- 
 ment), pp. 241-243 (the constant alternation in practice 
 of the inductive and deductive processes), and pp. 292, 
 293 (the Argument from Universal Consent). Several 
 minor alterations and additions have also been made. 
 
C O iN T E N T S. 
 
 CHAP. PAGE 
 
 '^I. The Nature of Inductive Inference ..... 3 
 
 / II. Processes subsidiary to Induction ...... 38 
 
 § I. Observation and Experiment . . . .38 
 
 § 2. Classification, Noliienclature, and Terminology . 50 
 ^'U,.' (i) Classification ....... 50 
 
 (2) Nomenclature . , . . . • ^7 
 
 (3) Terminology ........ 90 
 
 § 3. Hypothesis . . . . " . . . .95 
 
 /ni. The Inductive Methods 122 
 
 Method of Agreement . . . . . . .126 
 
 Method of Difference 144 
 
 Double Method of Agreement . . . . -156 
 Method of Residues . . . , . . .169 
 Method of Concomitant Variations . . . .179 
 
 IV. Imperfect Inductions . . . . . . . .214 
 
 Inductio per Simplicem Enumerationem . . . .214 
 
 Argument from Analogy . . . . . .221 
 
 Imperfect applications of the Inductive Methods (or In- 
 complete Inductions) . . . . . .232 
 
 C 
 
XXVI CONTENTS, 
 
 CHAP. PAGE 
 
 V. The Relation of Induction to Deduction, and Verification . 235 
 VI. The Fallacies incident to Induction . . . . .250 
 
 A. Fallacies incident to the subsidiary processes . . .250 
 
 I. Fallacy of Non-observation, consisting in neglect either 
 
 (i) of some of the instances ..... 250 
 or (2) of some of the circumstances attendant on a 
 
 given instance ...... 264 
 
 II. Fallacy of Mal-observation . . . . . . 268 
 
 HI. Errors incidental to the operations of Classification, 
 
 Nomenclature, Terminology, and Hypothesis . -273 
 
 B. Fallacies incident to the Inductive process itself, or Fallacies 
 
 of Generalisation . . . . . . -273 
 
 iv. Error originating in the employment of the Inductio 
 per Simplicem Enumerationem (including the illegiti- 
 mate use of the Argument from Authority) . . 275 
 V. Errors common to the employment of the various In- 
 ductive Methods ....... 293 
 
 (i) Mistaking a for the cause of b, when the real 
 cause is c- (of which one instance is neglecting 
 to take account of the Plurality of Causes) . 294 
 (2) Mistaking a for the sole cause, when a and c 
 are the joint causes, either as 
 (a) both contributing to the total effect . . 300 
 
 or {^) being both essential to the production of 
 
 any effect whatever .... 304 
 
 (3^) Mistaking joint eflfects for cause and effect . 309 
 
CONTENTS. xxvii 
 
 PAGE 
 
 (4) Mistaking the remote cause for the proximate 
 
 cause, or the reverse . . . . -313 
 
 (5) Neglecting to take into account the mutual action 
 
 (mutuality) of cause and effect . . • 317 
 
 (6) Inversion of cause and effect .... 32a_ 
 VI. False analogy (including the illegitimate use of the 
 
 Argument from Antiquity, and of the Argument 
 from Final Causes) . . . . .324 
 
 Index 353 
 
^Ek 7TpoyLvco(TKOfi€V(ov dc irao-a dLbaa-Kokia^ aycrnep koI iv rols 
 dvaXvTiKOLS Xeyojiev' rj fxev yap dt eTraycoyrjs, t) be (rvXXoyi(r/xw. 
 *H p,€v di) €7Tay<oyr] dp)(rj iari kcll rov KaOoKov, 6 de avk\oyL(Tp,6s 
 €K TODV KaOokov. 'EaI&lv CLpa dp^cu €^ hv 6 crvWoyiap^oSj hv ovk 
 tan (TvX\oyi(Tfi6s' eTraycoyr) apa. 
 
 Aristotle's Nicomachean Ethics, vi. 3 (3). 
 
 Quamvis ad scientiam quamlibet via unica pateat, qua nempe a 
 notioribus ad minus nota et a manifestis ad obscuriorum notitiam 
 progredimur, atque universalia nobis prsecipue nota sint (ab univer- 
 salibus enim ad particularia ratiocinando oritur scientia), ipsa tamen 
 universalium in intellectu comprehensio a singularium in sensibus 
 nostris perceptione exsurgit. 
 
 Preface to Harvey's Treatise De Generatione Animalium. 
 
ELEMENTS 
 
 OF 
 
 INDUCTIVE LOGIC. 
 
*.x.* The notes appended to the Chapters (as dis- 
 tinguished from the foot-notes) are designed to inform 
 the student of any divergences from the ordinary mode 
 of treatment, or to afford him information on disputed 
 questions which it appeared inconvenient to notice in 
 the text. They. may be omitted on the first reading. 
 
CHAPTER I. 
 On the Nature of Inductive Inference. 
 
 TWO bodies of unequal weight (say a guinea and 
 a feather) are placed at the same height under the ex- 
 hausted receiver of an air-pump. When released, they 
 are observed to reach the bottom of the vessel at the 
 same instant of time, or, in other words, to fall in equal 
 times. From this fact, it is inferred that a repetition of 
 the experiment either with these two bodies or wdth any 
 other bodies would be attended with the same result, and 
 that, if it were not for the resistance of the atmosphere 
 and other impeding circumstances, all bodies, whatever 
 their weight, would fall through equal vertical spaces in 
 equal times. Now, that these two bodies in this par- 
 ticular experiment fall to the bottom of the receiver in 
 equal times is merely a fact of observation, but that they 
 would do so if we repeated the experiment, or that the 
 next two bodies w^e selected, or any bodies, or all bodies, 
 would do so, is an inference, and is an inference of that 
 particular character which is called an Inductive Inference 
 or an Induction \ 
 
 ^ The student must throughout bear in mind the ambiguous use of 
 the words Induction, Inference, &c., as signifying both the result and 
 B 2 
 
4 NATURE OF 
 
 What assumptions underlie this inference, and on what 
 grounds does it rest ? 
 
 My object in placing the two bodies under the receiver 
 was obviously to answer a question which I had pre- 
 viously addressed to myself: viz. whether, when subject 
 to the action of gravity ^ only, they would fall in equal 
 or in unequal times. By exhausting the air in the re- 
 ceiver, I am able to isolate the phenomenon^ and thus, by 
 removing all circumstances affecting the bodies, except 
 the action of gravity, to watch the effect of this cause 
 operating alone. But in trying this experiment, in iso- 
 lating the phenomenon, and asking what will be the effect 
 of the action of gravity operating alone, I am evidently 
 assuming that the effect, whatever it may be, will be 
 entirely due to the cause or causes which are then and 
 ^ there in action ; in other words, I am assuming that 
 nothing can happen without a cause, that no change can 
 take place without being preceded or attended by circum- 
 stances which, if we were fully acquainted with them, 
 would fully account for that change. This assumption 
 (which may be called the Law of Universal Causation) 
 is universally admitted by mankind, or at least by the 
 
 the process by which the result is arrived at. See Deductive Logic, 
 Preface, and Part III. ch. i. note i. 
 
 ^ When I employ the expression ' action of gravity ' or ' force of 
 gravity,* I must not be understood as adopting any particular theory on 
 the nature of the phenomenon which we call ' gravitation.' I use these 
 terms simply because they are short and recognised phrases for expressing 
 the fact that all terrestrial bodies, when left entirely free, fall in the 
 direction of the earth's centre. 
 
INDUCTIVE INFEREKCE^. ^ y^ 5 V^ 
 
 V '<- 
 
 reflecting portion of mankind, though the grptods ofi 
 
 ^vhich it is admitted have been variously statea;Vspme /* 
 justifying it by an appeal to the continuous and unf^v 
 tradicted experience not only of the individual himsel|/ 
 but of the human race, others by an appeal to the neces- ^ 
 sities of thought. 
 
 Thus far, however, we have only ascertained that the 
 fact of these two particular bodies, in this particular 
 instance, falling to the ground in equal times is due to 
 the action of gravity, unimpeded by any other circum- 
 stances. But why should I infer that they, if the experi- 
 ment were repeated, or any other two bodies, if exposed 
 to the same circumstances, would behave in the same 
 way } It is not enough to feel assured that nothing can 
 happen without a cause, and that the only cause operating 
 in this particular instance is the action of gravity ; I must 
 also feel assured that the same cause will ^ invariably be 
 followed by the same effect, or, to speak more accurately, 
 that the same cause or combination of causes, will, if 
 unimpeded by the action of any other cause or combina- 
 tion of causes, be invariably followed by the same effect 
 or combination of effects, or, to state the same propo- 
 sition in somewhat different language, that, whenever the 
 same antecedents, and none others, are introduced, the 
 same consequents will invariably follow. This assump- 
 
 ^ The expression ' will ' is used for the sake of brevity. The 
 argument, however, is not simply from the present to the future, but v 
 from cases within the range of our experience to all cases, past, present, 
 or future, without that range. See p. 31, note 27. 
 
6 NATURE OF 
 
 tion (or law) is, like the former, universally admitted by 
 mankind, or the reflecting portion of mankind, though 
 the grounds on which it is admitted have been variously 
 stated, some, as in the case of the former law, referring it 
 to experience, others to certain necessities of thought 
 arising from the original constitution of the human mind. 
 This law may be called the Law of the Uniformity of 
 Nature *. 
 
 The argument, then, in the case which we have selected 
 as our instance, may be represented as follows : — 
 
 I observe that these two bodies (though of un- 
 equal weight) reach the bottom of the receiver 
 at the same moment. 
 This fact must be due to some cause or com- 
 bination of causes (Law of Universal Causation). 
 The only cause operating in this instance is the 
 action of gravity. 
 .*. The fact that these two bodies reach the bottom of 
 the receiver at the same moment is due to the 
 action of gravity, operating alone. 
 But, whenever the same cause or combination of 
 causes is in operation, and that only, the same 
 effect will invariably follow (Law of Uniformity of 
 Nature). 
 
 * It is, perhaps, necessary thus early to warn the student that the 
 converse of the Law of the Uniformity of Nature does not hold true. 
 Though the same cause, that is, the same antecedent or combination of 
 antecedents, is never followed by different effects, the same effect may 
 be due to different causes. We can, thus, always argue from the cause to 
 the effect, but we cannot always argue from the effect to the cause. 
 
INDUCTIVE INFERENCE. J 
 
 .\ Whenever these two bodies, or any other two or 
 more bodies (even though of unequal weight), are 
 subject to the action of gravity only, they will 
 reach the bottom of the receiver at the same 
 moment, or, in other words, will fall in equal 
 times. 
 
 The induction just examined has been arrived at by a 
 process of elimination, and takes for granted the concep- 
 tion of causation. It is representative of the inductionsy 
 with which science is mainly concemed/^^id'-of which we 
 shall have, for the most part, to treat in the present 
 work. But there ar^ other inductions of a simpler cha- 
 racter, the validity of which is assured not by any artificial 
 process of elimination, but merely by a series of uncon- 
 tradicted experiences. This kind of induction is usually 
 distinguished by logicians as Indudio per Enumerationem 
 Stmplicem. It is often (as will hereafter be pointed 
 out in the 4th chapter) exceedingly untrustworthy, but, 
 when the area of experience is very wide, the evidence 
 which it affords may approach to, and even amount to, 
 certainty. Often moreover, and especially in the case of 
 our widest generalisations, it is our only resource. 
 
 Amongst inductions of this kind must be included, as 
 we conceive, the Laws of Uniformity of Nature and Uni- 
 versal Causation themselves, as well as the axioms of 
 mathematics and certain facts of coexistence which have 
 not yet been resolved into, or possibly do not admit of 
 being resolved into, facts of causation. As examples of 
 the last class we may specify the coexistence throughout 
 
8 NATURE OF 
 
 matter of the properties of inertia and gravity, and the co- 
 inherence of attributes in the various kinds of animals, 
 plants, and minerals, as, for instance, fusibility at a certain 
 point together with a certain specific gravity in gold, or 
 the combination of rationality with a peculiar physical 
 form in man. Though coexisting facts of this nature 
 may possibly be due to some causal connection, and 
 might, if we had a perfect knowledge of all natural pro- 
 cesses, be explained in that manner, they are, as yet, 
 known to us only as facts of coexistence, and established 
 only by an inductio per enumerationem simplicem, or 
 uncontradicted experience. 
 
 Mr. Bain ^ enumerates three kinds of uniformities, which 
 ,may be established by induction, those of Coexistence, 
 Causation, and Equality. Uniformities of Coexistence and 
 Equality can be established only by Inductio per Enume- 
 rationem Simplicem, while those of Causation, though, in 
 the actual state of our knowledge, they often rest only 
 on this evidence, ought always to be established by the 
 more refined methods to be described in the sequel of 
 this book. To complete the list of inductions, we ought 
 to add to the above classification, the Laws of Uniformity 
 of Nature and Universal Causation, both of which, as 
 already remarked, we conceive to be established by un- 
 contradicted experience, or, in other words, by an Induc- 
 tio per enumerationem simplicem coextensive with all 
 human knowledge^. Of these fundamental laws, the 
 
 5 Logic, Bk. III. ch. ii. 
 
 * On the nature of the evidence on which these laws rest, see the 
 third appended note at the end of this chapter. 
 
INDUCTIVE INFERENCE, 9 
 
 former is a condition of, that is to say, is assumed in, all " 
 our inductions, whether of Coexistence, Causation, or 
 EquaHty, while the latter is assumed in inductions of 
 Causation alone. It is solely in virtue of the Law of the 
 Uniformity of Nature, that we are entitled to argue from 
 the past to the future, from the present to the absent, in 
 short, from the known to the unknown. 
 
 As the inductions of Causation are those with which 
 science is mainly concerned, and to which alone the more 
 refined rules of Inductive Logic are applicable, we shall 
 in the following work limit ourselves almost entirely to 
 their consideration. The inductions of Coexistence, with 
 which we shall, to some extent, be concerned in the 
 section on Classification, we shall regard as subservient 
 to these ^ 
 
 From what has been said above, as well as in distin-\ 
 guishing the various kinds of inference in the Manual \ 
 of Deductive Logic, it will be seen thaj: Induction may be y 
 defined as the legitimate inference of the unknown from the % 
 known, that is, of propositions applicable to cases hitherto / 
 unobserved and unexamined from propositions which are 
 known to be true of the cases observed and examinedy 
 Thus, from the proposition that a guinea and a feather, 
 if placed under the exhausted receiver of an air-pump, 
 will fall in equal times, may be inferred inductively the 
 
 ^ We shall briefly recur to the subject of Inductions of Coexistence 
 , in the fourth chapter, under the head of InducHo per Enutnerationem 
 Simplicem. 
 
lO NATURE OF 
 
 proposition that a shilling, a penny, 'and a straw will, if 
 exposed to the same circumstances, also fall in equal 
 times. But, as we can only draw this inference on 
 grounds which are equally applicable to all bodies what- 
 soever, when exposed to the same circumstances, and as 
 we might make the same assertion of any two or more 
 bodies, and consequently of all bodies, it will be seen 
 that Induction is not only an inference of the unkno wn 
 fr om the known ; but, in virtue of that fact, of the genera l 
 from the particu lar. I n every inductive argument, i n 
 fa ct, it is implied that wherever or whenever the same cir- 
 c umstances are repeated, the same effects will follow . 
 I nduction may, therefore, also be defined as the legitimat e 
 inference of the general from the partirular^ or (in order to 
 include those cases where general propositions are them- 
 selves employed as the starting-point of an inductive 
 argument, of which numerous instances will occur as we 
 proceed) .of the more general from the less general. 
 
 In trying the experiment which furnished our instance 
 at the beginning of the chapter, we were attempting to 
 find an answer to the question, * Do bodies, when 
 subject to the action of gravity only, fall through 
 equal vertical spaces in equal or in unequal times ? ' 
 The experiment may be regarded as an attempt to 
 decide between two rival theories (or hypothese s^ as they 
 are usually called), one being that bodies fall quicker in 
 proportion to their weights, the other that the weight of 
 the body, when the resistance of the atmosphere is re- 
 
INDUCTIVE INFERENCE, II 
 
 moved, does not affect the time of falling. The 
 experiment is decisive in favour of the latter hypothesis, 
 which is thus entitled to rank as a valid induction. Our 
 ind uctions are often , as in this case, the result of an 
 attempt to decide between rival hypotheses, or a rep ly 
 t p the question whether some particular hypothesis b e 
 tru e or not, the hypothesis or hypotheses suggesting the 
 parti cular experiment to be tried. S ometimes, however, 
 we have no assistance of this kind, and we try experi- 
 ments simply ' to see what will come of them.' Thus, 
 if a chemist discovers a new element, he will proceed to 
 try a variety of experiments in order to determine the 
 proportions in which it will combine with other elements, 
 as well as to discover the various properties of such 
 combinations. Su pposing the experiments to have been 
 pro perly rnndnrfpd^ thp indnrtinns af whirb hp arrivpQ 
 will he pprfpptly valid, though he may have formeil no 
 previo us theories as to the results of his researches. // Oc- 
 casionally, too, an induction will not be the result ofany 
 definite course of investigation^^fcut will be obtruded on 
 our notice, as in the following instance, adduced by Sir 
 John Herschel, to show that ' after much labour in vain, 
 and groping in the dark, accident or casual observation 
 will present a case which strikes us at once with a full 
 insight into a subject.' I ' The laws of crystallography 
 were obscure, and its causes still more so, till Hauy for- 
 tunately dropped a beautiful crystal of calcareous spar 
 on a stone pavement, and broke ,it. In piecing together 
 the fragments, he observed their facets not to correspond 
 
12 NATURE OF 
 
 with those of the crystal in its entire state, but to belong 
 
 to another form ; and following out the hint 
 
 thus casually obtruded on his notice, he discovered the 
 beautiful laws of the cleavage, and the primitive forms 
 of minerals ^/ 
 
 Thus, we perceive that our inductions are ^sometim es 
 pjTjeceded by - hypot heses, at other times noti/ In m ost 
 rasef y probably^ ^ ye have formed some theory (or hypo - 
 t hesis) as to the character of a phenomenon before we 
 ente pnlpon. or. at least, before we complete, its inves - 
 :ig a|ion. Such theories (or hypotheses) are often of the 
 [Utmost service in directing the course which our experi- 
 ments and observations shall take. Frequently, also, it is 
 impossible to perform any experiment, or to institute any 
 series of observations, which shall be decisive of the 
 question before us^ In this case, unless we altogether 
 suspend our judgment, we must rest content with an 
 unproved theory, and it becomes of prime importance to 
 ietermine to what conditions such a theory (or hypo- 
 hesis) must conform in order to entitle it to rank as a 
 probable or poss jble_solu tion of our difficultie s. A sub- 
 sequent section will be specially devoted to these ques- 
 tions, but meanwhile it seemed desirable at once to direct 
 the attention of the student to the distinction between 
 hypothesis and induction. . He_ must bear-m-Jaiftd-that, 
 
 ) though the formation of hypotheses is frequently an im- 
 portant step in the inductive process, a hypothesis must 
 
 * Herschel's Discourse on the Study of Natural Philosophy, § 191. 
 
INDUCTIVE INFERENCE, 1 3 
 
 be carefully distinguished from a valid induction. With- 
 lout at present attempting any formal definition of a 
 I hypothesis, it may be distinguished from an induction 
 [(that is, a valid, complete, or perfect induction) as a mere ^ 
 
 supposition or assumption from an ascertained truth./ 
 
 *^* The word * cause' is commonly used in a very 
 vague and indefinite sense. Of the various antecedents 
 whose presence or absence is essential to the event, 
 it is usual to single out one as the Cause, and either to 
 overlook the others, or to speak of them as ' conditions.' 
 
 (Strictly speaking, however, the Cause consists in the pre- , 
 sence of all those antecedents, the withdrawal of any of 
 which, and in the absence of all those antecedents, the \i ^ 
 introduction of any of which, might frustrate the event. 
 Thus, to take the homely instance of lighting a fire. The 
 application of the lighted match is what would ordinarily 
 be called the cause of the combustion. But there are 
 other conditions equally necessary, as, for instance, 
 amongst the positive conditions, the presence of fuel and 
 of atmospheric air, and, amongst the negative conditions, 
 the absence of such a quantity of moisture as would pre- 
 vent the fuel from igniting. In assigning the cause of a 
 phenomenon, it is seldom that the negative conditions are 
 mentioned. It is generally understood that we assign a 
 cause, subject to the qualification 'no counteracting 
 cause intervening.' Amongst the positive conditions, we 
 usually select that which, being last introduced, com- 
 pletes the assemblage of conditions, and stands in closest ^^^^ 
 
14 NATURE OF 
 
 proximity to the effect. Thus, in our example, the com- 
 bustion is said to be due to the application of the match, 
 and, when a man, who has previously been in a bad state 
 of health, is attacked by a fever, we speak of the fever as 
 the cause of his death. These, however, as observed by 
 Mr.'JVIill, are by no means invariable rules. * It must not 
 be supposed that in the employment of the term this or 
 any other rule is always adhered to. Nothing can better 
 show the absence of any scientific ground for the dis- 
 tinction between the cause of a phenomenon and its con- 
 ditions, than the capricious manner in which we select 
 from among the conditions that which we choose to 
 denominate the cause. However numerous, the con- 
 ditions may be, there is hardly any of them which may 
 not, according to the purpo'se of our immediate dis- 
 course, obtain that nominal pre-eminence.' Thus, if 
 a plot of dry heath is ignited by a spark from a railway- 
 engine, we may, in common parlance, attribute the fire 
 either to the spark, or to the dryness of the heath, or to the 
 ill construction of the engine ; the first of these assigned 
 causes being the proximate event, the second one of the 
 other positive conditions, the last a negative condition. 
 What, when employing popular language, we dignify 
 with the name of Cause is that condition which happens 
 to be most prominent in our minds at the time. It is, 
 perhaps, superfluous to add that, when aiming at scien- 
 tific accuracy, we ought to enumerate all the conditions, 
 or, at least, all the positive conditions, on which a phe- 
 nomenon depends, unless we have a right to presume 
 
INDUCTIVE INFERENCE, 1 5 
 
 that there is no Hkelihood of their being overlooked by 
 those whom we address ^ 
 
 In the science of Medicine, the cause which completes 
 the assemblage of conditions is often distinguished as the 
 exciting cause, the other causes being called pre-duposing. ' 
 Thus, the peculiarities of constitution, age, sex, occupa- 
 tion, &c., which render a person more than ordinarily 
 liable to any particular disorder, would be called the 
 pre-disposing causes; the contagion (by which the body 
 is brought into contact with some specific poison)^ a 
 sudden chill, bodily fatigue, mental depression, or any 
 circumstance, on the supervention of which the disease 
 is immediately consequent, would be called the exciting 
 cause ,^^. The pre-disposing causes of Asiatic Cholera, for 
 instance, are enumerated in Dr. Guy's edition of Dr. 
 Hooper's * Vade Mecum,' as ^ debility ; impaired health ; 
 intemperance ; impure air ; low and damp situations ; the 
 summer and autumn seasons : the exciting causes as 
 contagion ; a peculiar poison diffused through the atmo- 
 sphere/ The importance of attending to this distinction 
 in historical and political investigations is forcibly stated 
 and . illustrated by Sir G. C. Lewis, in his Methods of 
 Observation and Reasoning in Politics^ vol. i. ch. ix. 
 p. 333. &c. 
 
 '•* The subject of this paragraph is treated with great abiUty in 
 Mr. Mill's Logic, Bk. III. ch. v. § 3. 
 
 ^^ See Dr. Watson's Lectures on Physic, Lecture VI. 
 
1 6 NATURE OF 
 
 I Note I ^\— Mr. Mill {Logic, Book II. ch. iii.) maintains 
 / that in an act of induction we usually, though not 
 I invariably, argue directly from one particular case to 
 \ another. Dr. Whewell, on the other hand, holds that 
 \ all inductive inference is from the particular to the 
 \ general. {Philosophy of Discovery, ch. xxii. § 1-14.) 
 Though I have adopted Dr. Whewell's language (which 
 is that ordinarily employed), I cannot recognise the im- 
 portance of the difference which he believes to exist 
 between himself and Mr. Mill. To say that what I find 
 to be true of this case will be true of the next which 
 resembles it in certain assignable respects, whatever that 
 case may be, or that what I found to be true of that case 
 must be true of this, because this resembles that in certain 
 assignable respects, is virtually to say that it is true of any 
 and every case which presents these points of resemblance. 
 What is true of each or any case, taken indifferently, must 
 be true of all. ' The burnt child dreads the fire.' Why ? 
 Because it once suffered pain, from burning its finger. 
 Now, it appears to me indifferent whether we represent 
 the child as having in its mind the proposition 'That 
 object causes pain,' or the proposition ' That object will 
 cause me pain now, if I approach too near to it.' But, as 
 the former (the general) inference seems to be virtually 
 implied in the latter (the particular), and, as Mr. Mill 
 acknowledges, the particular inference can, on reflection, 
 only be justified by granting the truth of the general one, 
 
 '^ The student, unless he have some previous acquaintance with the 
 subjects discussed in them, is recommended to omit these notes on the 
 first reading. 
 
INDUCTIVE INFERENCE. 1 7 
 
 I prefer adhering to the common, and, as I think, the 
 more intelligible account of induction. Mr. Mill himself, 
 in one place, speaks of Induction as ' generalisation from 
 experience,' and, in another, as * the inference of a more 
 general from less general propositions ^^.' 
 
 Though agreeing with Dr. Whewell in his main 
 position, I must express my entire dissent from the 
 distinction which, throughout this discussion, he attempts 
 to draw between our reasonings in the ordinary affairs 
 of life, and Induction as employed in scientific research. 
 However various may be the conditions of their applica- 
 tion, I cannot but regard the mental processes as iden- 
 tical, on whatever classes of objects they may be exercised. 
 We may meet with insurmountable difficulties in the 
 attempt to apply Induction to some obscure question 
 of Physiology, and we may employ it with ease and 
 success a hundred times a day in avoiding pain or 
 securing ease, but 1 believe the mental process to be 
 essentially the same in both cases. 
 
 No/e 2. — -Since the time of Hume, the nature of our 
 conception of Cause has formed one of the principal 
 topics of philosophical controversy. Previously to his 
 time, it appears to have been taken for granted by the 
 
 ^^ Mr. Jevons {Principles of Science, vol.^i. pp. 261, 262) seems to have 
 slightly misapprehended my meaning in this note. While I believe that 
 we do, as a matter of fact, often argue from particular to particular, I 
 entirely agree with Mr. Jevons {Principles of Science, vol. ii. p. 243) in 
 holding that * what is inferred of a particular case might be inferred of all 
 similar cases/ or, in other words, that the logical justification of such 
 inferences is to be found in the general statement. 
 
 C 
 
1 8 NATURE OF 
 
 great majority of modern philosophers of all schools'^ 
 (if we except those who, like Malebranche, believed God 
 to be the only efficient cause in the universe, and so- 
 called acts of causation to be only the occasions of the 
 Divine interference^*), that the idea of causation neces- 
 sarily implies the idea of power or fiecessary connection ; 
 necessary connech'on, that is to say, between the cause and 
 effect, or power in the cause to produce the effect. Even 
 Locke, who effected a revolution in modern philosophy, 
 left this idea of Power unassailed, though he attempted 
 to account for its formation. * The mind,' says he ^^, 
 * being every day informed, by the senses, of the 
 alteration of those simple ideas it observes in things 
 without; and taking notice how one comes to an end, 
 and ceases to be, and another begins to exist, which 
 was not before; reflecting also on what passes within 
 itself, and observing a constant change of its ideas, 
 sometimes by the impression of outward objects on the 
 senses, and sometimes by the determination of its own 
 choice; and concluding from what it has so constantly 
 
 ^3 Dugald Stewart (in his Philosophy of the Human Mind, Notes C 
 and MM) has certainly succeeded in showing that Hume's views on the 
 nature of Cause were anticipated by casual remarks of several other 
 writers ; but it still remains true that Hume was the first philosopher 
 who definitely attacked the prevalent philosophical theory. 
 
 ^* Still, even according to these philosophers, every act of causation 
 implies an act of power; only the power is exerted not by the 
 so-called cause, but by the Deity himself. It will be noticed that I 
 speak only of modern philosophers. Into the difficult question of the 
 notions of causation entertained by ancient writers I do not enter. 
 
 ^ Locke's Essay, vol. ii. ch. xxi. § i. 
 
INDUCTIVE INFERENCE, 1 9 
 
 observed to have been, that the like changes will for the 
 future be made, in the same things, by like agents, and 
 by the like ways, considers in one thing the possibility of 
 having any of its simple ideas changed, and in another 
 the possibility of making that change ; an*d so comes by 
 that idea which we call Power. Thus we say, fire has 
 a power to melt gold, i. e. to destroy the consistency of 
 its insensible parts, and consequently its hardness, and 
 make it fluid ; and gold has a power to be melted : that 
 the sun has a power to blanch wax, and wax a power to 
 be blanched by the sun, whereby the yellowness is 
 destroyed, and whiteness made to exist in its room. In 
 which, and the like cases, the power we consider, is in 
 reference to the change of perceivable ideas. For we 
 cannot observe any alteration to be made in, or operation 
 upon anything, but by the observable change of its 
 sensible ideas ; nor conceive any alteration to be made, 
 but by conceiving a change of some of its ideas.' He 
 then proceeds to include our idea of Power amongst 
 our Simple Ideas. 
 
 Hume contested the validity of this idea by an appeal 
 to experience. Whence do we obtain this notion of 
 necessary connection between two events.? Do we ob- 
 serve any such connection in the events which take place 
 in the external world, or in the relation between volition ^ 
 and the motion of the organs of the body, or in the 
 act of the will by which it summons up, dwells on, or 
 dismisses ideas ? ' We have sought in vain for an idea 
 t)f power or necessary connection, in all the sources 
 
 c 2 
 
20 NATURE OF 
 
 from which we could suppose it to be derived. It ap- 
 pears, that, in single instances of the operation of bodies, 
 we never can, by our utmost scrutiny, discover anything 
 but one event following another; without being able to 
 comprehend aViy force or power, by which the cause 
 operates, or any connection between it and its supposed 
 effect. The same difficulty occurs in contemplating the 
 operations of mind on body, where we observe the 
 motion of the latter to follow upon the volition of the 
 former, but are not able to observe or conceive the tie, 
 which binds together the motion and volition, or the 
 energy by which the mind produces this effect. The 
 authority of the will over its own faculties and ideas is not 
 a whit more comprehensible: so that, upon the whole, 
 there appears not, throughout all nature, any one instance 
 of connection, which is conceivable by us. All events 
 seem entirely loose and separate. One event follows 
 another ; but we never can observe any tie between them. 
 They seem conjoined^ but never connected. And as we can 
 have no idea of anything, which never appeared to our 
 outward sense or inward sentiment, the necessary conclu- 
 sion seems to be, that we have no idea of connection or 
 power at all, and that these words are absolutely without 
 any meaning, when employed either in philosophical 
 reasonings, or common life^^' Does Hume then deny 
 the fact of causation^ namely, that, when we have been 
 accustomed to observe one event invariably followed by 
 another, we may confidently expect, other circumstances 
 
 ^^ Hume's Essays. Essay on the Idea of Necessary Causation. 
 
INDUCTIVE INFERENCE. 21 
 
 remaining the same, that it will continue to be followed 
 by it in the future, and that, if we pei;ceive a change in 
 any phenomenon, we may be confident that some other 
 event has preceded that change ? Certainly not. There 
 is, in Hume's writings, absolutely no foundation for the 
 virulence with which he is attacked by Reid ^\ What he 
 called in question was not the invariableness of the fact 
 of causation, but the grounds of the prevalent notions 
 attached to the word Cause. Whether his speculations 
 on this subject be well or ill-founded, he certainly did 
 not deny the correctness of the principles on which men 
 
 ^^ The following may serve as a specimen of Reid's diatribes against 
 Hume. *Of all the paradoxes this author has advanced, there is not 
 one more shocking to the human understanding than this, That things 
 may begin to exist without a cause. This would put at end to all 
 speculation, as well as to all the business of life. The employment of 
 speculative men, since the beginning of the world, has been to investigate 
 the causes of things. What pity is it, they never thought of putting the 
 previous question, Whether things have a cause or not ? This question 
 has at last been started ; and what is there so ridiculous as not to be 
 maintained by some philosopher? ' — Active Powers, Essay I. ch. iv. Sir 
 W. Hamilton and Dr. Mansel take a far juster view of Hume*s position. 
 Even Sir W. Hamilton, however, in commenting on Reid's statement, 
 says, ' This ' (namely. That things may begin to exist without a cause) 
 * is not Hume's assertion ; but that, on the psychological doctrine gener- 
 ally admitted, we have no valid assurance that they may not.* The 
 latter is, certainly, not Hume's assertion. It is true that he bases the 
 notion of causation on experience, but then he regards experience as the 
 sole source of all our knowledge. Sir William Hamilton's note requires 
 only to be compared with the following passage from the Essay : ' But ] 
 when one particular species of event has always, in all instances, been 
 conjoined with another, we make no longer any scruple of foretelling 
 one upon the appearance of the other, and of employing that reasoning 
 which can alone assure us of any matter of fact or existence.' 
 
22 . NATURE OF 
 
 act in ordinary life or which guide them in scientific 
 research. 
 
 There is another objection to the statements contained 
 in Hume's Essay which is better founded than the fore- 
 going. If the term * cause ' be convertible with the term 
 ' invariable antecedent/ it has been justly objected by 
 Reid ^^ that we might speak of day as the cause of night, 
 and of night as the cause of day. That there are loose 
 expressions in the Essay, in which the cause seems to 
 be confounded with the invariable antecedent or the 
 sum of the invariable antecedents, cannot be denied. 
 Such is the following : * Suitably to this experience, 
 therefore, we may define a cause to be an object, 
 followed by another, and when all the objects, similar 
 to the first, are followed by objects similar to the second.' 
 But then the sentence proceeds : * Or, in other words, 
 where ^ if the first object had 7iot been, the second never had 
 existed! Now this alternative definition is not open to 
 Reid's objection, though it is open to the objection of 
 ignoring the fact that the same event may be due to 
 distinct causes, as pointed out in p. 6, n. 4 ^^ When ^ 
 modified to meet this objection, it would run thus : ' Cause 
 [or causes] and Effect are two [or more] events, or sets of 
 events, which are so related, that, if the first [or one of the 
 first] had not been, the second had never existed.' Or, 
 
 ^^ Active Powers, Essay IV. ch. iri. 
 
 ^® I am indebted to Professor Park of Belfast for drawing my attention 
 to this objection, which had escaped my notice in the First Edition. It 
 was originally pointed out by Dr. Thomas Brown, in his Enquiry into 
 the Relation of Cause and Effect, Note A. 
 
INDUCTIVE INFERENCE. 23 
 
 perhaps, it might be more simply stated thus : ' An 
 Effect is so related to its Cause or its alternative Causes, 
 Hhat if the latter or one of the latter had not been, the 
 former had never existed?^.'* 
 
 Both Dr. Thomas Brown and Mr. Mill attempt to meet 
 Reid's objection. 
 
 Brown holds that the cause is that invariable antecedent . 
 which immediately precedes the effect ; thus the position 
 of the sun at a given moment, that which w^e call sun-rise, 
 is the cause of day. 
 
 Mill attempts to meet the same objection by having 
 recourse to the idea of * unconditionalness! The cause of ^ 
 a phenomenon is * the antecedent or concurrence of ante- 
 cedents on which it is invariably and unconditionally con- 
 sequent,' i. e. which not only invariably precedes it, but 
 which is followed by the effect without the occurrence of 
 any other condition. Now night cannot be called the 
 
 '^^ This definition is, it must be confessed, somewhat deficient in sim- 
 plicity. But I venture to suggest that it will bear closer examination 
 than that of Mr. Mill, who defines ' cause * as the ' unconditional invari- 
 able antecedent.* Whether by the term * unconditional ' he means * not 
 depending on any previous condition,' or ' not combined with any con- 
 current condition,' it may be objected that there is no such phenomenon 
 in nature. If, as seems clear from the context, the term be used in the 
 latter sense, we shall not only be excluded from saying that night is the 
 cause of day, but- also that solar light is the cause of day, for there 
 are other conditions, both positive and negative, essential to the produc- 
 tion of what we call day by the solar rays. In fact, according to the 
 terms of this definition, we could never, as we are constantly doing, 
 single out any one prominent phenomenon, and call it the cause of an 
 event, without enumerating all the other conditions, positive and nega- 
 tive, which are essential to its operation. 
 
24 NATURE OF 
 
 cause of day, because it might go on for ever without 
 being followed by day, unless the condition of the sun 
 rising were fulfilled. See Mill's Logic, Bk. III. ch. v. § 5. 
 
 The objection to Brown's account is that we fre- 
 quently speak without hesitation of A as the cause of B, 
 though we are by no means certain that it is, strictly 
 speaking, the immediate antecedent of B, nothing else 
 whatever intervening ; in fact, it is questionable whether in 
 any case we can ascertain to a certainty that nothing else 
 intervenes between two events. Similarly, it may be 
 objected to Mill's account that we frequently speak with- 
 out hesitation of A as being the cause of B, though we 
 are by no means certain that there are not other ante- 
 cedent conditions, positive and negative, which must be 
 satisfied before A can be followed by B ; and, indeed, as 
 in the former case, it may be questioned whether we can 
 ever be certain that there are no other conditions besides 
 those which we have selected ^\ 
 
 The first author of eminence who adopted Hume's 
 view of the nature of Cause was Dr. Thomas Brown; 
 singularly enough, however, so far from assuming with 
 Hume that its origin was to be found in experience, he 
 regarded it as instinctive. The notion of 'Power' he 
 supposed was simply a gratuitous hypothesis, needlessly 
 interpolated between the antecedent, which we call the 
 Cause, and the consequent, which we call the Effect. 
 *We are eager to supply, by a little guess-work of 
 
 ^^ It is curious that Mill, in attempting to answer Reid, takes no 
 notice of Brown's answer. 
 
INDUCTIVE INFERENCE. 25 
 
 fancy, the parts unobserved, and suppose deficiencies 
 in our observation where there may truly have been 
 none; till at length, by this habitual process, every 
 phenomenon becomes, to our imagination, the sign of 
 something intermediate as its cause, the discovery of 
 which is to be an explanation of the phenomenon. The 
 mere succession of one event to another appears, to us, 
 very difficult to be conceived, because it wants that inter- 
 vening something which we have learned to consider as 
 a cause : but there seems to be no longer any mystery, 
 if we can only suppose something intervening between 
 them, and can thus succeed in doubling the difficulty, 
 which we flatter ourselves with having removed; since, 
 by the insertion of another link, we must now have two 
 sequences of events instead of one simple sequence ^l' 
 Hume's position is also accepted by James Mill in his 
 Analysts of the Phejiomena of the Human Mind^ and by 
 John Stuart Mill in his System of Logic, 
 
 Hume's antagonists have generally (with Kant) com- 
 bated his arguments by denying the assumption on which 
 they are based, namely, that the origin of our conception 
 of Cause is to be sought in experience. Hume, it will be 
 recollected, challenges those who maintain the hypothesis 
 of ' power ' or ' necessary connection ' to show how we 
 can have become acquainted with it. Does it come from 
 our experience of the external world, or from our experi- 
 ence of the control of our will over our own acts or our own 
 
 22 Brown's Lectures on the Philosophy of the Human Mind, Lecture IX. 
 Cf. Lecture IL 
 
26 NATURE OF 
 
 thoughts ? The answer of the Kantian School would be 
 that it does not come from experience at all, that it is one 
 of those fundamental conceptions which are native to the 
 human mind, not given by experience but evoked by it. 
 Others, like Reid and Stewart, to whom we may add 
 M. Maine de Biran, surrender the notion of power as 
 applied to causation in the external world, while they 
 maintain it as applied to our own actions, which are the 
 results of will. We are conscious, they say, of power in 
 ourselves, though we perceive only succession in the ex- 
 ternal world. Dr. Mansel, following Cousin, adopts a 
 third view, and maintains that the notion of * Power ' is 
 given only in the control of the mind over its own opera- 
 tions. * The intuition of Power is not immediately given 
 in the action of matter upon matter ; nor yet can it be 
 given in the action of matter upon mind, nor in that of 
 mind upon matter ; for to this day we are utterly ignorant 
 how matter and mind operate upon each other. We 
 know not how the material refractions gf the eye are 
 connected with the mental sensation of seeing, or how 
 the determination of the will operates in bringing about 
 the motion of the muscles. We can investigate severally 
 the phenomena of matter and of mind, as we can examine 
 severally the constitution of the earth, and the architecture 
 of the heavens : we seek the boundary line of their junc- 
 tion, as the child chases the horizon, only to discover that 
 it flies as we pursue it. There is thus no alternative, but 
 either to abandon the inquiry after an immediate intuition 
 of power, or to seek for it in mind as determining its own 
 
INDUCTIVE INFERENCE, 27 
 
 modifications ; — a course open to those who admit an 
 immediate consciousness of self, and to them only. My 
 first and only presentation of power or causality is thus to 
 be found in my consciousness oi myself as willing'^'^ ! 
 
 The relation subsisting between an act of will and the 
 motion of the limbs, or between a physical antecedent and 
 its consequent, he regards as beyond our knowledge. 
 * Our clearest notion of efficiency is that of a relation 
 between two objects, similar to that which exists between 
 ourselves and our volitions. But what relation can exist 
 between the heat of fire and the melting of wax, similar 
 to that between a conscious mind and its self-determina- 
 tions ? Or, if there is nothing precisely similar, can there 
 be anything in any degree analogous? We cannot say 
 that there is, or, if there is, how far the analogy extends, 
 and how and where it fails. We can form no positive 
 conception of a power of this kind : we can only say, that 
 it is something different from the only power of which we 
 are intuitively conscious. But, on the other hand, we are 
 not warranted in denying the existence of anything of 
 the kind ; for denial is as much an act of positive thought 
 as affirmation, and a negative idea furnishes no data for 
 one or the other '^^! 
 
 It would, however, be beside my purpose to enter into 
 a detailed account of the history of this controversy. In 
 consequence, however, of its historical importance, it seemed 
 essential to take some notice of it, and to point out that, 
 whatever theory may be adopted as to the nature of Cause, 
 
 23 Prolegomena Logica, pp. 138, 139. "^^ Ibid. p. 140. 
 
28 NATURE OF 
 
 and however great our inability to conceive how one 
 event is followed by another, there is, at least, sufficient 
 definiteness in the conception to entitle it to be accepted 
 as the basis of scientific reasoning. Whether we acknow- 
 ledge that one event has invariably the power of producing 
 another, or whether we content ourselves with asserting 
 that it is invariably followed by that other, it is, in either 
 case, the element of invariahleness which makes the 
 connection or conjunction, whichever we may call it, a 
 fitting object of scientific research. But remove the 
 element of invariahleness, and suppose, if it be sup- 
 posable, that the same antecedent or set of antecedents 
 is sometimes followed by one consequent, and sometimes 
 by another, and sometimes by none at all ; in that case 
 science would be impossible. 
 
 The student who wishes to obtain further information 
 on this controversy (a controversy, however, which pos- 
 sesses a historical rather than a practical or scientific 
 interest), is referred to Hume's Essay on the Idea of 
 Necessary Connection ; Dugald Stewart's Dissertation, Part 
 11. sect. 8; Mill's Logic, Book III. ch. v; Sir W. Hamil- 
 ton's Lectures on Metaphysics, Lectures XXXIX, XL; 
 Hansel's Protegomena Logica, ch. v; Mill on Hamilton, 
 ch. xvi ; Lewes' History of Philosophy^ Articles on Hume 
 and Kant. I refer only to books likely to be within the 
 student's reach. In quoting or referring to Hume, I 
 have employed only his Essays. Many writers persist in 
 making references to his Treatise of Human Nature, a 
 work written at the early age of twenty-seven and after- 
 
INDUCTIVE INFERENCE, 29 
 
 wards repudiated by the author as containing an im- 
 mature expression of his opinions^^. In the Advertisement 
 to his Essays, he desires that ^ the following Pieces may 
 alone be regarded as containing the author's philosophical 
 sentiments and principles/ 
 
 Note 3. — That a cause is ; that ever} 
 
 event has a cause; that the same cause is always at- 
 tended with the same eifect ; are obviously three distinct 
 propositions, and still there are few writers who, in their 
 treatment of the question of Causation, have not more 
 or less confounded them. The first proposition ^f 
 completed) would be the Definition of Cause, the pre- 
 dicate, of course, depending on the view adopted with 
 reference to the question discussed in the previous note. 
 The second is a statement of the Law of Universal Causa- 
 tion, the third of the Law of the Uniformity of Nature. 
 
 It will be observed that in the text of this chapter I 
 have said of each of these laws that it 'is universally 
 admitted by mankind, or, at least, by the reflecting portion 
 of mankind.' The latter clause must be regarded as 
 emphatic, and suggests, I think, a sufficient answer 
 to those authors who call in question their universal 
 reception. Mr. Lewes, speaking of the Law of Universal 
 Causation, says, * All believe irresistibly in particular acts 
 
 2^ This work is undoubtedly of the highest philosophical interest, but 
 when we are concerned in determining the matured philosophical opinions 
 of Hume it cannot be regarded as authoritative. It is curious to find a 
 recent editor of Hume's Essays expressly defending the practice on which 
 I have animadverted in the text. See Mr. Grose's edition of Hume's 
 Essays^ vol. i. p. 39. 
 
30 NATURE OF 
 
 of causation. Few believe in universal causation; and 
 those few not till after considerable reflection "^^J He then 
 proceeds to adduce the case of a student of chemistry, 
 who could not be convinced of the truth of the Law, 
 but 'looked upon the argument as an unwarrantable 
 assumption/ Now T venture to thinK that this incapacity 
 was due to the terms of the proposition not being made 
 sufficiently intelligible to him. I question whether any 
 man of average powers of understanding could be found 
 who would maintain the contradictory of either of these 
 Laws ; who would assert, that is to say, that an event 
 might happen without anything to account for it, or that 
 a repetition of exactly the same circumstances might be 
 followed by a different effect. That a considerable 
 amount of intelligence is necessary in order to understand 
 the general terms in which the propositions are stated, 
 is undeniable, but, when once understood, I presume that 
 the propositions cannot fail to be acquiesced in, Like 
 all other propositions, however, of wide import, they may 
 be both understood and acquiesced in, without being 
 fully realised. It is the full and constant realisation of 
 these Laws, at all times and under all circumstances, 
 which mainly distinguishes the man of scientific from the 
 man of unscientific habits of thought. The unscientific 
 man either does not think of enquiring into the causes 
 of the phenomena around him, or notes with little pre- 
 cision the circumstances which he is investigating. The 
 scientific man, on the other hand, insists on invariably 
 ^^ Lewes' History of Philosophy, Article on Kant. 
 
INDUCTIVE INFEikENfin* /' ^P 
 
 ^^- I y ""' / '/ 
 referring the phenomena in which he i^mteresr(^d to / 
 
 their several causes, and is satisfied with notHir^ buri:)>^ 
 
 ;t rigorous enquiry into the relation betweod^ these * 
 ses and their effects. \. "^ f' > \ 
 
 most 
 
 causes and their effects. X "^ Vy^ \^^ 
 
 But, it may be asked, if the Laws of Universal Cau^ 
 tion and of the Uniformity of Nature are, on reflectic 
 thus universally received, by what mental process do 
 men assure themselves of their truth ? Of the origin of 
 these, as of kindred beliefs, two different explanations 
 are offered by rival schools of psychologists. According 
 to one school, the human mind is so constituted that it 
 cannot but accept them; they are fundamental beliefs 
 which exist in the mind prior to all experience, though 
 it is experience which occasions us to realise our pos- 
 session of them. We have never learnt them ; we have 
 simply discovered that we possess them. Thus Reid, 
 speaking of our conviction that the future will resemble 
 the past^^ (what we have called the Law of Uniformity 
 of Nature), says, ' The wise Author of our nature hath 
 
 ^ This, however, is a very inadequate statement of the Law of the 
 Uniformity of Nature. ' It has been well pointed out,' says Mr. Mill, 
 ' that Time, in its modifications of past, present, and future, has no con- 
 cern either with the belief itself, or with the grounds of it. We believe 
 that fire will burn to-morrow, because it burned to-day and yesterday ; 
 but we believe, on precisely the same grounds, that it burned before we 
 were born, and that it burns this very day in Cochin-China. It is not 
 from the past to the future, as past and future, that we infer, but from 
 the known to the unknown ; from facts observed to facts unobserved ; - 
 from what we have perceived, or been directly conscious of, to what has 
 not come within our experience. In this last predicament is the whole 
 region of the future ; but also the vastly greater portion of the present 
 and of the past.' — Mill's Logic^ Bk. III. ch. iii. 
 
3:Z NATURE OF 
 
 implanted in human minds an original principle by which 
 we believe and expect the continuance of the course of 
 nature, and the continuance of those connections which 
 we have observed in time past. It is by this general 
 principle of our nature, that, when two things have been 
 found connected in time past, the appearance of the one 
 produces the belief of the other^^' And Dr. Whewell, 
 speaking of the Law of Universal Causation, says, ^We 
 assert that " Every event must have a cause : and this 
 proposition we know to be true, not only probably, and 
 generally, and as far as we can see; but we cannot 
 suppose it to be false in any single instance. We are 
 as certain of it as of the truths of arithmetic or geometry. 
 We cannot doubt that it must apply to all events past 
 and future, in every part of the universe, just as truly 
 as to those occurrences which we have ourselves observed. 
 What causes produce what effects; — what is the cause 
 of any particular event ; — what will be the effect of any 
 peculiar process; — these are points on which experience 
 may enlighten us. Observation and experience may be 
 requisite, to enable us to judge respecting such matters. 
 But that every event has some cause, Experience cannot 
 prove any more than she can disprove. She can add 
 nothing to the evidence of the truth, however often she 
 may exemplify it. This doctrine, then, cannot have been 
 acquired by her teaching ^^.' 
 
 2* Raid's Inquiry into the Human Mind on the Principles of Common 
 Sense, ch. vi. § 24. 
 
 23 WhewelVs History of Scientific Ideas, Bk. III. ch. ii. § I. 
 
INDUCTIVE INFERENCE. 33 
 
 The opposite school of psychologists (of which Mr. 
 Mill and Mr. Alexander Bain may be taken as the modern 
 representatives) maintains that there is nothing in these 
 and kindred beliefs which compels us to distinguish them 
 generically from other truths, but that, like all other truths, 
 they are the result of Experience. From our earliest 
 years, we have been so constantly accustomed to observe 
 one change preceded by another change, and the same 
 antecedents followed by the same consequents, as well as 
 to find our own experience in these respects corroborated 
 by that of others, that, on reflection, we all acquiesce, and 
 cannot but acquiesce, in the statements which generalise 
 these facts. This, it is held, is a sufficient explanation of 
 that universality and necessity, which, by the advocates of 
 the intuitional theory, described in the last paragraph, are 
 supposed to distinguish the ' fundamental beliefs of the 
 human mind' or *the principles of common sense,' as 
 they are called by these authors, from all other truths. 
 The beliefs have acquired the character of universality 
 and necessity, not because they have sprung from any 
 other source than our ordinary beliefs, but because of the 
 constancy and variety of the experience from which they 
 are gained. ' In fact, our whole lives,' says James Mill, 
 * are but a series of changes, that is, of antecedents and 
 consequents. The conjunction, therefore, is incessant ; 
 and, of course, the union of the ideas perfectly insepa- 
 rable. We can no more have the idea of an event with- 
 out having the ideas of its antecedents and its conse- 
 quents, than we can have the idea and not have it at the 
 
 D 
 
34 NATURE OF 
 
 same time^^. But here occurs a difficulty. If the Laws 
 ^of Universal Causation and of the Uniformity of Nature 
 are inferred from particular facts of causation, are gene- 
 ralisations from experience, or, in other words, inductions, 
 how is it that they are rpade the grounds of all other 
 inductions ? Is not this to argue in a circle ? The 
 answer to this difficulty is that the Laws in question are 
 the result of an uniform and constant experience, co- 
 extensive not with the Hfe of the single individual who 
 employs them, but with the entire history of the human 
 race ; that, consequently, w^hen we adduce them as the 
 grounds on which our other inductions rest, we are per- 
 forming the perfectly legitimate process of resolving 
 narrower into wider cases of experience. The argument, 
 in short, is this : the inference from this narrow field of 
 observation (the particular induction w^hich we happen to 
 be making) must be allowed to be true, unless we are 
 •prepared to deny one or other of the much wider gene- 
 ralisations which constitute the Laws of Universal Causa- 
 tion and of the Uniformity of Nature. To recur to the 
 instance adopted in the text, the proposition that bodies, 
 subject to the action of gravity only, fall in equal times, 
 can be called in question only on peril of doubting one 
 or other of the laws ; thus, the doubt which might attach 
 to it is shifted to two other propositions which no one 
 
 ^ James 'NiiWs Analysis of the Phenomena of the Human Mind, ch. xi. 
 The position maintained by James Mill is that these beliefs owe their 
 universality to the fact of their being inseparably associated with all our 
 other cognitions. This is only another mode of stating the theory which 
 derives them from experience. 
 
INDUCTIVE INFERENCE, 35 
 
 would think of questioning. Or, to state the same posi- 
 tion in a slightly different form, this particular instance is 
 shown to be a member of an infinitely long series, the 
 other members of which have been examined and ap- 
 proved ; as, therefore, it differs in no essential respect 
 from them, it claims to be admitted also. There is, in- 
 deed, throughout this argument one assumption ; as the 
 rival theory assumed the trustworthiness of what it styled 
 our * fundamental beliefs,' so this assumes the validity of 
 experience. But, unless we make one or other of these 
 assumptions, we must be prepared to maintain that know- 
 ledge is altogether impossible ^\ 
 
 There is a third theory of the origin of universal beliefs 
 which combines, with certain modifications, both the 
 others. It would admit that all beliefs alike are ultimately 
 derived from experience, and still it would freely adopt 
 the language that there are some beliefs which are ' native 
 to the human mind.' The word * experience,' as or- 
 dinarily employed by psychologists, includes not only the 
 experience of the individual, but the recorded experience 
 of mankind. On the theory, however, of which we are 
 now speaking, it has a still more extended meaning ; it 
 
 ^^ It should be noticed that Dr. Mansel, while agreeing in the main, 
 as he usually does, with the intuitional school, in respect to the origin 
 of our belief in the Law of Universal Causation, refers to experience the 
 origin of our belief in the Uniformity of Nature. ' The belief in the ^ 
 uniformity of nature is not a necessary truth, however constantly guaran- 
 teed by our actual experience.* Mansel's Metaphysics^ Chapter on Neces- 
 sary Truths. Cf. Prolegomena Logica, ch. v. Dr. Mansel's treatment of 
 these questions is, in many respects, peculiar to himself. 
 
 D 2 
 
^6 NATURE OF 
 
 includes experience, or, to speak more strictly, a peculiar 
 facility for forming certain experiences, transmitted by 
 hereditary descent from generation to generation. While 
 some ideas occur only to particular individuals at particular 
 times, there are others which, from the frequency and 
 constancy with which they are obtruded upon the minds 
 of men at all times and under all circumstances, become, 
 after an accumulated experience of many generations, 
 connatural, as it were, to the human mind. We assume 
 them, often unconsciously, in our special perceptions, and 
 when the propositions, which embody them, are pro- 
 pounded to us, we find it impossible, on reflection, to 
 doubt their truth. It is by personal experience of ex- 
 ternal objects and their relations that each man recognises 
 them, but the tendency to recognise them is transmitted, 
 like the physical or mental peculiarities of race, from 
 preceding generations, and is anterior to any special ex- 
 perience whatever on the part of the individual. This 
 theory, to which much of modern speculation appears to 
 be converging, is advocated with great ability in the works 
 of Mr. Herbert Spencer ^l 
 
 The student who wishes for further information on the 
 questions discussed in this Note is referred to Dugald 
 Stewart's Philosophy of the Hwnan Mi?id, Part II. ch. v. 
 ^2^ ('Of that Permanence or Stability in the order of 
 Nature which is presupposed in our Reasonings concerning 
 
 '^ See especially his work on the Principles of Psychology, Part IV. 
 ^ In Sir W. Hamilton's edition of Stewart's Works, the corresponding 
 reference is Part II. Subdivision I. ch. ii. section 4, subsection 3. 
 
INDUCTIVE INFERENCE, 37 
 
 Contingent Truths') ; Reid's Intellectual Power s^ Essay VI. 
 ch. vi. ; Reid's Active Powers^ Essay I. ch. iv ; Hamilton's 
 Supplementary Dissertations to Reid's Works ^ Note A, § 3, 
 Note Q; Hamilton's Lectures on Metaphysics^ Lectures 
 XXXIX, XL ; James Mill's Analysis of the Phenomena 
 of the Human Mind, ch. xi; Mill's Logic, Book IIL 
 ch. iii-v, xxi ; ManseFs Prolegomena Logica, ch. v ; Man- 
 sefs Metaphysics, Section on Necessary Truths ; Mill on 
 Hamilton, ch. xvi ; Lewes' History of Philosophy, Article 
 on Kant; Bain's Moral and Mental Science, Book IL 
 ch. vi, with Appendix B ; Herbert Spencer's Principles of 
 Psychology, Part IV. The student, in employing these 
 references, must be careful to distinguish between what 
 relates to the Law of Universal Causation (sometimes 
 called the Principle of Causality) and the Law of the 
 Uniformity of Nature. The two Laws, as already 
 noticed, are not always distinguished with sufficient 
 care. 
 
CHAPTER II. 
 
 Of Processes subsidiary to Induction, 
 
 OF the various mental processes subsidiary to In- 
 duction proper, it will be sufficient for our purpose to 
 discuss Observation and Experiment, Classification (in- 
 cluding Nomenclature and Terminology), and Hypo- 
 thesis. 
 
 § I. Of Observation and Experiment, 
 
 These words are now so familiar, that they hardly 
 require any explanation. To observe is to watch with 
 attention phenomena as they occur, to experiment (or, to 
 adopt more ordinary language, to perform an experi ment^ 
 i s, not only to observe, but also to place the phenome na 
 under peculiarly favourable circumstances, as a pre- 
 liminary to observation. Thus, every experiment im- 
 plies an observation, but it also implies something more. 
 In an experiment, I arrange or create the circumstances 
 under which I wish to make my observation. Thus, if 
 two bodies are falling to the gound, and I attenid to the 
 phenomenon, I am said to observe it, but, if I place the 
 bodies under the exhausted receiver of an air-pump, or 
 cause them to be dropped under any special circum- 
 stances whatever, I may be said not only to make an 
 observation, but also to perform an experiment. Bacon 
 
OBSERVATION AND EXPERIMENT. 39 
 
 has not inaptly compared experiment with the torture of 
 witnesses ^ Mr. Mill distinguishes between the two pro- 
 cesses, by saying that in observation we find our instan ce 
 
 in.potn rP in pyp prim^nf w^ mnhp\\^\\y Qn nrtifin'il ar- 
 rangement of circums tances. ' When, as in astronomy, 
 we endeavour to ascertain causes by simply watching 
 their effects, we observe ; when, as in our laboratories, we 
 interfere arbitrarily with the causes or circumstances of 
 a phenomenon, we are said to experiment'^ J 
 
 As Observation often involves little or no conscious 
 effort, while Experiment always implies an artificial 
 arrangement of circumstances, it might be expected that 
 the general employment of the former for scientific pur- 
 poses would long precede that of the latter. And this 
 supposition is confirmed by the History of Science. 
 Though it is false to affirm that Experiment was never 
 employed by the Greeks^, its general neglect was cer- 
 tainly one cause of the little progress made by them in 
 the physical sciences. 
 
 In the attempt to ascertain the effect of a given cause, 
 there can be no question of the general superiority of 
 
 ^ ' Quemadmodum enim in civilibus ingenium cujusque, et occultus 
 animi affectuumque sensus, melius elicitur, cum quis in perturbatione 
 ponitur, quam alias : simili modo, et occulta naturae magis se produnt 
 per vexationes artium, quam cum cursu suo meant.' Nov. Org., Bk. I. 
 Aph. xcviii. 
 
 ^ Thomson and Tait's Natural Philosophy, vol. i. § 369. 
 
 ^ For a refutation of this popular misconception, see Mr. Lewes' work 
 on Aristotle^ ch. vi. Mr. Lewes, however, seems to me not sufficiently 
 to recognise the slight extent to which Experiment was employed in 
 ancient as compared with modern times. 
 
40 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 Experiment over Observation. To be able to vary the 
 circumstances as we choose, to produce the phenomenon 
 under investigation in the precise degree which is most 
 convenient to us, and as frequently as w^e wish to com- 
 bine it with other phenomena or to isolate it altogether, 
 are such obvious advantages that it is not necessary to 
 insist upon them. Without the aid of artificial experi- 
 ment, it would have been impossible, for instance, to 
 ascertain the laws of falling bodies. To disprove the old 
 theory that bodies fall in times inversely proportional to 
 their weights, it w^as necessary to try the experiment; to 
 be able to affirm with certainty that all bodies, if moving 
 in a non-resisting medium, would fall to the earth through 
 equal vertical spaces in equal times, it was essential to 
 possess the means of removing altogether the resisting 
 medium by some such contrivance as that of the air- 
 pump. In some of the sciences, such as Chemistry, the 
 Sciences of Heat, Light, and Electricity, it is next 
 to impossible, at least in their inductive stage, to ad- 
 vance a single step without the aid of Experiment. No 
 amount of mere Observation would ever have enabled 
 us to detect the chemical elements of which various 
 bodies are composed, or to ascertain the effects of these 
 elements in their pure state. Even when Observation 
 alone reveals to us a fact of nature. Experiment is often 
 necessary in order to give precision to our knowledge. 
 That the metals are fusible, and that some are fusible at 
 a lower temperature than others, is a fact which we can 
 conceive to have been obtruded upon man's observation, 
 
OBSERVATION AND EXPERIMENT. 4 1 
 
 but the precise temperature at which each metal begins 
 to change the solid for the liquid condition could be 
 learned only by artificial experiment. 
 
 But, though, in ascertaining the effect of a given cause. 
 Experiment is a far more potent instrument than Ob- 
 servation, the latter process is also available, and is 
 frequently of the greatest service. Thus, the Science of 
 Medicine equally avails itself, for this purpose, both of 
 observations and experiments. The scientific physician 
 will not only fry the effects of different medicaments, 
 different modes of diet, and the like, but he will also 
 wakk the effects on the organic system of various occu- 
 pations, habits, and pursuits. In some cases even, as 
 in all astronomical and many physiological phenomena, 
 the only means open to us of ascertaining the effect of 
 a given cause is Observation. If we wish to ascertain 
 the various phenomena attendant on a shower of meteors 
 or a total eclipse of the sun, we must wait till the shower 
 of. meteors occurs or the total eclipse takes place. If 
 we wish to learn the effects of the lesion of a particular 
 part of the nervous system, we must generally wait till 
 an instance offers itself; there are many experiments too 
 dangerous and too costly to be made, at least in the case 
 of man. 
 
 While, however, both Observation and Experiment are 
 available in ascertaining the effects of a given cause, 
 in the reverse process of ascertaining the cause of a 
 given effect. Observation alone is open to us. ^We 
 can take a cause/ says Mr. Mill, ^ and try what it will 
 
4^ PROCESSES SUBSIDIARY TO INDUCTION. 
 
 produce; but we cannot take an effect, and try' [that 
 is, experimentally], 'what it will be produced by. We 
 can only watch till we see it produced, or are enabled 
 to produce it by accident/ In those cases, consequently, 
 in which effects alone are patent to us, and the causes 
 are concealed from our view, we are compelled, unless we 
 are able to reverse the problem in the manner noticed 
 in the next paragraph, to have recourse to Observation. 
 A new disease makes its appearance : the mode of its 
 action, and the conditions favourable or unfavourable to 
 its diffusion, can only be learned by a careful observation 
 and comparison of cases. 
 
 It should, however, be noticed that the problem of 
 finding the cause of a given effect is, in practice, as, for 
 instance, in many cases of chemical analysis, often 
 reversed, and that, by setting in action a variety of causes, 
 we try to discover whether any one of them will produce 
 the effect in question. Experiment is thus substituted 
 for Observation. 
 
 It will readily be seen that those Sciences which de- 
 pend wholly or mainly on Observation are, as inductive 
 sciences, at a great disadvantage compared with those 
 in which it is possible largely to employ Experiment. 
 Where we wish to ascertain the effect of a given cause, 
 and we cannot make the instances for ourselves, the 
 want of appropriate and definite instances will often 
 completely baffle 'us. And, though the cause of a given 
 effect can only be learned by Observation, this is gene- 
 rally an enquiry of extreme difficulty, requiring to be 
 
OBSERVATION AND EXPERIMENT. 43 
 
 supplemented by experiment, or the actual production 
 of the given effect by the supposed cause, before we can 
 be certain that it has been conducted with the required 
 accuracy. Thus, mere observation of the electrical phe- 
 nomena which we witness in the heavens could never 
 have given us the Science of Electricity. The experiments 
 which we may conduct in an hour are often worth a 
 century spent in observations. 
 
 In the Science of Astronomy this defect is more than 
 compensated for by the extreme simplicity of the phe- 
 nomena, the heavenly bodies being regarded by us, not 
 in themselves, but only in their mutual relations. Hence, 
 we are, at a comparatively early stage, enabled to apply 
 the Deductive Method, and to solve the problems of 
 Astronomy by mathematical calculations. But in the 
 very complex Science of Physiology this resource is not 
 open to us, and hence the backwardness of those de- 
 partments of physiological science in which direct ex- 
 periment is not available. Any animal or vegetable 
 organism is so complex, the data are so numerous, and 
 bear to each other so many different relations, that, 
 hitherto, it has been found impracticable to subject 
 physiology, at least in any detail, to a deductive treat- 
 ment. In social and political speculations, the want of 
 experiment is, to some extent, supplied by statistics. A 
 social or political experiment is generally as impracticable 
 as an experiment in physiology, and the danger with 
 which it is attended is often incomparably greater. But 
 the number of observations open to us in these enquiries 
 
44 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 (as, for instance, in respect to crime, education, trade, 
 taxation, &c.) is often very large, and, by carefully 
 comparing and systematising them, we may frequently 
 detect some relation between two circumstances which 
 enables us, with great probability, to infer that one has 
 something to do with the production of the other. We are 
 here, however, trenching on the province of those chapters 
 which treat more peculiarly of inductive inference. 
 
 The f^]^<^wing "Rnl^g m ay be laid down for the rig ht 
 c pnduct of Observations and Experiments : — 
 
 Rule I. T hey must be precise . It is often of the 
 utmost importance to notice the exact time at which 
 an event occurs, the length of its duration, the position 
 of an object in space, its relation to surrounding objects, 
 and the like. We are all acquainted with the prime im- 
 portance of precision of detail in legal evidence ; it is no 
 less indispensable in scientific research. For the purpose 
 of enabling us to attain this object, various instruments 
 and methods have been invented. As instances of these 
 may be given, amongst instruments, the telescope, the 
 microscope, the thermometer, the barometer, measures 
 of various kinds, the balance, the dial, the clock, the 
 watch, the chronometer, the vernier, the goniometer, the 
 galvanometer, the thermo-electric pile ; amongst methods, 
 the decimal system of notation, fractions both vulgar 
 and decimal, the divisions of time, the various con- 
 trivances for the measurement of space, the method 
 of double-weighing, the method of least squares, the 
 personal equation in astronomical observations. To these 
 
OBSERVATION AND EXPERIMENT. 45 
 
 instances might be added numerous others, but these 
 will be sufficient to show the great aid derived by what 
 may be called the natural methods of observation from 
 artificial contrivances. The Thermometer and the Method 
 of Double -Weighing furnish such striking exemplifica- 
 tions of the assistance thus afforded, that, though they 
 are probably familiar to most of our readers, it may be 
 desirable to explain them, one as an example of an 
 instrument, the other of a method. 
 
 The Thermometer (it is not necessary here to describe 
 the different kinds of thermometers) is a contrivance for 
 determining the degree of temperature, irrespective of 
 the mode in which it affects individual organisms. As 
 our sensibility varies considerably under different circum- 
 stances, so that what at one time affects us with the 
 sensation of hot wall at another affect us with that of 
 cold, the sense of touch cannot be depended upon for 
 giving us accurate measurements of temperature. But 
 the fact that an augmentation of temperature, with cer- 
 tain rare exceptions (to be noticed hereafter), expands 
 the bodies subject to its influence furnishes us with such 
 a means of measurement. We take a substance which 
 notably exemplifies the power of heat in expansion, such 
 as mercury, alcohol, or, where it is necessary to ensure 
 great precision, atmospheric air carefully prepared, and, 
 by confining it within a tube, and marking off a scale 
 of measurements along the sid^ we are enabled, by 
 noting the degree of expansion of the substance in the 
 tube, to estimate, at least approximately, the exact degree 
 
46 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 of temperature in the atmosphere or any other body, the 
 conditions of which we are investigating. 
 
 The method of Double -Weighing is peculiarly simple 
 and ingenious. It is a contrivance for remedying any 
 possible defects in the construction of the Balance, The 
 body to be weighed is placed at one end of a balance, 
 and is exactly balanced by another body placed at the 
 other end ; the first body is then removed, and its place 
 supplied by a standard weight or weights, till these 
 exactly balance the second body ; we are thus, on the 
 principle that things which are equal to the same thing are 
 equal to one another, assured of the precise equivalence in 
 weight of the body to be weighed and the standard 
 weight or weights, whatever may be the imperfections ^ 
 of the instrument by which they are compared. 
 
 It frequently happens, however, that a single observa- 
 tion may greatly mislead us. I may be in a district at 
 one time, and find the air very temperate and agreeable ; 
 the next time I come, it may be peculiarly hot, or chill, 
 or moist. I may see a man, at the first shot, hit his 
 mark ; but at the subsequent shots, he may fire very wide 
 of it. Hence the importance, whenever there is any 
 liability to error, of taking an average of observations. 
 If a sufficient number of observations be taken, there is 
 every probability that an error in one direction will be 
 compensated by an error in the other, and that an ave- 
 rage, derived from all the observations, will approximate 
 much more nearly to the truth than any single observa- 
 tion is likely to do. Thus, if I wish to ascertain the true 
 
OBSERVATION AND EXPERIMENT, 47 
 
 character of the climate at any particular place, the obser- 
 vations I consult must extend over a considerable number 
 of years ; if I wish to estimate truly the skill of the marks- 
 man, I must watch, not a single shot, but many successive 
 ones. The average, it is true, is liable to error, but any 
 single observation is much more so. There is hardly 
 any department of science, depending upon observation, 
 in which, if it be our object to obtain precision, this 
 method is not indispensable *. 
 
 Rule II. But, though it is necessary to be precise i n 
 our ob servations and experime nts, it is also important, 
 in order to avoid distraction and waste of time, to attend 
 only to tTie"i^^/ ^7S7"r7r??^.y/^;^<rf^ of the case we are in- 
 ve stigating. A physician, for instance, in prescribing for 
 his patient, would not now think it necessary to take an 
 observation of the planets, nor would a chemist, in gather- 
 ing herbs for his decoctions, think it of any consequence 
 to notice the phase of the moon. A caution should, how- 
 ever, be added. Before neglecting any circumstance in 
 our observations, it is of the utmost importance to have 
 ascertained beyond doubt that it is not material to the 
 subject of our enquiries ^. To neglect this caution would 
 be a violation of the first Rule. 
 
 * The student who may wish for further information in connection 
 with Rule I. is referred to Dr. Whewell's Novum Organon RenovatutUy 
 Bk. III. ch. ii., and Herschel's Discourse on the Study of Natural Philo- 
 sophy, § 387-9. On the importance of taking an average of observations, 
 see Herschel's Discourse^ § 226-30. 
 
 ® The neophyte in science requires to be reminded that observations 
 which might at first be supposed to be immaterial are often afterwards 
 
48 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 Rule III. Tlj e- circumsta nces under which an observa- 
 tion^pr experiment is made should, except in the v ery 
 simp lest cases^ be varied as much as_pgs^le. A phy- 
 sician, in studying the character of a disease, will note its 
 effects on persons of different ages, constitutions, habits 
 of Ufe, and the like. An astronomical observer will not be 
 content with a single observation of a newly-discovered 
 comet, but will note the phenomena which attend it at va- , 
 rious stages in its passage through the heavens. A chemist 
 will combine a newly-discovered element with the various 
 other elements, and will try upon it the effect of heat, 
 pressure, &c. It is, of course, implied that some discretion 
 will be employed in the application of this Rule, and that 
 the variation of circumstances will not be carried beyond 
 the point at which there is some probability of its adding 
 to our knowledge. 
 
 Rule IV. Th e phenomenon under investigation s hould 
 if po ssible be i solated from all other phenomena, or, at 
 least, from all those which are lik ely to interfer e with our 
 study of. jt. . In studying the effects of the action of 
 gravity upon bodies, it was necessary to exhaust the 
 atmosphere and to withdraw the support, and, by thus 
 
 found to be amongst the circumstances most material to the enquiry. 
 ' Could anything' (says Dr. Rolleston, in his Address before the Medical 
 Association in 1868) 'have seemed at first sight to be more impertinent, 
 more otiosely curious and trifling, than to enquire during an epidemic of 
 cholera what was the nature of the subsoil in the area it was ravaging, 
 to what depth it was porous, and at what level the water was, and had 
 been previously, standing in it? Yet, as I think, Von Pettenkofer has 
 at last fought out and won his battle on these points.' 
 
OBSERVATION AND EXPERIMENT. 49 
 
 insulating the phenomenon, to enable us to perceive how 
 bodies behave when subject to the action of gravity only. 
 A physician, in trying the effects of a new drug, will, at 
 first at least, administer it alone, and not in combination 
 with other drugs which might augment or counteract its 
 influence on the system ^ 
 
 A beautiful instance of the isolation of a phenomenon 
 is afforded whenever there occurs a total eclipse of the 
 sun. As, on these occasions, the moon, by a curious 
 coincidence, exactly covers, or rather more than covers, 
 the sun*s surface, and thus intercepts all light from it, we 
 are able to see, what we see on no other occasion, cer- 
 tain rose-coloured protuberances, projecting, as it were, 
 from the dark edge of the moon, but really belonging to 
 the sun. The real nature of these * red flames' was long 
 a matter of dispute, but it seems now to be conclusively 
 settled that they are portions of an atmosphere of incan- 
 descent hydrogen in which the sun is enveloped, and 
 which shoots out in these flames to a distance estimated 
 at not less than forty or fifty thousand miles. Had it not 
 been for the insulation of the phenomenon thus produced 
 for us by the intervention of the moon, we should have 
 been ignorant of their existence. Here, to use a bold 
 metaphor, we might say that Nature herself performs an 
 experiment for us ^. 
 
 ® By observing the third of these rules we usually prepare our instances 
 for the application of what will hereafter be explained as the Method of 
 Agreement, and by observing the fourth for the application of what will 
 hereafter be explained as the Method of Difference. 
 
 '^ A method has recently been devised by which these protuberances 
 E 
 
50 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 When it is impossible entirely to isolate a phenomenon, 
 it is sometimes possible so far to diminish the action of 
 the concomitant circumstances as to be able accurately 
 or approximately to calculate what would be the effect, 
 if they were altogether absent. Thus, we can never 
 altogether remove the influence of friction on a moving 
 body, but we can so far diminish it as to be able to say 
 what the effect would be were no such influence at work. 
 We cannot altogether eliminate the influence of extraneous 
 circumstances on a patient subject to medical regime, 
 but, by due care, we may minimise the excitement, fatigue, 
 ennui, or other unfavourable conditions which might 
 interfere with our treatment. 
 
 The circumstances under which we perform our experi- 
 ments being more in our own power than those under 
 which we conduct our observations, it is obvious that 
 the foregoing rules, and especially the third and fourth, 
 can be more easily observed in experiments than in- 
 observations. 
 
 ^ 2. On Classification^ Nomenclature^ and Terminology. 
 
 (i) Of Classification. 
 
 A classification, in the widest sense of the te rm, is a 
 division, or a series of divisions and subdivisio ns ^. The 
 
 may be observed at any time when the sun is shining. Till quite re- 
 cently, however, a total eclipse of the sun afforded the only occasion for 
 observing them, and, if it had not been for the attention thus drawn to 
 them, ihey would probably never have been discovered. 
 8 See Deductive Logic, Part II. ch. viii. 
 
CLA SSIFICA TION, 5 1 
 
 process of classifying our own thoughts or feelings, or 
 the actions of ourselves or others, or the external objects 
 which surround us, is one of the most constant occupa- 
 tions of the mind. Thus, we are perpetually dividing 
 outward objects into those which are useful or those 
 which are useless or noxious to us ; those which are useful 
 into such as are within and such as are beyond our power 
 to attain; those which are useful and which it is within our 
 power to attain into such as are to be sought at once, 
 and those the effort to appropriate which may be more 
 advantageously postponed, — each of these divisions ad- 
 mitting of almost infinite subdivision. In fact, as has 
 frequently been remarked, every attribution of a general 
 name implies an act of division or classification. 
 When we speak of a horse, we are dividing all objects 
 into those which are horses and those which are not. 
 When we speak* of a bay horse, we are superadding to 
 this division the subdivision of horses into bay horses and 
 those of any other colour. 
 
 But the process of Classification of which we are about 
 to treat, though the same in kind with that which we 
 employ in the affairs 0/ ordinary life, is of a much more 
 complex and systematic character. The great difference 
 is that, whereas in the affairs of ordinary life we generally 
 classify objects with reference to some one principle, that 
 principle varying according to the particular purpose we 
 happen to have in view (thus we classify horses according 
 to their colour, their breed, their strength, &c., each classi- 
 fication being suggested by some distinct purpose), a 
 
 £ 2 
 
52 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 scientific classification must take account of all the points 
 of difference which are in any way likely to facilitate 
 the scientific investigation of the group. The purport of 
 the science being defined, the classification must be based, 
 not on one or two characters, selected arbitrarily, but on 
 the entire assemblage of characters which the science in- 
 vestigates. Thus, if Botany be defined as the science 
 which investigates the organisation (including under that 
 term the form, structure, and functions) of plants, a bota- 
 nical classification, in order to be strictly scientific, must 
 not omit to take into account any part of that organisa- 
 tion. But it is evident that such a requirement would 
 produce endless confusion, unless we could discover some 
 mode of subordinating the characters, so as to make the 
 more important points of difference the basis of the higher 
 divisions in the series. Hence we see already that a 
 scientific classification must be guided by at least two 
 principles, a review of all the characters or distinguishing 
 marks, so far as they are known and so far as they fall 
 within the scope of the science, and a subordination of 
 these characters one to another. To these principles 
 others will subsequently be added. 
 
 Before p roceeding to the attempt to ascertain ind uc- 
 tiv ely facts of co-existence or causation amongst a^v ast 
 m §iss of phenomena, it is often highly important, if not 
 essential, t o arrange these phenomena in gro ups^, as.,well 
 a s to determine the order in which these groups the m- 
 sel ves shall be arranged . Hence the importance of lay ing^ 
 do wn cor rex t rules for Cl assific ation in a System of^ 
 
CLASSIFICATION. 
 
 53 
 
 Inductive Logic. It is exclusively as subsidiary to In- 
 duction that we shall here consider the subject of Classi- 
 fication ^. 
 
 •^A scientific Classification, regarded as subsidiary to 
 Induction employed for scientific purposes, may be de- 
 fined as A Series of Divisions^ so arranged as best to 
 facilitate the complete and separate study of the several 
 groups which are the result of the divisions^ as well as of 
 the entire subject under investigation . *The general pro- 
 blem of classification,' says Mr. Mill ^^, ^ in reference to 
 these [namely, scientific] purposes may be stated as 
 
 ® It will probably occur to the student that the materials for Classifica- 
 tion can themselves only be obtained by Induction. And this is true. 
 All Classification implies the prior employment of an Inductio per Enu- 
 meratione}?i S'unplicem, by which we establish the fact of the co-inherence 
 of certain attributes. But these ' inductions of co-existence,' (see pp^ 
 7-9), which precede our classifications, are altogether of a different 
 order from the ' inductions of causation ' which it is the ultimate aim of 
 science to establish, and to which we regard Classification as mainly 
 subordinate. We say ' mainly subordinate/ for, of course, there is no 
 doubt that, when, by means of certain ' inductions of co-existence,' we 
 have constituted a class, we are in a more favourable position than before 
 for detecting additional facts of co-existence among the associated 
 phenomena. 
 
 When, from a wide experience, I find that the attributes a, b, c, d, e 
 invariably co-exist in the same objects, I generally constitute these objects 
 into a class, and designate them by a class-name. The name thus serves 
 to recall the fact of the co-inherence of the attributes, and I am far 
 more likely, than if I had never made the classification^ to discover 
 the co-existence with the other five of some sixth attribute, say/, or 
 to be able to trace some causal connection between, say, a and 6, or 
 a, h, and c. 
 
 10 Mill's Logic, Bk. IV. ch. vii. § i. 
 
54 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 follows: To provide that things shall be thought of in 
 such groups, and those groups in such an order, as will 
 best conduce to the remembrance and to the ascertain- 
 ment of their laws/ 
 
 The sciences of Botany and Zoology are rightly re- 
 garded as furnishing the best examples of Scientific Clas- 
 sification. The excellence of the classifications which 
 they present may be referred to two reasons. The first 
 is the extraordinary multiplicity of the difi'erent kinds 
 of animals and plants which are found on the surface of 
 the globe : this has, from the earliest times, exercised 
 man's ingenuity in the attempt to name them and reduce 
 them to order. The second reason may be found in the 
 imperfection of these sciences in their present condition : 
 the difficulty, amounting almost to impossibility, of dis- 
 covering laws of succession, or, in other words, relations 
 of cause and effect, in the animal and vegetable kingdoms 
 has naturally led scientific enquirers to concentrate their 
 attention on the far easier task of describing and ar- 
 ranging the objects themselves. Mineralogy, though its 
 classifications are less systematic and complete, is also, 
 in the present state of the science, mainly occupied in 
 attempting the work of classification. 
 
 The best means, perhaps, of making the student ac- 
 quainted with the nature of scientific classification is to 
 compare the method of natural classification (which aims 
 at being strictly scientific) with that of artificial classifica- 
 tion (which, so far as it is artificial, is not scientific), giving 
 illustrations from the sciences of Botany and Zoology. 
 
CLA SSIFICA TION. 55 
 
 An examination of the natural system will enable us to 
 lay clown certain rules for scientific classification, and 
 we shall conclude with such remarks as may seem ne- 
 cessary in order to preserve the student from erroneous 
 impressions. 
 
 A natural system of Classification aims at classifying 
 objects according to the whole of their resemblances and 
 differences, so far as these are recognised by the science 
 in whose service the classification is made. But amongst 
 these resemblances and differences some are found to be 
 invariably attended by a number of others, and conse- 
 quently these, as the more important^ are selected as the 
 characters by which to discriminate the higher divisions 
 of the series, the less important characters being, through- 
 out the whole serie s, subordinated to the r porf impnrfanf 
 This successive subordination of characters and the con- 
 sequent coincidence of the groups formed by our classi- 
 fications with what appear to be the great divisions of 
 nature are the peculiarities which mainly distinguish a 
 natural system. An artificial system, on the other hand, 
 is one w^hich selects arbitrarily some point of difference 
 amongst the objects to be classified, and then, so far as 
 possible, makes this or similar points the basis of its 
 classifications. No system, .however, as we shall see pre- 
 sently, is purely artificial. Though of litde use, except 
 as a preliminary effort, for the purposes of science, an 
 artificial system possesses one great advantage. As it 
 bases its divisions, where possible, on some one property, 
 and that generally something which at once strikes the 
 
56 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 eye (one of the earliest of the modern attempts to classify 
 plants took for its basis the form of the corolla), it is 
 peculiarly easy of application, and can be much more 
 readily learnt than a natural system. It thus often serves 
 the purposes of a key, by which we may easily discover 
 the place of a group in a natural system. We .now pro- 
 ceed to offer illustrations. 
 
 In Botany, the most celebrated artificial system is that 
 known as the Linnaean, though Linnseus also did much 
 towards the establishment of a natural system. In this 
 system, which was a great advance on preceding artificial 
 systems, the main basis of classification is the number of 
 stamens and pistils which are to be found in the flowering 
 plant. This character is, however, to some extent 
 modified by other considerations, such as the relative 
 lengths of the stamens, the shape of the fruit, &c. ; so far 
 as these modifications are admitted, the Linnaean system 
 approaches to a natural system. The annexed Tables 
 (extracted from Balfour's Manual of Botany ^^) will give 
 the student some idea of the manner in which the Classes 
 (higher divisions) and the Orders (divisions intermediate 
 between the Classes and Genera) are constituted accord- 
 ing to the Linnsean system. It should be premised that 
 the stamens are the male organs, and the pistils the 
 female organs of a plant. 
 
 " §§ 716,717- 
 
CLASSIFICATION. 57 
 
 Tabular View of the Classes of the Linnjean System. 
 
 A, Flowers present, or evident Stamens and Pistils (Phanerogamia). 
 I. Stamens and Pistil in every flower. 
 I. Stamens free. 
 
 a. Stamens of equal length, or not differing in certain pro- 
 portions ; 
 
 in number i Class I. Monandria. 
 
 — 2 II. Diandria. 
 
 — 3 III. Triandria. 
 
 — 4 IV. Tetrandria. 
 
 — 5 V. Pentandria. 
 
 6. VI. Hexandria. 
 
 — 7 VII. Heptandria. 
 
 — 8 VIII. Octandria. 
 
 — 9 IX. Enneandria. 
 
 — 10 X. Decandria. 
 
 — 12-19 ^I* Dodecandria. 
 
 20 1 inserted on Calyx — XII. Icosandria. 
 : J ( 
 
 or more J on Receptacle .... XIII. Polyandria. 
 b. Stamens of diflTerent lengths ; 
 
 two long and two short XIV, Didynamia. 
 
 four long and two short XV. Tetradynamia. 
 
 2. Stamens united ; 
 
 by Filaments in one bundle .... XVI. Monadelphia. 
 
 in two bundles XVII. Diadelphia. 
 
 in more than two bundles XVIII. Polyadelphia. 
 
 by Anthers (Compound flowers) XIX. Syngenesia. 
 
 with Pistil on a Column XX. Gynandria. 
 
 II. Stamens and Pistil in diflTerent flowers ; 
 
 on the same Plant XXI. Monoecia. 
 
 on diflTerent Plants XXII. Dioecia. 
 
 III. Stamens and Pistil in the same or in n 
 
 different flowers on the same or > XXIII. Polygamia. 
 on different Plants . . . 
 B. Flowers absent, or Stamens and Pistils not ] 
 evident 
 
 V XXIV. Cryptogamia. 
 
=;8 
 
 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 The Classes are sub-divided into Orders, as will be 
 
 seen from the next Table, on a less uniform plan than 
 
 that on which they were themselves constituted. 
 
 Tabular View of the Orders of the Linnjean System. 
 
 ~| Monogynia^^ I Free Style. 
 
 Digynia 2 Free Styles. 
 
 Trigynia 3 — 
 
 Tetragynia 4 — 
 
 Pentagynia 5 — 
 
 Hexagynia 6 
 
 y Heptagynia 7 — 
 
 Octogynia 8 — 
 
 Enneagynia 9 — 
 
 Decagynia lO — 
 
 Dodecagynia 12-19 — 
 
 Polygynia 20 and upwards. 
 
 Gymnospermia Fruit formed by four Achaenia. 
 
 Angiospermia Fruit, a two-celled Capsule with 
 
 many seeds. 
 
 r Siliculosa Fruit, a Silicula. 
 
 \ Siliquosa Fruit, a Siliqua. 
 
 ► Triandria, Decandria, &C. (number of Stamens), as in Classes. 
 
 Class I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 XV. 
 
 XVI. 
 XVII. 
 XVIII. 
 
 'Polygamia ^qualis . 
 Superflua . 
 
 XIX. <| 
 
 Frustranea 
 
 Necessaria 
 
 Florets all hermaphrodite. 
 
 Florets of the disk hermaphrodite, 
 those of the ray pistilliferous and 
 fertile. 
 
 Florets of the disk hermaphrodite, 
 those of the ray neuter. 
 
 Florets of the disk staminiferous, 
 those of the ray pistilliferous. 
 
 Each floret having a separate in- 
 volucre. 
 
 Segregata 
 
 Monogamia Anthers united, flowers compound. 
 
 ^^ It must not be supposed that all the Orders, Monogynia, &c., exist 
 in each of the first thirteen Classes. When an Order is absent, the next 
 Order which is present takes its place in the numerical arrangement. 
 Thus, if the Order Trigynia be absent, and the next Order which is 
 present be Tetragynia, as in Class IV, this latter will rank as the third 
 Order. 
 
XXII 
 XXIII. 
 
 XXIV. 
 
 CLA SSTFICA TION, 59 
 
 XX T 
 
 YVT* [ Monandria, Diandrla, &c. (number of Stamens), as in the 
 
 r^},' \ Classes. 
 
 'Moncecia Hermaphrodite, staminiferous,and 
 
 pistilliferous flowers on the same 
 plant. 
 
 Dioecia on two plants. 
 
 Trioecia on three plants. 
 
 Filices Ferns. 
 
 Musci Mosses. 
 
 Hepaticae Liverworts. 
 
 Lichenes Lichens. 
 
 Algae Sea-weeds. 
 
 Fungi Mushrooms. 
 
 'Even as an artificial method/ says Professor Balfour ^^ 
 ' this system has many imperfections. If plants are not in 
 full flower, with all the stamens and styles perfect, it is 
 impossible to determine their class and order. In many 
 instances, the different flowers on the same plant vary as 
 regards the number of the stamens. Again, if carried 
 out rigidly, it would separate in many instances the 
 species of the same genus ; but as Linnaeus did not wish 
 to break up his genera, which were founded on natural 
 affinities, he adopted an artifice by which he kept all the 
 species of a genus together. Thus, if in a genus nearly 
 all the species had both stamens and pistils in every 
 flower, while one or two were monoecious or dioecious, 
 he put the name of the latter in italics, in the classes and 
 orders to which they belonged according to his method, 
 and referred the student to the proper genus for the 
 description.' 
 
 The species of the Linnaean system coincide with those 
 of the natural system. The same is mostly the case with 
 
 " Balfour's Manual of Botany, § 718. 
 
6o PROCESSES SUBSIDIARY TO INDUCTION. 
 
 the genera, or next higher divisions. The Linnsean system 
 is, therefore, far from being purely artificial. In fact, when 
 we come to the lower groups of vegetables (genera and 
 species), we are compelled to discriminate them one from 
 another by a multiplicity of characters, so that a purely 
 artificial system of botany would be impossible. 
 
 The framers of natural systems of botany, instead of 
 selecting some one character, such as the number of 
 stamens and pistils, as the basis of the higher divisions, at- 
 tempt to discover a number of characters, any one of which, 
 if employed as the instrument of division, would give the 
 same results as any of the others. This coincidence of 
 divisions founded on various characters is a proof that we 
 have reached some real distinction in nature. The main 
 division of plants into cellular and vascular, or acoty- 
 ledonous and cotyledonous, and the sub-division of vas- 
 cular or cotyledonous plants into monoctyledonous and 
 dicotyledonous, furnish remarkable instances of such 
 a coincidence, and may consequently be regarded as cor- 
 responding with grand divisions in nature itself. 
 
 * In taking a survey of the Vegetable Kingdom, some 
 plants are found to be composed of cells only, and are 
 called Cellular ; while others consist of cells and vessels, 
 especially spiral vessels, and are denominated Vascular. 
 If the embryo is examined, it is found in some cases to 
 have cotyledons or seed-lobes, in other cases to want 
 them ; and thus some plants are cotyledonous, others 
 acotyledonous ; the former being divisible into nionocotyle- 
 donous^ having one cotyledon, and dicotyledonous^ having 
 
CLA SSIFICA TION, 6 1 
 
 two [or more] cotyledons. The radicle, or young root 
 of acotyledons, is heterorhizal, that of monocotyledons is 
 endorhizal, that of dicotyledons, exorhizal. When the 
 stems are taken into consideration, it is seen that marked 
 differences occur here also, acotyledons being acrogenous, 
 monocotyledons endogenous, and dicotyledons exogenous. 
 The venation of leaves, parallel, reticulated, or forked, 
 establishes the same great natural divisions ; and similar 
 results are obtained from a consideration of the flowers, 
 monocotyledons and dicotyledons being phanerogamous 
 and acotyledons cryptogamous' 
 
 ' Thus, the following grand natural divisions are arrived 
 at:— 
 
 I. Cellular . . Acotyledonous. Heterorhizal. Acro^enousJ '^^^ °" 
 •^ I gamous. 
 
 T r ^ , f Monocotyledonous. Endorhizal. Endogenous.! Phanero- 
 *\ Dicotyledonous. Exorhizal. Exogenous. J gamous^*.' 
 
 Having established these Primary Divisions of the 
 vegetable kingdom, the botanist, guiding himself as far as 
 possible by the same principles as those on which the 
 primary divisions were formed, proceeds to divide and 
 sub-divide till at last he arrives at species, which are 
 generally defined to be collections of individuals so nearly 
 resembling each other that they may be supposed to be 
 descended from a common stock. Thus, the Class 
 ' Dicotyledones or Exogense ' is sub-divided into four sub- 
 classes, one of which is the * Thalamiflorae,' characterised 
 as having ' calyx and corolla present, petals distinct and 
 
 " Balfour's Ma?iual of Botany, §§ 723, 7.24. 
 
62 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 inserted into the ♦thalamus or receptacle, stamens hy- 
 pogynous/ This sub-class is divided into a number of 
 orders (sixty in Professor Balfour's Manual), one of which 
 is Hypericacese, the Tutsan or St. John's-wort family, 
 thus described : — 
 
 ' Sepals 4-5, separate or united, persistent, usually with glandular dots, 
 unequal ; aestivation imbricated. Petals 4-5, oblique, often with black 
 dot?, aestivation contorted. Stamens hypogynous, indefinite in number ; 
 generally polyadelphous, very rarely 10, and monadelphous or distinct; 
 filaments filiform : anthers bilocular, with longitudinal dehiscence ; car- 
 pels 2-5, united round a central or basal placenta ; styles the same num- 
 ber as the carpels, usually separate ; stigmas capitate or simple. Fruit 
 either fleshy or capsular, multilocular, and multivalvular, rarely unilocu- 
 lar. Seeds usually indefinite in number, minute, anatropal, usually ex- 
 albuminous ; embryo usually straight. — Herbaceous plants, shrubs, or 
 trees, with exstipulate entire leaves, which are usually opposite and 
 dotted. Flowers often yellow.' 
 
 In this order there are fifteen known genera, one of 
 which is the Hypericum, which is thus described in . 
 Irvine's Handbook of British Plants : — 
 
 ' Hypericum, St. John's- wort. Herbaceous plants or shrubs, with 
 opposite simple, entire leaves, which are usually furnished with pellucid 
 dots (reservoirs of essential oil). Sepals five, free or united at the base, 
 ovate, slightly unequal, permanent. Petals as many as the sepals, obtuse. 
 Spreading. Stamens indefinite, combined at the base into three or five 
 sets, with small roimdish anthers. Ovary with three-five cells or carpels 
 and as many styles, with simple stigmas. Fruit capsular, rarely baccate, 
 three-five-celled, with numerous seeds.' 
 
 This genus is divided into sub-genera or sections, one 
 of which is thus described : 
 
 ' Stems herbaceous. Stamens in three parcels (triadelphous). Styles 
 three. Capsule three- celled, three-valved.* 
 
CLA SSIFICA TlOtf. / -O i. 
 
 \ O ' /. *' 
 
 The sub-genus or section is again dh/d^ in^cy^ub- ' / 
 
 sections, one of which is characterised as hayfng ' sfeips 
 round, sepals with ciliary glands/ This sub-sectfqa con- ' j 
 tains amongst its species the well-known Hype/ictm / 
 Pulchrum, * Elegant St. John's-wort,' thus described^: ^# 
 
 \ ^- 
 
 ' Stems erect, bent at the base, round, glabrous, simple or branchi H^._ ^ 
 Leaves ovate, clasping, coriaceous, smooth, with numerous translucent 
 dots. Flowers in opposite panicled cymes. Sepals obovate, roundish, with 
 a point, ciliated, with nearly sessile glands. Petals oblong, ribbed, with 
 black sessile glands'^.' 
 
 The first peculiarity which strikes us in thes^ descrip- 
 tions is the large number of characters which is employed 
 in constituting even the higher divisions of the series. 
 Instead of describing merely the number and distribution 
 of the stamens, as in the Linnsean system, we have, even in 
 the description of the Order, a reference to almost every 
 part of the plant. We next notice the much greater 
 definiteness which the characters assume, as we descend 
 lower in the series. Thus, to take the sepals as an in- 
 stance, the description of the sub-class simply informs 
 us of the presence of a calyx, while each successive divi- 
 sion (except the sub-genus) gives us more and more 
 definite information as to the number, position, form, &c. 
 of the sepals which constitute the calyx. Again, we 
 observe that, in the lower divisions, the stem, leaves, 
 sepals, and petals are the characters which are brought 
 into greatest prominence, whereas the stamens and the 
 various parts of the pistil (the carpels, styles, and stigmas), 
 
 ^^ See Irvine's Handbook of British Plants, under Order CIII. 
 
64 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 which are employed in the higher divisions, disappear 
 from the lower, as no longer affording grounds of differ- 
 ence. Now the stamens and pistil, inasmuch as any 
 peculiarity in them is generally accompanied by a larger 
 number of peculiarities in other parts of the plant, are 
 usually of far more importance than the corolla (petals) 
 and calyx (sepals), and therefore it is reasonable to suppose 
 that the grounds of difference furnished by them would 
 be likely to be exhausted in the higher divisions. At 
 the same time we see that, in the instance we have 
 taken, the sepals and petals furnish grounds of dif- 
 ference at a very early stage of the classification, and 
 consequently that even the less important characters 
 are often used concurrently with others to determine 
 the higher divisions. 
 
 In Zoology, the advantage of a natural over an artificial 
 classification is more readily recognised than in Botany, 
 the structure and functions of animals being more fa- 
 miliar and apparent than those of plants. A division of 
 animals, for instance, which adopted the number of limbs 
 as its sole distinguishing character, and thus brought 
 together, as quadrupeds^ the ox and the frog, would be so 
 absurd on the face of it, as to be rejected at once. ' No 
 arrangement of animals,' says Dr. WhewelF^, 'which, in 
 a large number of instances, violated strong and clear 
 natural affinities, would be tolerated because it answered 
 the purpose of enabling us easily to find the name and 
 place of the animal in the artificial system. Every system 
 
 ^® History of the Inductive Sciences, Bk. XVI. ch.vii. 
 
CLASSIFICATION. 65 
 
 of Zoological arrangement may be supposed to aspire 
 to be a natural system/ He then proceeds to give an 
 instance of an attempt to constitute an artificial classifica- 
 tion in the ichthyological branch of Zoology. ^Bloch, 
 whose ichthyological labours have been mentioned, fol- 
 lowed in his great work the method of Linnaeus/ (who 
 devoted much of his attention to the classification of 
 animals as well as of plants.) * But towards the end of 
 his life he had prepared a general system, founded upon 
 one single numerical principle — the number of fins ; just 
 as the sexual system of Linnaeus is founded upon the 
 number of stamina : and he made his sub-divisions ac- 
 cording to the position of the ventral and pectoral fins ; 
 the same character which Linnaeus had employed for his 
 primary division. He could not have done better, says 
 Cuvier, if his object had been to turn into ridicule all 
 artificial methods, and to show to what absurd combina- 
 tions they may lead.' 
 
 * By the natural method'^ says M. Milne Edwards ^^ 
 (whose remarks on Zoological Classifications and the 
 Primary Divisions and Classes of the Animal Kingdom 
 are well worthy of the attention of all students of induc- 
 tive logic), ' the divisions and subdivisions of the animal 
 kingdom are founded on the whole of the characters fur- 
 nished by each animal, arranged according to their degree 
 
 ^^ See Milne Edwards' Zoologie (in the Cours elementaire d'histoire 
 naturelle), septieme edition^ §§ 364, 365. There is an English translation 
 of this work by Dr. R. Knox. I have followed it, except in a few places 
 where it does not accurately represent the original. 
 
 F 
 
66 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 of respective importance; thus, in knowing the place 
 which the animal occupies, we also know the more re- 
 markable traits of its organisation, and the manner in 
 which its principal functions are exercised. 
 
 ' The rules to be observed in arriving at a natural clas- 
 sification of the animal kingdom are of extreme simplicity, 
 but often there is much difficulty in the application. They 
 may be reduced to two, for the object of the zoologist in 
 establishing such a classification is, — 
 
 ' I St. To arrange animals in natural series, according 
 to the degree of their respective affinities, — that is to say, 
 to distribute them in such a manner that those species 
 which most nearly resemble each other may occupy the 
 nearest places, while the distance of two species from 
 each other may, in some sort, be the measure of their 
 non-resemblance. 
 
 '2nd. To divide and subdivide this series according 
 to the principle of subordination of characters, — that is 
 to say, by reason of the importance of the differences 
 which these animals present between them/ 
 
 The Primary Divisions of the animal kingdom, ac- 
 cording to the natural system, are four, there being four 
 types of structure and of nervous organisation, to which 
 animal life conforms. 
 
 * These four principal forms may be understood by a 
 reference to four well-known animals — the dog, the cray- 
 fish or lobster, the snail, the asterias or sea-star. 
 
 ' In order that the zoological classification might be a 
 faithful representation of the more or less important 
 
CLASSIFICATION. 6y 
 
 tnodifications introduced into the structure of animals, it 
 was necessary to distribute these beings into four prin- 
 cipal groups or divisions; and this is, in fact, what 
 Cuvier did. 
 
 * The animal kingdom is divided into vertebrate animals^ 
 articulated or annulaied animals, molluscs, and zoophytes. 
 
 * The fundamental differences distinguishing these four 
 primary divisions depend chiefly on the mode of arrange- 
 ment of the different parts of the body and on the con- 
 formation of the nervous system. It is easy to under- 
 stand the importance of these two dominant characters : 
 to feel and to move is the especial character of animal life, 
 and these two functions belong to the nervous system. 
 It might readily, then, be anticipated that the mode of 
 conformation of this system would exert a powerful 
 influence over the nature of animals, and would furnish 
 characters of primary importance in classification. 
 
 * The general disposition or mode of reunion of the 
 different parts of the body exercises an equally im- 
 portant influence, as modifying the localisation of 
 the functions and the division of the physiological 
 result ^V 
 
 Vertebrate animals are thus described : 
 
 ' The vertebrate animals resemble man in the more important points 
 of their structure ; almost all the parts of their bodies are in pairs, and 
 disposed symmetrically on the two sides of a medial longitudinal plane ; 
 their nervous system is highly developed, and is composed of nerves and 
 ganglions, and of a brain and spinal marrow. To these we may add, 
 
 " Milne Edwards, §§ 372, 373. 
 F 2 
 
6S PROCESSES SUBSIDIARY TO INDUCTION. 
 
 that the principal muscles are attached to an internal skeleton, composed 
 of separate, pieces, connected together, an^ disposed so as to protect the 
 more important organs, and to form the passive instruments of loco- 
 motion; that the more important part of this skeleton forms a sheath 
 for the brain and spinal marrow, and results from the reunion of annular 
 portions, called vertebrae ; that the apparatus for the circulation is very 
 complete, and that the heart offers at least two distinct reservoirs ; that 
 the blood is red ; that the limbs are almost always four in number, and 
 never more ; finally, that there exist distinct organs lodged in the head 
 for sight, hearing, smell, and taste ^^.* 
 
 The Primary Division (embranchement) ' Vertebrate 
 Animals ' is sub-divided into the five classes, Mammals, 
 Birds, Reptiles, Batrachia, Fishes, of which Mammals 
 are thus described : 
 
 ' Organs of lactation. Hot blood. Circulation complete, and heart 
 with four cavities. Pulmonary respiration simple. Lobes of the cere- 
 bellum reunited by an annular protuberance. Lower jaw articulated 
 directly with the cranium. The body generally covered with hairs. 
 Viviparous.' 
 
 * There exist considerable differences amongst the 
 mammalia, and these modifications of structure serve 
 as the basis for the division of the class into groups 
 of an inferior rank, called orders. Most of these groups 
 are so distinct as to admit of no doubt in respect 
 of their limits : they constitute, in fact, natural divisions ; 
 but in others the line of demarcation is by no means so 
 distinct. Thus a mammal may have points of resemblance 
 so close to two groups as to render it almost indifferent 
 to which it be referred. To some naturalists, differences 
 appear important which are disregarded by others, and 
 
 ^* Milne Edwards, § 374. 
 
CLA SSIFICA TION, 69 
 
 hence a want of agreement on the subject of classification 
 has always prevailed. 
 
 ' The method followed here is nearly the same as that 
 proposed by Cuvier. It rests mainly on the differences 
 mammals show in respect of their extremities and teeth, 
 differences which always imply a crowd of others in 
 habits, structure, and even intelligence. 
 
 ' Keeping in view the ensemble of these characters, the 
 class mammalia may be divided into two groups, — the 
 monodelphic and didelphic. 
 
 * The monodelphic or monodelphian are the more nu- 
 merous, and are distinguished chiefly by their mode of 
 development. At birth they are already provided with all 
 their organs, and before birth they derive their nourish- 
 ment from the mother by means of a placenta. Their 
 brain is more perfect than the didelphian, by the presence 
 of a corpus callosum uniting the two cerebral hemispheres. 
 Finally, the walls of the abdomen have no osseous sup- 
 ports attached to the margins of the pelvis, as we find 
 in the second great class of mammals. The mammals 
 thus organised have been subdivided into two groups, — 
 namely, 07'dinhry mammals and pisciform mammals, 
 
 * The ordinary mammals are organised principally to 
 live on solid ground; the skin is provided with hairs. 
 These animals are further subdivided into ten orders : the 
 bimana, quadrumana, cheiroptera, insectivora, rodentia, 
 edentata, carnivora, amphibia, pachydermata, and rumi- 
 nantia. The first eight of these orders have flexible 
 fingers and toes, with nails covering only the dorsal aspect 
 
70 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 of the toe or finger, and comparatively small ; hence they 
 have been called unguiculata ; the last two, — namely, the 
 pachydermata and ruminantia, have the extremity of the 
 finger and toe entirely enclosed in a hoof; they are thus 
 called ungulata. 
 
 ' The order bimana includes only man : in him alone 
 the arms are destined for prehension, the limbs for pro- 
 gression and support in the erect attitude. Thus, his 
 natural position on the soil is unmistakeably vertical. The 
 teeth are of three kinds, and have their edges on the 
 same plane ; they are frugivorous : finally, the brain is 
 more perfect, more highly developed, than in any other 
 animal ^^/ 
 
 Here the Order is coextensive with the Species, but 
 usually the Order is divided into Genera, and each Genus 
 into Species. Thus, the Order 'Carnivora' is divided 
 into the Genera ' cat,' * hyaena,' ' dog,' ^ bear,' Src. Again, 
 the Genus * dog ' comprises the dog properly so called, the 
 wolf, and the fox. The genus * cat ' comprises not only 
 the cat properly so called, but the tiger, lion, panther, &c. 
 
 It may be as well to add an account of the characters 
 which distinguish respectively the Order ' Carnivora,' the 
 Genus * Felis,' and the Species * Leo,' in order to serve 
 as an example or illustration of the manner in which these 
 several degrees in the scale of Classification are usually 
 described : — 
 
 * The order of carnivora is composed of ordinary unguiculated mam- 
 mals ; the form of their dentition is complete, but they have no opposing 
 
 20 Milne Edwards, §§ 409-412. 
 
CLA SSIFICA TION, 7 1 
 
 thumb. According to the mode of life of these animals, their intestinal 
 canal is short ; their jaws and their muscles strong, in order to seize and 
 devour their prey ; their head from this circumstance seems large. The 
 jaws are short, thus favouring their strength, and the form of the tem- 
 poral-maxillary articulation proves that the teeth are made for tearing 
 and cutting, not for grinding or masticating. The canine teeth are 
 large, long, and very powerful ; the incisors, six in number in each jaw, 
 small ; the molars, sometimes adapted merely for cutting, in others sur- 
 mounted with rounded tubercles, presenting no conical points, arranged 
 as in the insectivora. One of these molar teeth is usually much longer 
 and more cutting than the others, and has therefore been called the car- 
 nivorous molar tooth ; behind these (on each side) are one or two molars, 
 almost flat, and between the carnivorous molar and the canine a variable 
 number of false molars. The food of the animal, whether exclusively 
 composed of flesh or mixed with other matters, may be judged of by the 
 varying proportions of these cutting or tuberculated molars. 
 
 'Animals of this order have generally the toes armed with claws 
 adapted to hold and to tear their prey ; usually also they have no collar- 
 bones.* 
 
 The following are the characteristics of the genus 
 ' Felis/ and of the species * Leo : ' — 
 
 ' Their jaws are short, and are acted on by muscles of extraordinary 
 strength ; their retractile nails, concealed between the toes in a state of 
 repose by means of elastic ligaments, are never blunted. Their toes are 
 five in number on the anterior limbs, and four on those behind. Their 
 hearing is exceedingly fine, and the best developed of all their senses. 
 They see well by day and night, but they are not far-sighted ; in some 
 the pupil is elongated vertically, in others it is round. They make great 
 use of the organ of smell ; they consult it before eating, and often when 
 anything disturbs them. Their tongue is covered with horny and very 
 rough points. Their coat is in general soft and fine, and the surface 
 of the body very sensible to the touch ; their whiskers especially seem 
 to be instruments of great sensibility. Though of prodigious vigour, 
 they generally do not attack animals openly, but employ cunning and 
 artifice. They never push their prey to flight, but watching by the 
 margins of rivers and pools in covert, they spring at once on their 
 victim. 
 
72 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 * At the head of this genus stands the lion, measuring frequently 
 twelve feet in length, or over six feet to the setting on of the tail ; about 
 three feet in height, and characterised by the square head, the tuft of 
 hair terminating the tail, and in the male by the mane which flows from 
 the head and neck^^.' 
 
 The process by which the Zoologist constitutes the 
 Primary Divisions of animal life, and then descends from 
 these to the Species, is distinguished by the same pecu- 
 liarities as those which we remarked in reviewing the 
 natural classifications of the Botanist. In one step or 
 other of the classification almost every known charac- 
 teristic of a species will be found. As we descend the 
 series, the characters gain in definiteness and, as a rule, 
 lose in importance. Moreover, even in the higher divi- 
 sions of the series, numerous characters are used, and 
 those not always of great apparent importance. Thus, 
 that *the body is generally covered with hairs' is one 
 of the characters of Mammalia. 
 
 The student will now be in a position to understand 
 the rules which may be laid down for the right conduct 
 of a Natural Classification. 
 
 I. Not only the lower, but the higher groups of the 
 series should be so constituted as to differ from one 
 another by a multitude of characters. It is only when, 
 as is the case in the primary divisions of Botany and 
 Zoology, we arrive at the same divisions from a variety 
 of different considerations, that we can feel assured that 
 our groups really correspond with distinctions in Nature. 
 
 21 Milne Edwards, § 414. 
 
CLA SSIFICA TION» 7 3 
 
 It is this coincidence^ in the higher groups of the series, 
 of divisions formed on different principles, that distin- 
 guishes a Natural from an Artificial Classification. 
 
 11. The more important characters should be selected 
 for the purpose of determining the higher groups. This 
 is called the principle of the subordination of characters. 
 But how are we to determine the relative importance 
 of characters ? ' We must consider as the most impor- 
 tant attributes,' says Mr. MilP^, ' those which contribute 
 most, either by themselves or by their effects, to render 
 the things like one another, and unlike other things ; 
 which give to the class composed of them the most 
 marked individuality; which fill, as it were, the largest 
 space in their existence, and would most impress the 
 attention of a spectator who knew all their properties but 
 was not specially interested in any.' This is perfectly 
 true, but it seems to be hardly sufficiently definite. The 
 following criteria may be proposed for the purpose of 
 discriminating between the more and the less important 
 properties of natural objects, (i) A character which is 
 found to furnish an invariable index to the possession 
 of certain other characters is of more importance than 
 a character which furnishes no such index. Thus, the 
 .internal structure of an animal is of more importance than 
 its size, and the mode of fructification of a plant than 
 the colour of its flowers. (2) Amongst such characters, 
 a character is regarded as of more or less importance, 
 according as it accompanies a greater or smaller number 
 22 Mill's Lo^ic, Bk. IV. ch. vii. § 2. 
 
74 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 of Other differences. Thus, in the classification of animals, 
 the characters from which the classes unguiculata and 
 . ungulata are so called are of more importance than 
 the form of the teeth, which is used in distinguishing the 
 orders. For the same reason, the mode of growth of 
 flowering plants (which leads to the distinction of en- 
 dogenous and exogenous plants) is of far more im- 
 portance, as a character, than the number of stamens 
 or pistils. Hence, in constituting the higher divisions 
 of a series we must look for those characters which are 
 accompanied by the largest number of differences. 
 
 III. The classification should be gradual, proceeding 
 by a series of divisions and subdivisions. When the 
 group to be classified consists of an enormous number 
 of species, as in the case of animals and plants, the 
 necessity of observing this rule is obvious. To descend 
 at once from the Primary Divisions to, say, Genera and 
 Species, would render the Classification comparatively 
 worthless. The object of a classification being to bring 
 together those groups which resemble each other and 
 to separate those groups which differ from each other, 
 we must take account of degrees of resemblance and 
 difference, so that, as a rule, the number of gradations 
 will increase with the number "of groups to be classified. 
 Both in Botany and Zoology, the grand divisions which 
 seem now to be universally recognised are Primary 
 Divisions, or Sub-Kingdoms (embranchements), Classes, 
 Orders, Genera, and Species. Between these various 
 other divisions are interpolated, according to the seeming 
 
CLASSIFICATION, 
 
 75 
 
 requirements of each particular system, and often accord- 
 ing to the views of each individual author. Moreover, 
 below Species are often reckoned Varieties, and even 
 Varieties are sometimes subdivided, this being especially 
 the case when animals have become domesticated or 
 plants cultivated. Taking as an instance the Anthyllis 
 Vulneraria (Common Lady's Finger), the divisions and 
 subdivisions of a natural classification may be illustrated 
 thus 23 :_ 
 
 I. 
 
 Primary Division 
 
 . Cotyledones. 
 
 II. 
 
 Class .... 
 
 . Dicotyledones. 
 
 
 Subclass 
 
 . Calyciflorae. 
 
 III. 
 
 Order .... 
 
 . Leguminosae. 
 
 
 Suborder 
 
 . Papilionaceae. 
 
 
 Tribe .... 
 
 . Loteae. 
 
 
 Subtribe 
 
 . Genisteae. 
 
 IV. 
 
 Genus .... 
 
 . Anthyllis. 
 
 
 Subgenus or Section 
 
 . Vulneraria. 
 
 V. 
 
 Species .... 
 
 . Vulneraria^*. 
 
 
 Variety . . . . 
 
 . Dillenii. 
 
 
 Race .... 
 
 . Floribus coccineis. 
 
 
 Variation 
 
 . Foliis hirsutissimis. 
 
 In very extensive groups, other divisions may be inter- 
 polated ; thus a subgenus or section is often divided into 
 a subsection. On the other hand, many of these divisions 
 often disappear; if a genus consist of only a small 
 number of species, and there be no very striking points 
 
 23 Balfour's Manual of Botany, § 725. 
 
 2* It is not uncommon in the classificatory sciences, as in this instance, 
 to assign the same name to a higher and lower division, the lower divi- 
 sion exhibiting in a marked manner the characters possessed in common 
 by the various members of the higher division. 
 
76 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 of diiference amongst them, we may descend at once, 
 without any intermediate divisions, from the Genus to 
 its various Species. Sometimes, even, an order may 
 contain only a single genus, or a genus a single species, 
 in which case the two may be regarded as coextensive. 
 In the case of Man, we saw that we descend at once from 
 the Order to the varieties, the order Bimana being co- 
 extensive with the genus and species Homo, so that here 
 three even of the grand divisions are coincident. 
 
 IV. The groups should be so arranged, that those 
 which have the closest affinities may be brought nearest 
 to each other, while the distance of one group from 
 another may be taken as a measure of its dissimilarity 
 from it. The observation of this rule would result in 
 what Mr. Mill calls 'the arrangement of the natural 
 groups into a natural series/ For the purposes of sub- 
 sequent induction, it is plain that it is of the utmost 
 importance not widely to dissever groups which present 
 many phenomena in common, or which we even suspect 
 may do so. The object aimed at by this rule is, to a 
 great extent, attained by the observation of the Subor- 
 dination of Characters (Rule 2), according to which, the 
 higher the place of the division in the series, the more 
 important is the collection of characters which serves to 
 constitute it. If Rule 2 were duly observed, it would be 
 impossible for any two widely dissimilar groups to be 
 brought into juxtaposition in the lower divisions of the 
 series. Thus, the ox and the frog, the primrose and the 
 mushroom, would in any natural system be at consider- 
 
CLASSIFICA TION, 7 J 
 
 able distances from each other. But it is not sufficient 
 to observe the rule of the Subordination of Characters. 
 The arrangement of the cognate groups in each division 
 should be such that at the head of the series may come 
 those groups which are most like the groups of the 
 preceding division, while at the bottom of the series may 
 come those groups which are most like the groups of 
 the subsequent division. Thus, suppose that we have 
 Orders A, B, C, of which B resembles A more than C 
 does, and that A is subdivided into the genera a'' a'^ a'' 
 1/ 1/^ c ; B into the genera m^ rd' n o f p' ; C into the 
 genera x' x^^ y ,y\y'\ z ; (of which the genera repre- 
 sented by the earlier letters of the alphabet are more akin 
 to each other than those represented by the later, and 
 conversely) ; in our arrangement we ought to place c in 
 juxtaposition with rd m\ 2sAp^ p'^ in juxtaposition with 
 x' x'\ the remaining groups being arranged, as above, 
 on the same principle. If such an arrangement could 
 be effected, it is plain that those groups which pre- 
 sented in the greatest intensity the principal phenomena 
 of the class of objects under investigation would come 
 first in the series, and that those which presented them 
 in the least intensity would come last. In Zoology, for 
 instance, those groups would come first which presented 
 in the greatest intensity the principal phenomena of 
 animal life, and in Botany those which presented in the 
 greatest intensity the principal phenomena of vegetable life. 
 It is, of course, seldom, in the arrangement of natural 
 objects, that we are able to draw up an exact table of 
 
78 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 precedency amongst the groups of any division, but we 
 are often able to say that this or that group or collection 
 of groups {a or a a^ a'^') should rank first in the series, 
 or that it should rank before some other group or collec- 
 tion of groups. Thus, no zoologist would hesitate to 
 assign to man (the Order Bimana) the highest place in 
 any classification of Mammalia, while he would place next 
 the Order Quadrumana, and in this Order he would select 
 apes, and, amongst apes, the anthropoid apes, to be 
 brought into closest juxtaposition with man. 
 
 This rule i& obviously of most difficult application. It 
 points out an ideal to be aimed at, but one which is never 
 likely to be perfectly realised. So many are the pro- 
 perties to be taken into consideration in every natural 
 object, that it is often impossible to say that this object 
 is, on the whole, more like another than that. The 
 groups of the higher divisions may often, those of the 
 lower may sometimes, be tabulated in some order of 
 precedency ; but there remains a large majority of cases 
 to which the Rule is inapplicable, or to which, at least, it 
 has not yet been successfully applied. This is especially 
 the case in Botany, where, though, in respect of com- 
 plexity of structure and perfection of organism. Vascular 
 plants may be ranked above Cellular, and Dicotyledons 
 above Monocotyledons, there are but few cases among 
 the subdivisions, especially of Monocotyledons and 
 Dicotyledons, where any order of precedency can be 
 established. But, even if the rule were of universal 
 application, and if we were perfectly acquainted with all 
 
CLASSIFICATION. 79 
 
 the properties of bodies and their relative value, it would 
 not follow that we could establish what Dr. Whewell, in 
 his opposition to this doctrine of Classification by Series, 
 calls * a mere linear progression in nature/ There might 
 still be many Orders, Genera, or Species, which, to use 
 a familiar expression, we should be obliged to bracket. 
 * It would surely be possible,' says Mr. Mill ^^, ' to arrange 
 all places (for example) in the order of their distance from 
 the North Pole, though there would be not merely a 
 plurality, but a whole circle of places at every single 
 gradation in the scale/ 
 
 Remark i . A natural classification is supposed to be com- 
 plete, when it has descended as low as species, — a species 
 being regarded as a group consisting of individuals, all of 
 which have descended from a common stock. Or, if the 
 process be reversed, and the classification be an ascend- 
 ing instead of a descending one, species are regarded as 
 the starting-point of the naturalist, and it is supposed that 
 the problem before him is to group them under higher 
 divisions. But a species may, as we have seen, be divided 
 into varieties, sub-varieties, &c. Now, in what consists 
 the difference between the relation of a variety to a species 
 and the relation of a species to a genus ? To this ques- 
 tion a very large section of naturalists now maintain that 
 no satisfactory answer can be given. If it be said that 
 varieties of the same species may be developed in the 
 course of time, but that species themselves must be 
 
 2« Bk. IV. ch. viii. § i. Note. 
 
8o PROCESSES SUBSIDIARY TO INDUCTION. 
 
 regarded as distinct, it may be asked on what grounds 
 this supposition rests. Different varieties of the same 
 species are certainly more like each other than different 
 species of the same genus, just as species of the same 
 genus have more resemblance than genera of the same 
 order, or members of any lower division than members of 
 any higher division ; but, given a larger amount of time, 
 is there more difBculty in supposing a common stock for 
 the different species of a genus than for the different 
 varieties of a species? This is the question originated 
 with so much ability by Mr. Darwin in his work on the 
 Origin of Species. His own solution of the question is 
 well known. 'It will be seen,' he says^^, *that I look at 
 the term species, as one arbitrarily given for the sake of 
 convenience to a set of individuals closely resembUng 
 each other, and that it does not essentially differ from the 
 term variety, which is given to less distinct and more 
 fluctuating forms. The term variety, again, in com- 
 parison with mere individual differences, is also applied 
 arbitrarily, and for mere convenience' sake.' It does not 
 fall within our province to discuss the question of the 
 ' Origin of Species,' but it is desirable that the student 
 should be aware that the practice of naturalists in stopping 
 at species, as if they were the ' infimae species ' of the old 
 logicians below which divisions need not proceed, is far 
 from being universally accepted. 
 
 Remark z. As our knowledge of the external world 
 becomes enlarged, the number of natural groups, recog- 
 
 ^^ Darwin's Origin of Species, ch. ii. 
 
CLA SSIFICA TION. 8 1 
 
 nised by the classificatory sciences, is being continually 
 increased. Botanists and zoologists (especially the former) 
 are constantly discovering or recognising new varieties, 
 frequently new species, and occasionally, even, new 
 genera and orders. ^ The known species of plants,' says 
 Dr. WhewelP'^, ^ were 10,000 at the time of Linnaeus, 
 and are now [a. d. 1858] probably 60,000.' The 
 increase in the number of recognised varieties, sub- 
 varieties, &c., is even still more rapid. One common 
 effect of these constant discoveries and recognitions is 
 to bridge over what previously appeared to be gaps in 
 nature, thus illustrating the fact that there are but few 
 breaks in natural phenomena, that there pervades nature 
 a Law of Continuity, according to which a group seldom 
 occurs to which some other group may not be found 
 very closely allied. So complete, sometimes, is this con- 
 tinuity, that it becomes very difficult to distinguish the 
 groups by any fixed characters. Two species (say) are 
 discriminated, and then a third group is found which 
 partakes of the character of each of the others. This is 
 constituted a new species, and then a fourth group is 
 found intermediate between this and the first, and so on. 
 * It has been shown,' says Dr. Carpenter, as quoted by 
 Sir W. Grove ^^, ' that a very wide range of variation exists 
 among Orbitolites, not merely as regards external form, 
 but also as to plan of developement ; and not merely as 
 
 ^ History of Scientific Ideas, Bk. VIII. ch. ii. § 6. 
 
 ^ Essay on Continuity, printed at the end of the Fifth Edition of ^ 
 The Correlation of Physical Forces, pp. 326, 327. 
 
 G 
 
S2 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 to the shape and aspect of the entire organism, but also 
 with respect to the size and configuration of its com- 
 ponent parts. It would have been easy, by selecting 
 only the most divergent types from amongst the whole 
 series of specimens which I have examined, to prefer an 
 apparently substantial claim on behalf of these to be 
 accounted as so many distinct species. But after having 
 classified the specimens which could be arranged around 
 these types, a large proportion would yet have remained, 
 either presenting characters intermediate between those 
 of two or more of them, or actually combining those 
 characters in different parts of their fabric ; thus showing 
 that no fines of demarcation can be drawn across any 
 part of the series that shall definitely separate it into any 
 number of groups, each characterised by features entirely 
 peculiar to itself.* We certainly find in nature a per- 
 sistency of type, which is the result of the laws of here- 
 ditary transmission ; if there were no such persistency, 
 the attempt to group natural objects would be fruitless 
 and absurd. But, at the same time, when we have esta- 
 blished groups, we constantly find that there are individual 
 members diverging more or less from the ordinary 
 type, and forming intermediate links between proximate 
 classes. To adopt and alter a metaphor employed 
 by Dr. Whewell, natural classes may be regarded as 
 the forests of neighbouring hills, the hills being seldom 
 separated by well-defined valleys, and the valleys being 
 frequently interspersed with straggling trees or clumps. 
 Remark 3. It sometimes happens that one of the 
 
CLASSIFICATION. 83 
 
 characters by which classes or groups are distinguished 
 from each other is to be found, not invariably, but only 
 usually or occasionally in the members of the group. 
 Thus, in the description of the Order Rosaceae, we find 
 that ' the seeds are erect or inverted, usually e^albumin- 
 ous Flowers sometimes unisexual/ Such in- 
 definite descriptions would be entirely out of place in an 
 artificial classification, but in a natural classification, where 
 the entire assemblage of the characters must be taken 
 into consideration, a character, though not found in- 
 variably, or even though found but seldom, may still be 
 valuable in distinguishing a group. 
 
 Remark 4. The most important characters are not 
 always those by which a group is most easily recognised. 
 For the purpose of recognition, some external and pro- 
 minent character or set of characters is generally best 
 adapted. Thus, if we wished to determine whether a 
 plant were monocotyledonous or dicotyledonous, our 
 easiest course would be to examine the stem ; if the stem 
 were endogenous, we should know that the plant was 
 a monocotyledon, if exogenous, that the plant was a 
 dicotyledon. A single character is often sufficient to 
 determine the place of a plant or animal in a series, 
 because we already know that the possession Qf this 
 character is a sign of the possession of the various other 
 characters which are enumerated in the description of the 
 natural class. The method of determining, by means of 
 one or a few characters, the place of a natural object in a 
 classification, is often called Diagnosis or Characteristick. 
 
 G 2 
 
84 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 * The Characteristick/ says Dr. Whewell ^^ ^ is an Ar- 
 tificial Key to a Natural System. As being Artificial, it 
 takes as few characters as possible; as being Natural, its 
 characters are not selected by any general or prescribed 
 rule, but follow the natural affinities/ ' The genera 
 Lamium and Galeopsis (Dead Nettle and Hemp Nettle) 
 are each formed into a separate group in virtue of their 
 general resemblances and differences, and not because 
 the former has one tooth on each side of the lower lip, 
 and the latter a notch in its upper lip, though they are 
 distinguished by these marks/ 
 
 Note.—'Dv, Whewell maintains that natural classes are 
 determined, not by definition, that is, by an enumeration 
 of characters, but by type, that is, by resemblance, more 
 or less complete, to some one member of the class, round 
 which the others are grouped. Thus, according to this 
 theory, the Class Mammalia would be determined, not by 
 an enumeration of characters, but by resemblance, more 
 or less complete, to some typical specimen, say Dog; the 
 genus Dog would be determined not by an eumeration 
 of the characters which are common to the dog, wolf, and 
 fox (the species comprised in the genus), but by approxi- 
 mation to the type-species dog : similarly, the Order Ro- 
 sacese would be determined not by an enumeration of 
 characters, common to a large number of genera, but by 
 the resemblance, more or less complete, of these genera 
 
 29 History of Scientific Ideas, Bk. VIII. ch. ii. § 7. 
 
CLA SSIFICA TION. 85 
 
 to the type-genus Rosa. Dr. Whewell's view will be un- 
 derstood from the following extract : — 
 
 *In a Natural Group the class is steadily 
 
 fixed, though not precisely limited ; it is given, though 
 not circumscribed; it is determined, not by a boundary 
 line without, but by a central . point within ; not by what 
 it strictly excludes, but by what it eminently includes ; by 
 an example, not by a precept; in short, instead of 
 Definition we have a Type for our director. 
 
 ' A Type is an example of any class, for instance, a 
 species of a genus, w^hich is considered as eminently pos- 
 sessing the characters of the class. All the species which 
 have a greater affinity with this Type-species than with 
 any others, form the genus, and are ranged about it, 
 deviating from it in various directions and different de- 
 grees. Thus a genus may consist of several species, 
 which approach very near the type, and of which the 
 claim to a place with it is obvious; while there may be 
 other species which straggle further from this central 
 knot, and which yet are clearly more connected with it 
 than with any other. And even if there should be some 
 species of which the place is dubious, and which appear 
 to be equally bound by two generic types, it is easily seen 
 that this would not destroy the reality of the generic 
 groups, any more than the scattered trees of the inter- 
 vening plain prevent our speaking intelligibly of the 
 distinct forests of two separate hills. 
 
 ' The Type-species of every genus, the Type-genus 
 of every family, is, then, one which possesses all the 
 
86 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 characters and properties of the genus in a marked and 
 prominent manner. The Type of the Rose family has 
 alternate stipulate leaves, wants the albumen, has the 
 ovules not erect, has the stigmata simple, and besides 
 these features, which distinguish it from the exceptions 
 or varieties of its class, it has the features which make it 
 prominent in its class. It is one of those which possess 
 clearly several leading attributes ; and thus, though we 
 cannot say of any one genus that it must be the Type of 
 the family, or of any one species that it must be the Type 
 of the genus, we are still not wholly to seek : the Type 
 must be connected by many affinities with most of the 
 others of its group; it must be near the centre of the 
 crowd, and not one of the stragglers ^^J 
 
 There is much force in what Dr. Whewell here says, 
 but his main position appears to me to be incorrect. 
 May not the various steps in the process of Classification 
 be described as follows .? We, first, observe a general 
 resemblance amongst a variety of groups. Prompted by 
 the observation of this resemblance, we determine to con- 
 stitute the groups into a distinct class. But it is not 
 
 ^ History of Scientific Ideas, Bk. VIII. ch. ii. § 3. art. 10. Mr. Mill 
 {Logic, Bk. IV. ch. vii. §§ 3, 4) examines Dr. Whewell's views at con- 
 siderable length. He appears to me, in this examination, to insist too 
 emphatically on what he calls ' distinctions of kind,' and to assert, 
 without sufficient warrant, that ' the species of Plants are not only real 
 kinds, but are probably, all of them, real lowest kinds, Infimae Species, 
 which if we were to subdivide into sub-classes, the subdivision would 
 necessarily be founded on definite distinctions, not pointing (apart from 
 what may be known of their causes or effects) to any difference beyond 
 themselves.' 
 
NOMENCLATURE. 87 
 
 sufficient simply to enumerate the groups which the class 
 contains ; it is incumbent upon us to state the principle 
 on which the classification is made. This statement 
 consists in an enumeration of those characters which are 
 common to all the members of the newly-constituted 
 class, and which, at the same time, distinguish them from 
 the members of other classes, with the addition, in some 
 cases, of certain characters which belong to most, or, 
 even, to a few only, of the members of the class. Thus, 
 the class is determmed (or ^ given ^ to use Dr. Whewell's 
 expression) by an enumeration of characters. But, when 
 the class is once familiar to us, the repetition of the class- 
 name suggests, not the characters, but some typical 
 specimen of the class, some one group which stands out 
 prominently as possessing the characters by which the 
 class was determined; and it is by reference to this central 
 specimen, as it were, that we fix the position of the other 
 groups and adjudicate on the claims of any newly-dis- 
 covered group to take its place by the side of the others. 
 Thus, the type-species, type-genus, or typical order, may 
 be of the greatest service as a convenient embodiment of 
 the characters, but the characters must be enumerated, 
 and the class determined, before we can select our typical 
 example. 
 
 (2) Of Nomenclature. 
 
 Nomenclature is intimately connected with Classifica- 
 tion. The groups, whether natural or artificial, into which 
 .objects are distributed, could neither be recollected by 
 
88 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 ourselves nor communicated to others, unless they were 
 fixed by the imposition of names. A Nomenclature is 
 a collection of such names, applied to the members of 
 the various divisions and subdivisions which constitute 
 a classification. The number of natural groups, however, 
 is so enormously large, that it would be next to im- 
 possible to devise, and, if possible to devise, it would 
 be impossible to remember, distinct names for each 
 group. Thus, the known species of plants, for instance, 
 amount to upwards of 60,000, and, if we took into 
 account varieties, sub-varieties, &c., the number of groups 
 would be represented by many multiples of this sum. 
 Some artifice, therefore, is necessary by which a com- 
 paratively small number of names may be made to dis- 
 tinguish a large number of groups. Botany and Chemistry 
 furnish admirable examples of the employment of such 
 an artifice, and some knowledge of the principles which 
 guide the imposition of names in those two sciences 
 (a knowledge which may be easily acquired) would 
 probably be of more service to the student than anything 
 which he might learn froni a body of rules for Nomen- 
 clature in general. 
 
 In Botany, the higher groups (including genera) have dis- 
 tinct names. Thus, we have Dicotyledones, Rosaceae, Rosa, 
 &c. But, when we arrive at the species, these are known 
 by the generic name with the addition of some distinctive 
 attribute. Thus, the genus Geranium is represented in 
 the British Isles by thirteen species, called respectively 
 Geranium phaeum, G. nodosum, G. sylvaticum, G. pratense, 
 
NOMENCLA TURE. 89 
 
 G. sanguitieum, G. pyrenaicum, G. pusillum, G. dis- 
 sectum, G. columbinum, G. rotundifolium, G. molle, G. 
 lucidum, G. robertianum. The specific names are se- 
 lected from various considerations ; sometimes in honour 
 of an individual (as Equisetum Mackaii, Rosa Wilsoni), 
 sometimes from the country or the district in which the 
 plant abounds, sometimes from the soil which is most 
 favourable to it, sometimes from some peculiarity in the 
 plant itself So arbitrary and fanciful sometimes are these 
 names, that Linnaeus (as w^e are told by Dr. WhewelP^) 
 ' gave the name of Bauhinia to a plant with leaves in 
 pairs, because the Bauhins were a pair of brothers, that 
 of Banisteria to a climbing plant, in honour of Banister, 
 who travelled among mountains/ It is plain that a name 
 which describes some peculiarity in the plant itself is 
 of most service to the learner ; but any name, easily re- 
 membered, serves the main purpose of a nomenclature, 
 which is to distinguish one group from another. Varieties, 
 sub-varieties, &c., are distinguished from each other on 
 the same principle as species. Thus, as we have seen, 
 of the species Anthyllis Vulneraria there is a variety 
 Dillenii, and of the variety Anthyllis Vulneraria Dillenii 
 there is a * race' Floribus coccineis, and of the race there 
 is a * variation ' Foliis hirsutissimis. The nomenclature 
 of Zoology is now generally constructed on the same 
 principle as that of Botany. In some systems of Miner- 
 alogy, three names are employed, namely, those of the 
 
 31 nktory of Scientific Ideas, Bk. VIII. ch. ii. § 6. 
 
90 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 Order, Genus, and Species, as for instance, Rhombohe- 
 dral Calc Haloide. 
 
 The nomenclature of Chemistry, or, at least, of In- 
 organic Chemistry, which, in some respects, furnishes 
 an interesting example of a scientific nomenclature, is 
 constructed on the principle of making the prefixes and 
 affixes of the words employed significant of the nature 
 of the substances for which they stand. Thus, we 
 have the affixes ide, ic^ ouSy ate, He, &c., and the pre- 
 fixes mono, di, tri, sesqut. Sec, each having a special 
 significance, though, unfortunately, not always an un- 
 ambiguous one. 
 
 It would transcend the Umits of this work to give an 
 account, sufficiently clear and precise, of the Nomenclature 
 of Inorganic Chemistry (which, moreover, is at present 
 in a transitional state), but the student who is anxious 
 to gain some idea of the principles on which it is con- 
 structed, can refer to Watts' Dictionary of Cheinistry, 
 vol. iv. art. Nomenclature. 
 
 (3) Of Terminology. 
 
 A Nomenclature of a Science is, as we have seen, 
 a collection of names of groups. A Terminology is a 
 collection of the names (or terms) which distinguish either 
 the properties or the parts of the individual objects which 
 the science recognises. Thus, when we speak of the 
 genus * Rosa,' we are employing the nomenclature of 
 Botany ; but, when we say that the individuals of the 
 o^enus ' Rosa ' have * their corolla imbricated before flower- 
 
TERMINOLOGY. 9 1 
 
 ing, their styles with lateral insertion, their carpels nu- 
 merous/ &c., we are employing not the nomenclature, 
 but the terminology, of the science. In botany we have 
 an almost perfect example of a complete and judiciously 
 constructed terminology. 
 
 * The formation of an exact and extensive descriptive 
 language for botany,' says Dr. Whewell ^^ * has been 
 
 • executed with a degree of skill and felicity, which, before 
 it was attained, could hardly have been dreamt of as 
 attainable. Every part of a plant has been named ; and 
 the form of every part, even the most minute, has had 
 a large assemblage of descriptive terms appropriated to it, 
 by means of which the botanist can convey and receive 
 knowledge of form and structure, as exactly as if each 
 minute part were presented to him vastly magnified. This 
 acquisition was part of the Linnsean Reform. " Tourne- 
 fort," says Decandolle, ^' appears to have been the first 
 who really perceived the utility of fixing the sense of terms 
 in such a way as always to employ the same word in the 
 same sense, and always to express the same idea by the 
 same word ; but it was Linnaeus who really created and 
 fixed this botanical language, and this is his fairest claim 
 to glory, for by this fixation of language he has shed 
 clearness and precision over all parts of the science." 
 
 * It is not necessary here to give any detailed account 
 of the terms of botany. The fundamental ones have 
 been gradually introduced, as the parts of plants were 
 more carefully and minutely examined. Thus the flower 
 
 32 History of Scientific Ideas, Bk. VIII. ch. ii. § 2. 
 
92 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 was successively distinguished into the caljyx, the corolla, 
 the stamens, and the pistils : the sections of the corolla 
 were termed petals by Columna ; those of the calyx were 
 called sepals by Necker. Sometimes terms of greater 
 generality were devised ; as perianth to include the calyx 
 and corolla, whether one or both of these were present ; 
 pericarp for the part inclosing the grain, of whatever kind 
 it be, fruit, nut, pod, &c. And it may easily be imagined 
 that descriptive terms may, by definition and combination, 
 become very numerous and distinct. Thus leaves may 
 be called pinnatifid, pinnatipartite, pinnatisect, pinnatilohale, 
 palmatijid, palmatipartite, &c., and each of these words 
 designates different combinations of the modes and extent 
 of the divisions of the leaf with the divisions of its outline. 
 In some cases arbitrary numerical relations are introduced 
 into the definition : thus a leaf is called hilohate when it 
 is divided into two parts by a notch; but if the notch 
 go to the middle of its length, it is bifid ; if it go near the 
 base of the leaf, it is bipartite ; if to the base, it is bisect. 
 Thus, too, a pod of a cruciferous plant is a siliqua if it be 
 four times as long as it is broad, but if it be shorter than 
 this it is a silicula. Such terms being established, the 
 form of the very complex leaf or frond of a fern is exactly 
 conveyed by the following phrase : " fronds rigid pinnate, 
 pinnae recurved subunilateral pinnatifid, the segments 
 linear undivided or bifid spinuloso-serrate." ' 
 
 A Terminology, we have said, comprises the terms 
 appropriated to express, not only the parts of objects, but 
 also their properties. Thus, in the foregoing example, 
 
TERMINOLOGY. 93 
 
 the words * sepals/ * petals/ &c., express parts of the 
 plant, the words 'pinnatifid/ ^bilobate/ &c., which are 
 applied to the shape of the leaves, express characters or 
 properties. A complete terminology must be so con- 
 structed as to express every shade of difference in all 
 those properties which are recognised in a scientific 
 treatment of the object. Thus, if colour be regarded as 
 of importance in the description of a plant, mineral, &c., 
 it is essential that there shall be some appropriate term 
 by which to describe every shade of colour. But there are 
 few terms which, from their mere signification, can call 
 up any precise idea in the mind. Hence it is necessary 
 to fix by convention the precise meaning of every tech- 
 nical term employed in science. Again, to appropriate 
 the words of Dr. Whewell, * The meaning of technical 
 terms can be fixed in the first instance only by conven- 
 tion, and can be made intelligible only by presenting to 
 the senses that which the terms are to signify. The 
 knowledge of a colour by its name can only be taught 
 through the. eye. No description can convey to a hearer 
 what we mean by apple-green or French grey. It might, 
 perhaps, be supposed that, in the first example, the term 
 apple, referring to so familiar an object, sufficiently 
 suggests the colour intended. But it may easily be seen 
 that this is not true; for apples are of many different 
 hues of green, and it is only by a conventional selection 
 that we can appropriate the term to one special shade. 
 When this appropriation is once made, the term refers 
 to the sensation, and not to the parts of this term ; for 
 
94 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 these enter into the compound merely as a help to the 
 memory, whether the suggestion be a natural connection 
 as in " apple-green," or a casual one as in " French 
 grey." In order to derive due advantage from technical 
 terms of this kind, they must be associated immediately 
 with the perception to which they belong ; and not con- 
 nected with it through the vague usages of common 
 language. The memory must retain the sensation ; and 
 the technical word must be understood as directly as the 
 most familiar word, and more distinctly. When we find 
 such terms as tin-white or pinchheck-hrown^ the metallic 
 colour so denoted ought to start up in our memory with- 
 out delay or search^^' When we have fixed, by convention, 
 the meaning of a term, it must invariably be employed 
 in this sense, and in no other. The least vagueness 
 or inconsistency in the use of terms may interpose a 
 fatal obstacle in the way, not only of the learners, but 
 even of the promoters of a science. The progress of the 
 Mechanical Sciences and of what are commonly called 
 Physics was long retarded by the vague and unintelligent 
 use of such words as * heavy,* Might,' 'hot,' 'cold,' 'moist,' 
 
 * dry,' &c. Even still such words as * force,' ' fluid,' 
 
 * attraction,' ' ether,' &c., are often employed without 
 sufficient precision. 
 
 A Terminology, as remarked by Dr. Whewell ^*, is in- 
 dispensably requisite in giving fixity to a Nomenclature. 
 Thus, in Botany, *the recognition of the kinds of plants 
 
 33 History of Scientific Ideas, Bk. VIII. ch. ii. § 2. 
 ^* Novum Organon Renovatum, Bk IV. Aphorism ii. 
 
HYPOTHESIS. 9J 
 
 must depend upon the exact comparison of their re- 
 semblances and differences ; and to become a part of 
 permanent science, this comparison must be recorded 
 in words/ 
 
 Dr. Whewell devotes the last Book of his Novum 
 Organon Renovatum to a series of aphorisms on the 
 * Language of Science,' including both Nomenclature and 
 Terminology. These aphorisms afford one of the best 
 examples of Dr. Whewell's style and mode of treatment, 
 and will well repay the attention of the student who is 
 desirous of acquainting himself further with the methods 
 of the Classificatory Sciences. Mr. Mill has some chapters 
 '{Logic, Bk. IV. ch. iii-vi) on * Naming' and the * Requi- 
 sites of a Philosophical Language,' and, in addition to 
 the passage already referred to, Dr. Whewell treats these 
 subjects in his History of Scientific Ideas, Bk. L ch. ii ; 
 Bk. VIIL ch. ii. §§ 2 and 6 ; Bk. VIIL ch. iii. art. 5. 
 In Mr. Bain's Inductive Logic, there is a special chapter 
 (Bk. IV. ch. iii) on Classification, and another (Bk. V. 
 ch. vi) on the Sciences of Classification. /. i.^J tt 
 
 §3. OnHypotkesis. '^^^^JJ^^-^ 
 
 Wh en the mind has before it a number of observed 
 facts, it is almost irresistibly driven to frame for itself 
 some theory as to the mode of their co-exist(^nj^ or 
 suc cession. It is from this irresistible impulse to refer to 
 some law the various phenomena around us that all 
 science as well as all scientific error has sprung. In some 
 
g6 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 cases, as we have seen in the first chapter^^, a single 
 observation or experiment may at once establish a true 
 theory or valid induction, independently of any previous 
 suppositions on our part. But in all the more intricate 
 branches of enquiry, true theories have usually been 
 preceded by a number of false ones, and it has not 
 unfrequently occurred that the false theories have been 
 mainly instrumental in conducting to the true. Thus, 
 the elliptical theory of planetary motion was preceded by 
 the circular theory, with its various modifications, and 
 the undulatory theory of light by the emission theory. 
 Rather ihan rest satisfied with a number of disconnected 
 facts, men have often imagined the most absurd relations 
 between phenomena, such as that a comet was the har- 
 binger of war, or that the future could be foretold by 
 birds. Tl^ese theorieSj^__assumptic^^^ 
 when employed provisionally in scientific enqu iry, and 
 fallin g short of asce rtained truths, are called hypotheses. 
 and hs ^e already been alluded to in the firjj„.chapter. 
 The w ord ^hvpothpsis/ as commonly employed, is ex- 
 clusi ve of propositions which rest upon absolute proof, 
 whe ther inductive or deductive, and is general ly used 
 ^^ c ontradistinc tion to ihem. Thus, we speak of a 
 science being only in a hypothetical stage, or of a 
 hypothesis being converted into an induction or being 
 brought deductively under some general law already 
 ascertained to be true. On the other hand, we should 
 hardly dignify with the name of * hypothesis' a supposition 
 ^^ See pp. II, 12. 
 
■^> -^ 
 
 HYPOTHESIS. i O ^^7 ^ 
 
 which, at least in the eyes of its framer, did |iot ^g^es^.y 
 some amount of plausibility. A hypothesis ^^ niay be^/le - 
 scribed as a supposition made without evidence or withoV /^ 
 sufficient evidence, in order that we may deduce fromyit ^ ^y 
 c onclusions agreeing with actual fa^J s. If these conclu^ 
 sions are correctly deduced, and really agree with the facts, 
 a presumption arises that the hypothesis is true. More- 
 over, if the hypothesis relates to the cause, or mode of 
 production of a phenomenon, it will serve, if admitted, 
 to explain such facts as are found capable of being de- 
 duced from it. And this explanation is the purpose of 
 many, if not most, hypotheses. Explanation, in the 
 scientific sense, means the reduction of a series of facts 
 which occur uniformly but are not connected by any 
 known law of causation into a series which is so con- 
 nected, or the reduction of complex laws of causation 
 into simpler laws. If no such laws of causation are 
 known to exist, we may suppose or imagine a law that 
 would fulfil the requirement ; and this supposed law would 
 be a hypothesis. 
 
 A hypothesis may be serviceable in many w ays. In 
 the first place, it may afford a solution, more or less 
 pr obable, of a problem which is incapa ble of any definite 
 s olution^ or which, at least, has not yet bee n definitely 
 solved. Thus, many of the advocates of the Darwinian 
 hypothesis maintain that it is the most probable solution 
 of an insoluble problem. Secondly, what was at first 
 
 ^ The following sentences, to the end of the paragraph, are slightly 
 altered from Mr. Mill's Logic, Bk. III. ch. xiv. § 4. 
 
 H 
 
98 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 Started as a hypothesis may ulti mately be established by 
 positive proo f, as has been the case with the elliptical 
 theory of planetary motion, and, as many suppose, with 
 the undulatory theory of light. T hirdly, even th ough 
 a hypothesis may nltimately bp discovered to be false, it 
 may be of great service in pointing the way to a truer 
 theory. Thus, as already remarked, the circular theory 
 of planetary motion, and the supplementary theory of 
 epicycles and eccentrics, undoubtedly contributed to the 
 formation of the hypothesis which was eventually proved 
 to be true. Kepler himself tried no less than nineteen 
 different hypotheses, before he hit upon the right one, and 
 his ultimate success was doubtless in no slight degree 
 due to his unsuccessful efforts. There is hardly any 
 branch of science in which it might not be affirmed 
 that, without a number of false guesses, true theories 
 could never have been attained. Lastly, a hypothesis, 
 whether true or false, if it be applicable to all the 
 known facts, serves as a means of binding those facts 
 together, of colligating them, to use a technical phrase, 
 and thus, by presenting them under one point of 
 view, plainly marks off the phenomena to be explained. 
 A theory, like the Phlogistic theory in Chemistry, or 
 the theory of epicycles and eccentrics (which, by being 
 sufficiently extended, might have been made to include 
 all the phenomena of planetary motion), may thus have 
 been of the greatest service in the history of science, 
 ' simply by keeping before the minds of investigators the 
 precise phenomena which demanded an explanation. 
 
HYPOTHESIS, 99 
 
 The formation , of hypotheses is obviously the work of 
 the imaginative faculty, a faculty of hardly less importance 
 in science than in art. To lay down rules for the ex- 
 ercise of this faculty has hitherto been found futile. The 
 object of Inductive Logic is rather to restrain the ex- 
 uberant, than to excite the sluggish, imagination. The 
 latter office is best fulfilled by recounting the great 
 achievements of science, and thus arousing the ambition 
 and kindling the enthusiasm of her votaries. The former 
 (which is no less necessary) may be promoted by de- 
 termining the conditions to which a hypothesis must 
 conform, in order that it may rank as a provisional 
 explanation of facts, and before it is entitled to demand 
 the honours of a rigorous inductive examination. These 
 conditions may be reduced to three : — 
 
 I. The hypothesis must not be known or suspected to 
 be untm e, that is to say, it must not be inconsistent wi th 
 facts already ascertained or the inferences to which they 
 J^^^ It w^ould be absurd, for instance, in the present 
 state of knowledge, to propose design or compact as 
 the cause of the divergences which are found in the 
 various dialects of a language, or to suppose the heavenly 
 bodies to move in perfect circles. So simple a rule as 
 this may appear to be superfluous, but it seems necessary 
 
 ^ The explanation of this rule, contained in the latter clause of the 
 sentence, has been suggested by Mr. Jevons' chapter on the Use of 
 Hypothesis, a chapter which may be read with advantage by the student. 
 His second condition of a legitimate hypothesis, which corresponds with 
 my first, is expressed thus: ' That it do not conflict with any laws of nature, 
 or of mind, which we hold as true.* Principles of Sciencs^ vol. ii. p. 139. 
 
 H 2 
 
lOO PROCESSES SUBSIDIARY TO INDUCTION. 
 
 to include it in the conditions to which a hypothesis must 
 conform, as, otherwise, a perverted ingenuity might suc- 
 ceed in framing numberless hypotheses which violated 
 none of the preliminary conditions. 
 
 II. The hypothesis must be of such a character as 
 t o admit of verification or disproof, or at least of being 
 re ndered more or less probable, by subsequent investiga - 
 tion s ^l Unless this restriction were placed on the for- 
 
 mation of hypotheses, there would be no limit to the 
 wildness of conjecture in which theorists might indulge. 
 It might, for instance, be maintained that falling bodies 
 are dragged to the earth by the action of invisible spirits, 
 and, wild as such a theory would be, there is nothing 
 positively to disprove it. Granted that, like many other 
 products of imagination, such a theory might possibly 
 be true, it .would still fall without the scope of science. 
 The aim of science is proof, present or prospective, and 
 consequently what neither admits of proof, nor, so far as 
 we can foresee, is ever likely to admit of it, or even ap- 
 proximate to it, is no fitting object of scientific enquiry. 
 As affording a caution against the unrestrained exercise 
 of the imagination in scientific speculation, it may be 
 
 ^^ It may occur to the student that we have not provided for the case 
 where a supposition is already supported by a certain amount of probable 
 evidence, but where it is not likely to be rendered more or less probable 
 by further investigation. But such a supposition, though it would be an 
 imperfect induction or deduction, could hardly be called a hypothesis, a 
 term which seems always to imply something provisional, something 
 which, on further enquiry, may be either confirmed or weakened, rendered 
 more or less probable than it now is. 
 
 3( ' 
 
HYPOTHESIS, lOI 
 
 useful to adduce a few instances of suppositions or 
 hypotheses, which were probably considered as perfectly 
 satisfactory by those who proposed them or amongst 
 whom they were prevalent, which would now be regarded 
 by all competent authorities as absurd, and which still do 
 not admit of being distinctly disproved. 
 
 It was once very generally held that the position ' 
 of the planets with reference to the earth at any par- 
 ticular moment determines not only the course of human 
 events at that time, but the subsequent life of each 
 person born under the * conjuncture/ Such an absurd 
 theory is now probably held by no single person of sound 
 understanding; but, so complicated is the web both of 
 society and of individual life, and so easy would it be 
 to explain ' apparent exceptions ' by having recourse to 
 ' counteracting causes,' that, if any ingenious person were 
 to maintain and defend this theory, it would probably 
 be impossible to disprove it. Palmistry affords another 
 instance of the same kind. The interlacing of the lines 
 on the palms of the hands is said to indicate a man's 
 ' fortunes.' Such a notion is too absurd to be discussed ; 
 but, if maintained, how could it be disproved .? It might 
 always be said that the general theory of palmistry was 
 true, though there might be some error in the particular 
 rules by which the * fortune ' in question was foretold ^^. 
 
 ^"^ The superstitions connected with dreams afford a similar instance : 
 * The ancients were convinced that dreams were usually supernatural. 
 If the dream was verified, this w'as plainly a prophecy. If the event was 
 the exact opposite of what the dream foreshadowed, the latter was still 
 supernatural, for it was a recognised principle that dreams should some- 
 
102 PROCESSJES SUBSIDIARY TO INDUCTION. 
 
 The early history of Geology is full of hypotheses of 
 this kind. The following examples of theories, which 
 no scientific man would now entertain, but which hardly 
 admit of disproof, are extracted from LyelFs Principles 
 of Geology ^''\— 
 
 * Andrea Mattioli, an eminent botanist, the illustrator of 
 Dioscorides, embraced the notion of Agricola, a skilful German 
 miner, that a certain " materia pinguis," or " fatty matter," 
 set into fermentation by heat, gave birth to fossil organic 
 shapes. Yet Mattioli had come to the conclusion, from his 
 own observations, that porous bodies, such as bones and shells, 
 might be converted into stone, as being permeable to what 
 he termed the " lapidifying juice." In like manner, Falloppio 
 of Padua conceived that petrified shells were generated by 
 fermentation in the spots where they are found, or that they 
 had in some cases acquired their form from " the tumultuous 
 movements of terrestrial exhalations." Although celebrated 
 as a professor of anatomy, he taught that certain tusks of 
 elephants, dug up in his time in Apulia, were mere earthy 
 concretions ; and, consistently with these principles, he even 
 went so far as to consider it probable, that the vases of Monte 
 Testaceo at Rome were natural impressions stamped in the 
 soil. In the same spirit, Mercati, who published, in 1574, 
 
 times be interpreted by contraries. If the dream bore no relation to 
 subsequent events unless it were transformed into a fantastic allegory, 
 it was still supernatural, for allegory was one of the most ordinary forms 
 of revelation. If no ingenuity of interpretation could find a prophetic 
 meaning in a dream, its supernatural character was even then not neces- 
 sarily destroyed, for Homer said there was a special portal through which 
 deceptive visions passed into the mind, and the Fathers declared that it 
 was one of the occupations of the daemons to perplex and bewilder us 
 with unmeaning dreams.* — Lecky's History of European Morals^ vol. i. 
 
 p. 3^5. 
 
 *® Lyell's Principles of Geology, ch. iii. 
 
HYPOTHESIS, 103 
 
 faithful figures of the fossil shells preserved by Pope Sixtus V. 
 in the Museum of the Vatican, expressed an opinion that they 
 were mere stones, which had assumed their peculiar con- 
 figuration from the influence of the heavenly bodies: and 
 Olivi of Cremona, who described the fossil remains of a rich 
 museum at Verona, was satisfied with considering them as 
 mere "sports of nature." Some of the fanciful notions of 
 those times were deemed less unreasonable, as being some- 
 what in harmony with the Aristotelian theory of spontaneous 
 generation, then taught in all the schools. For men who had 
 been taught in early youth, that a large proportion of living 
 animals and plants was formed from the fortuitous concourse 
 of atoms, or had sprung from the corruption of organic matter, 
 might easily persuade themselves, that organic shapes, often 
 imperfectly preserved in the interior of solid rocks, owed their 
 existence to causes equally obscure and mysterious.' 
 
 * As to the nature of petrified shells, Quirini conceived that 
 as earthy particles united in the sea to form the shells of mol- 
 lusca, the same crystallizing process might be effected on the 
 land ; and that, in the latter case, the germs of the animals 
 might have been disseminated through the substance of the 
 rocks, and afterwards developed by virtue of humidity. 
 Visionary as was this doctrine, it gained many proselytes even 
 amongst the more sober reasoners of Italy and Germany ; lor 
 it conceded that the position of fossil bodies could not be 
 accounted for by the diluvial theory.* 
 
 It has been maintained by theologians, more ardent 
 than discreet, that all fossils were the creations of the 
 Devil, whose object was either to mimic the Almighty 
 or to tempt mankind to disbelieve the Mosaic account 
 of the creation. Such theories admit of no refutation; 
 every argument, grounded on the resemblance of fossil 
 remains to living organisms, shows only more distinctly, 
 
I04 PROCESSES SUBSIDIARY TO INDUCTION, 
 
 to those who have once embraced the idea, the success 
 of the alleged agent as a mimic or as an impostor. 
 
 Other instances of hypotheses which violate this rule are 
 aiforded by the Vortices of Descartes and the Crystalline 
 Spheres of the ancient astronomers, both of which were 
 imagined for the purpose of accounting for the pheno- 
 mena of planetary motion. Both of these hypotheses 
 have been subsequently disproved by the free passage of 
 comets through the spaces supposed to be occupied, 
 according to the one theory, by the Vortices, according 
 to the other, by the solid Crystalline Spheres. But at 
 the time they were first started, there was no reasonable 
 ground for supposing that, if untrue, they could be dis- 
 proved, and, what is more important, there was no 
 possibility of proving them or even rendering them 
 more probable ; they were simply freaks of imagination, 
 incapable of proof and, to all appearance, of disproof. 
 Another theory more absurd even than that of the solid 
 crystalline spheres, but which has not, like that, been 
 positively disproved, is the curious hypothesis by which 
 Lodovico delle Colombe endeavoured to reconcile the 
 Aristotelian doctrine that the moon was a perfect body 
 with the recent discoveries of Galileo, who, by the aid 
 of his telescope, had found that its surface was full of 
 hollows, and was consequently charged by his enemies 
 with taking a fiendish delight in distorting the fairest 
 works of nature ; the apparently hollow parts, suggested 
 Lodovico, were filled with a pure transparent crystal, 
 and so both the astronomer and the Stagirite were right. 
 
HYPOTHESIS. 105 
 
 It will be observed that we regard hypotheses as ad- 
 missible, even though they are not likely ever to be 
 positively proved or disproved, provided that the accumu- 
 lation of further evidence is likely to render them more 
 or less probable. Between such theories and the theories 
 just exemplified, which are neither supported nor likely 
 to be supported by any evidence whatever, there is the 
 widest difference, and, while the one have no place in 
 Science, the other, we conceive, have a legitimate claim 
 to further consideration. The ideal of Science, it is true, 
 is proof; but, while it can never recognise mere freaks 
 of fancy, it is often compelled to rest content with pro- 
 babilities. Instances of hypotheses such as we have 
 in view are the Darwinian hypothesis and the Meteoric 
 theory of the repair of Solar Heat, to be noticed pre- 
 sently. 
 
 III. The hypothesis must be applicable to the descrip - 
 tion or explanation of all the observed phenomena, an d, 
 i f it assign a cause, must assign a cause fully adequa te 
 to have produced, then j i / A hypothesis, which does not 
 satisfy this requirement, may be at once rejected. Thus, 
 when the circular theory of planetary motion was found 
 inapplicable to describe several of the phenomena, it 
 was rightly abandoned, and the theory of epicycles and 
 eccentrics, which, though erroneous, was fully adequate 
 to explain all the known phenomena, was substituted for 
 it. One of the most familiar instances of an inadequate 
 hypothesis is the theory started by Voltaire, there is little 
 doubt in irony, that the marine shells found on the tops 
 
I06 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 of mountains are Eastern species, dropped from the hats 
 of pilgrims, as they returned from the Holy Land. Such 
 a theory would obviously be inadequate to account (i) for 
 the numbers of the shells, (2) for the fact that they are 
 found imbedded in the rocks, (3) for their existence far 
 away from the tracks of pilgrims, to say nothing of the 
 fact that many of these shells bear no resemblance to 
 recent Eastern species, while none resemble them exactly. 
 The contrast between an adequate and an inadequate 
 hypothesis is well illustrated by two of the rival hypo- 
 theses by which it is attempted to- account for the genera- 
 tion and the maintenance of solar heat. These are 
 respectively the Meteoric Theory and the Theory of 
 Chemical Combustion. In speaking of the former theory, 
 Professor Tyndall says^^ : — 
 
 * I have already alluded to another theory, which, however 
 bold it may at first sight appear, deserves our serious atten- 
 tion — the Meteoric Theory of the Sun. Kepler's celebrated 
 statement that " there are more comets in the heavens than 
 fish in the ocean," implies that a small portion only of the 
 total number of comets belonging to our system are seen 
 from the earth. But besides comets, and planets, and moons, 
 a numerous class of bodies belong to our system which, from 
 their smallness, might be regarded as cosmical atoms. Like 
 the planets and the comets, these smaller asteroids obey the 
 law of gravity, and revolve in elliptic orbits round the sun. 
 It is they which, when they come within the earth's atmo- 
 sphere, and are fired by friction, appear to us as meteors and 
 falling stars. 
 
 * On a bright night, twenty minutes rarely pass at any part 
 
 " Beat a Mode of Motion, §§ 689-693. 
 
HYPOTHESIS, 107 
 
 of the earth's surface, without the appearance of at least one 
 meteor. Twice a year (on the 12th of August and 14th of 
 November) they appear in enormous numbers. During nine 
 hours in Boston, when they were described as falling as thick 
 as snowflakes, 240,000 meteors were observed. The number 
 falling in a year might, perhaps, be estimated at hundreds or 
 thousands of millions, and even these would constitute but 
 a small portion of the total crowd of asteroids that circulate 
 round the sun. From the phenomena of light and heat, and 
 by direct observation on Encke's comet,' (the inference from 
 which * observation,' however, it may be remarked, is very 
 doubtful) *we learn that the universe is filled by a resisting 
 medium, through the friction of which all the masses of our 
 system are drawn gradually towards the sun. . And though the 
 larger planets show, in historic times, no diminution of their 
 periods of revolution, it may be otherwise with the smaller 
 bodies. In the time required for the mean distance of the 
 earth to alter a single yard, a small asteroid may have ap- 
 proached thousands of miles nearer to the sun. 
 
 ^ Following up these reflections, we should be led to the 
 conclusion that while an immeasurable stream of ponderable 
 meteoric matter moves unceasingly towards the sun, it must 
 augment in density as it approaches its centre of convergence. 
 And here the conjecture naturally rises, whether that vast 
 nebulous mass, the Zodiacal Light, which embraces the sun, 
 may not be a crowd of meteors. It is at least proved that 
 this luminous phenomenon arises from matter which circulates 
 in obedience to planetary laws ; hence, the entire mass of the 
 zodiacal light must be constantly approaching, and incessantly 
 raining its substance down upon the sun. 
 
 * It is easy to calculate both the maximum and the minimum 
 velocity, imparted by the sun's attraction to an asteroid circu- 
 lating round him. The maximum is generated when the body 
 approaches the sun from an infinite distance ; the entire pull 
 of the sun being then exerted upon it. The minimum is that 
 
Io8 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 velocity which would barely enable the body to revolve round 
 the sun close to his surface. The final velocity of the former, 
 just before striking the sun, would be 390 miles a second, that 
 of the latter 276 miles a second. The asteroid, on striking 
 the sun, with the former velocity, would develope more than 
 9000 times the heat generated by the combustion of an equal 
 asteroid of solid coal ; while the shock, in the latter case, 
 would generate heat equal to that of the combustion of up- 
 wards of 4000 such asteroids. It matters not, therefore, 
 whether the substances falling into the sun be combustible or 
 not ; their being combustible would not add sensibly to the 
 tremendous heat produced by their mechanical collision. 
 
 * Here, then, we have an agency competent to restore his 
 lost energy to the sun, and to maintain a temperature at his 
 surface which transcends all terrestrial combustion. In the 
 fall of asteroids we find the means of producing the solar light 
 and heat. It may be contended that this showering down of 
 matter necessitates the growth of the sun ; it does so ; ' but 
 the quantity necessary to maintain the observed calorific 
 emission for 4000 years, would defeat the scrutiny of our best 
 instruments. If the earth struck the sun, it would utterly 
 vanish from perception ; but the heat developed by its shock 
 would cover the expenditure of a century.' 
 
 Of the other theory. Professor Tyndall says ^^ : — 
 
 ^ Su* William Thomson adduces the following forcible 
 considerations to show the inadequacy of chemical com- 
 bination to produce the sun's heat. " Let us consider," he 
 says, *'how much chemical action would be required to 
 produce the same effects. . . . Taking the former estimate, 
 2781 thermal units *^ centigrade (each 1390 foot pounds) 
 
 *^ Heat a Mode of Motion, § 700. 
 
 *3 The thermal unit is the quantity of heat necessary to raise the 
 temperature of a pound of water one degree. If the degree be centi- 
 grade, this is equivalent to the heat generated by a pound weight falling 
 
HYPOTHESIS, 109 
 
 or 3,869,000 foot pounds, which is equivalent to 7000 horse- 
 power, as the rate per second of emission of energy from 
 every square foot of the sun's surface, we find that more 
 than 0.42 of a pound of coal per second, 1500 lbs. per hour, 
 would be required to produce heat at the same rate. Now 
 if all the fires of the whole Baltic fleet (this was written in 
 1854) were heaped up and kept in full combustion over one 
 or two square yards of ;surface, and if the surface of a globe 
 all round had every square yard so occupied, where could 
 a sufficient supply of air come from to sustain the com- 
 bustion? Yet such is the condition we must suppose the 
 sun to be in, according to the hypothesis now under con- 
 sideration. . . . If the products of combustion were gaseous, 
 they would, in rising, check the necessary supplies of fresh 
 air ; if they were solid and liquid (as they might be if the 
 fuel were metallic), they would interfere with the supply of 
 elements from below. In either, or in both ways, the fire 
 would be choked, and I think it may be safely affirmed that 
 no such fire could keep alight for more than a few minutes, 
 by any conceivable adaptation of air and fuel. If the sun 
 be a burning mass it must be more analogous to burning 
 gunpowder than to a fire burning in air ; and it is quite 
 conceivable that a solid mass, containing within itself all the 
 elements required for combustion, provided the products of 
 combustion are permanently gaseous, could burn off at its 
 surface all round, and actually emit heat as copiously as the 
 sun. Thus, an enormous globe of gun-cotton might, if at 
 first cold, and once set on fire round its surface, get to a 
 permanent rate of burning, in which any internal part would 
 become heated sufficiently to ignite, only when nearly ap- 
 proached by the burning surface. It is highly probable 
 indeed that such a body niight for a time be as large as the 
 
 from a height of 1390 feet against the earth. The term foot-pound 
 expresses the energy requisite to lift one pound to the height of a foot. 
 
no PROCESSES SUBSIDIARY TO INDUCTION, 
 
 sun and give out luminous heat as copiously, to be freely- 
 radiated into space, without suffering more absorption from 
 its atmosphere of transparent gaseous products than the light 
 of the sun actually does experience from the dense atmo- 
 sphere through which it passes. Let us therefore consider 
 at what rate such a body, giving out heat so copiously, would 
 burn away ; the heat of combustion could probably not be so 
 much as 4000 thermal units per pound of matter burned, the 
 greatest thermal equivalent of chemical action yet ascertained 
 falling considerably short of this. But 2781 thermal units 
 (as found above) are emitted per second from each square 
 foot of the sun ; hence there would be a loss of about 0.7 
 of a pound of matter per square foot per second. ... or 
 a layer half a foot thick in a minute, or 55 miles thick in 
 a year. At the same rate continued, a mass as large as the 
 sun is at present would burn away in 8000 years. If the sun 
 has been burning at that rate in past time he must have been 
 of double diameter, of quadruple heating power, and of eight- 
 fold mass only 8000 years ago. We may therefore quite 
 safely conclude that the sun does not get its heat by chemical 
 action . . . and we must therefore look to the meteoric theory 
 for fuel.* 
 
 A hypothesis which fulfils these three conditions is a 
 legi timate hypothesi s, though it must conform to still more 
 rigor ous requirements beiore it Cclli bu accepted as a 
 com plete Inductlc^. or even be regarded as posse ssing 
 any great amount of probabili ty. Thus, the Meteoric 
 Theory, though it is not yet proved, and perhaps never 
 may be proved, to be the true explanation of the pheno- 
 menon of solar heat, is perfectly tenable as a hypothesis. 
 For, to take the conditions in the reverse order to that 
 in which they have been enumerated above, the impact 
 
HYPOTHESIS, 1 I r 
 
 of a large number of meteors on a dense body, such as 
 the sun probably is, would be competent or adequate to 
 produce the given effect ; the theory in question is likely, 
 if not to be proved or disproved, at least to be rendered 
 more or less probable by the progress of astronomical 
 science ; lastly, we do not know, nor have we any reason 
 to suppose, that the hypothesis is an untrue explanation 
 of the facts. But, though legitimate as a hypothesis, 
 before we could accept the Meteoric Theory as a Valid 
 or Complete Induction, that is to say, an ascertained 
 truth, we should require to know not only that there is 
 a large number of meteors circulating round the sun, that 
 these meteors have a tendency to fall into the central body, 
 and that, j/* they were falling or had falJen in sufficient 
 quantities, they would be competent or would have been 
 competent to produce the present amount of solar heat, 
 but also that they do, as a matter of fact, fall in sufficient 
 quantities to account for the phenomenon, or, at least, 
 that nothing else but the showering down of asteroids and 
 meteors could account for it. 
 
 It was by availing himself of the latter mode of proof 
 that Newton demonstrated the existence in the sun of a 
 central force attracting the planets towards it. Assuming 
 Kepler's hypothesis (then sufficiently verified by obser- 
 vation to be universally accepted as a true statement 
 of the facts), that equal areas are described by the 
 radii vectores of the planets in equal times, Newton 
 showed that this fact could be due to only one cause, 
 namely, the deflection of the planets from their recti- 
 
112 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 linear course by a force acting in the direction of the 
 sun's centre. The existence of the central force was, 
 at first, started by him as a hypothesis. * He then proved 
 that,' on the supposition of the existence of such a force, 
 *the planet will describe, as we know by Kepler's first 
 law that it does describe, equal areas in equal times; and, 
 lastly, he proved that if the force acted in any other di- 
 rection whatever, the planet would not describe equal 
 areas in equal times. It being thus shown that no other 
 hypothesis would accord with the facts, the assumption 
 was proved; the hypothesis became an inductive truth. 
 Not only did Newton ascertain by this hypothetical pro- 
 cess the direction of the deflecting force; he proceeded 
 in exactly the same manner to ascertain the law of varia- 
 tion of the quantity of that force. He assumed that the 
 force varied inversely as the square of the distance ; 
 showed that from this assumption the remaining two of 
 Kepler's laws might be deduced; and finally, that any 
 other law of variation would give results inconsistent with 
 those laws, and inconsistent, therefore, with the real 
 motions of the planets, of which Kepler's laws were 
 known to be a correct expression^*.' 
 
 It will be noticed that the course of demonstration pur- 
 sued in this instance is the following : (i) we have certain 
 observed facts ; (2) these observed facts are generalised 
 in what are called Kepler's Laws; (3) we have the 
 assumption of the central force ; (4) it is shown that the 
 central force will account for Kepler s Laws, and there- 
 
 ** Mill's Logic, Bk. III. ch. xiv. § 4. 
 
HYPOTHESIS. 113 
 
 fore, of course, for the particular facts of observation on 
 which those Laws were founded; (5) it is shown (and 
 this, together with the next step, is what properly consti- 
 tutes the demonstration) that this assumption is the only 
 one which will account for the Laws or the particular 
 facts expressed by them ; (6) it is inferred inductively, 
 by means of the Method of Difference (to be hereafter 
 described), that the assumption of the central force, as it 
 will account for, and is the only supposition which will 
 account for, the observed facts, must be accepted as true ; 
 (7) Kepler's Laws (which had hitherto been accepted as 
 correct statements of observed facts, though they had not 
 yet been explained by reference to any cause competent 
 to account for them) are now proved deductively from 
 what we have ascertained to be the Valid Induction of 
 the Central Force. 
 
 A Hypothesis can only be converted into a Valid 
 Ind uction ^^ by the application of one or other of the 
 Ind uctive Method s (to be described in the next Chapter), 
 or, if we insist on strict accuracy of proof, of such of 
 them as furnish absolutely certain conclusions. 
 
 Note I. — According to the view here taken, which 
 
 *^ Though a hypothesis is usually contrasted with a Valid or Complete 
 Induction, it must not be forgotten that we have admitted, as legitimate, 
 hypotheses which are never likely to rest on more than probable evi- 
 dence. These can, of course, receive accessions of proof only by 
 the same means as those by which we establish Imperfect Inductions. 
 It should also be remembered that the truth of a hypothesis may be 
 demonstrated by deductive as well as by inductive methods. 
 
 1 
 
114 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 agrees with that of Mr. Mill, a hypothesis cannot claim 
 to be regarded as an established truth, till it has con- 
 formed to the requirements of one or other of the 
 inductive methods, or has been shown to admit of 
 being deduced from some previously established In- 
 duction. Thus, when Newton proves the existence of 
 a central force, deflecting the planets from the recti- 
 lineal course which they would otherwise describe and 
 making them describe curves round the sun, by showing 
 that no other supposition would account for the fact that 
 their radii vectores describe equal areas in equal times, he 
 is, as Mr. Mill says, employing the Method of Difference. 
 The demonstration 'affords the two instances, A B C, 
 a d c, and B C, d c. A represents central force ; A B C. 
 the planets plus a central force ; B C, the planets as they 
 would be without a central force. The planets with a 
 central force give a (areas proportional to the times) ; the 
 planets without a central force give 5 c (a set of motions) 
 without a, or with something else instead of a. This is 
 the Method of Difference in all its strictness. It is true, 
 the two instances which the method requires are obtained 
 in this case, not by experiment, but by a prior deduction. 
 But that is of no consequence. It is immaterial what is 
 the nature of the evidence from which we derive the as- 
 surance that ABC will produce a d c, and B C only d c ; 
 it is enough that we have that assurance. In the present 
 case, a process of reasoning furnished Newton with the 
 very instances, which, if the nature of the case had ad- 
 mitted of it, he would have sought by experiment *^.' 
 *« Mill's Lo^k, Bk. III. ch. xiv. § 4. 
 
HYPOTHESIS, 115 
 
 Dr. Whewell, who does not acknowledge the utility of 
 Mr. Mill's methods, appears to regard the inductive pro- 
 cess as consisting simply in the framing of successive 
 hypotheses, the comparison of these hypotheses with the 
 ascertained facts of nature, and the introduction into 
 them of such modifications as that comparison may 
 render necessary*"^. The first requisite in a hypothesis, 
 according to Dr. Whewell, is that it shall explain all 
 the observed facts. But its probability, he urges, will 
 be considerably enhanced, if, in addition to explaining 
 observed facts, it enables us to predict the future. 
 ' Thus the hypotheses which we accept ought to explain 
 phenomena which we have observed. But they ought 
 to do more than this : our hypotheses ought to foretel 
 phenomena which have not yet been observed ; at least 
 all phenomena of the same kind as those which the 
 hypothesis was invented to explain. For our assent to 
 the hypothesis implies that it is held to be true of all 
 particular instances. That these cases belong to past 
 or to .future times, that they have or have not already 
 occurred, makes no difference in the applicability of the 
 rule to them. Because the rule prevails, it includes all 
 cases ; and will determine them all, if we can only cal- 
 culate its real consequences. Hence it will predict the 
 
 *'' A theory of Induction almost identical with that of Dr. Whewell 
 (though, I venture to suggest, not so clearly stated or so carefully 
 guarded), has been recently propounded by Professor Stanley Jevons in 
 his Principles of Science. This, together with other points of difference 
 between Professor Jevons and myself, I have noticed in the Preface to 
 the present edition. 
 
 I 2 
 
Il6 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 results of new combinations, as well as explain the ap- 
 pearances which have occurred in old ones. And that 
 it does this with certainty and correctness, is one mode 
 in which the hypothesis is to be verified as right and 
 usefuP^ 
 
 Curiously enough, the first hypothesis which Dr. 
 Whewell cites as having' fulfilled both these conditions, 
 is also one which eventually proved to be false. ' For 
 example, the Epicyclical Theory of the heavens was 
 confirmed by its predicting truly eclipses of the sun 
 and moon, configurations of the planets, and other 
 celestial phenomena \ and by its leading to the con- 
 struction of Tables by which the places of the heavenly 
 bodies were given at every moment of time. The truth 
 and accuracy of these predictions were a proof that the 
 hypothesis was valuable, and, at least to a great extent, 
 true ; although, as was afterwards found, it involved a 
 false representation of the structure of the heavens.' A 
 theory may thus not only enable us to explain known 
 facts, but even to predict the future, and still be untrue. 
 Notwithstanding, however, the infelicitous character of the 
 example selected, Dr. Whewell attaches the greatest impor- 
 tance to the fulfilment of this condition by a hypothesis. 
 * Men cannot help believing that the laws laid down by 
 discoverers must be in a great measure identical with the 
 real laws of nature, when the discoverers thus determine 
 effects beforehand in the same manner in which nature 
 herself determines them when the occasion occurs. Those 
 
 ** Novum Orgafion Renovatum, Bk. II. ch. v. art. lo. 
 
HYPOTHESIS. 117 
 
 who can do this must, to a considerable extent, have 
 detected nature's secret ; — must have fixed upon the con- 
 ditions to which she attends, and must havp seized the 
 rules by which she applies them. Such a coincidence of 
 untried facts with speculative assertions cannot be the 
 work of chance, but implies some large portion of truth 
 in the principles on which the reasoning is founded. To 
 trace order and law in that which has been observed, may 
 be considered as interpreting what nature has written 
 down for us, and will commonly prove that we under- 
 stand her alphabet. But to predict what has not been 
 observed, is to attempt ourselves to use the legislative 
 phrases of nature; and when she responds plainly and 
 precisely to that which we thus utter, we cannot but sup- 
 pose that we have in a great measure made ourselves 
 masters of the meaning and structure of her language. 
 The prediction of results, even of the same kind as those 
 which have been observed, in new cases, is a proof of real 
 success in our inductive processes.' 
 
 But what appears to Dr. Whewell to establish the truth 
 of a hypothesis beyond all question is what he calls a 
 Consilience of Inductions. ' We have here spoken of the 
 prediction of facts 0/ the same kind as those from which 
 our rule was collected. But the evidence in favour of our 
 induction is of a much higher and more forcible character 
 when it enables us to explain and determine cases of 
 a kind different from those which were contemplated in 
 the formation of our hypothesis. The instances in which 
 this has occurred, indeed, impress us with a conviction 
 
Il8 PROCESSES SUBSIDIARF TO INDUCTION. 
 
 that the truth of our hypothesis is certain. No accident 
 could give rise to such an extraordinary coincidence. No 
 false supposition could, after being adjusted to one class 
 of phenomena, exactly represent a different class, where 
 the agreement was unforeseen and uncontemplated. That 
 rules springing from remote and unconnected quarters 
 should thus leap to the same point, can only arise from 
 //laf being the point where truth resides. 
 
 * Accordingly the cases in which inductions from classes 
 of facts altogether different have thus jumped together, 
 belong only to the best established theories which the 
 history of science contains. And as I shall have occasion 
 to refer to this peculiar feature in their evidence, I will 
 take the liberty of describing it by a particular phrase ; 
 and will term it the Consilience of Inductions. 
 
 ' It is exemplified principally in some of the greatest 
 discoveries. Thus it was found by Newton that the 
 doctrine of the Attraction of the Sun varying according 
 to the Inverse Square of the distance, which explained 
 Kepler s Third Law, of the proportionality of the cubes 
 of the distances to the squares of the periodic times of 
 the planets, explained also his First and Second Laws, 
 of the elliptical motion of each planet ; although no con- 
 nection of these laws had been visible before. Again, it 
 appeared that the force of Universal Gravitation, which 
 had been inferred from the Perturbations of the moon 
 and planets by the sun and by each other, also accounted 
 for the fact, apparently altogether dissimilar and remote, 
 of the Precession of the equinoxes. Here was a most 
 
HYPOTHESIS, 119 
 
 Striking and surprising coincidence, which gave to the 
 theory a stamp of truth beyond the power of ingenuity to 
 counterfeit ^^J 
 
 It is undeniable that a theory which thus appears to 
 afford an explanation of different classes of facts strikes 
 the imagination with considerable force, and that its very 
 simplicity furnishes primd facie evidence of its truth. 
 But what is required before a hypothesis can be placed 
 beyond suspicion is formal proof, and that, it appears 
 to me, is furnished by Mr. Mill's 'methods,' and not 
 by Dr. Whewell's requisitions of explanation, prediction, 
 and co7isilience of inductions. For the questions at issue 
 between Mr. Mill and Dr. Whewell, see Whewell's 
 Novum Organon Renovatum (where his views are stated 
 in their latest and most matured form), Bk. II. ch. v. 
 § 3, and Mill's Logic, Bk. III. ch. xiv. § 6. 
 
 Note 2. — In attempting to determine the conditions to 
 which a legitimate hypothesis must conform, I have 
 avoided the employment of the expressions vera causa 
 and adcequata causa. In the first place, a hypothesis may 
 simply attempt to find a general expression for a number 
 of isolated facts without referring them to any cause, as 
 was the case with the various hypotheses respecting the 
 shape of the planetary orbits, and hence to speak as if 
 a hypothesis always assigned a cause is an undue limita- 
 tion of the meaning of the word. But to the expression 
 vera causa there is a more special exception. Its meaning 
 
 ^ Novum Organon Renovatum, Bk. II. ch. v. art. 1 1 . 
 
l:ZO PROCESSES SUBSIDIARY TO INDUCTION. 
 
 is ambiguous. Is it the actual cause which produces a 
 phenomenon, or a cause which we know to be actually 
 existent, or a cause analogous to an existent cause? 
 The student will find a criticism of this expression (first 
 employed by Newton) in Dr. WhewelFs Philosophy of 
 Discovery^ ch. xviii. § 5, &c. The expression cannot 
 have been used in the first, which is its most obvious, 
 sense, for, as Dr. Whewell says, ' although it is the 
 philosopher's aim to discover such causes, he would be 
 litde aided in his search of truth, by being told that it 
 is truth which he is to seek.' But in the second of 
 the two remaining senses, the requirement, as would now 
 be generally acknowledged, is too stringent, and, if it 
 had been invariably observed, would have prevented us 
 from reaping some of the greatest discoveries in science, 
 while in the last it is so vague as to be of no practical 
 service. It has been attempted to affix other meanings 
 to the phrase ; but there can be little doubt that Newton, 
 having in mind the Vortices of Descartes, intended to 
 protest against the introduction of causes of whose ex- 
 istence we have no direct knowledge, and consequently 
 laid down a rule, which the subsequent history of science 
 has shown to be needlessly stringent. 
 
 Note 3. — We sometimes find the expression a ^gratuitous 
 hypothesis.' By this is meant the assumption of an 
 unknown cause, when the phenomenon is capable of 
 being explained by the operation of known causes, or 
 the introduction of an extraneous (though it may be 
 
HYPOTHESIS, 121 
 
 known) cause, when the phenomenon is capable of being 
 accounted for by the causes already known to be in 
 operation. Of the latter case we should have instances, 
 where a man is supposed to have acted at the suggestion 
 of another, though his own motives would supply a 
 sufficient explanation of his conduct, or where a man is 
 supposed to have been poisoned, though he was already 
 known to have been suffering from a fatal disease. Of 
 the former case we should have instances in the crystalline 
 spheres of the ancient astronomers and in the masses 
 of crystal which were supposed by Lodovico delle 
 Colombe to fill up the cavities of the moon (there being 
 no instances known to us of the existence of crystal in 
 these huge masses, and the phenomena being capable of 
 explanation without making the supposition) ; in the 
 caloric (which was supposed to be a distinct substance) 
 of the early writers on heat^ and in the ^ electrical fluid ' 
 of the early electricians. In all these instances, under 
 whichever of the two cases they may fall, the objection 
 to the hypothesis is that it seems * not to be needed.' 
 
 I have said nothing of ^ gratuitous hypotheses ' in the 
 text, as a hypothesis, though it may appear to be gra- 
 tuitous, may still be legitimate, and may even ultimately 
 turn out to be true. 
 
CHAPTER III. 
 
 On the Inductive Methods. 
 
 INDUCTION has been defined to V>^ a Ip^irima tp 
 inference from t he known to the nnVnnwn ^ T^ii±--44^fi 
 . u nknow n must not be entirely unknown. It must be 
 knoa ^to agree in certain circumstances with the know n, 
 and ^ is in virtue of this agreement that the inferenc e 
 i& made. Now, how are we to ascertain what are the 
 common circumstances which justify the inductive infer- 
 ence ? X and Y may both agree in exhibiting the circum- 
 stances a^ bj <r, but it will not follow because X exhibits 
 the quality m, that therefore this quality will also neces- 
 sarily be found in Y. Nor even, if twenty, thirty, a 
 hundred, or a thousand cases could be adduced in which 
 the circumstances a, b, c were found to be accompanied 
 by the circumstance m, would it follow necessarily (it 
 might not even follow probably) that the next case in 
 which we detected the circumstances a, b, c would also 
 exhibit the quality m. We might pass through a field 
 containing thousands of blue hyacinths, but this would 
 not justify us in expecting that the next time we saw 
 
INDUCTIVE METHODS, 1 23 
 
 a hyacinth, it would be a blue one. This form of induc- 
 tion {Induciio per SimpUcem Enumerationem) may have no 
 value whatever. In most cases, the condemnation passed 
 on it by Bacon ^ is perfectly just: 'Inductio quae pro- 
 cedit per enumerationem simplicem, res puerilis est, et 
 precario concludit, et periculo exponitur ab instantia con- 
 tradictoria, et plerumque secundum pauciora quam par 
 est, et ex his tantummodo quae praesto sunt, pronunciat.' 
 But when we have reason to think that any instances to 
 the contrary, if there were such, would be known to us, 
 the argument may possess considerable value, and when, 
 as in the case of the Laws of Causation and of the 
 Uniformity of Nature, we feel certain, from a wide and 
 various experience, that there are no cases to the contrary, 
 no stronger argument (to us individually) can be adduced. 
 It is rarely, however, that an Inductio per Simplicem 
 Enumerationem can afford us this certainty^. Our trust- 
 worthy inductions are, in the great majority of cases, the 
 result of our detecting some fact of causation among the 
 observed phenomena. We find, for instance, that, amongst 
 the observed phenomena, a, b, c, ^ of X, a is the cause 
 of r, and, consequently, if we observe the phenomenon 
 a in Y, we infer that, if there are no counteracting cir- 
 cumstances, Y will possess the quality c as well ; or, if we 
 
 ^ Novum Organum, Lib. I. aph. cv. 
 
 2 It must be remembered that a complete enumeration of instances, 
 when we know the enumeration to be complete, inasmuch as it leaves 
 no room for an inference from the known to the unknown, does not 
 furnish an inductive but a deductive argument. See Elements of De- 
 ductive Logic, Part III. ch. i. appended Note 2. 
 
124 INDUCTIVE METHODS, 
 
 observe the phenomenon c in Y, we infer that it is not 
 unlikely * that a may be present as well The problem 
 of Induction, therefore, resolves itself (except in the rare 
 cases in which we may legitimately employ Inductio per 
 Enumerationem Simplicem, or in which we have no other 
 resource) into the problem of detecting facts of Causation. \ 
 Certain rules for this purpose have been laid down by 
 Mr. Mill, called by him the Experimental Methods, but 
 which we shall distinguish as the Inductive Methods. 
 
 These Methods, it will be noticed as we proceed, are all 
 methods of elimination, or devices by which we are enabled 
 to argue from a comparatively small number of instances 
 with the same certainty as if they were ever so numerous. 
 
 Before proceeding to state and explain these Rules or 
 Methods, it may be useful to make some preliminary 
 remarks on the nature of the causal relations which 
 subsist among phenomena. / 
 
 (i) The same cause, unless there are counteracting 
 circumstances, that is, other causes which prevent it from 
 acting or which modify its action, is invariably followed 
 by the same effect. 
 
 (2) As already shown (Chapter I. pp. 13-15), several 
 causes may have co-operated in producing any given 
 effect. In this case, it is not unusual to speak of the 
 * combination of causes ' or the * sum of the causes.' 
 
 2 We say ' not unlikely,' for c might be due to some other cause as well 
 as a, and, therefore, the presence of c does not enable us to infer with 
 certainty the presence of a, as does that of a the presence of c. 
 
INDUCTIVE METHODS, 125 
 
 (3) The same effect may be due to several distinct 
 causes, or combinations of causes, being due sometimes 
 10 one and sometimes to another, and, hence, though we 
 may always argue from a particular cause to its effect, we 
 cannot always argue from an effect to any particular 
 cause. Thus, ignition may be due, not only to the con- 
 centration of the rays of solar heat, but also to friction, 
 electricity, &c. This fact has given occasion to the 
 expression * Plurality of Causes' 
 
 (4) It frequently happens that between the original 
 cause and the ultimate effect there intervene a number 
 of intermediate causes. Thus, suppose we make an 
 experiment by which motion is converted into heat, heat 
 into electricity, and electricity into chemical affinity ; we 
 may, roughly speaking, say that motion has been 
 the cause of the chemical affinity, or chemical affinity 
 the effect of the motion, but, speaking strictly, we ought 
 to enumerate the intervening causes. 
 
 (5) Sometimes a number of effects appear to be 
 produced simultaneously by the same cause. Thus, it 
 would appear that there are many cases in which, if one of 
 the agents, motion, heat, light, electricity, magnetism, and 
 chemical action, is excited, the rest are developed simul- 
 taneously*. These simultaneous effects, whether we 
 conceive that they are really or only apparently simul- 
 taneous, would be called joint or common effects of the 
 cause. Similarly the expression 'joint effects' would be 
 employed for the effects produced by the same cause on 
 
 * See Grove's Correlation of Physical Forces, Concluding Remarks. 
 
126 INDUCTIVE METHODS. 
 
 different bodies, or different portions of the same body. 
 Thus, if a blow bruises my forehead, and at the same time 
 gives me a headache, the bruise and the headache may 
 be called joint effects of the blow. These joint effects 
 may be, as it were, in different degrees of descent from 
 the same cause. Thus, if the headache incapacitates me 
 for work, my incapacity for work and the bruise on my 
 forehead will be joint effects, but in different degrees 
 of descent from the original cause. 
 
 Any phenomena which are connected, either as cause 
 and effect, and that either immediately or remotely, or as 
 joint effects, and that either in the same or in different 
 degrees of descent from the same cause, may be spoken 
 of as being causally connected, or as causal relations, or 
 as being related to one another through some fact of 
 causation. 
 
 We now proceed to the statement of the Inductive 
 Methods. 
 
 METHOD OF AGREEMENT. 
 CANON ^ 
 
 I If two or more instances of the phenomenon under inves- 
 tigation have only one other circumstance in common, that 
 circumstance may he regarded, with more or les'^ of proha- 
 
 V— - 
 
 ^ The statement of the Canons is taken, with some modifications, from 
 Mr. Mill's Logic. The authorities for the various examples, when these 
 are not of a familiar character, are cited at the foot of the page. 
 
METHOD OF AGREEMENT. 12/ 
 
 dt'h'/y, as the cause (or effect) of the given phenomenon, or^ at 
 leasts as connected ivith it through some fact of causation. 
 
 Wherever the phenomenon a is found, we observe th at 
 ^-is founds eit her invariably or frequently ^, in conjunctio n 
 with it. This fact leads us to suspect that there is som e 
 causal connection between them. On what grounds, 
 and un der what circumstances^ are we justified in drawi ng 
 such an inferen ce ? And what is the particular character 
 of the inference which we are justified in drawing? 
 The answer to these questions involves many difficulties, 
 of which we shall now attempt to offer a solution. 
 
 When antecedents and consequents are discriminated 
 in this discussion, antecedents will be represented by 
 Roman capitals, A, B, C, &c., and consequents by Greek 
 characters, a, jS, y, &c. When circumstances are not 
 distinguished as antecedents and consequents, we shall 
 employ the small Roman letters, a, b, c, &c. 
 
 No w^ suppose that we have A B followed by a ft and 
 
 A C , by g y; it mig hty at first sight, appear that A mus^ 
 be the cause^^of _a, or, if we wer e attempti ng to ascertain 
 the eff'ect of a given cause (>yhich, however^ is a much 
 rarer applic ation of this method), that a rnust be the 
 effect of A. And there is much plausibility in this sup- 
 position, for whatever can, in any given instance, be ex- 
 cluded, or, to use the technical term, eliminated without 
 
 ^ We add ' or frequently,' as it is not necessary that the conjunction 
 shall be invariable. The student need not, however, at present trouble 
 himself with this distinction, which will be fully explained hplow. See 
 ^p. 134, 141-143. A .Lj^ M V :' vl^ tficA^ I ' ^ -^ 
 
 ''^l-'^y'^i'TM 
 
128 INDUCTIVE METHODS. 
 
 [prejudice to a phenomenon^, cannot have any influence 
 /on it in the way of causation, nor can an effect which 
 I disappears be due to a cause which continues to 
 I operate. Thus, if we were attempting to find the 
 cause of a given effect a, it might be argued that B 
 cannot be its cause, for it is absent in one of the cases 
 where a is present, and similarly of C ; but that a must be 
 due to some cause; and, consequently, it is due to A, the 
 only antecedent remaining. Or, if we were attempting to 
 find the effect of a given cause A, it might be argued that 
 ^ cannot be its effect, for it is absent in one of the cases 
 where A is present, and similarly of y ; but that, as a has 
 been permanently present, A must be its cause. If it 
 were not for the fact that the same event may be due to 
 a great number of distinct causes (as is exempHfied in the 
 familiar cases of motion, death, disease, &c.), this reason- 
 ing would be perfectly just. Now it will be observed that, 
 when B was removed, it was replaced by C. It is, there- 
 fore, conceivable that a may have been due to B in the 
 first instance, and to C in the second, it being, of course, 
 in each case, only a portion of the effect, the remaining 
 portions being respectively ft y, and A having been 
 throughout inoperative. This consideration, it is plain, 
 vitiates the reasoning, whether we are attempting to dis- 
 cover the effect of a given cause or the cause of a given 
 effect. Thus, suppose that there are two distinct drugs, 
 either of which is potent to remove a given disease, and 
 that, in administering each of them, we mix it with some 
 perfectly inert substance, which is the same in each 
 
/ 
 
 METHOD OF AGREEMENT, 1 29 
 
 case; if the principles of the' above reasoning were cor- 
 rect, and we were justified in neglecting to take account 
 of what may be called the Plurality of Causes, we should 
 be at liberty to argue (if we were seeking the cause of a 
 given effect) that the restoration of the patients to health 
 was, in each case, due to the inert substance, or (if we 
 were seeking the effect of a given cause) that the inert 
 substance was the cause of their restoration to health. 
 
 But, if the M et hod of Agreenient is open to 'so serious 
 a n objection, it may be asked on what p^rounds is it 
 rec ognised a s an Inductive Method.?' The answer is 
 thai^ by thp multiplication and variation of ins tances, 
 the possible error due Jo_t.he„JPlurality of Causes may „^ 
 
 be rendered le ss and less_prQbable,_till, at last, for_ all 
 
 practical purp oses, it ma y be regarded as. having dis- 
 appeared. Thus, if to the instances A B, ag ; A C, ay ; 
 we r,an add A D,M;.,.A-£.,-af> &c. Slq. ; it is. plain t hnt wo 
 may, at each step, be very considerably diminishing the 
 possibility of an error i n our reasoning , and, after a certain 
 numb er of instances , may be justified in feeling morally 
 certain Jha.t wa^iiay^ . avgide-d JL^lt is not likely that, 
 in a number of instances, each agreeing in some one 
 circumstance (besides the phenomenon which is being 
 investigated) but differing as widely as possible in all 
 other circumstances, the same event should in each case, 
 or in a majority of cases, or in even a great number of 
 ,c ases, be due to differ ent^causes. The chance of an inert 
 substance being successively mixed with two potent 
 drugs, and of the effects which are really due to them 
 
130 INDUCTIVE METHODS, 
 
 being erroneously ascribed to it, is, in the present state 
 of medical science, but a very slight one ; but the pro- 
 bability is obviously considerably diminished, if instead 
 of two such errors we suppose three, instead of three 
 we suppose four, and so on. 
 
 For the sake of simplicity, we have assumed groups 
 of two antecedents and two consequents (A B, a /3 ; AC, 
 ay; &c. &c.), but it is extremely seldom that we find in 
 nature combinations so simple. We have usually a vast 
 mass of antecedents and a vast mass of consequents 
 (or, to state the same proposition in more scientific 
 language, a vast mass of antecedents all, or most of them, 
 contributing to a complex eifect), and hence it often 
 becomes a matter of extreme difficulty to discover a 
 collection of instances which, presenting the phenomenon 
 in question, agree in only one other circumstance or even 
 in a small number of other circumstances. The diffi- 
 c ulty, therefore, of rigidly satisfying the requiremen ts of 
 the Method must be added to what Mr. Mill ca lls its. 
 ch aracteristic imperfection, namely, the uncertainty a ttach- 
 ing to its conclusions f rom the consideration of the 
 Elurality of Causes. 
 
 But there is still a t hird difficulty incident to the 
 Method of Agreement , which however is, in a majority 
 of cases, o f a theoretical rather than a practical nature. 
 If we insisted literally on the fulfilment of the con dition 
 that the i nstances presenting the given phenomenon should 
 have only one other circumstance in common, it would 
 
 / 
 
METHOD OF AGREEMENT, I3I 
 
 wi ll be found to ^gr^e in a number of circumstanc es 
 which are im material to the point under investigation. 
 Thus, if we are enquiring into the properties of a group 
 of external objects, they will all agree in the fact that they 
 are subject to the action of gravity, and probably also 
 in the facts that they are surrounded by atmospheric air 
 and exposed to the light of the sun ; but, if these facts 
 do not affect the subject of our enquiry, we may pass 
 them over as if they had no existence. When, therefore, 
 we employ the expression ' only one circumstance in 
 common,' we must be understood to mean 'only one 
 material circumstance,' and to exclude all circumstances 
 which a wide experience or previous inductions have 
 shown to be immaterial to the question before us. It 
 need hardly be added that, in forming this judgment 
 as to the material or immaterial character of the circum- 
 stances, the greatest caution is often required. 
 
 But, suppose we have ascertained (when enquiring 
 into the cause of a given effect) that the instances agree 
 in only one antecedent (or rather one material ante- 
 cedent), namely A, and that we have so multiplied and 
 varied the instances as to have satisfied ourselves that 
 we have excluded the possibility of a Plurality of 
 Causes, are we justified in drawing the inference that 
 A is the cause of a .? We are so justified, for a must 
 be due to something which went before it, and, as it 
 has been shown that it is not due to any of the other 
 antecedents, it must be due to A. Similarly, if our 
 object be to enquire into the effect of a given cause A, 
 
1^2 INDUCTIVE METHODS. 
 
 we are justified, if we discover a consequent a, of which 
 we can assure ourselves that it is not due to any of the 
 other antecedents, in regarding it as the effect of A. 
 
 Hitherto, we have supposed the antecedents and con- 
 sequents to be discriminated. But, suppose that we have 
 a number of phenomena a b c d e, a d e f g, &c., in which 
 we cannot discriminate them, how will the conclusions 
 of the Method of Agreement be affected ? There will, 
 as in the former cases, obviously be the difficulti es arisin g 
 fro m Plurality of Causes and the complexity of the 
 phenomena . Supposing, however, these to be overcome, 
 an d two circumstances only, a and b, to have been as cer- 
 tai ned to be common to all the instances, what con clusion 
 shalI^.ar.e-J:}e justifi ed in drawing with -reference t o the 
 co nnection between a and b? I t is only reaso nable 
 to .Suppose that they must be causally conn ected in 
 so me way, else their connection would be a mere 
 casual coinciden ce ; a supposition which wq assume to 
 have been excluded by the number and variety of the 
 instances examined. B ut they need not necessarily stand 
 to £a £h other in the relation of cause and effect, fo r they 
 ma^^Jji e common effects (in the sam e, or in different de- 
 grees of d escent) of some cause which has itself ceased 
 JiO jQIi£i:^te. In social and physiological phenome na this 
 is frequently the, ras e. A disease will leave effects behind 
 it which will continue to co-exist for years after the disease 
 itself has passed away, and which, though not standing 
 to each other in the relation of cause and effect, are thus 
 causally connected. The social condition of any old 
 
METHOD OF AGREEMENT. 1 33 
 
 country is, to a great extent, an aggregate of such effects, 
 the original cause or causes of which have long ceased to 
 have any existence. 
 
 It s hould be noticed ]that the Method of Agreement i s 
 m ainlvp though not exclusively, a Method of Observation 
 r?th^^ ^^^Ti of ]^,x penment, and that it is applied far more 
 fr equently for the purpose of enquiring into the causes of 
 given effects than into the effects of given causes . The 
 reason of this peculiarity is that in trying an experiment, 
 or in enquiring into the effect of a given cause, we are 
 generally able to employ one of the other Methods, 
 which, as will be seen hereafter, are not exposed to the 
 same difficulties as the Method of Agreement. 
 
 It should also be noticed that where, after a careful 
 ' elimination and an examination of a sufficiently large 
 number of instances, we have, instead of two, some three, 
 four, or more circumstances common to all the instances, 
 we may, with much probability, regard them all, unless 
 we know or suspect any of them to be immaterial cir- 
 
 r^^pgtanrpq, cig-.hpinor rangally connected. If the COmmOU 
 
 circumstances be a, b, c, d, this is all that we can infer. 
 But, if they be A, B, C, a, we may infer that the cause 
 of a is certainly either A or B or C, or some two of them 
 acting jointly, or all acting together, while those common 
 antecedents, which do not either constitute or contribute 
 to the cause, probably stand in some causal relation to 
 it, and consequently to its effect a. Similar conclusions 
 may be drawn, if the common circumstances left after 
 elimination be A, a, /3, y. Thus, for instance, a, ft y 
 
134 INDUCTIVE METHODS, 
 
 might all be joint effects of A, or a might be its im-* 
 mediate effect, and /3, y effects of a, and so on. 
 
 It is perhaps not superfluous to remind the student 
 that, in the application of this Method, he should be 
 peculiarly careful not to overlook any instance in which 
 the given phenomenon is unaccompanied by the other 
 circumstance. Such an instance should at once lead him 
 to suspect that some third common circumstance, which 
 may be the true cause (or effect) of the given phenomenon, 
 has' escaped his attention, but this, if it be so, does not 
 necessarily vitiate his conclusion. If the given phe- 
 nomenon be the consequent, and this other circumstance 
 the antecedent, such an instance may only point to some 
 other and independent cause of the phenomenon in ad- 
 dition to the cause he supposes himself to have ascer- 
 tained. If, on the other hand, the given phenomenon 
 be the antecedent, and this other circumstance the conse- 
 quent, such an instance may only point to a counteracting 
 cause which, in this exceptional case, fmstrates the sup- 
 posed effect. The only condition essential to an appl ica- 
 ti on of the Method of Agreement is that the c ases on 
 w bicb^ the inference is founded shall present on ly two ^ 
 circ umstances in common . It is not necessary that these 
 circumstances should invariably be found in conjunction, 
 provided that in the cases where they are found in con- 
 junction no other common circumstance can be detected. 
 We shall recur to this subject below '^. , 
 
 In the statement of the Canon, we have thought it 
 ■^ See pp. 141-143- 
 
\ 
 
 METHOD OF AGREEMENT, 1 35 
 
 desirable to in tjfoduce the expression * with more or less 
 of ^rohahility/ in order to show that, under no r.irrnm- 
 stan c^^s^ does an inference drawn in accordance with the 
 Method of Agreement: attain to absolute an d formal cer - 
 taint y» though, as we have seen, it may attain to mo ral 
 certainty 
 
 As^familiar .e xamples of the employment of the Metho d 
 of Agreement, the following may be adduced : — 
 
 A particular kind of food, whatever else I may eat 
 or drink, and however various my general state of health, 
 the temperature of the air, the climate in which I am 
 living, and my divers other surroundings, invariably makes 
 me ill; I am justified in regarding it as the probable 
 cause of my illness, and avoid it accordingly. This ex- 
 ample furnishes a good illustration both of the difficulties 
 and of the possible cogency of the Method of Agree- 
 ment. What made me ill on each of two, three, or four 
 occasions, may have been some viand different from the 
 one in question, but it is very unlikely, if the number of 
 occasions on which the inference is based be considerable, 
 that it has been a different viand on each of them. 
 
 1 find that a certain plant always grows luxuriantly 
 on a particular kind of soil; if my experience of the 
 Dther conditions be sufficiently various, I am justified in 
 concluding that the soil probably possesses certain chemi- 
 cal constituents which are peculiarly favourable to the 
 I )roduction of the plant. 
 
 Trade is observed to be in a languishing condition 
 wherever there exist certain restrictions, such as high 
 
136 INDUCTIVE METHODS. 
 
 duties, difficulties thrown in the way of landing or loco- 
 motion, &c. ; if it could be ascertained that these countries 
 agreed in no other respect which could influence the 
 condition of trade, except in being subject to these 
 restrictions, it might be inferred with considerable proba- 
 bility that the commercial depression was due to the 
 restrictions as a cause. 
 
 In all these cases, it will be seen that the great diffi- 
 culty consists in ascertaining that the supposed cause 
 is the only circumstance, or the only material circum- 
 stance, which, in addition to the phenomenon itself, the 
 various instances possess in common. 
 
 We now append a few instances of a less familiar 
 nature :- — 
 
 The occurrence of Aurora Borealis has, under me- 
 teorological conditions of very different character, been 
 invariably found to be accompanied by considerable 
 magnetic disturbances. It is rightly inferred that there 
 is some causal connection between magnetic disturbance 
 and the occurrence of the Aurora Borealis. 
 
 It has been observed uniformly, and under a variety 
 of circumstances, that, wherever an indiscriminate sys- 
 tem of almsgiving has prevailed, the population has, 
 sooner or later, become indolent and pauperised. This 
 may be noticed especially in the neighbourhood of large 
 monasteries, in parishes where large sums of money 
 are distributed in the shape of ' doles,' in places which 
 are the residence of rich and charitable but injudicious 
 persons, and the like. The reason is not difficult to 
 
METHOD OF AGREEMENT, 1 37 
 
 discover. The unfortunate recipients of the charity are 
 left without the ordinary motives to exertion, and con- 
 sequently, when the abnormal supply ceases, or becomes 
 too small for the wants of an increased population, being 
 without self-reliance or any special skill, they have no 
 resource but beggary. 
 
 After a variety of experiments on substances of the 
 most different kinds, and under the most different cir- 
 cumstances, it has been found that, as a body passes 
 from a lower degree of temperature to a higher, it in- 
 variably undergoes a change of volume, though that 
 change may not always be in the same direction, it being, 
 in the great majority of cases, in the direction of expan- 
 sion, but, occasionally, in that of contraction. Hence it 
 has been inferred that change of volume is an invariable 
 effect of change of temperature. It has been supposed 
 by some writers on physics that we may go further than 
 this, and state that augmentation of temperature is invari- 
 ably followed by augmentation of volume, and diminution 
 of temperature by diminution of volume, the exceptions 
 of water ^ as well as of bismuth and of the casting-metals 
 
 ^ Water follows the general rule, and continues to contract in bulk 
 as its temperature is lowered, till it reaches about 39° Fahrenheit or 4^ 
 Centigrade, when it begins to expand, and continues to do so till after its 
 conversion into ice, so that a given weight of water at the temperature 
 (say) of 37°, or when frozen, occupies more space than it occupied at 
 (say) the temperature of 40°. This anomaly is somewhat boldly ex- 
 plained by Sir W. Grove as due to the setting in of the process of crystal- 
 lization, which he supposes to begin at 39°, and to interfere with the 
 ordinary law of contraction and expansion. (See Grove's Correlation of 
 Physical Forces, fifth ed. p. 58, &c.) 
 
138 INDUCTIVE METHODS, 
 
 generally (which suddenly expand at the moment of 
 solidification) being explained as anomalies due to some 
 interfering cause. We are, however, at present so little 
 acquainted with the intimate constitution of bodies, that 
 it might be rash to state the proposition in this form, 
 and, stated as above, it is open to no exception ^ 
 
 The following example, which also illustrates the 
 caution necessary to be observed in framing a general 
 proposition, is extracted from Sir John Herschel's Dis- 
 course on the Study of Natural Philosophy ^^ : — 
 
 ' A great number of transparent substances, when exposed 
 in a certain particular manner, to a beam of light which has 
 
 ^ I adduce this as an example of the Method of Agreement rather 
 than of the Method of Concomitant Variations, because the argument, 
 as here stated, rests rather upon the variation of circumstances and the 
 great diversity of bodies in which the law is foimd to hold good, than 
 upon the relation between the various degrees of expansion or contraction 
 and the various degrees of temperature in the same body. Had the stress 
 been laid upon the latter consideration, the argument would undoubtedly 
 have been an instance of the Method of Concomitant Variations. 
 
 It frequently happens, in fact, that two or more Methods are com- 
 bined in the same proof. In the present instance, as will be seen below, 
 the argument as applied to each particular kind of body (mercury, for 
 instance) is an argument based on the Method of Concomitant Varia- 
 tions ; but when we proceed to extend the experiment to other bodies, 
 and then argue from the variety of the bodies examined that a body, in 
 passing from one degree of temperature to another, invariably undergoes 
 a change of volume, it appears to me that we are no longer employing 
 the Method of Concomitant Variations but the Method of Agreement. 
 It must be borne in mind that the object of our enquiry is not strictly 
 the effects of heat (for the total effects of heat, inasmuch as we cannot 
 wholly exhaust any body of its heat, must be unknown to us), but the 
 effects of a change of temperature. ^ ^'^ § 90. 
 
METHOD OF AGREEMENT. 1 39 
 
 been prepared by undergoing certain reflexions or refractions 
 (and has thereby acquired peculiar properties, and is said 
 to be *^ polarized ")j exhibit very vivid and beautiful colours, 
 disposed in streaks, bands, &c. of great regularity, which seem 
 to arise within the substance, and which, from a certain 
 regular succession observed in their appearance, are called 
 "periodical colours." Among the substances which exhibit 
 these periodical colours occur a great variety of transparent 
 solids, but no fluids and no opaque solids. Here, then, there 
 seems to be sufficient community of nature to enable us to 
 use a general term, and to state the proposition as a law, 
 viz. transparent solids exhibit periodical colours by exposure 
 to polarized light. However, this, though true of many, does 
 not apply to all transparent solids, and therefore we cannot 
 state it as a general truth or law of nature in this form; 
 although the reverse proposition, that all solids which exhibit 
 such colours in such circumstances are transparent, would 
 be correct and general. It becomes necessary, then, to make 
 a - list of those to which it does apply ; and thus a great 
 number of substances of all kinds become grouped together 
 in a class linked by this common property. If we examine 
 the individuals of this group, we find among them the utmost 
 variety of colour, texture, weight, hardness, form, and com- 
 position ; so that, in these respects, we seem to have fallen 
 upon an assemblage of contraries. But when we come to 
 examine them closely in all their properties, we find they have 
 all one point of agreement, in the property of double refrac- 
 tion, and therefore we may describe them all truly as doubly 
 refracting substances. We may, therefore, state the fact in 
 the form, " Doubly refracting substances exhibit periodical 
 colours by exposure to polarized light;" and in this form 
 it is found, on further examination, to be true, not only for 
 those particular instances which we had in view when we 
 first propounded it, but in all cases which have since occurred 
 on further enquiry, without a single exception ; so that the 
 
140 INDUCTIVE METHODS. 
 
 proposition is general, and entitled to be regarded as a law 
 of nature.' 
 
 The experiments by which Dr. Wells ^^ established his 
 Theory of Dew afford a remarkable example of the 
 Method of Agreement. By employing various objects 
 of different material under a variety of circumstances, 
 he showed that, whatever the texture of the object, the 
 state of the atmosphere, &c., it is an invariable condition 
 of the deposition of dew that the object on which it is 
 deposited shall be colder than the surrounding atmo- 
 sphere, the greater coldness of the object being itself 
 produced by the radiation of heat from its surface. This, 
 to quote the words of Sir John Herschel, is the case not 
 only with * nocturnal dew,' but with ^ the analogous phe- 
 nomena ' of ' the moisture which bedews a cold metal or 
 stone when we breathe upon it ; that which appears on 
 a glass of water fresh from the well in hot weather ; that 
 which appears on the inside of windows when sudden 
 rain or hail chills the external air ; that which runs down 
 our walls when, after a long frost, a warm moist thaw 
 comes on.' 
 |lt is by the Method of Agreement that we discover the 
 
 ^* Dr. Wells' Memoir on the Theory of Dew, which had become very 
 scarce, was reprinted by Longmans and Co. in 1866. It is very brief, 
 and well deserves to be carefully read by every student of scientific 
 method. Sir John Herschel {Natural Philosophy, § 168) speaks of the 
 speculation as ' one of the most beautiful specimens ' he can call to mind 
 * of inductive experimental enquiry lying within a moderate compass.' 
 Mr. Mill also employs it as one of his Miscellaneous Examples in Bk. III. 
 ch. ix. of his Logic. 
 
METHOD OF AGREEMENT, ^ /4I 
 
 > ■ '/ \ 
 
 symptoms of a disease, the signs of a politifcol r^iflu^on, ''5^ 
 
 national characteristics, the order of superposition anx^itjg 
 
 geological strata, grammatical rules, and the like. . /y> 
 
 The first division of Bacon's instantice solitaricB coih^ ' 
 cides with the cases contemplated in the Method of n^ 
 Agreement, as the second coincides with the cases con- 
 templated in the Method of Difference. The example 
 employed in the first is so remarkable both in itself, and 
 as an anticipation of Newton's Speculations on Colour, 
 that we may adduce it as an additional instance of the 
 Method of Agreement : — 
 
 * Exempli gratia : si fiat inquisitio de natura colons, 
 instaniicB solitarice sunt prismata, gemmae crystallinse, quae 
 reddunt colores, non solum in se, sed exterius supra 
 parietem. Item rores, &c. Istae enim nil habent com- 
 mune cum coloribus fixis in floribus, gemmis coloratis, 
 metallis, lignis, &c. praeter ipsum colorem. Unde facile 
 colligitur, quod color nil aliud sit quam modificatio ima- 
 ginis lucis immissae et receptae : in priore genere, per 
 gradus diversos incidentiae ; in posteriore, per texturas et 
 schematismos varios Corporis. Istae autem instantice sunt 
 solitarice quatenus ad similitudinem ^^.' 
 
 In attempting to ascertain the cause of a given effect, 
 a, it may happen that we find a particular antecedent, 
 A, frequently, but not invariably, accompanying it. If, 
 in those cases which present both a and A, no other 
 common circumstance can be detected, we may infer 
 that A is probably a cause of a. We say * a cause/ for 
 
 " Novum OrgafiujUy Lib. II. aph. xxii. 
 
J^T, INDUCTIVE METHODS. 
 
 the fact that a may be present without A is a proof that 
 A is not the only cause. Our meaning will be plain from 
 the following example : — 
 
 We compare instances in which bodies are known to 
 assume a crystalline structure, but which have no other 
 point of agreement; in the great majority of instances, 
 though not in all, we find that these bodies have assumed 
 their crystalline structure during the process of solidifica- 
 tion from a fluid state, either gaseous or liquid, and, 
 so far as we can ascertain, these cases have no other 
 circumstance in common. From this it may be reason- 
 ably inferred that the passage from a fluid to a solid 
 state is a cause, though not the only cause, of crystal- 
 lization ^^. 
 
 Again, when A is frequently, though not invariably, 
 followed by a, and there is, so far as we can ascertain, 
 no other common antecedent, we are justified in sus- 
 pecting that A is a cause of a, and that, in the cases 
 where a does not occur, the operation of A is counter- 
 acted by some other cause. If, for example, a certain 
 occupation or mode of living is found to be usually, 
 though not invariably, attended by a particular form of 
 
 '^ This example is adopted, with considerable modifications, from one 
 which occurs in Mr. Mill's Logic, Bk. III. ch. viii. § I. I am indebted 
 to Sir John Herschel for pointing out to me that Mr. Mill's example 
 (which I had originally adopted as it stood) is too broadly stated. * The 
 solidification of a substance from a liquid [it should be fluid] state' is not 
 * an invariable,' but only an usual ' antecedent of its crystallization.' The 
 reader will find several exceptions noticed in Watts' Dictionary of 
 Chemistry, art. Crystallization. 
 
METHOD OF AGREEMENT. I43 
 
 disease, we seem to be justified in regarding this occupa- 
 tion or mode of living as a cause of the disease, and 
 in explaining the few cases in which the disease does 
 not occur as due to exceptional and counteracting 
 circumstances. 
 
 Similarly, when a and b are found in frequent, though 
 not invariable, conjunction ^*, and, in the cases where they 
 are found together, there occurs, so far as we can ascer- 
 tain, no other common circumstance, we are justified in 
 suspecting that there exists some causal connection 
 between them. 
 
 The student who is acquainted with the science of 
 Medicine, will find a good illustration of the extreme 
 difficulty attending the application of the Method of 
 
 ^* The invariable conjunction of two phenomena, when the presence 
 of the one implies the presence of the other, and the absence of the one 
 the absence of the other, is a case falling under the Double Method of 
 Agreement, to be explained presently ; but those cases in which we 
 simply know that a given phenomenon is invariably preceded or in- 
 variably followed by another, fall under the Method of Agreement just 
 discussed. If a given phenomenon is, so far as we know, invariably 
 preceded by another, this fact justifies us in suspecting (though it does 
 not prove) that the antecedent is not only a cause, but the only cause, 
 of the given phenomenon. Such a conclusion can only be proved (even 
 approximately) by the Double Method of Agreement. It is, how- 
 ever, as already pointed out, not in the invariableness of the conjunc- 
 tion, but in the fact that the instances examined present, so far as 
 we can ascertain, only two phenomena in common, that the cogency of 
 the Method of Agreement consists. But of this fact invariableness of 
 antecedence (or of consequence) furnishes one of the strongest proofs, 
 inasmuch as such invariableness implies a very wide variation of 
 circumstances; hence the stress laid upon it in some of the examples 
 adduced above. 
 
144 INDUCTIVE METHODS. 
 
 Agreement, as well as of the Joint Method of Agreement 
 and Difference (to be noticed presently), in the disputes 
 which still occur as to the cause of the mental disease 
 which is known as Atactic Aphasia, that is, the condition 
 in which, with reference to certain sounds, the patient has 
 lost the power of co-ordinating the muscles of speech. 
 The French physiologist, M. Broca, laid down the posi- 
 tion that this disease is invariably due to a lesion of the 
 third frontal convolution of the left hemisphere of the 
 brain, the disease being invariably attended by the specific 
 lesion, and the lesion never occurring without the disease. 
 His followers maintain that the instances are decisive in 
 favour of this theory, while the apparent exceptions admit 
 of a satisfactory explanation; his opponents, on the 
 other hand, assert that there are well-established cases 
 both of atactic aphasia without the specific lesion, and 
 of the lesion without aphasia ^^. 
 
 METHOD OF DIFFERENCE. 
 CANON. 
 
 f' If an instance m which the phenomenon under investi- 
 \gation occurSj and an instance in ivhich it does not occur ^ 
 
 *5 See a paper by Dr. William Ogle in the St. George's Hospital Reports, 
 vol. ii. ; a Pamphlet by Dr. Frederic Bateman of Norwich, published by 
 J. E. Adlard, Bartholomew Close, London, 1868 ; Dr. Reynolds' System 
 of Medicine, vol. ii. pp. 442-444 ; and various reports of discussions 
 published in the Lancet and other medical journals. I have to thank 
 my friends, Professors Acland and RoUeston, for their kindness in supply- 
 ing me with information on this interesting subject, and regret that my 
 *space prevents me from pursuing it at greater length. , .. -. > ^ 
 
METHOD OF DIFFERENCE. 1 45 
 
 /lave every circumstance in common save one, that one oc- 
 \curring only in the former ; the circumstance in which 
 \atone the two instances differ ^ is the effect, or cause, or a 
 \iecessary part of the cause, of the phenomenon, 
 
 I The circumstances a, b, c are found in conjunction 
 kvith d, e, f, and the ormlsion or disappearance of the cir- 
 cumstance a is found to be attended by the disappearance 
 of the circumstance d. It is inferred that a and d are 
 so connected that one is cause (or a necessary part of 
 the cause) and the other effect. If, moreover, it can 
 be ascertained that a is the antecedent and d the con- 
 sequent, or that, though there are instances in which d 
 occurs without a, there are no instances in which a occurs 
 without d, we may proceed to infer (in the latter case, on 
 the ground that a phenomenon may have more than one 
 cause, but that a cause, unless counteracted by some other 
 cause, must be attended by its effect) that a is the cause, 
 Vaud— d-JJi£_^ffect. Similarly, if the circumstances a, b, c 
 are found in conjunction with d, e, f, and the introduction 
 of the circumstance x into the former set of phenomena 
 is found to be attended by the appearance of the cir- 
 cumstance y in the latter set of phenomena (so that they 
 may be represented respectively as a, b, c, x ; d, e, f, y), 
 it may be inferred that x and y are related as cause 
 and effect; or, if x be the antecedent and y the con- 
 sequent, or the appearance of x be invariably attended 
 by the appearance of y while the appearance of y is 
 not invariably attended by the appearance of x, that x 
 
146 INDUCTIVE METHODS. 
 
 is the cause and y the effect. The reasons on which 
 the Canon rests are obvious. All other circumstances 
 remaining the same, if the introduction or omission of 
 any circumstance be followed by a change in the remain- 
 ing circumstances, that change must be due to such 
 introduction or omission, as an effect to a cause; or, 
 if two new circumstances enter simultaneously, without 
 producing any other change in the phenomenon, these 
 two circumstances (except on the improbable suppo- 
 sition that they are two causes exactly counteracting each 
 other) must be related as cause and effect, though we 
 may be unable to say which of the two is cause and 
 which effect. ' The Metho d of Agreement / says Mr. 
 Mill, 'sta nds on the ground that whatever can be e li- 
 min ated, is not connected with the phenomenon by anv 
 law. The Method of Difference has for its fo undation 
 that w hatever can not be elimjnated, is conne cted with,,^ 
 t he.4Ji^apmenon by a law.' In the Method of Differ- 
 ence, the instances agree in everything, except in the 
 possession of two circumstances which are present in 
 the one instance and absent in the other. In the Method 
 of Agreement, the various instances compared (for here 
 w^e generally require more than two instances) agree in 
 nothing, except in the possession of two circumstances 
 which are common to all the instances. One Method 
 is called the Method of Agreement, because we compare 
 vari ous instances to see in what they agree ; the oth er 
 is called the Method of Difference, because we c ompare 
 an instance in which the phenomenon occur s with 
 
METHOD OF DIFFERENCE, I47 
 
 a nother in which it ^ne.fi not nrrnr^ in r\rr\ f\ r fn no in 
 
 what they differ. 
 
 Instances of the Method of Difference are not far 
 to seek. A piece of paper is thrown into a stove: we 
 
 /have no hesitation in regarding its apparent consumption 
 as the effect of the heat of the fire, for we feel assured 
 that the sudden increase of temperature is the only new 
 circumstance to which the piece of paper is exposed, and 
 that, therefore, any change in the condition of the paper 
 
 ^jmiTfttir^^ (]\W, \(ljhc^t cause. A bullet is fired from a gun, 
 or a dose of prussic acid is administered, and an animal 
 instantly falls down dead. There is no hesitation in 
 ascribing the death to the gun-shot wound or the dose 
 of poison. Nor is this confidence the effect of any 
 wide experience, for, if it were the first time that we 
 had seen a gun fired or a dose of poison administered, 
 we should have no hesitation in ascribing the altered 
 condition of the animal to this novel cause ; we should 
 know that there was only one new circumstance operating 
 upon it, and, consequently, that any change in its con- 
 dition must be due to that one circumstance. In rH these 
 instance s, there is the introduction of a new antecede nt. 
 X, to -which^the new consequent, y, must be due,,. Bul;^ 
 if thfi ^omission of one circumstanc e b^ attended by thp 
 oniis§i Qn of another, we may argue with equal confidence . 
 I withdraw my hand from this book which is resting 
 upon it, and the book instantly falls to the ground ; there 
 is no hesitation in referring the altered position of the 
 
 'boQjL tothe ^ithd r^w^^ of my gii j:Lport, A man is 
 
 L 2 
 
148 INDUCTIVE METHODS, 
 
 deprived of food, and he dies ; we have no hesitation in 
 ascribing the disappearance of the phenomenon we call 
 life to the withdrawal of the means by which it is main- 
 tained. In these instances, we have certain antece- 
 dents, followed by certain consequents, and, observing the 
 simultaneous or successive disappearance of A and a, 
 we have no hesitation in connecting the two as cause and 
 effect. 
 
 All cruc ial i nstances (instantiae ^^ crucis, as they are 
 
 called by Bacon) a re applications of the Method of . Ldf- 
 
 feren( ; e. A crucial instance is some observ? \tinp or ex- 
 
 peri iyient w hich enable s us at once to decide be tween two 
 
 r rn o^^ n yal hypotheses. It will be familiar to every one 
 
 the form of the chefuical test, as where we apply an 
 
 ^^ ' Inter praerogativas instantiarum ponemus loco decimo quarto in- 
 stantias crucis ; translato vocabulo a crucibus, quae, erectae in biviis, indi- 
 cant et signant viarum separationes. Has etiam instantias decisorias, et 
 judicialeSf et in casibus nonnuUis instantias oraculi, et mandati, appellare 
 consuevimus. Earum ratio talis est. Cum in inquisitione naturae alicujus, 
 intellectus ponitur tanquam in aequilibrio, ut incertus sit, utri naturarum 
 e duabus, vel quandoque pluribus, causa naturae inquisitae attribui aut 
 assignari debeat, propter complurium naturarum concursum frequentem 
 et ordinarium ; instantice crucis ostendunt consortium unins ex naturis 
 (quoad naturam inquisitam) fidum et indissolubile, alterius autem varium 
 et separabile ; unde terminatur quaestio, et recipitur natura ilia prior pro 
 causa, missa altera et repudiata. Itaque hujusmodi instantiae sunt max- 
 imae lucis, et quasi magnae auctoritatis ; ita ut curriculum interpretationis 
 quandoque in illas desinat, et per illas perficiatur. Interdum autem 
 instanticB crucis illae occurrunt et inveniuntur inter jampridem notatas ; 
 at ut plurimum novae sunt, et de industria atque ex composito quaesitae 
 et applicatae.et diligentia sedula et acri tandem erutae.* — Novum OrganutUy 
 Lib. II, aph. xxxvi. 
 
METHOD OF DIFFERENCE. 1 49 
 
 acid for the purpose of determining the character of 
 a metal, or a metal for the purpose of detecting latent 
 poison. According to the metaphor, there are two or 
 more ways before us, and the observation or experiment 
 acts as a ' guide-post ' (crux) in determining us which to 
 take. The following beautiful example of a Crucial 
 Instance is borrowed from Sir John Herschel ^''. 
 
 ' A curious example is given by M. Fresnel, as decisive, 
 in his mind, of the question between the two great opinions 
 on the nature of light, which, since the time of Newton 
 and Huyghens, have divided philosophers ; ' — that is, be- 
 tween what is called ' the emission theory,' according to 
 which light consists of actual particles emitted from lumir 
 nous bodies, and what is called * the undulatory theory,' 
 according to which light consists in the vibrations of an 
 elastic medium pervading all space. 
 
 'When two very clean glasses are laid one on the other, 
 if they be not perfectly flat, but one or both in an almost im- 
 perceptible degree convex or prominent, beautiful and vivid 
 colours will be seen between them ; and if these be viewed 
 through a red glass, their appearance will be that of alternate 
 dark and bright stripes. These stripes are formed bet^veen 
 the two surfaces in apparent contact, as any one may satisfy 
 himself by using, instead of a flat plate of glass for the upper 
 one, a triangular-shaped piece, called a prism, like a three- 
 cornered stick, and looking through the inclined side of it 
 next the eye, by which arrangement the reflection of light 
 from the upper surface is prevented from intermixing with 
 that from the surfaces in contact. Now, the coloured stripes 
 thus produced are explicable on both theories, and are appealed 
 
 " Discourse on the Study of Natural Philosophy, § 218. 
 
150 INDUCTIVE METHODS, 
 
 to by both as strong confirmatory facts ; but there is a dif- 
 ference in one circumstance according as one or the other 
 theory is employed to explain them. In the case of the 
 Huyghenian doctrine, the intervals between the bright stripes 
 ought to appear absolutely black ; in the other, half bright, 
 when so viewed through a prism. This curious case of dif- 
 ference was tried as soon as the opposing consequences of 
 the two theories were noted by M. Fresnel, and the re- 
 sult is stated by him to be decisive in favour of that theory 
 which makes light to consist in the vibrations of an elastic 
 medium ^^.' 
 
 The following is an example of a similar kind. It 
 had been determined, from theoretical considerations, 
 that, on the assumption of the undulatory theory, the 
 velocity of light must be less in the more highly refracting 
 medium, while, according to the emission theory, it ought 
 to be greater. When M. Foucault had invented his 
 apparatus for determining the velocity of light, it became 
 possible to submit the question to direct experiment; 
 and it was estabhshed by M. Fizeau that the velocity 
 of light is less in water (the more highly refracting 
 medium) than in air, in the inverse proportion of the 
 refractive indices. The result is, therefore, decisive in 
 
 ^® Mr. Mill {Logicy Bk. III. ch. xiv. § 6) maintains that it does not 
 follow from this experiment that ' the phenomena of light are results of 
 the laws of elastic fluids, but at most that they are governed by laws 
 partially identical with these.' But though the experiment may not be 
 decisive as in favour of the Undulatory Theory, it is undoubtedly de- 
 cisive as against the Emission Theory. It may be necessary to add that 
 the term ' fluids ' would now be repudiated by those who hold the 
 Undulatory Theory. 
 
METHOD OF DIFFERENCE. 151 
 
 favour of the undulatory, or at least, against the emission 
 theory ^^. 
 
 There is no science, perhaps, in which the Method 
 of Difference is so extensively used as the science of 
 Chemistry, and that because chemistry is emphatically a 
 science of experiment. Almost any chemical e2L|i£rim£nt 
 I will serve as an instance of the Method of Difference. 
 [Mix, for example, chloride of mercury with iodide of 
 /potassium, and the result will be a colourless liquid at 
 (the top of the vessel with a briUiant red precipitate at 
 uhe bottom. There can be no hesitation in ascribing 
 this result to the mixture of the two liq uids ; and two 
 similar experiments will enable us to determine that the 
 chlorine has been set free from the mercury and united 
 with the potassium, which itself has been set free from 
 the iodine with which it was previously united, while 
 the iodine has united with the mercury, the former pro- 
 ducing chloride of potassium (dissolved in the colourless 
 liquid), the latter iodide of mercury (the red precipitate). 
 
 The science of Heat (or, as Dr. Whewell proposes to 
 call it, Thermotics) also furnishes excellent examples of 
 the Method of Difference. The following instances are 
 adapted from Professor Tyndall's Heat a Mode of 
 Motion'^''',— 
 
 * Here is a brass tube, four inches long, and of three- 
 quarters of an inch interior diameter. It is stopped at the 
 
 ^ See Lloyd's Wave Theory of Light, Art. 37 ; Ganot's Physics, 
 English translation, third edition, Art. 436. 
 20 Third Edition, ch. i. §§ 14-16. 
 
15^ INDUCTIVE METHODS, 
 
 bottom, and screwed on to a whirling table, by means of 
 which the upright tube can be caused to rotate very rapidly. 
 These two pieces of oak are united by a hinge, in which are 
 two semicircular grooves, intended to embrace the brass tube. 
 Thus the pieces of wood form a kind of tongs, the gentle 
 squeezing of which produces friction when the tube rotates. 
 I partially fill the tube with cold water, stop it with a cork 
 to prevent the splashing out of the liquid, and now put the 
 machine in motion. As the action continues, the temperature 
 of the water rises, and now the tube is too hot to be held in 
 the fingers. Continuing the action a little longer, the cork 
 is driven out with explosive violence, the steam which follows 
 it producing by its precipitation a small cloud in the atmo- 
 sphere.* 
 
 In this experiment it will be noticed that only one new 
 antecedent is introduced, namely the motion of the ma- 
 chine ; hence the increased temperature of the water and 
 the various effects which follow upon it are due to the 
 motion as a cause. The experiment, then, shows that 
 heat is generated by the action of mechanical force. 
 
 The converse of this proposition, namely that heat is 
 consumed in mechanical work, or, as it is often stated, 
 transmuted into mechanical energy, is proved by the two 
 next experiments. 
 
 * This strong vessel is filled at the present moment with 
 compressed air. It has lain here for some hours, so that the 
 temperature of the air within the vessel is now the same as 
 that of the air of the room without it. At the present mo- 
 ment this inner air is pressing against the sides of the vessel, 
 and if this cock be opened a portion of the air will rush 
 violently out. The word " rush," however, but vaguely ex- 
 presses the true state of things ; the air which issues is driven 
 
METHOD OF DIFFERENCE. 1 53 
 
 out by the air behind it ; this latter accomplishes the work of 
 urging forward the stream of air. And what will be the con- 
 dition of the (wording air during this process ? It will be 
 chilled. The air executes work, and the only agent it can 
 call upon to perform the work is the heat to which the elastic 
 force with which it presses against the sides of the vessel is 
 entirely due. A portion of this heat will be consumed, and 
 a lowering of temperature will be the consequence. Observe 
 the experiment. I will turn the cock, and allow the current 
 of air from the vessel to strike against the face of the pile^\ 
 The magnetic needle instantly responds ; its red end is driven 
 towards me, thus declaring that the pile has been chilled by 
 the current of air.' 
 
 * Here moreover is a bottle of soda-water, slightly warmer 
 than the pile, as you see by the deflection it produces. Cut 
 the string which holds it, the cork is driven out by the elastic 
 force of the carbonic acid gas; the gas performs work, in so 
 doing it consumes heat, and now the deflection produced by 
 the bottle is that of cold.' 
 
 The last experiment furnishes a good instance of the 
 extreme simplicity of the examples by which scientific 
 truths may often be illustrated. 
 
 The uncertainty which, as we have seen, always at- 
 taches to conclusions arrived at by the Method of 
 ' Agreement renders it desirable that they should, wherever 
 it is possible, be confirmed by an application of the 
 Method of Difference. A beautiful instance of such a 
 confirmation is adduced by Mr. Mill in the case of 
 
 ^^ That is the thermo-electric pile, a delicate instrument for indicating 
 very small changes of temperature. It is by means of this instrument 
 that it has recently been shown that we receive heat (though, of course, 
 in infinitesimal quantities) from the moon's rays. 
 
154 INDUCTIVE METHODS, 
 
 Crystallization. The Method of Agreement has already 
 led us to the conclusion that the solidification of a sub- 
 stance from a fluid state is a very frequent antecedent 
 of its crystallization, and consequently, in all probability, 
 one, at least, of its causes. But the Method of Difference 
 completes the evidence, and enables us to state positively 
 that it is a cause. 
 
 * For in this case we are able, after detecting the antece- 
 dent A, to produce it artificially, and by finding that a follows 
 it, verify the result of our induction. The importance of 
 thus reversing the proof was never more strikingly manifested 
 than when, by keeping a phial of water charged with siliceous 
 particles undisturbed for years, a chemist (I believe Dr. Wol- 
 laston) succeeded in obtaining crystals of quartz; and in 
 the equally interesting experiment in which Sir James Hall 
 produced artificial marble, by the cooling of its materials 
 from fusion under immense pressure : two admirable ex- 
 amples of the light which may be thrown upon the most 
 secret processes of nature by well-contrived interrogation 
 of her^^.' 
 
 It will be noticed that the Method o f Difference i s 
 s pecially adapted to the discovery of the effects of given 
 ca uses, whereas , where it is our object to discov er the 
 ca use of a given effect, we are generally compelled to 
 have recourse to the Method of Agreement . The 
 Method of Agreement is, in fact, mainly a Method of 
 
 ^"^ Mill's Logic y Bk. III. ch. viii. § i. I have been obliged, in accord- 
 ance with what has been said on p. 142, to state, with considerable 
 modifications, the conclusion in this instance as arrived at by the Method 
 of Agreement. The account of the application to it of the Method of 
 Difference has been stated in Mr. Mill's own words. 
 
METHOD OF DIFFERENCE. 1 55 
 
 Observation, whereas the Meth od of Difference is main ly 
 a M^ tJiod of Experiment. We may indeed arrange the ^ 
 conditions of an experiment so as to satisfy the require- 
 ments of the Method of Agreement, and Nature may 
 (as in the familiar case of lightning) herself satisfy the 
 requirements of the Method of Difference, but, as a rule, 
 it will be found that arguments based on observations 
 fall under the former, and arguments based on experi- 
 ments under the latter Method. It is hardly necessary 
 to add that, wherever we have ^"r rhoirp b^twp^^n tht^ 
 two, methods, we should invariably select t,hft Method 
 of DifTerPDce. 
 
 I n the emp loym ent of the Method of Difference^ the 
 gre atest care shoul d b <" tal^ e" ^<^ introdnre only one new 
 
 can-^in fluence the result. As the whole forr e of the 
 ar g ument bnse d on this Method depends on the assump- 
 tion that any rhangp w hich takcs placc in the phe aomer, 
 non is due to the anJ^cedenLthea and there introduredj 
 it is plainthatwje can place no reliance. Qa^aur..aQiiciusion 
 unless we feel perfectly assured that no other antecedent 
 
 has intervened. If, for instance, it is our object to 
 
 ascertain the temperature of the atmosphere, we must 
 take the greatest care that our thermometer is not affected 
 by the heat radiated from or conducted by other bodies. 
 The most curious examples of the disregard of this 
 caution may be found in the History of Medicine. 
 Something perfectly inert has been administered to a 
 patient in combination with some powerful drug, some 
 
15$ INDUCTIVE METHODS. 
 
 important alterations in his diet, or some strict regime ; 
 then the effects of the drug, diet, or regime have been 
 unwittingly ascribed to the inert substance. Had the 
 ancients recognised that. instead of one cause acting on 
 falling bodies, as appeared to them to be the case, there 
 were really two, the action of gravity tending downwards 
 and the resistance of the atmosphere pressing upwards, 
 they could never have fallen into the gross error of 
 supposing that bodies fall in times inversely proportional 
 to their weights. 
 
 DOUBLE METHOD OF AGREEMENT. 
 
 CANON. 
 
 If two or more instances in which the phenomenon occurs 
 have only one other circumstance in co7nmon^ while two or 
 more instances, falling within the same department of in- 
 vestigation'^^, from which* the phefiomenon is absent have 
 ^j^hing in common save the absence of that circumstance ; 
 
 ^ In this edition I have inserted in the statement of the Canon the 
 words ' falling within the same department of investigation,' because, as 
 has been pointed out to me, the student might otherwise not see that, 
 for the purposes of comparison, the positive and negative instances must 
 be in pari materia. Thus, if the subject of enquiry is language, the 
 negative as well as the positive instances must be sought in the depart- 
 ment of language ; or, if the subject of enquiry liesj within the sphere of 
 morals, or of physical forces, or of living organisms, the negative as well 
 as the positive instances must be sought within those respective depart- 
 ments. Practically, however, there is no occasion for definite rules on 
 this head, as the common-sense of the investigator is quite sufficient to 
 j^^ keep him within the limits of the enquiry. •«/ ^^.^^yt^JiAA'tiA^ 
 
DOUBLE METHOD OF AGREEMENT. . 1 57 
 
 //la/ circumstance is the effect^ or the cause, or a necessary 
 part of the cause, of the phe?iomenon. Moreover {supposing 
 
 e' requirements of the Method to be rigorously fulfilled), the 
 cumstance proved by the Method to be the cause is the only 
 ise of the phenomenon. 
 
 The uncertainty attaching; to^the Method of Agreement 
 may, even where it is impossible to have recourse to the 
 Method of Difference, be, to some-e xt o nt, r om cdiod by 
 the e mployment of what is called by Mr. Mill the Toint 
 Me thod of Agreement and P jfference ^ or the Tndirprt 
 Method of Difference. T his consists in a double employ- 
 , mentolthe-M^thod of Agreement and a comparison of 
 the results thus obtained, the comparison assimilating it 
 to the Method of Difference. We, first of all, compare 
 jcases in which the phenomenon occurs, and, so far as we ^ 
 :an ascertain, find them to agree in the possession of 
 )nly one other circumstance. But, though we may not 
 be justified in regarding this inference as certain, we may 
 increase our assurance by proceeding to compare cases 
 in which the phenomenon does not occur. If these 
 agree in nothing but the non-possession of the circum- 
 stance which the other cases agreed in possessing, we 
 have a set of negative instances agreeing in nothing but 
 the absence of the given phenomenon and the absence 
 of the aforesaid circumstance. The set of negative 
 instances may now be compared with the set of positive 
 linstances, and we may argue thus : The positive in- 
 Wnces agree in nothing but the presence of the given 
 
158 INDUCTIVE METHODS. 
 
 /phenomenon and this other circumstance, and the nega- 
 tive instances agree in nothing but the absence of the 
 given phenomenon and this other circumstance. Hence 
 we may regard it as a highly probable inference that 
 they are connected together as cause and effect. We 
 say * highly probable/ for, as we are not absolutely 
 certain that the conditions of the Method of Agreement 
 have been satisfied in the case of the positive instances, 
 so, from the extreme difficulty of proving a negative, 
 we must be still less certain that they have been satisfied 
 in the case of the negative instances. What (in addition 
 to another advantage, to be noticed presently) is gained 
 by the Method is a sort of double assurance, so far 
 as the assurance goes. If the one set of instances 
 agreed in nothing but the presence of the two circum- 
 stances, and if the other set of instances agreed in 
 nothing but the absence of the two circumstances, then 
 we should be able to infer, by the Method of Difference, 
 that the introduction of the given phenomenon (which 
 we will suppose to be the consequent) always follows 
 on the introduction of the other circumstance (which 
 we will suppose to be the antecedent), and, vice versd, 
 that the removal of the given phenomenon always follows 
 on the removal of the other circumstance, or, in other 
 words, that the given phenomenon is the effect and the 
 other circumstance the cause. 
 
 But this Method, supposing its conditions to be 
 rigorously satisfied, possesses one advantage peculiar to 
 itself. \V The Single Method of Agreement, as we have 
 
DOUBLE METHOD OF AGREEMENT, 1 59 
 
 seen, is always theoretically open to the objection arising 
 \ from Plurality of Causes, but this Method, if the set of 
 negative instances be perfect, is not only free from that 
 objection, but also sustains the conclusion that the in- 
 ferred cause is the only cause of the phenomenon in 
 question (or, in case we do not know which is ante- 
 cedent and which is consequent, that a and b are so 
 connected that one of them is the cause and the only 
 I cause of the other). ' In the joint method,' says Mr. 
 \ MilP*, *it is supposed not only that the instances in 
 I which a is ^ agree only in containing A, but also that the 
 \instances in which a is not^agree only in not containing 
 JA^ Now, if this be so, A must be not only the cause of 
 a, but the only possible cause : for if there were another, 
 as for example B, then in the instances in which a is not, 
 B must have been absent as well as A, and it would not 
 be true that these instances agree only in not containing 
 A/ It may be asked, then, if the negative branch of the 
 argument be so forcible, why should we employ the posi- 
 tive branch ? It is by means of the positive branch that 
 we are, as it were, put on the track of the one other cir- 
 cumstance in which the instances presenting the given 
 phenomenon agree, and by means of the negative branch 
 that we prove the accuracy of our conclusion. * It is 
 generally,' continues Mr. Mill, ' altogether impossible to 
 work the Method of Agreement by negative instances 
 without positive ones : it is so much more difficult to 
 exhaust the field of negation than that of affirmation.' 
 2* Mill's Logic, Bk. IIL ch. x. § 2, 
 
l6o INDUCTIVE METHODS, 
 
 It is plain that the conditions of the Joint Method can 
 only be rigorously fulfilled where there is an invariable 
 conjunction between two phenomena, so that the two 
 are (unless counteracting circumstances intervene^ always 
 present together and always absent together. For, if A 
 be the only cause of a, the effect a cannot be present 
 without the cause A, nor can the cause A be present 
 without being attended by the effect a. Hence, invariable 
 conjunction may be regarded as a sign that the con- 
 ditions of this Method are fulfilled, and it is from the 
 observation of such an invariable conjunction that the 
 argument frequently proceeds. In such cases, the number 
 of instances, both positive and negative, which have been 
 observed, is supposed to be so great and of such variety 
 as to have excluded all other common circumstances 
 except the presence or absence of the two phenomena 
 in question. 
 
 The_ Joint Method of Agreement and Difference (or, 
 the Indir ect Method of Difference, or, as I should prefer 
 to call it, the Double Method of Agreement) is b eing 
 contin udly employed by us in the ordinary affairs of life. 
 If, when I take a particular kind of food, I find that 
 I invariably suffer from some particular form of illness, 
 whereas, when I leave it off, I cease to suffer, I entertain 
 a double assurance that the food is the cause of my 
 illness. ^ have observed that a pertain pla ntj^jn^riably 
 
 / plentiful oiT ^ p AMimlai coil; if. with - ^wide exper ience^ 
 I fail to find it growing on any other soil, I feel con- 
 
 (firmed in my belief that there is in this particular soil 
 
DOUBLE METHOD OF AGREEMENT. l6l 
 
 Ene chemical constituent, or some peculiar combination 
 chemical constituents, which is highly favourable, if 
 t essential, to the growth of the plant. 
 Dr. Wells' Essay on the Theory of Dew presents an 
 extremely instructive instance of the application of the 
 Double Method of Agreement : — 
 
 ' It appears ' (I am here quoting from Mr. MilP^) * that the 
 instances in which much dew is deposited, which are very 
 various, agree in this, and, so far as we are able to observe, 
 in this only, that they either radiate heat rapidly or conduct 
 it slowly : qualities between which there is no other circum- 
 stance of agreement than that, by virtue of either, the body 
 tends to lose heat from the surface more rapidly than it can 
 be restored from withi^. The instances, on the contrary, 
 in which no dew, or but a small quantity of it, is formed, and 
 which are also extremely various, agree (as far as we can 
 observe) in nothing except in not having this same property. 
 We seem, therefore, to have detected the characteristic 
 difference between the substances on which dew is produced, 
 and those on which it is not produced. And thus have been 
 realized the requisitions of what we have termed the Indirect 
 Method of Difference, or the Joint Method of Agreement 
 and Difference,' 
 
 Several beautiful illustrations of the Joint Method of 
 Agreement and Difference may be found in the recent 
 discoveries made by means of Spectrum Analysis. We 
 shall select one which is peculiarly interesting on account 
 of its employment in the attempt to determine the con- 
 
 ^ Miirs Logic, Bk. III. ch. ix. § 3. 
 M 
 
l62 INDUCTIVE METHODS. 
 
 stitution of the sun and some of the other heavenly 
 bodies. 
 
 A ray of light proceeding from incandescent hydrogen 
 is passed through a prism, and it is invariably found that 
 in the spectrum thus obtained there are two bright lines 
 occupying precisely the same position. Moreover, rays 
 of white light proceeding from various incandescent sub- 
 stances are passed through incandescent hydrogen, and 
 the emergent light is then broken up by a prism. In 
 the spectra thus obtained it is found that there ^ are 
 invariably two dark (or, under certain circumstances, 
 bright ^^) Hues occupying exactly the same positions in 
 the spectrum as the lines above mentioned. Hence it is 
 inferred, by the Method of Agreement, that a ray of light, 
 whether it proceed directly from incandescent hydrogen 
 itself, or be transmitted through it from some other 
 incandescent substance, will invariably produce these two 
 lines. But, if we try the same experiments with any 
 other element than incandescent hydrogen, although we 
 may obtain bright or dark lines, we never find these 
 lines occupying the same positions in the spectrum as 
 the two lines in question. 
 y^ Here, then, we have the negative instances of the 
 
 2^ The darkness of the lines is due to the property possessed by incan- 
 descent media of absorbing rays of light of the same refrangibility as 
 those emitted by them. When the absorption exerted upon the trans- 
 mitted light is more than compensated by the luminosity of the hydrogen 
 light, these lines, instead of being dark, appear bright, as is also the 
 case when the ray of light proceeds directly from incandescent hydrogen 
 itself. 
 
DOUBLE METHOD OF AGREEMENT. 163 
 
 Double Method ; and it is inferred (subject, of course, to 
 the assumption that our knowledge of the negative in- 
 stances is sufficiently complete) that the presence in the 
 spectrum of these two lines is invariably due either to a 
 ray of light proceeding directly from incandescent hydro- 
 gen, or to a ray transmitted through it from some other 
 incandescent substance ; that is to say, that one or other 
 of these is the cause, and the only cause of the presence 
 in the spectrum of these two particular lines. When 
 these lines are bright, it is doubtful whether the rays 
 proceed directly from incandescent hydrogen or have 
 been transmitted through it, but, when they are dark, 
 the rays must have been transmitted. Wherever, there- 
 fore, two dark lines occupying these positions occur in 
 the spectrum we may infer (deductively) the passage 
 of the ray of light through a medium composed wholly 
 or partially of incandescent hydrogen. But we detect 
 such lines in the spectrum of the sun and several of 
 the stars, and hence (unless we suppose it possible or 
 not improbable that there is in the sun or other stars 
 some element agreeing in this respect with hydrogen, 
 but differing in others) we may conclude that the sun 
 and these other stars are surrounded with an atmo- 
 sphere of incandescent hydrogen 2"^. 
 
 ^ It must be understood that, in this example, I have not stated the 
 historical steps by which the discovery was arrived at, but simply 
 attempted to give a logical analysis of the arguments by which it would 
 now be established. It may be added that the lines in question are 
 known as C and F in the solar spectrum. It was the exact coincidence 
 M 2 
 
1 54 INDUCTIVE METHODS. 
 
 The following examples are selected from a subject of 
 a widely different character, the History of Language. 
 M. Auguste Brachet, in his Historical Grammar of the 
 French Tongue ^^, lays down that there are three sure tests 
 by which we can discriminate between popular words 
 derived from the Peasant Latin (lingua Latina rustica) 
 by a regular process, and Latin words of learned origin 
 imported into Modern French by scholars. These tests 
 are (i) the continuance of the tonic accent; (2) the sup- 
 pression of the short vowel; (3) the loss of the middle 
 or medial consonant. It will be seen that it is by the 
 employment of the Double Method of Agreement that 
 M. Brachet arrives at these conclusions. 
 
 ' Look at such words (i. e. words of popular origin) carefully, and you 
 will see that the syllable accented in Latin continues to be so in French ; 
 or, in other words, that the accent remains where it was in Latin. This 
 continuance of the accent is a general and absolute law : all words be- 
 longing to popular and real French respect the Latin accent : all such 
 words as portique from porticus, or viatique from vidticnm, which 
 break this law, will be found to be of learned origin, introduced into the 
 language at a later time by men who were ignorant of the laws which 
 nature had imposed on the transformation from Latin to French. We 
 may lay it down as an infallible law, that The Latin accent continues in 
 
 of the bright lines In the hydrogen spectrum with the dark lines C and 
 F in the solar spectrum, which first led to the belief that hydrogen enters 
 into the constitution of the solar atmosphere. It is now, however, ren- 
 dered possible, through an ingenious contrivance, to separate, as it were, 
 the solar atmosphere from the glowing body within it, and thus to obtain 
 these lines bright instead of dark. The student will find a brief account 
 of these discoveries in Professor Stokes' Address to the British Association 
 in 1869. 
 
 2® Mr. Kitchin's Translation, p. 32. 
 
DOUBLE METHOD OF AGREEMENT. 
 
 165 
 
 French in all words 0/ popular origin ; all words which violate this law 
 
 are of learned origin : thus- 
 
 - 
 
 
 LATIN. 
 
 POPULAR WORDS. 
 
 LEARNED WORDS. 
 
 Alumine 
 
 al&n 
 
 alumine 
 
 Angelas 
 
 dnge 
 
 angelh 
 
 Bldsphemum 
 
 blame 
 
 blaspheme 
 
 Cancer 
 
 chancre 
 
 cancer 
 
 C6mputum 
 
 cdmpte 
 
 comp{it 
 
 Debitum 
 
 dette 
 
 d^bit 
 
 D^cima 
 
 dime 
 
 decime. Sec. 
 
 ' We have seen that the tonic accent is a sure touchstone by which to 
 distinguish popular from learned words. There is another means, as 
 certain, by which to recognise the age and origin of words — the loss of . 
 the short vowel. Every Latin word, as we have said, is made up of one 
 accented vowel, and others not accented — one tonic and others atonic. 
 The tonic ahvays remains ; but of the atonies the short vowel, which 
 immediately precedes the tonic vowel, always disappears in French : 
 
 Bon(i)tdtem 
 
 San(i)tdtem 
 
 Pos(i)tiira 
 
 Clar(i)tdtem 
 
 Sep(ti)indna 
 
 Coin(i)tdtus 
 
 Pop(u)latus 
 
 bonte 
 sante 
 posture 
 clarte 
 
 semaine (O. Fr. sepmaine) 
 comte 
 peuple, &c. 
 
 * Words such as circuler, circuMre, which break this law and keep 
 the short vowel, are always of learned origin ; all words of popular origin 
 lose it, as cercler. This will be seen from the following examples : — 
 
 LATIN. POPXJLAR WORDS. LEARNED WORDS. 
 
 Ang(u)latus angle angule 
 
 Blasph(e)mdre blamer (0. Fr. blasmer) blasphemer 
 
 Cap(i)tdle cheptel capital 
 
 Car(i)t^tein cherte charite 
 
 Circ(u)ldre cercler circuler^ &c. 
 
1 65 INDUCTIVE METHODS, 
 
 * The third characteristic, serving to distinguish popular from learned 
 words, is the loss of the medial consonant, i. e. of the consonant which 
 stands between two vowels, like the t in matiirus. We will at once 
 give the law of this change : — All French words which drop the medial 
 consonant are popular in origin, while words of learned origin retain it. 
 Thus the Latin vocalis becomes, in popular French, voyelle, in learned 
 French, vocale. There are innumerable examples of this : as — 
 
 LATIN. 
 
 POPULAR WORDS. 
 
 LEARNED WORDS. 
 
 Au(g)Tistus 
 
 aoUt 
 
 auguste 
 
 Advo(c)atus 
 
 avoue 
 
 avocat 
 
 Anti(pli)6na 
 
 antienne 
 
 antiphone 
 
 Cre(d)entia 
 
 creance 
 
 credence 
 
 Communi(c)dre 
 
 communier 
 
 communiquer, &c. 
 
 The requisitions of the Double Method of Agree- 
 ment may be far from being rigorously fulfilled, and still 
 two phenomena may be so frequently present together 
 and so frequently absent together, that we may be justi- 
 fied in suspecting some causal connection between them. 
 Unless they were invariably absent together, as well as 
 invariably present, and unless they were the only cir- 
 cumstances which were invariably present and absent 
 together, we should not be justified in regarding one as 
 the cause, and the onfy cause, of the other ; but the mere 
 detection of the fact that they are frequently present and 
 absent together may justify us in believing that there 
 is between them some causal connection. The precise 
 character of this causal connection may hereafter be 
 determined by one of the other inductive methods, or 
 by bringing the case under a previous deduction. The 
 following instances will serve as illustrations of what has 
 been here said. 
 
DOUBLE METHOD OF AGREEMENT. 167 
 
 Sir John Herschel conceives that he has detected a 
 connection between a full moon and a calm night : * The 
 only effect distinctly connected with its [the moon s] 
 position with regard to the sun, which can be reckoned 
 upon with any degree of certainty, is its tendency to clear 
 the sky of cloud, and to produce not only a serene but a 
 calm night, when so near the full as to appear round to 
 the eye — a tendency of which we have assured ourselves 
 by long-continued and registered observation/ The pre- 
 cise nature of the causal connection can here be deter- 
 mined : ' The effect in question, so far as the clearance 
 of the sky is concerned, is traceable to a distinct physical 
 cause, the warmth radiated from its [the full moon's] 
 highly-heated surface ; though why the effect should 
 not continue for several nights after the full, remains 
 problematic ^^' 
 
 In this example, there is not, of course, an invariable 
 connection between the clear night and the full moon ; 
 for, in the determination of the weather, there are so 
 many and so various causes at work that they must 
 necessarily modify or counteract each other. The moon 
 might exercise considerable influence, might, as Sir John 
 Herschel says, have a tendency to produce a calm night 
 and still be overpowered by other influences. It is suffi- 
 cient, in order to lead us to suspect some causal connec- 
 tion between the two phenomena, that we should find a 
 calm night proportionably oftener, and oftener in a con- 
 siderable proportion, when there is a full moon than 
 
 2^ Herschel's Familiar Lectures on Scientific Subjects, pp. 146, 147. 
 
1 68 INDUCTIVE METHODS. 
 
 when there is not. Thus, suppose that, after a long 
 series of observations of nights when there is a full 
 moon, we find the proportion of calm nights to nights 
 which cannot be called calm to be as 5 to 2 (we are, of 
 course, taking an imaginary case), and the proportion on 
 ordinary nights to be as 3 to 2, there can be little doubt 
 that the full moon is, in some way or other, connected 
 with the larger proportion of calm nights. 
 
 The employment of the Double Method of Agreement 
 may lead to the detection of facts of causation in many 
 instances of a similar kind. Thus, suppose that, in a 
 particular part of the country, a particular wind is found 
 to be proportionably oftener attended with rain than 
 other winds, we begin to suspect that there is some 
 causal connection between rain and this wind, so that, 
 when the wind blows, we may expect rain, at least with 
 more confidence than when other winds blow ; and, if the 
 proportion in which rain accompanies this wind be much 
 greater than that in which it accompanies other winds, 
 our expectation is proportionably strengthened, and we 
 have no hesitation in speaking of the quarter from which 
 the wind blows as ' the rainy quarter/ In this case, the 
 cause is, of course, to be sought in the character of the 
 tract over which the wind blows. Similarly, if, after 
 sufficiently long observation, we find the death-rate in 
 some particular place decidedly larger than in the sur- 
 rounding neighbourhood, we have no hesitation in ascrib- 
 ing the fact to some peculiarity either in the place or the 
 population, and we at once begin to consider whether 
 
METHOD OF RESIDUES, 1 69 
 
 there is anything exceptional in the soil, the climate, the 
 habits or occupations of the people, and the Uke, which, 
 either alone or in conjunction with other circumstances, 
 would account for the phenomenon. 
 
 In all cases of this kind, we are, as it were, set on the 
 track of a cause by discovering that some phenomenon is 
 present in a proportionably greater number of instances 
 when some other phenomenon is present than when it is 
 absent. The cause itself may hereafter be detected either 
 by one of the other inductive methods, or by bringing the 
 case under a previous deduction. Thus, we know that 
 the surface of that part of the moon which we call * full ' 
 is highly heated, and that it is the tendency of warmth 
 radiated from a highly-heated surface to clear the atmo- 
 sphere. Hence the series of observed phenomena is, 
 in this case, accounted for by being brought deductively 
 under previous inductions. 
 
 METHOD OF RESIDUES. 
 
 CANON. ^-rvCt/VIA' 
 
 Subtract from any phenomenon such part as is known 
 to he the effect of certain antecedents^ and the residue of the 
 phenomenon is the effect of the remaining antecedents. 
 
 If the antecedents are A, B, C, D, and the complex 
 phenomenon can be resolved into the consequents a, jS, 
 7, S, 6, of which 7, S, 6 are ascertained by previous induc- 
 tions or deductions to be due to C, D, then the remain- 
 ing consequents a, /3 must be referred to the remaining 
 
170 INDUCTIVE METHODS. 
 
 antecedents A, B. Gi Yen that the total result is due to a 
 certain number of antecedents, and that part, of the result . 
 is due to a portion of those antecedents ; the r esidue 
 o f the result must necessarily be due to the re maining 
 anter g Hf^ptg . This rule appears so obvious as to be 
 hardly worth stating ; it has, however, as will be seen 
 from the examples given below, been mainly instrumental 
 in leading to many of the most important discoveries of 
 modern times. * It is by this process, in fact/ says Sir 
 John Herschel ^^, ' that science, in its present advanced 
 state, is chiefly promoted. Most of the phenomena which 
 nature presents are very complicated ; and when the 
 effects of all known causes are estimated with exactness, 
 and subducted, the residual facts are constantly appearing 
 in the form of phenomena altogether new, and leading 
 to the most important conclusions.' 
 
 T here is one difficulty connected with this Meth od. 
 
 of Residues included among the inductive methods ? The 
 MpfhoH^ it must be confessed, is strictly deductive, but, as 
 iHs~-g £nerallv applied to the result of previous ind uctions 
 and ^^e ner ally suggests subsequent inductions, it may 
 vi ndicate its claim to discussion in this place. It is by 
 induction that we ascertain that y, 5, e are due to C, D ; 
 by the Method of Residues we determine that the re- 
 maining consequents a, /S must be due to the remaining 
 antecedents A, B ; we then generally proceed to decide 
 by one of the other inductive methods which of the 
 
 ^® Discourse on the Study of Natural Philosophy, § 158. 
 
METHOD OF RESIDUES. I7I 
 
 remaining consequents is due to which of the remaining 
 antecedents. 
 
 The following are instances of the employment of the 
 Method of Residues, and it will be noticed that the 
 science of astronomy is peculiarly rich in ^such ex- 
 amples ^^ : — 
 
 *The planet Jupiter is attended by four satellites which 
 revolve round it in orbits very nearly circular, and whose 
 dimensions, forms, and situations with respect to that of the 
 planet itself are now perfectly well known. The periodical 
 times of their respective revolutions are also ascertained with 
 extreme precision, and all the particulars of their motions 
 have been investigated with extraordinary care and persever- 
 ance. The three interior of them are so near the planet, and 
 the planes of their orbits so little incHned to that in which it 
 revolves round the sun, that they pass through its shadow, 
 and therefore undergo eclipse, at every revolution. These 
 eclipses have been assiduously observed ever since the dis- 
 covery of the satellites, and their times of occurrence regis- 
 tered. As they afford a means of determining the longitudes 
 of places, the prediction beforehand of the exact times of their 
 occurrence becomes an object of great importance : and it is 
 evident enough that, all the particulars of their motions being 
 known (as well as of that of the planet itself, and therefore of 
 the size and situation of its shadow), there would be no diffi- 
 culty in making such prediction (starting from the time of 
 some one observed eclipse of each as an epoch) ; pro'vided always 
 
 ^^ In the former editions the acceleration (or diminution of the periodic 
 times) of Encke's comet (see Herschel's Discourse on the Study of Natural 
 Philosophy, § 159) was given as an example of residual phenomena. 
 The cause of this phenomenon is, however, so doubtful, that I have 
 thought it best to omit the instance in the present edition. 
 
172 INDUCTIVE METHODS. 
 
 each eclipse were seen at the identical moment ewhen it actually 
 happened. Moreover, on that supposition, the times recorded 
 of all the subsequent eclipses ought to agree with the times so 
 predicted. This, however, proved not to be the case. The 
 observed times were sometimes earlier, sometimes later than 
 the predicted ; not, however, capriciously, but according to 
 a regular law of increase and decrease in the amount of dis- 
 cordance, the difference either way increasing to a maximum, 
 — then diminishing, vanishing, and passing over to a maxi- 
 mum the other way, and the total amount of fluctuation to 
 and fro being about i6"i 27^. Soon after this discrepancy 
 between the predicted and observed times of eclipse was 
 noticed, it was suggested that such a disagreement would 
 necessarily arise if the transmission of light were not instan- 
 taneous. This suggestion was converted into a certainty by 
 Roemer, a Danish astronomer, who ascertained that they 
 always happened earlier than their calculated time when the 
 earth in the course of its annual revolution approached 
 nearest to Jupiter, and later when receding farthest : so that 
 in effect the extreme difference of the errors or total extent 
 of fluctuation — the 16™ 27s in question — is no other than the 
 time taken by light to travel over the diameter of the earth's 
 orbit, that being the extreme difference of the distances of 
 the two planets at different points of their respective revolu- 
 tions. At present, in our almanacs a due allowance of time 
 for the transmission of light at this rate, assuming a uniform 
 velocity, is made in the calculation of these eclipses ; and the 
 discrepancy in question between the observed and predicted 
 times has ceased to exist ^^.' 
 
 The circumstances which led to the discovery of the 
 planet Neptune furnish, perhaps, the most striking in- 
 stance of the employment of the Method of Residues. 
 From the year 1804 it had been noticed that the orbit 
 
 ^ Herschel's Familiar Lectures on Scientific Subjects, p. 226, &c. 
 
METHOD OF RES t DUES. 1 73 
 
 of the planet Uranus was subject to an amount of per- 
 turbation which could not be accounted for from the 
 influence of the known planets. 
 
 * Of the various hypotheses formed to account for it (the 
 perturbation), during the progress of its development, none 
 seemed to have any degree of rational probability but that of 
 the existence of an exterior, and hitherto undiscovered, planet, 
 disturbing, according to the received laws of planetary dis- 
 turbance, the motion of Uranus by its attraction, or rather 
 superposing its disturbance on those produced by Jupiter and 
 Saturn, the only two of the old planets which exercise any 
 sensible disturbing action on that planet. Accordingly, this 
 was the explanation which naturally, and almost of necessity, 
 suggested itself to those conversant with the planetary per- 
 turbations who considered the subject with any degree of 
 attention. The idea, however, of setting out from the ob- 
 served Anomalous deviations, and employing them as data 
 to ascertain the distance and situation of the unknown body, 
 or, in other words, to resolve the inverse problem of pertur- 
 bations, ^'gi'ven the disturbances to Jind the orbit ^ and place in 
 that orbit of the disturbing planet ^^ appears to have occurred 
 only to two mathematicians, Mr. Adams in England and 
 M. Leverrier in France, with sufficient distinctness and hope- 
 fulness of success to induce them to attempt its solution. 
 Both succeeded, and their solutions, arrived at with perfect 
 independence, and by each in entire ignorance of the other's 
 attempt, were found to agree in a surprising manner when 
 the nature and difficulty of the problem is considered; the 
 calculations of M. Leverrier assigning for the heliocentric 
 longitude of the disturbing planet for the 23rd Sept. 1846, 
 326° o', and those of Mr. Adams (brought to the same date) 
 329° 19', differing only 3° 19'; the plane of its orbit deviating 
 very slightly, if at all, from that of the ecliptic. 
 
 * On the day above mentioned — a day for ever memorable 
 
174 INDUCTIVE METHODS, 
 
 in the annals of astronomy — Dr. Galle, one of the astronomers 
 of the Royal Observatory at Berlin, received a letter from 
 M. Leverrier, announcing to him the result he had arrived 
 at, and requesting him to look for the disturbing planet in 
 or near the place assigned by his calculation. He did so, and 
 on that 'very night actually found it, A star of the eighth mag- 
 nitude was seen by him and by M. Encke in a situation where 
 no star was marked as existing in Dr. Bremiker's chart, then 
 recently published by the Berlin Academy. The next night 
 it was found to have moved from its place, and was therefore 
 assuredly a planet. Subsequent observations and calculations 
 have fully demonstrated this planet, to which the name of 
 Neptune has been assigned, to be really that body to whose 
 disturbing attraction, according to the Newtonian law of 
 gravity, the observed anomalies in the motion of Uranus were 
 owing ^^' 
 
 Besides furnishing an instance of the method of Residues, 
 the above example is also a happy illustration of th'e com- 
 bination of deduction with observation which has been 
 so eminently fertile in astronomical research. 
 
 * Almost all the greatest discoveries in astronomy have re- 
 sulted from the consideration of what we have elsewhere 
 termed residual phenomena, of a quantitative or numerical 
 kind, that is to say, of such portions of the numerical or 
 quantitative results of observation as remain outstanding and 
 unaccounted for after subducting and allowing for all that 
 would result from the strict application of known principles ^*. 
 
 ^3 Herschers Outlines of Astronomy, Fourth Edition, §§ 767, 768. 
 
 ^* A very striking example of the employment of the Method of Resi- 
 dues is to be found in the recent investigations by which Mr. Huggins 
 has shown that the slight deviation of the lines C and F in the spectrum 
 of Sirius is to be accounted for on the supposition that the solar system 
 and that star are mutually receding from each other at the rate of 29*4 
 
METHOD OF RESIDUES. 1/5 
 
 It was thus that the grand discovery of the precession of the 
 equinoxes resulted as a residual phenomenon, from the im- 
 perfect explanation of the return of the seasons by the return 
 of the sun to the same apparent place among the fixed stars. 
 Thus, also, aberration and nutation resulted as residual phe- 
 nomena from that portion of the changes of the apparent 
 places of the fixed stars which are left unaccounted for by 
 precession. And thus again the apparent proper motions of 
 the stars are the observed residues of their apparent move- 
 ments outstanding and unaccounted for by strict calculation 
 of the effects of precession, nutation, and aberration. The 
 nearest approach which human theories can make to per- 
 fection is to diminish this residue, this caput mortuum of 
 observation, as it may be considered, as much as practicable, 
 and, if possible, to reduce it to nothing, either by showing 
 that something has been neglected in our estimation of 
 known causes, or by reasoning upon it as a new fact, and on 
 the principle of the inductive philosophy ascending from the 
 effect to its cause or causes ^^.* 
 
 * Many of the new elements of chemistry have been 
 detected in the investigation of residual phenomena. Thus, 
 Arfwedson discovered lithia by perceiving an excess of (iveight 
 in the sulphate produced from a small portion of what he 
 considered as magnesia present in a mineral he had analysed. 
 It is on this principle, too, that the small concentrated residues 
 of great operations in the arts are almost sure to be the lurking 
 places of new chemical ingredients: witness iodine, brome, 
 selenium, and the new metals accompanying platina in the 
 experiments of Wollaston and Tennant. It was a happy 
 
 miles a second. A brief account of this speculation may be found in 
 Professor Stokes' Address before the British Association in 1869. 
 35 Herschel's Outlines of Astronomy, § 856. 
 
1/6 INDUCTIVE METHODS. 
 
 thought of Glauber to examine what everybody else threw 
 away ^^.' 
 
 * The unforeseen effects of 'changes in legislation, or of 
 improvements in the useful arts, may often be discerned by 
 the Method of Residues. In comparing statistical accounts, 
 for example, or other registers of facts, for a series of .years, 
 we perceive at a certain period an altered state of circum- 
 stances, which is unexplained by the ordinary course of 
 events, but which must have some cause. For this residuary 
 phenomenon, we seek an explanation until it is furnished by the 
 incidental operation of some collateral cause. For example, 
 on comparing the accounts of live cattle and sheep annually 
 sold in Smithfield market for some years past, it appears that 
 there is a large increase in cattle, while the sheep are nearly 
 stationary. The consumption of meat in London may be 
 presumed to have increased, at least in proportion to the 
 increase of its population; and there is no reason for sup- 
 posing that the consumption of beef has increased faster than 
 that of mutton. There is, therefore, a residuary pheno- 
 menon — viz. the stationary numbers of the sheep sold in 
 Smithfield — for which we have to find a cause. This cause is 
 the increased transport of dead meat to the metropolis, owing 
 to steam navigation and railways, and the greater convenience 
 of sending mutton than beef in a slaughtered state. 
 
 'Again; on comparing the consumption of wine with that of 
 spirits and beer in England during the last sixty years ^^, we 
 find that the former has remained stationary, while the latter 
 has undergone a great increase. The general causes, such as 
 increase of population and wealth, which have increased the 
 
 ^^ Herschel's D/scowrs« on the Study of Natural Philosophy ^ § i6r. 
 
 ^ This was written in 1852. Since that time, owing to the reduction 
 of the duties, the greater familiarity of Englishmen with foreign countries 
 and habits, and, perhaps, the taste for a more refined style of living, the 
 consumption of wine has enormously increased. 
 
METHOD OF RESIDUES. 177 
 
 consumption of spirits and beer, have not increased the con- 
 sumption of wine. For this residuary phenomenon, a special 
 cause must be sought ; and it may be found principally in the 
 alteration of habits among the upper classes with respect to 
 drinking ^^' 
 
 We shall conclude our instances with what Sir John 
 Herschel truly calls ^ a very elegant example,' the differ- 
 ence between the observed and calculated velocities of 
 sound. We quote from Professor Tyndall's Lectures 
 on Sound : — 
 
 '■ I now come to one of the most delicate points in the 
 whole theory of sound. The velocity through air has been 
 determined by direct experiment ; but knowing the elasticity 
 and density of the air, it is possible without any experiment 
 at all to calculate the velocity with which a sound-wave is 
 transmitted through it. Sir Isaac Newton made this cal- 
 culation, and found the velocity at the freezing temperature 
 to be 916 feet a second. This is about one-sixth less than 
 actual observation had proved the velocity to be, and the 
 most curious suppositions were made to account for the dis- 
 crepancy. Newton himself threw out the conjecture that it 
 was only in passing from particle to particle of the air that 
 sound required time for its transmission ; that it moved in- 
 stantaneously through the particles themsehes. He then sup- 
 posed the line along which sound passes to be occupied by 
 air-particles for one-sixth of its extent, and thus he sought to 
 make good the missing velocity. The very art and ingenuity 
 of this assumption were sufficient to ensure its rejection ; 
 other theories were therefore advanced, but the great French 
 mathematician Laplace was the first to completely solve the 
 
 ^* Sir George Cornewall Lewis on the Methods of Observation and 
 Reasoning in l^olitics, vol. i. p. 356. 
 
178 INDUCTIVE METHODS, 
 
 enigma. I shall now endeavour to make you thoroughly 
 acquainted with his solution. 
 
 * I hold in my hand a strong cylinder of glass, accurately 
 bored, and quite smooth within. Into this cylinder, which 
 is closed at the bottom, fits this air-tight piston. By pushing 
 the piston down, I condense the air beneath it ; and when I 
 do so heat is developed. Attaching a scrap of amadou to the 
 bottom of the piston, I can ignite it by the heat generated by 
 compression. Dipping a bit of cotton wool into bisulphide 
 of carbon, and attaching it to the piston, when the latter is 
 forced down, a flash of light, due to the ignition of the bisul- 
 phide of carbon vapour, is observed within the tube. It is 
 thus proved that when air is compressed, heat is generated. 
 By another experiment, I can show you that when air is rare- 
 fied, cold is developed. This brass box contains a quantity of 
 condensed air. I open the cock, and permit the air to dis- 
 charge itself against a suitable thermometer ; the sinking of 
 the instrument declares the chilling of the air. 
 
 * All that you have heard regarding the transmission of a 
 sonorous pulse through air, is, I trust, still fresh in your 
 minds. As the pulse advances, it squeezes the particles of air 
 together, and two results follow from this compression of the 
 air. Firstly, its elasticity is augmented through the mere 
 augmentation of its density. Secondly, its elasticity is aug- 
 mented by the heat developed by compression. It was the 
 change of elasticity which resulted from a change of density 
 that Newton took into account, and he entirely overlooked 
 the augmentation of elasticity due to the second cause above 
 mentioned. Over and above, then, the elasticity involved in 
 Newton's calculation, we have an additional elasticity due to 
 changes of temperature produced by the sound itself. When 
 both are taken into account, the calculated and the observed 
 velocity agree perfectly ^^ 
 
 ^ Lectures on Sounds ch. i. 
 
METHOD OF CONCOMITANT VARIATIONS, 1 79 
 
 It is not necessary, for our purposes, to pursue the 
 quotation, but the student who wishes to see a n example 
 of the extreme delicacy and caution with which it is 
 requisite to conduct physical researches, may with great 
 advantage read the remainder of the chapter. 
 
 METHOD OF CONCOMITANT VARIATIONS. 
 
 CANON. 
 
 \ i Whatever phenomenon varies in any manner whenever 
 \ another phenomenon varies in some particular manner^ is 
 I either a cause or an effect of that phenomenon^ or is connected 
 I with it through some /act o/" causation ^^, ^ 
 
 This. Method is really a peculiar application, or ser ies 
 of a pp l ications^ of t)ie Method of Differeiice. It is em - 
 pl oyed in those cases where a phenomenon cannot b e 
 nxade tn (ljc^appea,r altog-ether, but where we havp thp — 
 power of augmentin g or diminishing its quantity^ or at least 
 wher^ Na,ture presents it in greater_ or sm^ amount s. 
 Thus, suppose we drop a quantity of quicksilver into a 
 glass tube, we shall find that every sensible augmenta- 
 tion of the temperature of the surrounding atmosphere 
 is accompanied by a sensible augmentation of the volume 
 of the quicksilver in the tube, and, vice versd, that every 
 sensible diminution of the temperature is accompanied 
 
 ^ On p. 182 will be found a. cider ta this Canon. 
 
 N 2 y 
 
l80 INDUCTIVE METHODS. 
 
 by a sensibh diminution of the volume of the quicksilver. 
 Now each particular experiment is an application of the 
 Method of Difference, and, providing we have ascertained 
 that the conditions of that Method have been rigorously 
 satisfied, partakes of its cogency. That certain definite 
 augmentations of temperature will increase the volume of 
 quicksilver by, say, one-twentieth, one-thirtieth, or one- 
 fiftieth part, is an absolutely certain inference, supposing 
 due care to have been taken in the performance of the 
 experiments, and is simply a result of the Method of 
 •DifFerence. But, inasmuch as there are limits above and 
 below which we cannot try the experiment, or inter- 
 mediate points of temperature at which we do not find 
 it convenient to do so, the question arises whether we 
 are justified, in virtue of the experiments already tried, in 
 asserting that the volume of the quicksilver will invariably 
 expand or contract in proportion to the increasing 
 or diminishing temperature of the surrounding media. 
 We are' justified in making such an assertion, and for 
 this reason. The cause which occasions the quicksilver 
 to expand or contract at two definite points must, if it 
 continue to act, and if it be counteracted by no other 
 cause, operate at all intermediate poin.ts ; and, similarly, 
 the cause which occasions it to expand or contract up 
 to a certain point must, on the same suppositions, go on 
 producing a like effect. This is implied in the very 
 notion of Causation. We arrive, then, at the conclusion 
 that the volume of the quicksilver is invariably de- 
 pendent on the temperature of the surrounding medium ; 
 
METHOD OF CONCOMITANT VARIATIONS, l8l 
 
 in other words, that augmentation of temperature is ihe 
 cause of its expansion *^ 
 
 It may be asked, Why not employ the Method of 
 Difference once and for all ? Because, ex hypothesis the 
 phenomenon is one which is only capable of augmenta- 
 tion or diminution, and cannot be made to vanish. We 
 may reduce to a minimum the resistance to motion, but 
 we cannot remove the resistance altogether. We may 
 more and more diminish the heat of a body, but we 
 cannot wholly deprive the body of its heat. Hence we 
 can apply the Method of Difference to the several aug- 
 mentations and diminutions of the phenomenon, but we 
 cannot apply it to the phenomenon as a whole. 
 
 In the example given above, we know that augmenta- 
 tion of temperature and augmentation of volume are 
 related as cause and effect, because, in the experiments, 
 we can assure ourselves that they are the only two cir- 
 cumstances which vary in common ; if we were not 
 certain of this fact, there might be some third circum- 
 stance which was the cause of both. Moreover, we know 
 that augmentation of temperature is the cause and aug- 
 mentation of volume the effect, because, in this case, the 
 former is the antecedent and the latter the consequent. 
 There is another class of cases where, though we are not 
 able to determine which of two circumstances is cause 
 
 *^ The student acquainted with the phraseology of Mathematics will 
 understand our meaning, when we say that the Method of Concomitant 
 Variations is really an integration of a (supposed) infinite number of 
 applications of the Method of Difference. 
 
l8:i INDUCTIVE METHODS. 
 
 and which is effect, we may regard the relation as being 
 one of cause and effect, inasmuch as we feel confident 
 that there is present no third circumstance varying pro- 
 portionately with the other two. But, if we cannot be 
 confident even of this fact, the two circumstances may, 
 for aught we know, both be effects of the same cause ; 
 as, for instance, the loudness of a clap of thunder varies 
 with the intensity of a flash of lightning, though neither 
 is the cause of the other, both alike being effects of the 
 electrical condition of the atmosphere. Hence will be seen 
 the importance of the concluding words of the Canon, ''or is 
 connected with it through some fact of causation/ The 
 first and second cases differ from the third in this, that 
 in both of them we suppose a rigorous fulfilment of the 
 requisitions of the Method of Difference as applied to those 
 individual observations or experiments on which the Method 
 of Concomitant Variations is founded, and which it, as it 
 were, sums up. In the last case, however, we suppose 
 that there is some uncertainty as to whether the requisi- 
 tions of the Method of Difference have been rigorously 
 fulfilled or not. It will thus be seen that the statement 
 of the Canon, as given above, is adapted to the weakest 
 case. We may add to it the following rider : — 
 
 If we can assure ourselves that there is no third pheno- 
 menon varying concurrently with these two, we niay affirm 
 that the one phenomenon is either a cause or an effect of 
 
 the other. 
 V 
 
 The Method of Concomitant Variations may be used 
 
METHOD OF CONCOMITANT VARIATIONS, 183 
 
 for two purposes, either to establish a causal connection, 
 or to determine the law according to which two pheno- 
 mena vary. Thiis, it may either establish the fact that 
 any increase of temperature causes quicksilver to expand, 
 or it may determine the exact rate according to which 
 this expansion takes place, a determination which is, in 
 fact, effected by the ordinary thermometer. In the latter 
 case, the application of the Method is not confined to 
 those permanent natural agents referred to above, the 
 influence of which we cannot altogether remove ; it may 
 come in as supplementary to the Method of Difference. 
 Thus it is by the Method of Difference that we discover 
 that certain kinds of impurity in the atmosphere produce 
 certain kinds of disease, but, if we could ascertain the 
 relation subsisting between the amount of impurity in 
 the atmosphere and the amount of disease, it would be 
 by an application of the Method of Concomitant Vari- 
 ations. 
 
 In the latter class of enquiries, the attempt to determine 
 the numerical relations according to which two pheno- 
 mena vary, the utmost caution is required as soon as 
 our inference outsteps the limits of our observations. In 
 the first place, there is always the possibility of the in- 
 tervention of some counteracting cause. In the case of 
 water, we found that, at 39°, instead of continuing to 
 contract as it becomes colder, it ceases at that point to 
 do so, and thenceforward begins to expand. ' No coun- 
 teracting cause intervening' is, however, a qualification 
 with which we must understand all our inductions, by 
 
1 84 INDUCTIVE METHODS. 
 
 whatever method they may have been arrived at. But 
 there is an element of uncertainty which is peculiar to 
 the Method of Concomitant Variations as applied to 
 determine the law or rate of variation between two 
 phenomena, especially when the range of our obser- 
 vations is confined within comparatively narrow limits. 
 ' Any one/ says Mr. Mill ^^ who has the slightest acquaint- 
 ance with mathematics, is aware that very different laws 
 of variation may produce numerical results which differ 
 but slightly from one another within narrow Hmits ; and 
 it is often only when the absolute amounts of variation 
 are considerable, that the difference between the results 
 given by one law and by another becomes appreciable. 
 When, therefore, such variations in the quantity of the 
 antecedents as we have the means of observing are small 
 in comparison with the total quantities, there is much 
 danger lest we should mistake the numerical law, and 
 be led to miscalculate the variations which would take 
 place beyond the limits; a miscalculation which would 
 vitiate any conclusion respecting the dependence of the 
 effect upon the cause, that could be founded on those 
 variations. Examples are not wanting of such mis- 
 takes. " The formulae," says Sir John Herschel, " which 
 have been empirically deduced for the elasticity of 
 steam (till very recently), and those for the resistance 
 of fluids, and other similar subjects," when relied on 
 beyond the limits of the observations from which they 
 were deduced, '' have almost invariably failed to support 
 
 *2 Mill's Logic, Bk. III. ch. viii. § 7. 
 
METHOD OF CONCOMITANT VARIATIONS. 1 85 
 
 the theoretical structures which have been erected on 
 them." ' This, however, it must be noticed, is an un- 
 certainty which does not vitiate the method, but simply 
 renders necessary the exercise of the utmost caution in 
 its appHcation. 
 
 Perhaps no simpler instance of the Method of Con- 
 comitant Variations can be given than the experimental 
 proof of the First Law of Motion, which Law may be 
 stated thus : that all bodies in motion continue to move 
 in a straight line with uniform velocity until acted upon 
 by some new force. 
 
 * This assertion,' I am quoting from Mr. Mill *', * is in 
 open opposition to first appearances ; all terrestrial objects, 
 when in motion, gradually abate their velocity and at last 
 stop ; which accordingly the ancients, with their inductio per 
 enumerationem simpHcem, imagined to be the law. Every 
 moving body, however, encounters various obstacles, as 
 friction, the resistance of the atmosphere, &c., which we 
 know by daily experience to be causes capable of destroying 
 motion. It was suggested that the whole of the retardation 
 might be owing to these causes. How was this enquired into ? 
 If the obstacles could have been entirely removed, the case 
 would have been amenable to the Method of Difference. 
 They could not be removed, they could only .be diminished, 
 and the case, therefore, sKlmitted only of the Method of 
 Concomitant Variations. This accordingly being employed, 
 it was found that every diminution of the obstacles diminished 
 the retardation of the motion : and inasmuch as in this case 
 (unlike the case of heat) the total quantities both of the 
 antecedent and of the consequent were known ; it was prac- 
 ticable to estimate, with an approach to accuracy, both the 
 
 *3 Mill's Logic, Bk. III. ch. viii. § 7. 
 
1 86 INDUCTIVE METHODS, 
 
 amount of the retardation and the amount of the retarding 
 causes or resistances, and to judge how near they both were 
 to being exhausted ; and it appeared that the effect dwindled 
 as rapidly [as the cause], and at each step was as far on the road 
 towards annihilation as the cause was. The simple oscillation 
 of a weight suspended from a fixed point, and moved a little 
 out of the perpendicular, which in ordinary circumstances lasts 
 but a few minutes, was prolonged in Borda's experiments to 
 more than thirty hours, by diminishing as much as possible 
 the friction at the point of suspension, and by making the 
 body oscillate in a space exhausted as nearly as possible of 
 its air. There could therefore be no hesitation in assigning 
 the whole of the retardation of motion to the influence of the 
 obstacles : and since, after subducting this retardation from 
 the total phenomenon, the remainder was an uniform velocity, 
 the result was the proposition known as the first law of 
 motion.' 
 
 We have already employed as an illustration the fact 
 that a change in the temperature of a body is always 
 accompanied by a change in its volume. The following 
 extract places the same fact in a new light, and shows 
 that the nature of substance (whether soKd, liquid, or aeri- 
 form) depends on, and, at considerable intervals, varies 
 with, the temperature to which it is exposed. 
 
 * The most striking and important of the effects of heat 
 consist, however, in the liquefaction of soHd substances, and 
 the conversion of the liquids so produced into vapour. There 
 is no solid substance known which, by a sufficiently intense 
 heat, may not be melted, and finally dissipated in vapour; 
 and this analogy is so extensive and cogent, that we cannot 
 but suppose that all those bodies which are liquid under 
 ordinary circumstances, owe their liquidity to heat, and would 
 
METHOD OF CONCOMITANT VA%IATjpNS. T!&7 
 
 freeze or become solid if their heat could be suflji^ttntly < - 
 reduced. In many we see this to be the case in ordmipy 
 winters ; for some, severe frosts are requisite ; others freeze | . 
 only with the most Intense artificial colds ; and some have / 
 hitherto resisted all our endeavours ; yet the number of 
 these last is few, and they will probably cease to be excep- 
 tions as our means of producing cold become enlarged. 
 
 * A similar analogy leads us to conclude that all aeriform 
 fluids are merely liquids kept in the state of vapour by heat. 
 Many of them have been actually condensed into the Hquid 
 state by cold accompanied with violent pressure ; and as our 
 means of applying these causes of condensation have improved, 
 more and more refractory ones have successively yielded. 
 Hence we are fairly entitled to extend our conclusion to those , 
 which we have not yet been able to succeed with ; and thus 
 we are led to regard it as a general fact, that the liquid and 
 aeriform or vaporous states are entirely dependent on heat ; 
 that were it not for this cause, there would be nothing but 
 solids in nature ; and that, on the other hand, nothing but a 
 sufficient intensity of heat is requisite to destroy the cohesion 
 of every substance, and reduce all bodies, first to liquids, and 
 then into vapour ^. 
 
 An interesting appHcation of the Method of Concomi- 
 tant Variations is found in the arguments by which it is 
 established that refrigeration at night (when the sun's rays 
 are withdrawn) is, ccBteris paribus, proportional to the 
 dryness of the atmosphere. Thus, in the British Isles, 
 where the atmosphere almost always contains a large 
 amount of aqueous vapour, the difference between the 
 temperature at day and night is comparatively slight, 
 
 ** Herschel's Discourse on the Study of Natural Philosophy^ §§ 357, 
 
 358. 
 
^8S INDUCTIVE METHODS, 
 
 whereas, in countries far inland, where the atmosphere is 
 extremely dry, the variations of temperature are compara- 
 tively large. This phenomenon is due to the fact that 
 masses of aqueous vapour, though they intercept, also 
 radiate heat. Hence, while during the day they protect 
 us from the excessive heat of the sun, they intercept the 
 heat which is radiated from the earth's surface during 
 the night, and, at the same time, return to it some 
 portion of the heat they have absorbed during the day. 
 
 * A freedom of escape,' says Professor Tyndall *^, * would 
 occur at the earth's surface generally, were the aqueous 
 vapour removed from the air above it, for the great body 
 of the atmosphere is a practical vacuum, as regards the 
 transmission of radiant heat. The withdrawal of the sun 
 from any region over which the atmosphere is dry, must 
 be followed by quick refrigeration. The moon would be 
 rendered entirely uninhabitable by beings like ourselves 
 through the operation of this single cause ; with a radiation, 
 uninterrupted by aqueous vapour, the difference between 
 her monthly maxima and minima must be enormous. The 
 winters of Thibet are almost unendurable, from the same 
 cause. Witness how the isothermal lines dip from the 
 north into Asia, in winter, as a proof of the low tempera- 
 ture of this region. Humboldt has dwelt upon the " frigo- 
 rific power" of the central portions of this continent, and 
 controverted the idea that it was to be explained by reference 
 to the elevation ; there being vast expanses of country, not 
 much above the sea-level, with an exceedingly low tempera- 
 ture. But not knowing the influence which we are now 
 studying, Humboldt, I imagine, omitted the most potent 
 cause of the cold. The refrigeration at night is extreme 
 
 *5 Tyndall's Heat a Mode of Motion, § 49a. 
 
METHOD OF CONCOMITANT VARIATIONS. 1 89 
 
 when the air is dry. The removal, for a single summer 
 night, of the aqueous vapour from the atmosphere which 
 covers England, would be attended by the destruction of 
 every plant which a freezing temperature could kill. In 
 Sahara, where " the soil is fire and the wind is flame," the 
 cold at night is often painful to bear. Ice has been formed 
 in this region at night. In Australia, also, the diurnal range 
 of temperature is very great, amounting, commonly, to 
 between 40 and 50 degrees. In short, it may be safely 
 predicted, that wherever the air is dry, the daily thermo- 
 metric range will be great. This, however, is quite different 
 from saying that where the air is clear^ the thermometric 
 range will be great. Great clearness to light is perfectly 
 compatible with great opacity to heat ; the atmosphere may 
 be charged with aqueous vapour while a deep blue sky is 
 overhead, and on such occasions the terrestrial radiation 
 would, notwithstanding the ^'clearness," be intercepted.' 
 
 The science of Geology abounds in instances of the 
 employment of the Method of Concomitant Variations. 
 In fact, as the agents with which it is concerned, land and 
 water, subsidence and elevation, deposition and denuda- 
 tion, are constantly present and acting on the earth*s 
 surface, and as it is impossible to cause the influence of any 
 one of them to vanish altogether, the geologist is compelled 
 in his explanations and arguments to avail himself mainly 
 of this method. The following extract from Ly ell's Prin- 
 ciples of Geology furnishes a good illustration, and will be 
 peculiarly interesting to any one who has visited the 
 place. It is designed as an explanation of the alternate 
 subsidence and elevation of the famous temple of Jupiter 
 Serapis, at Pozzuoli, on the Bay of Naples. 
 
 * We can scarcely avoid the conclusion, as Mr. Babbage has 
 
190 INDUCTIVE METHODS, 
 
 hinted, " that the action of heat is in some way or other the 
 cause of the phenomena of the change of level of the temple. 
 Its own hot spring, its immediate contiguity to the Solfatara, 
 its nearness to the Monte Nuovo, the hot spring at the baths 
 of Nero, on the opposite side of the Bay of Baiae ; the boihng 
 springs and ancient volcanos of Ischia on one side and Vesu- 
 vius on the other, are the most prominent of a multitude of 
 facts which point to that conclusion." And when we reflect 
 on the dates of the principal oscillations of level, and the 
 volcanic history of the country before described, we seem to 
 discover a connection between each era of upheaval and a 
 local development of volcanic heat, and again between each 
 era of depression and the local quiescence or dormant condi- 
 tion of the subterranean igneous causes. Thus for example, 
 before the Christian era, when so many vents were in frequent 
 eruption in Ischia, and when Avernus and other points in the 
 Phlegraean Fields were celebrated for their volcanic aspect 
 and character, the ground on which the temple stood was 
 several feet above water. Vesuvius was then regarded as a 
 spent volcano ; but when, after the Christian era, the fires of 
 that mountain were rekindled, scarcely a single outburst was 
 ever witnessed in Ischia, or around the Bay of Baiae. Then 
 the temple was sinking. Vesuvius, at a subsequent period, 
 became nearly dormant for five centuries preceding the great 
 outbreak of 1631, and in that interval the Solfatara was in 
 eruption a.d. 1198, Ischia in 1302, and Monte >s^uovo was 
 formed in 1538. Then the foundations on which the temple 
 stood were rising again. Lastly, Vesuvius once more became 
 a most active vent, and has been so ever since, and during the 
 same lapse of time the area of the temple, so far as we know 
 anything of its history, has been subsiding. 
 
 ' These phenomena would agree well with the hypothesis, 
 that when the subterranean heat is on the increase, and when 
 lava is forming without obtaining an easy vent, like that 
 afforded by a great habitual chimney, such as Vesuvius, the 
 
METHOD OF CONCOMITANT VARIATIONS, I9I 
 
 incumbent surface is uplifted, but when the heated rocks 
 below are cooling and contracting, and sheets of lava are 
 slowly consolidating and diminishing in volume, then the 
 incumbent land subsides *^.* 
 
 Laplace's Nebular Hypothesis, that stellar systems, like 
 our solar system, are formed from the gradual condensa- 
 tion of nebular masses, is supported by an appeal to 
 this method. * We see,' conceives Laplace, ^ among these 
 nebulae' (which are diffused along the Milky Way), 'in- 
 stances of all degrees of condensation, from the most 
 loosely diffused fluid, to that separation and solidification 
 of parts by which suns and satellites and planets are 
 formed ; and thus we have before us instances of systems 
 in all their stages ; as in a forest we see trees in every 
 period of growth ^'^! 
 
 Physiology (so far as it is based on Anatomy, as dis- 
 tinct from direct experiment), for like reasons with 
 Geology, mainly employs the Method of Concomitant 
 Variations. It is very seldom, in this science, that we 
 obtain a phenomenon present in one set of instances 
 and entirely absent in another ; but we frequently find a 
 phenomenon which, within certain limits, presents itself 
 in the most variable quantities. If, then, we find another 
 
 *® Lyell's Principles of Geology, tenth edition, ch. xxx. 
 
 *^ Wheweirs Novum Organum Renovatum, Bk. III. ch. viii. sect. 2. 
 § 9. This example is adduced by Dr. Whewell as an instance of what 
 he calls the Method of Gradation, which, however, must not be con- 
 founded with Mill's Method of Concomitant Variations. The example, 
 so far as it can be relied on, serves equally well as an instance of either 
 method. 
 
19^ INDUCTIVE METHODS. 
 
 phenomenon varying as it varies, we may argue with 
 tolerable confidence that the two phenomena either stand 
 to each other in the relation of cause and effect, or are, at 
 least, common effects of some unknown cause. Thus, it 
 appears to be established that, not only in different 
 species, but in different individuals of the same species, 
 there is some relation between the manifestations of in- 
 telligence and the amount of cerebral development, under- 
 standing the latter expression to include not only bulk of 
 brain but also complexity and depth of convolutions. 
 
 *With some apparent exceptions,' says Dr. Carpenter*^, a 
 classical authority on most physiological questions, ^ which 
 there would probably be no great difficulty in explaining 
 if we were in possession of all the requisite data, there is a 
 very close correspondence between the relative development 
 of the Cerebrum in the several tribes of Vertebrata and the 
 degree of Intelligence they respectively possess — using the 
 latter term as a comprehensive expression for that series of 
 mental actions which consists in the intentional adaptation 
 of means to ends, based on definite ideas as to the nature 
 of both.' 
 
 And again : — 
 
 *As we ascend the MammaHan series, we find the Cere- 
 brum becoming more and more elongated posteriorly by the 
 development of the middle lobes, and the intercerebral con- 
 missure becomes more complete; but we must ascend as 
 high as the Carnivora, before we find the least vestige of the 
 posterior lobes ; and the rudiment which these possess is so 
 rapidly enlarged in the Quadrumana, that in some of that 
 group the posterior lobes are as fully developed in reference 
 
 *' Carpenter's Principles of Human Physiology, sixth edition. 1864. 
 
METHOD OF CONCOMITANT VARIATIONS. 193 
 
 to the Cerebrum as a whole, and as completely cover in the 
 Cerebellum, as in the human subject. The attention which 
 has yet been given to this department of enquiry, has not 
 hitherto done more than confirm the statement already made, 
 W'ith regard to the general correspondence between the de- 
 velopment of the Cerebrum and the manifestations of Intelli- 
 gence; very decided evidence of which is furnished by the 
 great enlargement of the Cerebrum, and the corresponding 
 alteration in the form of the Cranium, which present them- 
 selves in those races of Dogs most distinguished for their 
 educability, when compared with those whose condition ap- 
 proximates most closely to what was probably their original 
 state of wildness. 
 
 * This general inference drawn from Comparative Anatomy, 
 is borne out by observation of the human species. When the 
 Cerebrum is fully developed, it offers innumerable diversities 
 of form and size among various individuals; and there are 
 as many diversities of character. It may be doubted if two 
 individuals were ever exactly alike in this respect. That a 
 Cerebrum which is greatly under the average size is incapable 
 of performing its proper functions, and that the possessor 
 of it must necessarily be more or less idiotic, there can be 
 no reasonable doubt. On the other hand, that a large, well- 
 developed Cerebrum is found to exist in persons who have 
 made themselves conspicuous in the world in virtue of their 
 intellectual achievements, may be stated as a proposition of 
 equal generality.' 
 
 Dr. Thurnam*^, taking the brain- weights of ten dis- 
 tinguished men, who died between the ages of fifty and 
 seventy, calculates the average weight of their brains 
 to have been 54-7 ounces. The average weight of the 
 
 ** On the Weight of the Braitif by John Thurnam, M.D. London, 
 J. E. Adlard. 1866. 
 
194 INDUCTIVE METHODS, 
 
 brains of ordinary men, dying between the same ages, 
 is 47*1 ounces. This gives in favour of ^cultivated and 
 intellectual man' an excess of 7-6 ounces, or 15 per 
 cent. Though, as a general rule, the connection between 
 intellectual and cerebral development appears to be sub- 
 stantiated, we must, however, be very cautious in draw- 
 ing any inferences as to particular cases. Megalo- 
 cephaly, or pathological enlargement of the brain, is a 
 recognised disease, and is frequently attended with idiotcy. 
 In this class of cases, no doubt, if our means of investi- 
 gation were adequate, we should discover some peculiarity 
 either in the chemical composition or in the anatomical 
 structure of the brain which would enable us to explain 
 the exceptions in conformity with the rule. 
 
 It is, perhaps, needless to add that we are not justified 
 in drawing any further inference from these data, than 
 that the brain is the organ of intelligence, and that there 
 is some definite relation between the organ and its 
 functions. 
 
 Another interesting application of the Method of Con- 
 comitant Variations may be found in one of the 
 arguments by which the distinction between Formed and 
 Germinal Material is established. Any piece of glandular 
 tissue, if examined under a microscope, will be found 
 to consist of two parts, one of which will take a tint 
 from carmine, the other not. The portion which takes 
 the tint is called Germinal, the portion which will not 
 take it is called Formed Material. The former is living 
 matter, capable of growth and germina,tion ; the latter 
 
METHOD OF CONCOMITANT VARIATIONS, 195 
 
 is dead matter, capable of no change but decay. Now, 
 if this distinction between the two kinds of matter be 
 well founded, we may reasonably expect to find the ger- 
 minal matter developed in much larger proportions in the 
 younger than in the older specimens of animals and 
 plants, and in what may be called the more active than 
 in what may be called the more passive parts of animal 
 and vegetable organisms. And this is the case. In the 
 pith of rush, elder, &c. we find that, in the spring, there 
 are many portions of the cells which will take the car- 
 mine tint ; in summer, few ; in autumn, none. In the 
 crystalline lens of the eyes of young animals the portions 
 which will take it preponderate, becoming proportionately 
 fewer as we examine the eyes of older specimens. Jn 
 the grey matter of the brain we find many parts which 
 will take the carmine tint, in the white matter but few. 
 In a grain of wheat, when formed, there is, in the peri- 
 sperm, no portion which will take it, in the white matter 
 but a small portion, while in the embryo it is often 
 difficult to discover any part which does not take it. 
 These instances might be multiplied to any extent ^^ 
 
 In physiological and medical researches, we must be 
 peculiarly careful to bear in mind that, though two pheno- 
 mena may vary proportionately, it by no means follows 
 that one is cause and the other effect. They may both 
 be common effects of the same cause. Thus, though the 
 
 ^ The student will find this subject fully treated in Dr. Lionel Beale's 
 Jjectures on the Simple Tissue of the Human Body, and in other works 
 of the same author. 
 
 2 
 
196 INDUCTIVE METHODS. 
 
 prevalence of cholera is said to be constantly attended 
 by the appearance of certain low forms of organic life, 
 namely, fungi or phytozoa, it by no means follows that 
 these fungi or phytozoa are the cause of cholera. Both 
 phenomena alike may be effects of certain conditions of 
 the^ atmosphere. Nothing but a direct experiment could 
 determine between these two theories. 
 
 The Method of Concomitant Variations, or, as it is 
 often called, when employed on subjects not strictly 
 physical, the Method of Comparison, is that which is 
 most frequently employed in the Science of Language. 
 It is found, for instance, that between two dissimilar words 
 employed at different epochs to express the same idea 
 may be interpolated a number of intermediate forms 
 employed at intermediate epochs, which make the transi- 
 tion from the one word to the other gradual and natural. 
 From this it is inferred that the word used at the later 
 epoch is derived from that used at the earlier epoch, certain 
 tendencies of speech being regarded as the cause of the 
 i^divergence. ' Thus, at first sight,' says M. Brachet ^^, 
 ' it is hard to see that dme is derived from anima ; but 
 history, our guiding-line, shows us that in the thirteenth 
 century the word was written anme, in the eleventh ajiemey 
 in the tenth anime, which leads us straight to the Latin 
 aftimaJ In this case there can be no doubt of the truth 
 of the conclusion. 
 
 Similarly, the loss of declension in the transition from 
 
 ^^ M. Brachet 's Historical Grammar of the French Tongue y Mr. 
 Kitchin*s Translation, p. 42. 
 
METHOD OF CONCOMITANT VARIATIONS, 197 
 
 the Latin Language to the French is easily explained 
 when we take into account the following considera- 
 tions : — 
 
 * The tendency to simplify and reduce the number of cases 
 was early felt in the popular Latin : the cases expressed shades 
 of thought too delicate and subtle for the coarse mind of the 
 Barbarian. And so, being unable to handle the learned and 
 complicated machinery of the Latin declensions, he con- 
 structed a system of his own, simplifying its springs, and 
 reducing the number of the effects at the price of frequently 
 reproducing the same form. Thus the Roman distinguished 
 by means of case-terminations the place where one is, from 
 the place to which one is going : " veniunt ad domum," 
 " sunt in domo." But the Barbarian, unable to grasp these 
 finer shades, saw no use in this distinction, and said, in either 
 case alike, "sum in domum," "venio ad domum." 
 
 * Thus, from the fifth century downwards, long before the 
 first written records of the French language, popular Latin 
 reduced the number of cases to two: (i) the nominative to 
 mark the subject; and (2) that case which occurred most 
 frequently in conversation, the accusative, to mark the object 
 or relation. From that time onwards the Latin declension 
 was reduced to this : — subject, murus ; object, murum, 
 
 * The French language is the product of the slow develop- 
 ment of popular Latin; and French grammar, which was 
 originally nothing but a continuation of the Latin grammar, 
 inherited, and in fact possessed from its infancy, a completely 
 regular declension: subject, murs^ murus ; object, mur, murum : 
 and people said "ce murs est haut;" "j'ai construit un 
 w«r." 
 
 * This declension in two cases forms the exact difference 
 between ancient and modern French. It disappeared in the 
 fourteenth century, not without leaving many traces in the 
 language, which look like so many insoluble exceptions, but 
 
198 INDUCTIVE METHODS, 
 
 find their explanation and historic justification in our know- 
 ledge of the Old French declension ^2.' 
 
 Here the conclusion is that French Grammar is derived 
 from Latin Grammar, certain pecuHarities of the period 
 intervening between the use of the Latin and modern 
 French languages being regarded as the cause of the 
 differences between them. 
 
 Again, nothing at first sight would appear more im- 
 probable than that the French word sms and the Greek 
 word cijut are derived from the same root. But, when 
 we compare the old French word sui, the Latin sum, 
 the Old Latin esum, and the Old Greek form cVftt, the 
 connection of the two words and their ultimate derivation 
 from a common root becomes a certainty. Here the 
 divergence may be definitely accounted for by the vari- 
 ous influences operating upon people (like the Latins 
 and Greeks) occupying different tracts of country, ex- 
 posed to different circumstances, having the organs of 
 speech differently modified, and the like. 
 
 Amongst the above examples it will be noticed that 
 some have been included, the conclusions of which are 
 by no means absolutely certain. In these cases, the 
 deficiency of proof is due not to any formal inconclusive- 
 ness in the Method of Concomitant Variations, or in that 
 of Difference, on which it is based, but to the existence 
 of a doubt as to whether the requirements of those 
 methods have been stringently fulfilled. In any but the 
 
 ^^ M. Brachet's Historical Grammar of the French Tongue, Mr. 
 Kitchin*s Translation, p. 88. 
 
METHOD OF CONCOMITANT VARIATIONS, 1 99 
 
 Experimental Sciences it is always extremely difficult to 
 assure ourselves that we are acquainted with all the cir- 
 cumstances which may influence, or may be influenced 
 by, any given phenomenon. Moreover, as is the case, for 
 instance, with regard to the concomitance between cere- 
 bral development and the manifestation of intelligence, 
 there may be many known points of difference between 
 the observed cases besides those which are taken into ac- 
 count, and the value of the conclusion will depend on the 
 extent to which we have ascertained that these other points 
 of diff'erence are not pertinent, or not equally pertinent 
 with those which we have taken into account, to the cir- 
 cumstance or circumstances which we are investigating. 
 
 The application of the Method of Concomitant Varia- 
 tions to determine the numerical relations subsisting 
 between two phenomena may be illustrated from the ex- 
 periments by which the measure of the accelerating force 
 of gravity was established. The fact, that the higher the 
 point from which a body falls, the greater is the velocity 
 acquired, is patent to observation, though, if we analyse 
 the process by which we arrive at the conclusion, it 
 is by the Method of Concomitant Variations. The rale 
 of acceleration, however, is a very difficult and delicate 
 problem to solve. By Attwood's machine (which it is 
 unnecessary to describe here) it is shown (i) that gravity 
 is an uniformly accelerating force, that is, that the incre- 
 ments of velocity in equal times are equal ; (2) that the rate 
 of increase varies slightly at diff'erent places on the earth's 
 surface; (3) that, in the latitude of Greenwich, in vacuo, 
 
200 INDUCTIVE METHODS, 
 
 and at high-water mark, the rate of acceleration for every 
 second of time is 32-19 inches, the space traversed in the 
 first second of time, if the body fall from rest, being half 
 that quantity, so that the spaces traversed in successive 
 units of time vary as the odd numbers i, 3, 5 .^ • - 
 (2«— i). A slight degree of attention will show that 
 it is by the Method of Concomitant Variations that all 
 these conclusions are obtained ^^ 
 
 The conclusions based on statistics in moral and 
 social enquiries are also instances of this application of 
 the Method of Concomitant Variations. It is argued 
 that, if the same causes continue to operate with like 
 intensity and no new causes intervene, the numerical 
 relations established between two classes of social pheno- 
 mena, as, for instance, deficient education and crime, 
 may be expected to remain constant. 
 *" Another very important application of the Method of 
 Concomitant Variations is what is now commonly known 
 as the Historical Method. A certain institution, custom, 
 or opinion is traced throughout various stages of society, 
 and its growth or decline is connected with the general 
 state of civilisation prevalent throughout these periods, it 
 being argued that, as civilisation advances, the institution, 
 custom, or opinion has grown or declined, as the case 
 may be. This method has of late years been employed 
 with great success in the domains of law, morals, religion, 
 
 ^^ The student who wishes for more detailed information on this sub- 
 ject is referred to Professor Price's Infinitesimal Calculus^ vol. iii. chap, 
 viii. sect. 3. 
 
METHOD OF CONCOMITANT VARIATIONS. 20I 
 
 art, and language ; and it is sufficient to refer the student 
 for examples to works such as those of Sir Henry Maine, 
 Sir John Lubbock, Professor Max Mliller, and Mr. 
 Tylor. The gradual process by which the organisation 
 of the family passes into that of the state, or by which 
 the primitive feeling of resentment is developed into that 
 strict sense of justice which distinguishes civilised man 
 would be amongst the many striking illustrations of this 
 method which are afforded by writers on morals and 
 society, both ancient and modern. When the method is 
 combined with deductions from the science of Psychology, \ 
 staung a priori what might be expected from a general | 
 knowledge of human nature, it is called by Mr. Mill the I 
 Inverse Deductive Method, Under this head we shall 
 briefly advert to it again, in the chapter on the Relation 
 of Induction to Deduction ^*. ^ 
 
 -I 
 
 ^ There is one objection to the employment of the Historical Method, 
 which at least demands an answer. The progress, say, of morality, art, 
 or some particular institution, is compared with the progress of general 
 civilisation. But perhaps this very circumstance is amongst the most 
 important considerations to be taken into account in estimating the 
 stage of civilisation to which any people or class has attahied. The 
 scientific enquirer, therefore, who employs the Historical Method seems 
 to be open to the objection that he is making one quality vary as an 
 aggregate of qualities of which it is itself one ; for, supposing the ex- 
 treme case of the other qualities which make up the aggregate being all 
 constant, we should then have the identical proposition that the quality 
 or institution in question varies as itself. But, as a matter of fact, we 
 know that the other qualities which make up the aggregate of circum- 
 stances which we call civilisation are far from being constant. More- 
 over, they are all so mtertwined with one another that almost any one of 
 them varies directly as almost, any other. Amongst these various circum- 
 
20a INDUCTIVE METHODS, 
 
 Briefly to review these Methods, it will be seen that 
 we can only arrive at absolute certainty by means of 
 one or other of the Methods of Difference, Residues, or 
 Concomitant Variations, while the Method of Agreement 
 and the Joint Method of Agreement and Difference give 
 conclusions only of more or less probability, a probability, 
 however, which sometimes amounts to moral certainty. 
 The Joint Method of Agreement and Difference, or the 
 Double Method of Agreement, possesses one advantage 
 ever all the other Methods, namely that, supposing it to 
 have been satisfactorily ascertained by this Method that A 
 is the cause of a, it will follow that it is the only cause. 
 
 It should also be borne in mind that a wide distinction 
 exists between those cases in which the induction indicates 
 the precise character of the causal connection which 
 subsists between two or more phenomena and those in 
 which it simply points out that there exists a causal 
 
 stances, however, we are able to detect one on which all the others seem 
 to be specially dependent. This is, to state it in the most general terms, 
 the intellectual condition prevalent at the given time, in the given place, 
 or amongst the given class. Not only do we find, as a matter of fact, 
 that the current intellectual beliefs and the degree of development of the 
 intellectual faculties is ther best index to the state of the other con- 
 stituents which make up civilisation, but also we should expect a priori 
 that these latter circumstances would be mainly determined by the 
 former. For it is by the exercise of reason that man learns, in an 
 infinite variety of ways, to adapt himself to the various circumstances 
 which surround him, that he discovers the means of gratifying his higher 
 tastes, and that he is enabled to enter into the feelings and understand 
 the wants of others. On this relation between the state of the intel- 
 lectual faculties and the aggregate of circumstances which constitute 
 civilisation, the student may consult Mr. Mi\W Logic, Bk. VI. ch. x. § 7. 
 
INDUCTIVE METHODS. 203 
 
 connection of some kind or other. In the latter case 
 a new induction is required in order to show what the 
 nature of the causal connection is. 
 
 It may be noticed, finally, that the Inductive Methods 
 are strictly reducible to two only, the Method of Agree- 
 ment and the Method of Difference ; the Joint Method of 
 Agreement and Difference being a double employment of 
 the Method of Agreement, supplemented by an employ- 
 ment of the Method of Difference, the Method of Con- 
 comitant Variations being a series of employments of the 
 Method of Difference, and the Method of Residues being, 
 strictly speaking, a deductive method employed in an 
 inductive enquiry. 
 
 Note I. — In the preceding chapter no allusion, or only 
 a casual one, has been made to a circumstance which 
 frequently occasions an insuperable difficulty in the appli- 
 cation of the Inductive Methods, namely, the Intermixture 
 of Effects. It has been supposed that the antecedents 
 A, B, C, D, &c. are followed by the consequents a, /3, y] S, 6, 
 &c., the effects being regarded as heterogeneous and not 
 homogeneous. But, suppose the effect of A to be a, of B to 
 
 a. y y 
 
 be , of C to be y, of D to be -, and of E to be , the 
 
 2 3.2 
 
 total effect of A, B, C, D, E will be- +^. It is obvious 
 
 20 
 
 how difficult it would be in this case to discover either 
 
 the exact portion of the effect which is due to each cause 
 
 or the several causes which operate to produce the total 
 
a04 INDUCTIVE METHODS, 
 
 effect. We might have, in fact, as in mechanical action 
 and reaction, A producing a and B producing — a, each 
 cause thus neutraHsing the effect of the other, so that 
 we might entertain no suspicion that the causes A and B 
 were in operation at all. In these cases, our main re- 
 source is Deduction. Having ascertained separately by 
 one or other of the various inductive methods, or from 
 previous deductions, the effects, say of A, B, C, D, we 
 calculate deductively their combined effect, and then, by 
 subtracting, according to the Method of Residues, the 
 sum of the known causes from the total aggregate of 
 causes and the known portion of the effect from the 
 total effect, we simplify, if we do not solve, the problem. 
 On the insufficiency, under ordinary circumstances, of 
 the Inductive Methods, without the aid of Deduction, to 
 grapple with cases of this kind^^ and on the nature of 
 
 ^ Since the appearance of the first edition of this work, it has been 
 pointed out by Mr. Bain that * Concomitant Variation is the only one of 
 the [Inductive] Methods that can operate to advantage in such cases.* 
 I take the liberty of transcribing the passage : ' If a cause happens to 
 vary alone, the effect will also vary alone, and cause and effect may be 
 thus singled out under the greatest complications. Thus, when the 
 appetite for food increases with the cold, we have a strong evidence of 
 connexion between those two facts, although other circumstances may 
 operate in the same direction. 
 
 ' The assigning of the respective parts of the sun and moon, in the 
 action of the Tides, may be effected, to a certain degree of exactness, by 
 the variation of the amount according to the positions of the two 
 attracting bodies. ^ 
 
 * By a series of experiments of Concomitant Variations, directed to 
 ascertain the elimination of nitrogen in the human body under varieties 
 of muscular exercise. Dr. Parkes obtained the remarkable conclusion, 
 
INDUCTIVE METHODS, 20^ 
 
 the assistance rendered by Deduction, the reader may con- 
 sult Mr. MilFs Logic, Bk. "ill. ch. x. § 4-8, and ch. xi. 
 
 In cases of this kind, where the action of one cause 
 is augmented, diminished, or wholly counteracted by that 
 of another, it must not be supposed that any part of its 
 appropriate effect has failed to be produced, even though 
 it may have disappeared wholly or partially in the total 
 result. An object may remain at rest, when subject 
 to two equal forces acting in opposite directions, but 
 we cannot say of either of these forces that it is in- 
 operative : each, it is true, prevents any visible effect 
 resulting from the other ; but then this is the very effect 
 which it produces, and the correct mode of describing 
 either o^ the opposing forces would be to say that 
 it has a tendency to make the given object move with 
 a certain velocity in a certain direction. The student 
 cannot too constantly bear in mind that every cause 
 invariably produces its full effect, though other causes 
 may prevent that effect from manifesting itself with all 
 the intensity with which it would manifest itself, if it acted 
 alone ; that there are, strictly speaking, no exceptions to 
 laws of nature, though these laws, in their manifold action 
 and reaction, may modify or even neutralise each other. 
 The aphorism ' Every rule has an exception,','is only true, 
 even in Grammar, either because the rule is inexactly 
 stated or because it conflicts with some other rule known 
 or unknown. 
 
 that a muscle grows during exercise and loses bulk during the subsequent 
 rest.' — Bain's Logic^ Bk. III. ch. viii. § 6. 
 
2,06 INDUCTIVE METHODS, 
 
 Note 2. — The Canons for the Inductive Methods were 
 first stated by Mr. Mill, and the importance now attached 
 to them in most analyses of inductive enquiries is mainly 
 due to his influence. The methods are, however, as 
 Mr. Mill himself states, ' distinctly recognised ' in Sir John 
 Herschel's Discourse o?i the Study of Natural Philosophy^ 
 so often quoted in this work, ' though not so clearly 
 characterised and defined, nor their correlation so fully 
 shown, as has appeared to me desirable.' In the Second 
 Book of Bacon's Novum Organum, we find some ap- 
 proximations, very rough, it is true, to formal inductive 
 methods. The ' instantiae crucis ' have already been ad- 
 duced as examples of the Method of Diff"erence, and the 
 * instantiae solitarise' as including examples of both the 
 Method of Agreement and the Method of Difference ; 
 but the part of the Novum Organum to which I am now 
 alluding, and which is intended to be of more universal 
 application than the ' instantiae crucis ' and the ^ instantiae 
 solitariae,' is contained in the early Aphorisms of the 
 Second Book. Certain Tables of Instances are there 
 given for the purpose of providing materials with which 
 to conduct an investigation into what Bacon called the 
 ' Form,' corresponding pretty nearly to what we should 
 call the ^ Cause,' of Heat. The instances are very far 
 from satisfying the conditions of Mr. Mill's Methods, but 
 the principles on which they are arranged in Tables 
 bear a close analogy to the principles on which the 
 Canons are constructed. The best mode, perhaps, of 
 enabling the student to perceive the extent of the resem- 
 
INDUCTIVE METHODS. 207 
 
 blance is to state the conditions to which the instances 
 in Bacon's Tables would be required to conform, in order 
 to satisfy the requirements of Mr. Mill's Methods. 
 
 If the ' Instantiae convenientes in natura calidi * ^^ were 
 so related to one another that, besides the given pheno- 
 menon (heat), only one other circumstance were common 
 to them all, that other circumstance might be regarded, 
 with more or less probability, as the cause (or effect) of 
 heat, or, at least, as connected with it through some fact 
 of causation. Such instances would then come under the 
 Method of Agreement. 
 
 If one instance in the Table of Agreement (^ Instantiae 
 convenientes in natura calidi') were so related to one 
 of the instances in the Table of Privation (' Instantiae in 
 proximo, quae privantur natura calidi ') ^^ as to have every 
 circumstance in common with it, except that the former, 
 besides presenting the phenomenon of heat which is 
 supposed to be absent in the latter, also presented some 
 other circumstance which was absent from the latter, this 
 other circumstance would be the cause, or a necessary 
 part of the cause (or effect), of heat. We should here 
 have the Method of Difference. 
 
 If, in the * Tabula graduum, sive comparativae in 
 calido ' ^^ we could discover some one phenomenon which 
 increased or diminished proportionately with the increase 
 or diminution of heat, that phenomenon would be the 
 cause or the effect of heat, or, at least, connected with it 
 
 ^^ Novum Organum, Lib. II. Aph. xi. ^^ Id. Aph. xii. 
 
 ^^ Id. Aph. xiii. 
 
208 INDUCTIVE METHODS, 
 
 through some fact of causation, and would conform to 
 the requirements of the Method of Concomitant Variations. 
 If it could be shown that this phenomenon and heat were 
 the only circumstances which varied concurrently, then 
 the phenomenon would be proved to be either the cause 
 or the effect of heat, and would conform to the require- 
 ments of the rider to this last Method (p. 182). 
 
 The * Exemplum exclusivae, sive rejectionis naturarum 
 a forma calidi ' ^^ bears some, though, it must be acknow- 
 ledged, a very slight, resemblance to the Method of 
 Residues. These ' rejectiones ' consist in excluding some 
 possible explanation of the phenomenon, either because 
 an instance, which does not present the phenomenon, 
 does present the assigned cause, or because an in- 
 stance, which does present the phenomenon, does not 
 present the assigned cause ^^ As an instance of the 
 former, we may take the following * rejectio ' : ^ Per radios 
 lunse (which were then supposed to be cold) et aliarum 
 stellarum rejice lucem et lumen.' As instances of the 
 latter, we may take the two following : ' Per radios solis, 
 rejice naturam elementarem (that is, ' terrestrial nature/ 
 which is composed of ^ the four elements'); Per ignem 
 communem, et maxime per ignes subterraneos (qui re- 
 motissimi sunt, et plurimum intercluduntur a radiis cceles- 
 tibus) rejice naturam coelestem.' By a succession of these 
 
 ** Novum Organum, Lib. II. Aph. xvi'i. 
 
 ^ The latter, of course, is not a legitimate argument. The effect 
 may be due to several distinct causes, a fact which was not recognised 
 by Bacon. 
 
INDUCTIVE METHODS, 209 
 
 * rejectiones/ we limit the number of possible explana- 
 tions, amongst which we are to look for the true one. 
 Bacon's ' rejections,' however, not being, as a matter of 
 fact, exhaustive, lead to a purely negative result ; they 
 may save us from unnecessary trouble in seeking for a 
 cause where it cannot be found, but they do not, like the 
 Method of Residues, leave a definite number of ante- 
 cedents which either constitute the cause, or amongst 
 which we know that the cause is to be sought. 
 
 It is plain that if there were a certain number only of 
 possible causes of the given phenomenon, and by the 
 method of rejections we could exclude all but one, this 
 one remaining cause would be the undoubted cause of 
 the given phenomenon. This case Bacon appears to 
 have regarded as the perfect type of Induction, and as 
 alone capable of affording certainty ^^ 
 
 Note 3. — Dr. Whewell (in a pamphlet published in 
 1849, which is now embodied in the Philosophy 0/ Dis- 
 covery^'^) questions the utility of the Four Methods. 
 ' Upon these methods,' he says, * the obvious thing to 
 
 *^ It must be understood that, in this note, I am simply comparing 
 the * Tables ' of Bacon with the * Methods * of Mr. Mill. On the rela- 
 tion of the 'Tables' to each other and on the special importance 
 attached by Bacon to the * Rejections,* the student may consult Mr. Ellis' 
 General Preface to Bacon's Philosophical Works, Ellis and Spedding*s 
 Bacon, vol. i. pp. 32-39. Some of Mr. Ellis' criticisms of Bacon's 
 method I should be disposed to modify, but it Would be beside my purpose 
 to enter on this question in the present place. 
 
 ^2 See Philosophy of Discovery, oh. xxii. The criticism of Mr. Mill's 
 Methods will be found in §§ 38-48. Mr. Mill replies in a note at the 
 end of Bk. III. ch. ix. 
 
:^10 INDUCTIVE METHODS. 
 
 remark is, that they take for granted the very thing which 
 is most difficult to discover, the reduction of the pheno- 
 mena to formulae such as are here presented to us/ He 
 also objects that, as a matter of fact, no discoveries have 
 ever been made by the employment of these methods. 
 ' Who will carry these formulae through the history of 
 the sciences, as they have really grown up, and show us 
 that these four methods have been operative in their for- 
 mation; or that any light is thrown upon the steps of 
 their progress by reference to these formulae ? ' 
 
 The first objection is, as Mr. Mill points out, of the 
 same character with the objections raised by Locke and 
 other writers of the eighteenth century against the Rules 
 of Syllogistic Reasoning. The reply, in either case, is 
 that Logic does not profess to supply arguments, but to 
 test them. Men have certainly reasoned, and reasoned 
 with the greatest force, w:ithout any conscious use of the 
 rules of Logic. But it is the province of a system of 
 Logic to analyse the arguments commonly employed, to 
 discriminate between those which are correct and those 
 which are incorrect, and thus to enable men to detect, 
 in the case of others, and to avoid, in their own case, 
 erroneous methods of reasoning. To think of appro- 
 priate arguments is undoubtedly more difficult than to 
 test them ; but this does not obviate the necessity of sub- 
 mitting them to a test. Nor is it a more real objection 
 that men, who know nothing of the technical rules of 
 Logic, often reason faultlessly themselves, and show re- 
 markable acuteness in detecting inconclusive reasoning 
 
INDUCTIVE METHODS. 211 
 
 in the arguments of others. Many men speak gram- 
 matically without having learnt any system of grammar ; 
 in the same manner, many men reason logically with- 
 out having learnt any system of Logic. But the great 
 majority of men, there can be little doubt, may derive 
 assistance both from one and the other. Grammar 
 fulfils its functions when it raises the student to the level 
 of the most correct speakers; similarly, Logic fulfils its 
 functions when it raises the student to the level of the 
 best reasoners. As applied to the syllogistic rules and 
 formulae, this defence would now be generally admitted, 
 but it holds equally good of the methods under which it 
 may be shown that our inductive arguments may ulti- 
 mately be arranged. ' The business of Inductive Logic,' 
 says Mr. Mill, ' is to provide rules and models (such as 
 the Syllogism and its rules are for ratiocination) to which 
 if inductive arguments conform, those arguments are 
 conclusive, and not otherwise. This is what the Four 
 Methods profess to be, and what I believe they are 
 universally considered to be by experimental philoso- 
 phers, who had practised all of them long before any 
 one sought to reduce the practice to theory.' 
 
 With regard to the second objection, that these me- 
 thods have not been operative in the formation of the 
 sciences. Dr. Whewell seems to ignore the distinction 
 between the conscious and the unconscious employment 
 of a method. It is undoubtedly true that in records of 
 scientific investigations we seldom find the formal lan- 
 guage in which the Inductive Canons are expressed. It 
 p 2 
 
213 INDUCTIVE METHODS. 
 
 seems to me equally true that in such records we inva- 
 riably detect the employment of the Canons themselves. 
 Discoveries are of two kinds : they are either entirely the 
 result of patient research, or they are first suggested to 
 the mind by some brilliant thought, and afterwards 
 verified by rigorous proof In the former case, the 
 discoverer must have made sure of his ground as he 
 proceeded, and, so far as his method was inductive, he 
 ] could only do so by appealing, consciously or uncon- 
 sciously, to one or more of the inductive methods ; if he 
 acted otherwise, he arrived at a true result by mere 
 accident. In discussing the latter case, we must repeat 
 what has already been stated, that it is not the office of 
 Logic, either inductive or deductive, to suggest thoughts, 
 but to analyse and to test them. Now, in the case we are 
 supposing, the discovery really consists of two parts — 
 the original conception and the subsequent process by 
 which it is determined to be the true explanation of 
 the phenomenon. However striking and appropriate 
 the conception, we have no right to regard it as the 
 true explanation of the phenomenon till it has been 
 subjected to the most rigorous investigation. This inves- 
 tigation must be either inductive or deductive, or both. 
 But, so far as it is inductive, it must conform to the 
 requirements of the Inductive Canons, or else it will not 
 result in positive proof, or even approximate closely 
 to it. As in the former case, unless the discoverer 
 has, consciously or unconsciously, reasoned in strict 
 conformity with the requirements of Logic, he has no 
 
INDUCTIVE METHODS. 21^ 
 
 right to feel any confidence in the result of his re- 
 searches. 
 
 It may be added that appropriate conceptions, promising 
 to be fertile in scientific results, are only likely, as a rule, 
 to occur to persons whose minds have been habitually 
 disciplined by the strict observance, conscious or un- 
 conscious, of the laws of reasoning. Originality is not 
 a quality, as some seem to think, which admits of no 
 psychological explanation. 
 
CHAPTER IV. 
 
 Of Imperfect Inductions, 
 
 AN argument from the particular to the general, or 
 from particulars to adjacent particulars, may fall short of 
 absolute proof, or even of moral certainty, while it com- 
 Unends itself as possessing. mQrg . px Jess _ OLLl)Iohabili^^ 
 Arguments of this character may be called Imperfect 
 Inductions. Under this head fall imperfect applications 
 of the experimental or inductive methods, the argument 
 from analogy, and incomplete cases of InducHo per sim- 
 plicem enumerationem. 
 
 The InducHo per simplicem enumerationem is, as al- 
 ready noticed^, when complete {InducHo Completd], a, 
 deductive, and not an inductive, argument. When m- 
 comple/e, it is an inductive argument, for it is an inference 
 of the unknown from the known. This form of Induc- 
 tion affords certainty only when, as in the case of the 
 Laws of Universal Causation and of the Uniformity of 
 Nature, or of the Mathematical Axioms, it is grounded 
 
 ' See p. 123, note 2, and Deductive Logic, Part III. chap. i. appended 
 note a. 
 
INDUCTIO PER SIMP. ENUM, 21 ^ 
 
 upon universal experience, and we feel assured that, if 
 there had been at any time or were now in any place 
 any instance to the contrary, it would not have escaped 
 our notice. But, in ordinary cases, the incomplete In- 
 duetto per simplicem enumerationem affords only a pre- 
 sumption, sometimes very slight, sometimes tolerably 
 strong, in favour of the position which it is adduced to 
 establish. I__^erc.dve, say in five, ten, or twenty cases, 
 that the phenomenon a is attended by the phenomenon 
 h, and, knowing of no cases in which the one phe- 
 nomenon is not attended by the other, I begm to suspect 
 that a and b are connected together in the w^y of 
 causation. Such a surmise may afterwards be proved by 
 the aid of one or other of the five methods to be correct, 
 and, in that case, it is taken out of the category of 
 inductions per simplicem enumerationem, and becomes an 
 instance of a scientific induction. But, if neither proved 
 nor disproved, it still has a certain amount of probability 
 in its favour, that amount depending on the two following 
 considerations : (i) the number of positive instances 
 which have occurred to us; (2) the Hkelihood, if there 
 be any negative instances, of our having met with them. 
 The first of these considerations deserves Httle weight, 
 runkas ^supported by the^othex. A native of the North 
 of Europe, some centuries ago, might, if the mere accu- 
 mulation of positive instances were sufficient, have taken 
 it for a certain truth that all men had white complexions. 
 His own personal observation, as well as the reports of 
 travellers and the traditions of his race, would have 
 
2l6 IMPERFECT INDUCTIONS, 
 
 furnished numberless instances in favour of the position. 
 But, before drawing the inference, he ought to have 
 reflected that he possessed information about a small 
 portion only of the inhabitants of the earth's surface, 
 that a difference of climate might produce a difference 
 of complexion, and that there was no reason for sup- 
 posing that the anatomical structure of man, or the 
 various characteristics which we denominate human, are 
 necessarily connected with a skin of one particular colour. 
 But, on the other hand, we may affirm with tolerable 
 certainty that all the varieties of beings possessing the 
 physical structure of man have the capacity of articulate 
 speech ; for, if there were any races exhibiting the 
 one set of phenomena without the other, there is every 
 probability, with our present knowledge of the earth's 
 surface, that we should be acquainted with their existence. 
 In this instance the first consideration, which in itself 
 would deserve little weight, is converted into a certainty 
 almost absolute by the support which it derives from 
 the second. 
 
 It cannot be too strongly impressed on the mind of 
 the student that a mere simplex enumeratw, that is, a mere 
 assemblage of positive instances, unless we have reason to 
 suppose that, were there any instances to the contrary, 
 they would have become known to us, is simply worthless. 
 * Inductio qucB procedit per enumerationem simplicem res 
 puerilis est.' But if the enumeratio simplex be accom- 
 panied by a well-grounded conviction that there are no 
 instances to the contrary, it may afford a very high 
 
INDUCTIO PER SIMP. ENUM. 2,1 J 
 
 degree of probability, and, if we can assure ourselves 
 that there are no instances to the contrary, to us indi- 
 vidually it will afford certainty. 
 
 It might seem that an Inductio per Simplicem Enum- 
 erationem is always an employment of the Method of 
 Agreement. But there is this essential difference. The 
 Method of Agreement is a method of elimination^ selecting 
 some and rejecting other instances, and founding its con- 
 clusion not on the quantity but on the character of the 
 instances which it selects. The Inductio per Enumera- 
 tionem Simplicem, on the other hand, depends for its 
 validity on the number of instances ; the instances, indeed, 
 must be gathered from every available .field, and hence 
 sometimes we speak of their variety as well as their 
 quantity, but the one essential characteristic of the 
 method is that it does not select, but accumulate in- 
 stances. A few well-selected instances are often suffi- 
 cient to satisfy the requirements of the Method of 
 Agreement. The same number, when we abstract the 
 grounds on which they were selected, would be utterly 
 insufficient to justify an Inductio per Enumerationem 
 Simplicem. 
 
 It may in fact be remarked of all the Experimental 
 Methods that they are devices for saving labour. The 
 range of our experience is often insufficient to justify 
 an argument founded on an Inductio per Enumerationem 
 Simplicem, but by means of the Experimental or In- 
 ductive Methods we so select our instances as to bring 
 the particular case which we are investigating under the 
 
2,l8 IMPERFECT INDUCTIONS. 
 
 general laws of Universal Causation and the Uniformity 
 of Nature. The validity of the induction in question 
 is thus artificially connected with the validity of these 
 universally accepted inductions, and we are enabled to 
 argue from the truth of the latter to that of the former. 
 
 Uncontradicted experience, of course, implies a great 
 variety of instances, and, from this point of view, every 
 well-grounded Inductio per Enumerationem Simplicem 
 might be represented as an application of the Method 
 of Agreement. But to represent it in this form would 
 often weaken its force. For, while our experience may 
 be so wide as to justify us in affirming the constant 
 union of two or more circumstances, the number of 
 other common circumstances, known or suspected, with 
 which these are found in invariable combination, may 
 be so large as to render it impossible for us to satisfy 
 even approximately the conditions of the Method of 
 Agreement. Here, as elsewhere, an argument often 
 admits of being stated in two ways, and it is the office 
 of the logician to state it in that form in which it 
 carries the largest amount of conviction, or rather offers 
 the most satisfactory kind of proof. 
 
 It is, as we have already pointed out in the First 
 Chapter ^, by means of an Inductio per Enumerationem 
 Simplicem that w^e establish what have been called 
 'Inductions of Co-existence/ This is the case, when, 
 as the result of a wide experience, two phenomena 
 
 ' Pp. 7-9- 
 
INDUCTIO PER SIMP. ENUM, 21 9 
 
 are found to be invariably co-existent, but we have no 
 evidence to connect them as cause and effect, or even 
 as effects of the same cause. Such are the attributes 
 which are found to be invariably united in the same 
 Natural Kinds, that is to say, in the same species of 
 plants, animals, and minerals; such are the two pro- 
 perties of Inertia and Gravity which are found united 
 in all matter. In all these cases, there is probably some 
 causal connection, hitherto undetected, between the co- 
 existing phenomena; but while we are unable to apply 
 with any success the more refined inductive methods, 
 we must content ourselves with regarding the uniformity 
 as simply one of co-existence. If we made any pro- 
 gress towards the discovery of a causal connection, the 
 uniformity would be transferred to another category, 
 and would rank amongst the inductions discussed in 
 the last chapter. Meanwhile, these inductions, depend- 
 ing simply on uncontradicted experience, and being at 
 present inaccessible to the Methods of Elimination, must 
 be regarded as generalisations awaiting further inves- 
 tigation I 
 
 The term 'Empirical Generalisation' or * Empirical 
 Law ' might be conveniently appropriated to express the 
 
 ^ For a further discussion of the Uniformities of Co-existence, the 
 reader is referred to Mr. Bain's Logic, Bk. iii. ch. 3. I am disposed to 
 estimate more highly than Mr. Bain the probability that these uni- 
 formities might, if our knowledge were extended, be ultimately resolved 
 into Uniformities of Causation, and hence they do not appear to me to 
 require any separate or detailed treatment in a work on Logic. 
 
«20 IMPERFECT INDUCTIONS, 
 
 result of an Inductio per Simplicem Enumerationem. 
 Though these expressions are employed with great lati- 
 tude, it is usually regarded as characteristic of an Em- 
 pirical Law or Generalisation that it can only be received 
 as true within the limits of the data from which it is 
 derived, that at another time, at another place, or under 
 different circumstances from those under which the 
 observations were made, it might be found to break 
 down*. It is true that, owing to the conflict of causes, 
 this description applies to many of the conclusions 
 arrived at by means of the Inductive Methods, but it 
 is peculiarly applicable to the results of the Inductio 
 per Simplicem Enumerationem, and it would be ex- 
 tremely convenient to possess an expression by which 
 the results of this method might be at once distinguished 
 from those of scientific induction on the one hand, and 
 those of analogy (to be discussed presently) on the 
 other. Instances of Empirical Laws in this restricted 
 sense are such generalisations as that certain animals or 
 flowers are of a certain colour, that certain tribes of 
 men are less capable of civilisation than others, and, 
 perhaps, that certain appearances of sky are indicative of 
 certain changes of weather. There are, of course, some 
 cases in which it is difficult to determine whether a 
 given conclusion has been arrived at by the Inductio 
 per Simplicem Enumerationem or by an imperfect ap- 
 plication of the Method of Agreement, that is to say, 
 
 * See Herschel's Discourse on the Study of Natural Philosophy, § 187, 
 and Mill's Logic, Bk. III. ch. xvi. § 4. 
 
ANALOGV. 221 
 
 whether it is based on instances taken indifferently, or 
 on selected instances ^ 
 
 Another form of imperfect induction is the Argument 
 from Analogy^. Here we do not argue from a number 
 
 * I have avoided any special discussion of what are called ' Empirical 
 Laws,' both on account of the extremely indeterminate use of the ex- 
 pression, and because such a discussion is calculated, in my opinion, 
 needlessly to perplex the student by the complicated questions to which 
 it leads. The advanced student can refer to Mr. Mill's Logic, Bk. III. 
 ch. XV., and Bk. V. ch. v. § 4, but he will be introduced, I venture to 
 suggest, to more difficulties than he will find solved. 
 
 ^ It will be observed that the word 'Analogy' is here employed in the 
 sense of ' resemblance.' In the stricter and more ancient meaning of the 
 term, it signifies an equality of relations (Ictottjs \6yojv). See Aristotle's 
 Ethics, Bk. V. 3 (8). The reader will find the two significations of the 
 word * Analogy' discriminated in the Elements of Deductive Logic, 
 Part III. ch. i. note 2. 
 
 Archbishop Whately defines Analogy as a Resemblance of Relations. 
 This definition, if intended to represent the ancient signification of the 
 word, is incorrect. The Aristotelian Analogy is an equality, not a 
 resemblance of relations. The instance given in Eth. Nic. i. 6 (12) is 
 that, in man, the reason (vovs) bears to the living principle {ipvxq) the 
 same relation that the faculty of vision {oipis) bears to the body (ffco/xa) : 
 us yap €1/ (Tdo/xari o^is, kv ^vxf} vovs. The assertion, in this instance, 
 it will be noticed, is that the relation to each other of the two former 
 members of the analogy is, not similar to, but the same as, that of the 
 two latter. The Aristotelian term dvaXoyia, in fact, exactly corresponds 
 with the term Proportion as employed by mathematicians, and it was 
 by the word Proportio, when not availing themselves of the Greek word 
 Analogia itself, that the Romans expressed this form of argument. See 
 Quinctilian, Inst. Orat. i. 6 : ' Analogies quam proxime ex Graeco trans- 
 ferentes in Latinum proportionem vocaverunt, haec vis est : Ut id, quod 
 dubium est, ad aliquid simile, de quo non quaeritur, referat ; ut incerta 
 
i^Z2 IMPERFECT INDUCTIONS, 
 
 of instances, as in the case of Inductio per Simplicem 
 Enumerationem, but from a number of points of resem- 
 blance. The argument is not, that because S, T, U, V, 
 W, &c. exhibit the union of m with a, b, r, we may 
 therefore expect to find m in Z, or wherever else a, 
 b, c may occur; but that, because X and Y (any two 
 or more instances) agree in the possession of certain 
 qualities a, 3, c, we may expect to find the quality m 
 which is presented by X exhibited also in Y. The 
 argument is based, not on the number of instances in 
 which the two sets of qualities are found united, but on 
 the number of qualities which are found to be common 
 to two or more instances : the argument is not that 
 I have so often observed a, b, c in conjunction with m 
 that I believe these qualities to be conjoined invariably, 
 but that I know X and Y to resemble each other in so 
 many points that I believe them to resemble each other 
 in all. 
 
 Thus, because the moon resembles the earth in being 
 a large spheroid revolving round another body, as well 
 as in various other particulars, it may be argued that 
 it probably resembles the earth also in sustaining animal 
 and vegetable life on its surface. But, if every ground 
 of resemblance furnishes a probable reason for assigning 
 to the one body any property known to belong to the 
 other, it is evident that every ground of dissimilarity will 
 also furnish a probable reason for denying of the first 
 
 certis probet.' I am indebted for this quotation to Mr. Austin's Lectures 
 on Jurisprudence ^ vol. iii. p. 255. 
 
ANALOGY, 2,2^ 
 
 body any property known to belong to the second. In 
 estimating, therefore, the value of an analogical argument, 
 we must strike a balance between the known points of 
 resemblance and the known points of difference, and 
 according as the one or the other preponderate, and in 
 the proportion in which the one or the other prepon-? 
 derate, is .the weight of the argument to be regarded 
 as inclining. If, for instance, the phenomenon A is known 
 to resemble the phenomenon B in four points, whereas 
 the known points of difference between them are three, 
 and it is discovered that some new property belongs to 
 A but it is uncertain whether it also belongs to B, the 
 value of the analogical argument that it does belong to 
 B will be represented by 4:3. 
 
 Before, however, we are justified in drawing this in- 
 ference, it is necessary to observe certain cautions. 
 
 In the first place, we must have no evidence that there 
 is any causal connection between the new property and 
 any of the known points of resemblance or difference. 
 If we have such , evidence, the argument ceases to be 
 analogical, and, if not a perfect induction, is an imper- 
 fect induction of the kind to be described presently. 
 We know, for instance, that animal and vegetable life on 
 the surface of the earth could not exist without moisture ; 
 but, so far as we are able to ascertain, there is no moisture 
 on the surface of the moon. Hence we appear to be 
 justified in concluding, not by analogy, but by the Method 
 of Difference (assuming, of course, the accuracy of the 
 observations), that animal and vegetable life, in the sense 
 
^24 IMPERFECT INDUCTIONS, 
 
 ordinarily attached to those terms, are not to be found on 
 the moon's surface I Again, we happen to know two men 
 who bear a considerable resemblance to each other in 
 character and opinions. One of these men acts in a par- 
 ticular way, and we infer, analogically, that the other will 
 act similarly. But, suppose we ascertain that the act of 
 the former man was due to some particular characteristic, 
 say avarice. The inference will now no longer depend 
 on the ratio of the known points of resemblance to the 
 known points of difference in the characters and opinions 
 of the two men, that is, on analogy, but it will depend 
 mainly on the presence or absence, the strength or weak- 
 ness, of this particular characteristic in the second man, 
 and, in a subsidiary degree, on the presence or absence, 
 the • strength or weakness, of corroborating or counter- 
 vailing motives ; that is, it will depend, not on analogy, 
 but on other modes of induction. 
 
 Secondly, though there must be no evidence to con- 
 nect the property in question with any of the known 
 points of resemblance or difference, there must, on the 
 other hand, be no evidence to disconnect it. If there 
 be such evidence, the point of resemblance or difference 
 with which we know or believe it to be unconnected 
 must, in estimating the value of the analogy, be left out 
 of consideration. The reason is obvious. When we are 
 
 / '^ See the essay Of the Plurality of Worlds (usually attributed to 
 / Dr. Whewell), ch. ix. sect. 7-9. The whole of this essay furnishes ex- 
 cellent examples of the employment of the Argument from Analogy, and 
 also illustrates the extreme caution and delicacy which are requisite in 
 estimating its value. 
 
ANALOGY. 225 
 
 enquiring whether this property is more Hkely to be 
 connected with the known points of resemblance or the 
 known points of difference, it is plain that we must only 
 take into account those points with which there is, at 
 least, some chance of its being connected. 
 
 Thirdly, we must have no reason to suspect that any 
 of the known points of resemblance or difference of 
 which the argument takes account, are causally connected 
 with each other. If the compared phenomena agree in 
 the possession of the properties a, h, c, d^ e, and of these 
 properties b is an effect of (or causally connected with) 
 a, and d is an effect of (or causally connected with) c, 
 the only properties which ought to be taken into account 
 in estimating the value of the analogy are a, c, e. The 
 moon is supposed to differ from the earth in having 
 no clouds and no water, but, as these two properties 
 are mutually connected in the way of cause and 
 effect, they can only be allowed to count as one 
 item in instituting a comparison, for the purposes 
 of analogy, between the known points of resemblance 
 and the known points of difference in the two bodies. 
 The enormous difference, on the other hand, between the 
 maximum and minimum temperature of any place on the 
 moon's surface, owing to the extreme length of the lunar 
 days and nights and the absence of any sensible atmo- 
 sphere, constitutes a distinct point of difference, and, 
 as such, furnishes an additional argument against the 
 habitation of the moon. When we ask to which side 
 the argument from analogy inclines, we are asking 
 
 Q 
 
!Z26 IMPERFECT INDUCTIONS, 
 
 /whether it is more probable that the property in question 
 (known to belong to the one phenomenon, but not 
 known either to belong or not to belong to the other) is 
 connected, by way of causation, with one of the known 
 points of resemblance or with one of the known points of 
 difference ; but, in calculating the probability, it is essen- 
 tial that every point should, so far as we know, be in- 
 dependent of every other ; for it is only in virtue of each 
 being supposed to be an ultimate property or to point to 
 an ultimate property that it has any claim to be taken 
 into the account. Thus, if any two of the properties 
 are found to be joint effects of the same cause or to 
 stand to each other in the relation of cause and effect, 
 they furnish only one argument instead of two. If we 
 say of A that he is likely, under some particular con- 
 juncture of circumstances, to act in the same manner as 
 B, because they are both of them vain and selfish, we 
 should not strengthen our argument by adding a number 
 of characteristics which are deducible from vanity and 
 selfishness, or by adducing a number of individual acts 
 in which these qualities have been exhibited. 
 
 Fourthly, it is only when we have reason to suppose 
 that we are acquainted with a considerable proportion of 
 the properties of two objects, that the argument from 
 analogy can have much weight. If we know only a few 
 properties out of a large number, they may happen to be 
 precisely those which are exceptional rather than repre- 
 sentative, points of similarity where the objects themselves 
 are mainly dissimilar, or points of dissimilarity where the 
 
ANALOGY, 22J 
 
 objects are mainly similar. Thus, we know that in some 
 respects the planet Mars closely resembles the earth, as, 
 for instance, in having an atmosphere, a surface dis- 
 tributed into land and water, and a temperature in which 
 life similar to that on our own globe might exist; 
 but it would be very rash to conclude from these data 
 that it also resembles the earth in sustaining animal and 
 vegetable life on its surface ; for, though life, such as we 
 understand it, does not appear to be impossible on the 
 planet Mars as it appears to be on many of the other 
 celestial bodies, the number of properties with which we 
 are acquainted is so small as compared with the number 
 of properties with which we are unacquainted that there 
 is little or nothing on which to ground even a probable 
 conclusion. On the other hand, the analogy by which 
 Kepler boldly extended the three laws gained from the 
 observation of the motion of Mars to the remaining 
 planets was a perfectly sound one; for the orbit of a 
 planet, as compared with the condition of its surface, is 
 a very simple phenomenon, and what was known of the 
 orbits of the other planets made it appear more likely < 
 that they would correspond with the orbit of Mars than 
 that they would differ from it. 
 
 The value of the Argument from Analogy, then, we see, 
 depends on the ratio of the ascertained points of resem- 
 blance to (i) the ascertained points of difference, (2) the 
 entire assemblage of the properties of the objects com- 
 pared. If the ascertained resemblances are numerous, 
 the ascertained differences few, and we have reason to 
 Q 2 
 
!2,%8 IMPERFECT INDUCTIONS. 
 
 think that we are well acquainted with the objects com- 
 pared, the argument from analogy is very forcible. If, 
 on the other hand, the ascertained resemblances only 
 slightly exceed in number the ascertained differences, or 
 if we have reason to suppose that there are numerous 
 properties in the compared objects with which we are un- 
 acquainted, the value of the argument from analogy may 
 be very slight. It is commonly said that the value of an 
 argument from analogy ranges from certainty to zero. 
 If it reaches certainty, the argument becomes a com- 
 plete induction ; if it falls to zero, it ceases to be an 
 argument at all; if the probability is expressed by 
 less than one-half, that is, if the number of ascertained 
 resemblances be less than the number of ascertained 
 differences, it is usual to say that analogy is against 
 the possession by the one object of a quality known 
 to belong to the other, or, in other words, in favour 
 of their differing in the possession of this quality rather 
 than agreeing in it. 
 
 ^ Besides the competition between analogy and diver- 
 sity,' says Mr. Mill^, 'there may be a competition of 
 conflicting analogies.' An object may be known to 
 resemble one object in some particulars and another in 
 others, and it may be a question with which of the two 
 it ought to be classed, or which of the two it is the more 
 likely to resemble in some unknown property. Thus, 
 for some time it was a question whether a sponge was 
 an animal or a vegetable substance ; and it is often by 
 
 '^ « Mill's Logic, Bk. III. ch. xx. § 2. 
 
ANALOGY. 229 
 
 conflicting analogies that we attempt to determine to 
 which of two or more masters a painting or a statue 
 should be ascribed. 
 
 The extreme caution which is requisite in employing 
 the Argument from Analogy may be illustrated by the 
 following scientific errors which have resulted from a 
 hasty and inconsiderate employment of this mode of 
 reasoning. 
 
 Sir W. Grove, in his Correlation of Physical Forces '\ 
 while combating the once fashionable doctrine of electrical 
 fluids, brings into juxta-position two very interesting in- 
 stances of hasty analogies. 
 
 * The progressive stages,' he says, * in the History of Phy- 
 sical Philosophy will account in a great measure for the adop- 
 tion by the early electricians of the theories of fluids. 
 
 ^ The ancients, when they witnessed a natural phenomenon, 
 removed from ordinary analogies, and unexplained by any 
 mechanical action known to them, referred it to a soul, a 
 spiritual or preternatural power : thus amber and the magnet 
 were supposed by Thales to have a soul ; the functions of 
 digestion, assimilation, &c., were supposed by Paracelsus to 
 be effected by a spirit (the Archaeus). Air and gases were 
 also at first deemed spiritual, but subsequently became in- 
 vested with a more material character; and the word gas, 
 from ge'ut, a ghost or spirit, affords us an instance of the 
 gradual transmission of a spiritual into a physical conception, 
 
 * The establishment by Torricelli of the ponderable cha- 
 racter of air and gas, showed that substances which had been 
 deemed spiritual and essentially different from ponderable 
 matters were possessed of its attributes. A less superstitious 
 
 ^ Fifth edition, p. 135. 
 
230 IMPERFECT INDUCTIONS. 
 
 mode of reasoning ensued, and now aeriform fluids were 
 shewn to be analogous in many of their actions to liquids or 
 known fluids. A belief in the existence of other fluids, diff"er- 
 ing from air as this differed from water, grew up, and when 
 a new phenomenon presented itself, recourse was had to a 
 hypothetic fluid for explaining the phenomenon and connect- 
 ing it with others; the mind once possessed of the idea of 
 a fluid, soon invested it with the necessary powers and pro- 
 perties, and grafted upon it a luxuriant vegetation of imaginary 
 off"shoots.* 
 
 Most of our readers will be aware of the difficulties 
 experienced by the early geologists in accounting for 
 the fact that the strata of our own and other northern 
 countries often contain remains of animals and shells 
 akin to those which are now to be found only in the 
 torrid zone. This difficulty is easily explained by sup- 
 posing a different distribution of land and water over the 
 surface of the globe from that which at present exists. 
 But we must pause before we admit the inference that, 
 because these animals and shells are ah'n to those which 
 are now found only in warm climates, they must, there- 
 fore, have subsisted in a similar temperature. 
 
 * When reasoning on such phenomena,' says Sir Charles 
 Lyell ^^, * the reader must always bear in mind that the fossil 
 individuals belonged to species of elephant, rhinoceros, hippo- 
 potamus, bear, tiger, and hyaena, distinct from those which 
 now dwell within or near the tropics. Dr. Fleming, in a 
 discussion on this subject, has well remarked that a near 
 resemblance in form and osteological structure is not always 
 
 /^ ^^ Lyell's Principles of Geology, ch. vi. (ninth edition) ; ch. x. (tenth 
 . edition). 
 
ANALOGY. 231 
 
 followed, in the existing creation, by a similarity of geo- 
 graphical distribution ; and we must therefore be on our 
 guard against deciding too confidently, from mere analogy of 
 anatomical structure, respecting the habits and physiological 
 peculiarities of species now no more. " The zebra delights to 
 roam over the tropical plains ; while the horse can maintain 
 its existence throughout an Iceland winter. The buffalo, like 
 the zebra, prefers a high temperature, and cannot thrive even 
 where the common ox prospers. The musk ox, on the other 
 hand, though nearly resembling the buffalo, prefers the stinted 
 herbage of the arctic regions, and is able, by its periodical 
 migrations, to outlive a northern winter. The jackal {Cams 
 aureus^ inhabits Africa, the warmer parts of Asia, and Greece ; 
 while the isatis (Canis lagopus) resides in the arctic regions. 
 The African hare and the polar hare have their geographical 
 distribution expressed in their trivial names ; " and different 
 species of bears thrive in tropical, temperate, and arctic 
 latitudes. 
 
 ' Recent investigations have placed beyond all doubt the 
 important fact that a species of tiger, identical with that of 
 Bengal, is common in the neighbourhood of Lake Aral, near 
 Sussac, in the forty-fifth degree of north latitude ; and from 
 time to time this animal is now seen in Siberia, in a latitude 
 as far north as the parallel of Berlin and Hamburgh. Hum- 
 boldt remarks that the part of Southern Asia now inhabited 
 by this Indian species of tiger is separated from the Himalaya 
 by two great chains of mountains, each covered with perpetual 
 snow, — the chain of Kuenlun, lat. 35° N., and that of Mouz- 
 tagh, lat. 42°, — so that it is impossible that these animals 
 should merely have made excursions from India, so as to 
 have penetrated in summer to the forty-eighth and fifty-third 
 degrees of north latitude. They must remain all the winter 
 north of the Mouztagh, or Celestial Mountains. The last 
 tiger, killed in 1828, on the Lena, in lat. 52^°, was in a climate 
 colder than that of Petersburg and Stockholm.' 
 
23^ IMPERFECT INDUCTIONS. 
 
 Neither through Analogy nor through Induction by 
 Simple Enumeration can we establish a fact of Causation, 
 though the conclusions of either of these methods may 
 suggest to us such a fact. When we begin to suspect 
 that any one circumstance or set of circumstances is the 
 cause or the effect of another, or connected with it in the 
 way of causation, we ought at once to attempt to apply, 
 if possible, one or more of the Experimental Methods. 
 If we can satisfy ourselves that their conditions, or those 
 of any one of them, have been rigorously fulfilled, we 
 have, of course, obtained a Valid Induction, giving us 
 either absolute or moral certainty. But something con- 
 siderably short of a rigorous fulfilment of these conditions 
 may still lead to a conclusion, possessing more or less of 
 probability. We may, for instance, to take the Method 
 of Agreement, feel uncertain whether a and b (any two 
 circumstances) are the only material circumstances which 
 the cases we have examined exhibit in common ; but still 
 we may have examined so many, so various, and so well 
 selected instances, that we may be justified in regarding 
 it as highly probable that the two circumstances stand to 
 each other in the relation of cause and effect, or are, at 
 least, connected in the way of causation. Similarly, to 
 take the Method of Difference, in the act of introducing 
 a new antecedent, we may have unwittingly introduced 
 some other new antecedent, or, in omitting an antecedent, 
 we may have unwittingly introduced or omitted some 
 other antecedent ; but still we may have exercised such 
 extreme caution as to justify us in feeling an assurance 
 
INCOMPLETE INDUCTIONS. 233 
 
 amounting almost, though not altogether, to certainty 
 that the experiment has been rightly performed. The 
 less our assurance of this fact, the slighter is the prob- 
 ability of the conclusion. 
 
 There remains one case, which is attended with some 
 perplexity. It sometimes happens that, though we may 
 be unable to establish a fact of causation between two 
 particular phenomena, we may be able to show that some 
 one phenomenon stands in a causal relation to some one 
 or other of a definite number of other phenomena. Thus, 
 supposing a vegetable to be transplanted to a distant 
 part of the world, we may be able to assure ourselves, 
 by excluding other causes of difference, that any new 
 qualities which it may assume are due either to difference 
 of climate, or to difference of soil, or to both these causes 
 conjointly, though our knowledge may not enable us to 
 assign amongst these alternatives the particular cause or 
 combination of causes to which the effect is due. Now 
 ought such an Inference to be classified as a perfect or 
 an imperfect Induction.? If we content ourselves with 
 stating the alternatives, the inference should be regarded, 
 so far as it goes, as a Perfect Induction ; for within the 
 limits stated the conclusion may be considered absolutely 
 certain. But if, on any grounds, we suppose one o^ 
 these alternatives to be more probable than the others, 
 and we state this as our conclusion, the inference is, of 
 course, only a probable one, and should rank as an Im- 
 perfect Induction. 
 
234 IMPERFECT INDUCTIONS. 
 
 The same remarks will apply to those cases in which 
 there is any uncertainty as to the nature of the fact of 
 causation. If the inference be, say, that the two pheno- 
 mena either are one cause and the other effect, or stand 
 to each other in the relation of cause and effect, though 
 we may be unable to determine which of the two is 
 cause and which is effect, or are both of them effects of 
 the same cause (adding any other alternatives which the 
 particular case may require), the inference is, so far as it 
 goes, a Perfect Induction. But, if one or some only of 
 these alternatives be selected, on any grounds short of 
 absolute or moral certainty, to the exclusion of the 
 others, the inference is only probable, and must be re- 
 garded as merely an Imperfect Induction. 
 
 Briefly to sum up the contents of this chapter, Imper- 
 fect Inductions are the results either of an Inductio per 
 Simplicem Enumerationem (to which we propose to ap- 
 propriate the expression * Empirical Generalisations'), or 
 of the Argument from Analogy (which we call Analogies), 
 or of an imperfect fulfilment of one or other of the Induc- 
 tive Methods (to which we might, perhaps, advantageously 
 appropriate the expression ^ Incomplete Inductions '). In 
 the two former cases there can be no more than an 
 intimation of a Fact of Causation, while in the last we 
 conceive ourselves to be on the way towards establishing 
 one. 
 
CHAPTER V. 
 
 On the relation of Induction to Dedtcction, 
 and on Verification, 
 
 THE results of our inductions are summed up in 
 general propositions, which are not unfrequently stated 
 in the shape of mathematical formulae. These general 
 propositions, the results of inductive reasoning, become, 
 in turn, the data from which deductive reasoning pro- 
 ceeds. Though the major premiss of any single deduc- 
 tive argument may itself be the result of deduction, it 
 will invariably be found, as pointed out long ago by 
 Aristotle ^, that the ultimate major premiss of a chain of 
 deductive reasoning is a result of induction. There must 
 be some limit to the generality of the propositions under 
 which our deductive inferences can be subsumed, and, 
 when we have reached this limit, the only evidence on 
 which the ultimate major premiss can repose, if it depend 
 on evidence at all, must be inductive. Thus, most of 
 the deductions in the science of Astronomy, and many 
 
 ^ 'H fjilu d^ kirayooy^ ^PXl ^^^' '^"^ "^^^ Ka96\ov, 6 be avWoyifffios 
 €K ruv KaOoXov. ^ialv dpa dpxcd k^ wv 6 avWoyifffibs, wv ovk €(Tti 
 avWoyiff/jLos- kirayojy^ dpa. — Eth. Nic. vi. 3 (3). Cf. Eth. Nic. vi. 
 6, 8 (9); Metaphysics^ i. i ; Posterior Analytics, ii. 19. 
 
2^6 RELATION OF INDUCTION TO DEDUCTION^ 
 
 of those in the science of Mechanics, depend ultimately 
 on the Law of Universal Gravitation ; but this Law itself 
 is the result of an induction based upon a variety of facts, 
 including both the fall of bodies to the earth and the 
 motion of the planets in their orbits. Again, a large 
 number of geometrical deductions may be traced up to 
 the ultimate major premiss : ' Things that are equal to 
 the same thing are equal to one another/ But this 
 proposition, if not referred directly to induction, is 
 classed under the head of intuitive conceptions, the most 
 probable, though perhaps not the most commonly re- 
 ceived, explanation of which is that which derives them 
 from the accumulated experience of generations, trans- 
 mitted hereditarily from father to son. 
 
 A Deductive Inference combines the results of previous 
 inductions or deductions, and evolves new propositions 
 as the consequence, or, to put the matter in a slightly 
 different point of view, as expre'ssing the total result, 
 of these combinations. We append a few easy examples 
 of the manner in which the results of induction are em- 
 ployed in a deductive argumerlt. 
 
 To begin with a very simple instance, but one which 
 will serve as a good illustration of the stage at which 
 our investigations cease to be inductive and become 
 deductive; — suppose we have ascertained, by previous 
 inductions, that A produces a, B produces b, C pro- 
 duces — f, D produces |, and E produces |, we know, 
 by calculation — that is, by deductive reasoning — that the 
 total effect of A, B, C, D, E is b -f f. In this case the 
 
AND VERIFICATION. 237 
 
 simple rules of Algebra, governing the addition and sub- 
 traction of quantities, combined with the special data 
 here furnished, are the premisses from which our de- 
 deductive reasoning proceeds. 
 
 The proposition proved in Euclid, Book i. Prop. 38, 
 that ' Triangles upon equal bases, and between the same 
 parallels, are equal to one another,' is derived from, or 
 is the total result of, the previous deductions (i) that 
 * Parallelograms upon equal bases, and between the same 
 parallels, are equal to one another,' (2) that ' Triangles 
 formed by the diagonal of a parallelogram are each of 
 them equal to half the parallelogram' (i. 34), and (3) the 
 previous induction that 'the halves of equal things are 
 equal/ 
 
 What is called the Hydrostatic Paradox, namely, that 
 a man standing on the upper of two boards, which 
 form the ends of an air-tight leather bag, and blowing 
 through a small tube opening into the space between the 
 board, can easily raise his own weight, is a combination 
 of two propositions, both gained from experience by 
 means of induction, these propositions being (i) that 
 fluids transmit pressure equally in all directions, (2) that 
 the greater the pressure brought to bear on any surface 
 from below, the greater the weight which it will sustain 
 (otherwise expressed by the Mechanical Law that action 
 and reaction are equal). 
 
 To take another very simple instance of a similar kind. 
 One of the earliest and easiest problems in the Science 
 of Optics is the following : ' A conical pencil of rays is 
 
IJ38 RELATION OF INDUCTION TO DEDUCTION^ 
 
 incident upon a plane reflecting surface ; to determine 
 the form of the reflected pencil/ The solution, that the 
 reflected pencil will be a cone having for its vertex a 
 certain imaginary point, which can be geometrically deter- 
 mined, on the other side of the surface, is derived from a 
 combination of the experimental truth, gained by induc- 
 tion, that ^ the angle of reflexion is equal to the angle 
 of incidence ' with the geometrical propositions stated in 
 Euclid i. 8 and i. 29I 
 
 In the Science of Political Economy, Ricardo's Theory 
 of Rent, when stated in the slightly modified form that 
 * the rent of land represents the pecuniary value of the 
 advantages which such land possesses over the least 
 valuable land in cultivation,' is an easy deduction from 
 two principles which are supplied by every one's ex- 
 perience, namely, (i) that land varies in value, and (2) 
 that there is some land either so bad or so disadvan- 
 tageously situated as to be not worth the cultivating ^. 
 
 Professor Cairnes' work on the Slave Power furnishes 
 a remarkable example of the successful application of the 
 deductive method to the determination of economical 
 questions. The economical effects of slavery are thus 
 traced. We learn from observation and induction that 
 slave labour is subject to certain characteristic defects: 
 
 ^ The student will find an easy exposition of this Theory in Fawcett's 
 Manual of Political Economy, Bk. II. ch. iii. ad init. As originally stated, 
 Ricardo's theory neglected to take account of advantages of situation, 
 such as proximity to a market, and regarded the value of land as 
 depending solely on Its fertility. 
 
AND VERIFICATION, 239 
 
 it is given reluctantly ; it is unskilful ; and, lastly, it is 
 wanting in versatility. As a consequence of these cha- 
 racteristics, it can only be employed with profit when it 
 is possible to organise it on a large scale. It requires 
 constant supervision, and this for small numbers or 
 for dispersed workmen would be too costly to be re- 
 munerative. The slaves must, consequently, be worked 
 in large gangs. Now there are only four products which 
 repay this mode of cultivation, namely, cotton, sugar, 
 tobacco, and rice. Hence a country in which slave 
 labour prevails is practically restricted to these four 
 products, for it is another characteristic of slave labour, 
 under its modern form, that free labour cannot exist 
 side by side with it. But, besides restricting cultivation 
 to these four products, some or all of which have a 
 peculiar tendency to exhaust the soil, slave labour, from 
 its want of versatility, imposes a still further restriction. , 
 * The difficulty of teaching the slave anything is so great 
 — the result of the compulsory ignorance in which he is 
 kept, combined with want of intelligent interest in his 
 work— that the only chance of rendering his labour 
 profitable is, when he has once learned a lesson, to keep 
 him to that lesson for life. Accordingly where agricul- 
 tural operations are carried on by slaves, the business of 
 each gang is always restricted to the raising of a single 
 product. Whatever crop be best suited to the character 
 of the soil and the nature of slave industry, whether 
 cotton, tobacco, sugar, or rice, that crop is cultivated, 
 and that crop only. Rotation of crops is thus precluded 
 
240 RELATION OF INDUCTION TO DEDUCTION, 
 
 by the conditions of the case. The soil is tasked again 
 and again to yield the same product, and the inevitable 
 result follows. After a short series of years its fertility 
 is completely exhausted, the planter abandons the ground 
 which he has rendered worthless, and passes on to seek 
 in new soils for that fertility under which alone the 
 agencies at his disposal can be profitably employed.' 
 Thus, from the characteristics of slave labour may be 
 deduced the economical effect of exhaustion of the soil 
 on which it prevails, and the consequent necessity of 
 constantly seeking to extend the area of cultivation. 
 From the peculiar character of the crops which can 
 alone be successfully raised by slave labour may be ex- 
 plained the former prevalence of slavery in the Southern, 
 and its absence in the Northern, States of the American 
 Union ; and from the necessity of constantly seeking 
 fertile virgin soil for the employment of slave labour may 
 be explained the former policy of the Southern States, 
 which was invariably endeavouring to bring newly consti- 
 tuted States under the dominion of slave institutions ^. 
 
 These examples of the combination of inductive with 
 deductive reasoning might be multiplied to any extent. 
 Mechanics, Astronomy, and the Mathematico-physical 
 sciences generally, furnish, perhaps, the most striking 
 instances of them. The great importance of deduction 
 as an instrument for the ascertainment of physical truths 
 
 ^ See Professor Cairnes on the Slave Power, ch. ii. His arguments are 
 stated in a condensed form in Fawcett's Manual of Political Economy, 
 Bk. II. ch. xi. 
 
AND VERIFICATION, 24 1 
 
 could hardly be illustrated more appropriately than by the 
 following cases adduced by Sir John Herschel * : — 
 
 * It had been objected to the doctrine of Copernicus, that, 
 were it true, Venus [and, it might have been added. Mercury, 
 as the other inferior planet] should appear sometimes horned 
 like the moon. To this he answered by admitting the con- 
 clusion, and averring that, should we ever be able to see its 
 actual shape, it ^ould appear so. It is easy to imagine with 
 what force the application would strike every mind when the 
 telescope confirmed this prediction, and showed the planet 
 just as both the philosopher and his objectors had agreed it 
 ought to appear. The history of science affords perhaps only 
 one instance analogous to this. When Dr. Hutton expounded 
 his theory of the consolidation of rocks by the application of 
 heat, at a great depth below the bed of the ocean, and espe- 
 cially of that of marble by actual fusion ; it was objected that, 
 whatever might be the case with others, with calcareous or 
 marble rocks, at least, it was impossible to grant such a cause 
 of consolidation, since heat decomposes their substance and 
 converts it into quicklime, by. driving off the carbonic acid, 
 and leaving a substance perfectly infusible, and incapable even 
 of agglutination by heat. To this he replied, that the pressure 
 under which the heat was applied would prevent the escape 
 of the carbonic acid ; and that being retained, it might be 
 expected to give that fusibility to the compound which the 
 simple quicklime wanted. The next generation saw this 
 anticipation converted into an observed fact, and verified by 
 the direct experiments of Sir James Hall, who actually suc- 
 ceeded in melting marble, by retaining its carbonic acid under 
 violent pressure.' 
 
 It should be noticed that, for the most part, in the 
 actual conduct of scientific enquiry, there is a constant 
 
 * Discourse on the Study of Natural Philosophy^ § 299. 
 R 
 
2^4^ RELATION OF INDUCTION TO DEDUCTION, 
 
 alternation of the processes of Induction and Deduction. 
 A truth obtained inductively is often at once used, either 
 by itself or in combination with other propositions, for 
 the purpose of evolving new truths by deduction, while it 
 may also be subsequently employed together with other 
 inductions of the same order for the purpose of leading 
 up inductively to propositions of a higher degree of 
 generality. We are constantly passing from the one 
 process to the other, and back again, and often it becomes 
 exceedingly difficult to determine exactly how much of 
 our ultimate conclusion is due to the one method, and 
 how much to the other. It is an error (though this error 
 has received the countenance of Bacon) to suppose that 
 the process of induction should always be pursued con- 
 tinuously up to a certain point, and that from that point 
 the process of deduction should proceed equally uninter- 
 ruptedly. We may, and in fact should, frequently pause 
 to consider to what deductive conclusions our inductive 
 inferences lead, or to try whether they may not be con- 
 nected by a chain of deductive reasoning with wider 
 truths previously ascertained^. 
 
 A very common instance of the constant interlacing of 
 the inductive and deductive processes just noticed is to 
 be found in the ordinary mode of framing and employing 
 hypotheses. First, our hypotheses are always suggested 
 by some fact, or facts, within our experience. They are 
 thus based on a rough kind of induction. When framed, 
 
 ^ On this subject, see the excellent criticism on Bacon in Mr. Mill's 
 Logic, Bk. VI. ch. v. § 5. 
 
AND VERIFICATION. 243 
 
 we generally proceed to trace the consequences which 
 would ensue on the supposition of their truth. This is 
 a deductive process. Individual facts or inductions from 
 individual facts are then compared with these results, and, 
 if they agree with them, are regarded as confirmatory of 
 the hypothesis. Of course, these processes may be fre- 
 quently repeated, and are often so repeated, the hypo- 
 thesis thus constantly gaining in probability, even though 
 it may as yet have no claim to be regarded as an esta- 
 blished truth. Lastly, if it attain the position of a valid 
 induction, it must be by the application of one or other 
 of the inductive methods, which converts its previous pro- 
 bability into scientific certainty. Or, perhaps, it may be 
 finally established not by induction at all, but by being 
 brought deductively under some more general law. 
 
 These remarks and the instances adduced above natu- 
 rally lead to a discussion of the place to be assigned in 
 scientific enquiry to the process called Verification. In 
 Deductive Reasoning, especially when it involves elaborate 
 calculations, there is always great danger lest we should 
 have omitted to take into account some particular agency 
 or element, or have miscalculated its effects, or have 
 formed a false estimate of the combined effect of the 
 various agencies or elements in operation. The only 
 remedy against these possible errors, besides the employ- 
 ment of great caution in the conduct of the deductive 
 process itself, is to be found in Verification, a word which, 
 
244 RELATION OF INDUCTION TO DEDUCTION, 
 
 in its stricter sense, appears to be applied to the process 
 of testing, by means of an appeal to facts, the validity of 
 the conclusions already arrived at by a course of deduc- 
 tive reasoning. Thus it had been deductively inferred 
 from the Copernican theory that the planets Venus and 
 Mercury ought to pass through phases, like the moon, 
 and the application of the telescope, by means of which 
 they were actually seen to assume these phases, furnished 
 a triumphant verification of the inference. Every occur- 
 rence of an eclipse of the sun or moon or of the transit 
 or occultation of a star, when it accords with the previous 
 calculations of astronomers, is also an instance of Verifi- 
 cation in this, the stricter, sense of the term. But the 
 word is often used in a looser sense and extended to all 
 cases in which an appeal is made to facts, as, for instance, 
 when we perform an experiment in order to test the truth 
 of a hypothesis, or where we put in action the Method of 
 Difference in order to supplement the characteristic un- 
 certainty attaching to the employment of the Method of 
 Agreement. Of the process denoted by this looser sense 
 of the word, instances will readily occur to every one. 
 Thus, the diminution in the periods of Encke's comet has 
 been regarded by some astronomers (though, perhaps, 
 erroneously) as a verification of the theory that space 
 is filled with an interstellar medium; or, to take an in- 
 stance from a very different class of subjects, the recent 
 breaking-up of the slave-system in the Southern States of 
 America may be regarded as a verification of the pre- 
 diction that slave and free institutions could not long 
 
AND VERIFICATION. 245 
 
 co-exist under the same political form of government. 
 For an instance of a case in which the Method of Dif- 
 ference is called in to verify a previous employment of 
 the Method of Agreement, we may refer back to the 
 enquiry into the cause of crystallization, already adduced 
 in our discussion of those two methods ^ 
 
 There is a still wider appHcation of the word Veri- "* 
 fication, by which it is extended to any corroboration of 
 one mode of proof by means of another. It thus in- j 
 eludes a deductive proof adduced in corroboration of an 
 inductive one. The most common instance of this kind 
 of verification is the inclusion of a partial under a 
 more general law, the partial law having been arrived 
 at inductively, and it being subsequently shown that the 
 more general law leads deductively to it. Thus, the 
 phenomena of the Tides had, prior to the epoch of 
 Newton, been partially explained by the inductive me- 
 thod. Newton, by deducing these phenomena from the 
 Law of Universal Gravitation, not only afforded a much 
 more complete explanation, but also furnished the most 
 convincing verification of the results already arrived at. 
 Similarly, the laws of falling bodies on the earth's sur- 
 face, which had already been proved inductively, were, 
 from the time of Newton, brought under the law of uni- 
 versal gravitation, and proved deductively from it. The 
 same was also the case with Kepler's Laws, when they 
 were proved deductively from the theorem of the Central 
 Force. This mode of Verification is recommended by^ 
 « See pp. 142, 153, 154. 
 
2,4^ RELATION OF INDUCTION TO DEDUCTION, 
 
 Mr. Mill, under the name of the Inverse Deductive or His- 
 torical Method, as specially applicable to generalisations 
 on society which have been inferred inductively from the 
 study of history or the observation of mankind. These 
 are subsequently verified by being connected deductively 
 with the general laws of mind or conduct which are fur- 
 nished by the study of Psychology or Ethology '^. It is 
 thus shown that the generalisations of history are such 
 as we might have anticipated a priori from a general 
 knowledge of human nature, and each branch of the 
 enquiry is made in this manner to afford a striking con- 
 ^ firmation of the results arrived at by the other. 
 
 It frequently happens that what may be called a re- 
 sidual phenomenon affords an unexpected, and, on that 
 account, a striking verification of some law which is not 
 immediately the object of investigation. Thus, to recur 
 to an instance already adduced for another purpose, 
 when it was found that the difference between the ob- 
 served and calculated velocities of sound was exactly 
 accounted for by the law of the development of heat by 
 compression, this law acquired so nove^ and striking a 
 
 ^ "^ See above pp. 200-202, and Mill's Logic^ Bk. VI. ch. x. I cannot 
 agree with Mr. Mill in attaching any special importance to the order 
 in which the respective Methods are used in this enquiry. Though the 
 inductive investigation, based on the facts of history or observation, 
 generally precedes the deductive verification from the laws of psycho- 
 logy, we may, and sometimes do, begin with psychological generalisa- 
 tions, and subsequently verify them by an appeal to observed facts. 
 The only essential point is, that the two Methods should be combined, 
 so that the results arrived at by the one may corroborate the results 
 arrived at by the other. 
 
AND VERIFICATION, ^47 
 
 eonfirmation as to leave no doubt of its truth or univer- 
 sality. 
 
 The following examples, both taken from LyelFs 
 Principles of Geology ^^ will be interesting, the one as 
 affording a verification, though by no means a complete 
 one, of the bold theory of cosmical clouds, the other as 
 presenting an instance of a very plausible theory which 
 fails to receive any verification from an appeal to facts. 
 
 * There is still another astronomical suggestion respecting 
 the possible causes of secular variations in the terrestrial 
 climates which deserves notice. It has long been known that 
 certain stars are liable to great and periodical fluctuations in 
 splendour, and Sir J. Herschel has lately ascertained (Jan. 
 1840), that a large and brilliant star, called alpha Orionis, 
 sustained, in the course of six v^eeks, a loss of nearly half 
 its light. " This phenomenon," he remarks, " cannot fail to 
 awaken attention, and revive those speculations which were 
 first put forth by my father Sir W. Herschel, respecting the 
 possibility of a change in the lustre of our sun itself. If there 
 really be a community of nature between the sun and fixed 
 stars, every proof that we obtain of the extensive prevalence 
 of such periodical changes in those remote bodies, adds to the 
 probability of finding something of the kind nearer home." 
 Referring then to the possible bearing of such facts on an- 
 cient revolutions in terrestrial climates, he says, that ** it is 
 a matter of observed fact, that many stars han^e undergone, in 
 past ages, within the records of astronomical history, very 
 
 ' Ch. viii. (ninth edition) ; ch. xiii. (tenth edition). The former 
 passage appears not to be embodied in the last edition. Various other 
 theories have been proposed in order to account for the appearance of 
 temporary stars. See Guillemin, The Heavens, and Lardner's Handbook 
 of A stronomy, third edition, edited and revised by E. Dunkin. 
 
0,4^ RELATION OF INDUCTION TO DEDUCTION, 
 
 extensive changes in apparent lustre, without a change of 
 distance adequate to producing such an effect. If our sun 
 were even intrinsically much brighter than at present, the 
 mean temperature of the surface of our globe would, of 
 course, be proportionally greater. I speak now not of perio- 
 dical, but of secular changes. But the argument is compli- 
 cated with the consideration of the possibly imperfect 
 transparency of the celestial spaces, and with the cause of 
 that imperfect transparency, which may be due to material 
 non-luminous particles diffused irregularly in patches analo- 
 gous to nebulae, but of greater extent — to cosmical clouds, in 
 short — of whose existence we have, I think, some indication 
 in the singular and apparently capricious phenomena of tem- 
 porary stars, and perhaps in the recent extraordinary sudden 
 increase and hardly less sudden diminution of ArgusT ' 
 
 * The gradual diminution of the supposed primitive heat 
 of the globe has been resorted to by many geologists as the 
 principal cause of alterations of climate. The matter of our 
 planet is imagined, in accordance with the conjectures of 
 Leibnitz, to have been originally in an intensely heated state, 
 and to have been parting ever since with portions of its heat, 
 and at the same time contracting its dimensions. There are, 
 undoubtedly, good grounds for inferring from recent observa- 
 tion and experiment, that the temperature of the earth in- 
 creases as we descend from the surface to that slight depth 
 to which man can penetrate : but there are no positive proofs 
 of a secular decrease of internal heat accompanied by con- 
 traction. On the contrary, La Place has shown, by reference 
 to astronomical observations made in the time of Hipparchus, 
 that in the last two thousand years at least there has been 
 no sensible contraction of the globe by cooling; for had 
 this been the case, even to an extremely small amount, the 
 day would have been shortened, whereas its length has 
 certainly not diminished during that period by ^th of a 
 second.' 
 
AND VERIFICATION, 249 
 
 In this case, however, no argument can fairly be de- 
 duced from the non-verification of the theory, as the 
 period of our observation, when compared with the 
 enormous geological eras of which it is necessary to 
 take account in these speculations, is so short as possibly 
 to be infinitesimal. The theory receives no verification 
 from the facts to which we appeal, but we cannot say 
 that it is disproved, or even rendered improbable, by 
 their failure to support it. 
 
 It need hardly be remarked that any verification of 
 one inductive proof by another, or of an induction by 
 a deduction, or of a deduction by an induction, should 
 conform to the laws of deductive or inductive reasoning 
 as the case may be. Verification is not a distinct mode 
 of proof, but is simply a confirmation of one proof by 
 another, sometimes of a deduction by an induction, 
 sometimes of an induction by a deduction, and, finally, 
 sometimes of one induction or deduction by another. 
 
 The student will, of course, understand that it is not 
 always necessary to employ Verification. A proof may 
 be so cogent as to need no confirmation. It would be 
 absurd, for instance, to appeal to actual measurement 
 as a verification of the proposition enunciated in Euclid^ 
 i. 47. 
 
CHAPTER VI. 
 On the Fallacies incident to Induction, 
 
 THE errors incidental to inductive reasoning and to 
 its various subsidiary processes have already, to a great 
 extent, been noticed in the preceding chapters. In 
 laying down the conditions essential to the correct 
 conduct of a process, the mistakes which result from 
 its incorrect conduct necessarily form part of our enquiry. 
 Though, therefore, it may be convenient to pass the 
 inductive fallacies in review, it is assumed that the student 
 is already acquainted with the principal errors to which 
 his processes and methods are liable. 
 
 A. To begin with the subsidiary processes, the errors 
 incident to the process of observation, or ^ the fallacies 
 of mis-observation,' are well classified by Mr. Mill as 
 those which arise from Non-observation and those which 
 arise from Mal-observation. 
 
 I. Non-observation may consist either (i) in neglecting 
 some of the instances, or (2) in neglecting some of the 
 circumstances attendant on a given instance. 
 
 ( I ) With respect to the non-observation of instances, it 
 
FALLACIES INCIDENT TO INDUCTION, 2^1 
 
 was long ago pointed out by Bacon ^ that there is in the 
 human mind a peculiar tendency to dwell on affirmative 
 and to overlook negative instances. Familiar examples 
 of this tendency will readily occur to every one. We 
 think it a ' curious coincidence ' that we should suddenly 
 meet a man of whom we have just been talking, that 
 some event should happen of which we dreamed the night 
 before, or that the predictions of a fortune-teller or an 
 almanac should be verified by the facts. The expla- 
 nation of these * curious coincidences ' is that our at- 
 tention is arrested by the affirmative instances, whereas 
 
 ^ * Intellectus humanus in iis quae semel placuerunt (aut quia recepta 
 sunt et credita, aut quia delectant) alia etiam omnia trahit ad suiFraga- 
 tionem et consensum cum illis : et licet major sit instantiarum vis et 
 copia, quae occurrunt in contrarium ; tamen eas aut non observat, aut 
 contemnit, aut distinguendo summovet et rejicit, non sine magno et 
 pernicioso prejudicio, quo prioribus illis syllepsibus auctoritas maneat in- 
 violata. Itaque recte respondit ille, qui, cum suspensa tabula in templo 
 ei monstraretur eorum qui vota solverant quod naufragii periculo elapsi 
 sint, atque interrogando premeretur, anne turn quidem Deorum numen 
 agnosceret, quaesivit denuo, " At ubi sunt illi depicti qui post vota nun- 
 cupata perierint ? " Eadem ratio est fere omnis superstitionis, ut in astro- 
 logicis, in somniis, ominibus, nemesibus, et hujusmodi ; in quibus homines 
 delectati hujusmodi vanitatibus advertunt eventus, ubi implenturj ast 
 ubi fallunt, licet multo frequentius, tamen negligunt et praetereunt. At 
 longe subtilius serpit hoc malum in philosophiis et scientiis ; in quibus 
 quod semel placuit reliqua (licet multo firmiora et potiora) inficit, et in 
 ordinem redigit. Quinetiam licet abfuerit ea, quam diximus, delectatio 
 et vanitas, is tamen humaiio intellectui error est proprius et perpetuus, ut 
 niagis moveatur et excitetur affirmativis, quam negativis ; cum rite et 
 ordiue aequum se utrique praebere debeat ; quin contra, in omni axiomate 
 vero constituendo, major est vis instantiae negativae.' — Novum Organum, 
 Lib. I. Aph. xlvi. 
 
25^ FALLACIES INCIDENT 
 
 the numberless instances in which there is no corre- 
 spondence between the one set of facts and the other 
 altogether escape our notice. We probably talk scores 
 of times during the day of persons whom we do not 
 meet immediately afterwards ; we frequently dream in 
 the most circumstantial manner of events which never 
 occur; and, where one prediction of a fortune-teller is 
 verified, scores are probably falsified. The weather-pro- 
 phets of the almanacs possess a considerable advantage 
 in the fact that, whereas, at all times, there is at least a 
 considerable chance of their predictions turning out true, 
 there are certain periods, such as the equinoxes, at which 
 particular kinds of weather may be anticipated with a 
 probability amounting almost to certainty. 
 
 In former generations ' coincidences ' of this kind were 
 regarded not simply as ' curious ' and ' remarkable,' but 
 as proofs of some causal connection between the events. 
 To talk of a person was supposed to render his presence 
 more likely ; a verified prediction was regarded as evi- 
 dence of second-sight ; and a comet which was observed 
 to be followed by a war was supposed to be, if not 
 the cause of the war, at least a messenger sent from 
 Heaven to proclaim its approach. The tendency to take 
 note of affirmative, and to overlook negative instances, 
 is one of the causes of that hasty generalisation of which 
 we shall speak in a subsequent part of this chapter'^. 
 
 ^ The following remarks of Sir John Herschel, in speaking of the 
 verification of ' signs of the weather,' are so apposite, that I append them 
 in a note. 
 
TO INDUCTION. 253 
 
 This tendency is considerably intensified, if the af- 
 firmative instances are regarded as illustrations of some 
 preconceived theory^, or if the evidence afforded by 
 them be supplemented by some powerful affection of 
 the mind*. It seldom happens that men can hold 
 themselves entirely indifferent with respect to two rival 
 opinions and apply themselves to the comparatively 
 
 ' We would strongly recommend any of our readers whose occupations 
 lead them to attend to the " signs of the weather," and who, from 
 hearing a particular weather adage often repeated, and from noticing 
 themselves a few remarkable instances of its verification, have " begun 
 to put faith in it," to commence keeping a note-book, and to set down 
 without bias all the instances which occur to them of the recognised 
 antecedent, and the occurrence or non-occurence of the expected con- 
 sequent, not omitting also to set down the cases in which it is left 
 undecided ; and after so collecting a considerable number of instances 
 (not less than a hundred), proceed to form his judgment on a fair com- 
 parison of the favourable, the unfavourable, and the undecided cases ; 
 remembering always that the absence of a majority one way or the other 
 would be in itself an improbability, and that, therefore, to have any 
 weight, the majority should be a very decided one, and that not only in 
 itself, but in reference to the neutral instances. We are all involuntarily 
 much more strongly impressed by the fulfilment than by the failure of 
 a prediction, and it is only when thus placin'g ourselves face to face with 
 fact and experience, that we can fully divest ourselves of this bias.' — 
 Familiar Lectures on Scientific Subjects^ Lecture IV. 
 
 ' * Habet enim unusquisque (praeter aberrationes naturae humanae in 
 genere) specum sive cavernam quandam individuam, quae lumen naturae 
 
 frangit et corrumpit ; vel propter differentias impressionum, 
 
 prout occurrunt in animo praeoccupato et praedisposito, aut in animo 
 aequo et sedato.' — Bacon's Novum Organum, Lib. L Aph. xlii. 
 
 * * Intellectus humanus luminis sicci non est ; sed recipit infusionem a 
 voluntate et affectibus ; id quod generat ad quod vult scientias : quod 
 enim mavult homo verum esse, id potius credit.* — Novum Organum, 
 Lib. \. Aoh. xlix. 
 
r^54 FALLACIES INCIDENT 
 
 unexciting task of collecting evidence impartially on 
 either side. To avoid taking a side on imperfect informa- 
 tion, even where our interests or passions are not directly 
 concerned, is one of the last and most difficult lessons 
 learned by the scientific intellect, and by ordinary men 
 it is regarded as a sign of a peculiarly frigid temper- 
 ament, if not of an indifference to truth. Thus, when 
 the theory involved in the idea of witchcraft had once 
 been conceived and accepted, and especially when it 
 had led to the invention of a new crime, it came to 
 be held that the burden of proof lay with those who 
 called its reality in question. Every story which con- 
 firmed the theory would be greedily received, while 
 instances in which the supposed powers of the witch 
 had failed, if noticed at all, would either leave but 
 a slight impression on the mind, or be easily ac- 
 counted for by supposing the intervention of a higher 
 power. To the numerous class engaged in the ad- 
 ministration of the laws, a not unnatural reluctance 
 to question the justice, of the principles on which they 
 and their predecessors had been in the habit of act- 
 ing would furnish an additional inducement to pass 
 lightly over negative instances. Fear, or dread of 
 eccentricity, would operate in the case of others ; 
 and thus a theory of the most preposterous character, 
 which, to a mind not preoccupied, received little or no 
 confirmation from facts ^, and the truth of which could 
 
 ^ When a person was convinced that he was subject to the evil prac- 
 tices of a witch, this conviction would, of course, sometimes produce the 
 
TO INDUCTION, ^55 
 
 easily have been brought to the test, maintained its 
 ground, and throughout many centuries continued to pro- 
 duce the most mischievous results. The extent of the 
 bias to which the mind, in its observation of instances, is 
 exposed from the influence of strong affections, is patent 
 to every one. A man of a desponding temperament will 
 dwell on the number of those who have failed, a man of 
 a sanguine temperament on the number of those who have 
 succeeded, in their respective professions. A man with 
 strong sympathies will see only virtues or good traits of 
 character, where one of a malevolent or critical dispo- 
 sition will see only vices or blemishes. An ardent ad- 
 herent of a religious sect or a political party will see 
 nothing but good in those who agree with him, nothing 
 but evil in those who adopt a different creed or profess 
 to be guided by different principles of policy. 
 
 Many of the above errors might be otherwise described 
 as arising from the confusion between absolute and relative 
 frequency. We notice how often an event occurs, but we 
 do not notice how much oftener it does not occur. 
 
 Not only will a preconceived opinion or a powerful 
 affection come in aid of the natural tendency of men to 
 dwell on affirmative and overlook negative instances, but 
 they will often cause them to adhere to theories for which, 
 whatever may have been the history of their formation, 
 there is absolutely no. support whatever in fact. Thus, 
 
 ill effects attributed to witchcraft itself. In other cases, some event, such 
 as a death or an illness, which occurred in the ordinary course of nature, 
 would confirm the suspicion. 
 
256 FALLACIES INCIDENT 
 
 the theory which prevailed down to the time of Galileo ^, 
 that bodies fall to the earth in times inversely propor- 
 tional to their weights, so that a body weighing, say, 
 five pounds, would fall in a time five times as short as 
 a body weighing one pound, rested on absolutely no 
 evidence except the fact that, in consequence of the re- 
 sistance of the air, the heavier body reaches the ground 
 in a somewhat shorter time than the lighter one; still, 
 till Galileo made his experiments, at the end of the 
 sixteenth century, from the leaning tower of Pisa, no 
 one thought of bringing to a decisive test a theory which 
 it was so easy to prove or disprove. Even, without 
 having recourse to experiment, one would have imagined 
 that the most casual observations of falling bodies would 
 have revealed, to a mind not strongly pre-occupied, the 
 strange inaccuracy of this theory. The reception accorded 
 to the theory that the weight of the elements increases in 
 a tenfold ratio, so that earth is ten times heavier than 
 water, water ten times heavier than air, and air ten times 
 heavier than fire, seems still more astounding ^. 
 
 In Sir Thomas Browne's Enquiries into Vulgar and 
 Common Errors ^, we have an examination of the proposi- 
 tion that ' men weigh heavier dead than alive, and before 
 meat than after/ Here are two extraordinary paradoxes 
 
 • Galilcei Sy sterna Cosmicumj Dial. II. 
 
 ■^ This theory appears to have originated in a mistaken interpretation 
 of a passage in Aristotle, De Generatione et Corruptione^ II. 6. See Ellis 
 and Spedding's note on Bacon's Novum Organum, Lib. I. Aph. xlv. 
 
 * Bk. IV. ch. vii. 
 
TO INDUCTION. 2^7 
 
 which it was perfectly easy for any one to bring to a 
 decisive test ; and still, though an appeal to facts would 
 at once have been fatal to them, they appear to have met 
 with a very general reception. The grounds assigned 
 for the prevalence of the latter opinion are so curious 
 that they deserve to be transcribed. * Many are also of 
 opinion, and some learned men maintain, that men are 
 lighter after meals than before, and that by a supply 
 and addition of spirits obscuring the gross ponderosity 
 of the aliment ingested ; but the contrary hereof we have 
 found in the trial of sundry persons in different sex and 
 ages. And we conceive men may mistake, if they dis- 
 tinguish not the sense of levity unto themselves, and in 
 regard of the scale, or decision of trutination. For after 
 a draught of wine, a man may seem lighter in himself 
 from sudden refection, although he be heavier in the 
 balance, from a corporal and ponderous addition; but 
 a man in the morning is lighter in the scale, because 
 in sleep some pounds have perspired; and is also lighter 
 unto himself, because he is refected.' It will be noticed 
 that ' spirits ' are supposed to possess the property of 
 positive levity, and that, consequently, they are regarded 
 as making any body into which they enter lighter than 
 it was before. The theory that certain bodies are 
 positively light is itself an instance of a fallacy of 
 non-observation, but, as will be seen presently, of non- 
 observation of circumstances not of instances. 
 
 Another extraordinary instance of a statement which 
 obtained acceptance without any foundation whatever in 
 
 s 
 
258 FALLACIES INCIDENT 
 
 fact is noticed in an article in the Quarterly Review for 
 January, 1865, on ' Aristotle's History of Animals.' Here, 
 however, there appears to be no assignable reason for the 
 mistake. 
 
 * Aristotle held some peculiar notions with respect to the 
 skull. He says, '* that part of the head which is covered with 
 hair is called the cranium ; the fore part of this is called 
 the sinciput; this is the last formed, being the last part in 
 the body which becomes hard." He correctly alludes here 
 to the opening in the frontal bone of a young infant, which 
 gradually becomes hardened by ossification ; " the hinder part 
 is the occiput, and between the occiput and sinciput is the 
 crown of the head : the brain is placed beneath the sinciput, 
 and the occiput is empty (!). The skull has sutures ; in women 
 there is but one placed in a circle (!) ; men have generally 
 three joined in one, and a man's skull has been seen without 
 any sutures at all." The often repeated question as to how 
 far Aristotle's observations are the result of his own investi- 
 gation, naturally suggests itself again here ; had Aristotle ever 
 dissected a human body, he never would have asserted a 
 proposition so manifestly false as that the back of the head 
 is empty, or that women have one only suture placed in a 
 circle.' 
 
 The passage here noticed occurs in the Historia Ani- 
 malium, Bk, I. ch. vii. Cp. Bk. HI. ch. vii. 
 
 A still more remarkable instance of this description of 
 fallacy is noticed in Mr. Lecky's History of European 
 Morals from Augustus to Charlemagne^. 
 
 *■ Aristotle, the greatest naturalist of Greece, had observed 
 that it was a curious fact, that on the sea-shore no animal 
 
 » Vol. i. p. 394. 
 
TO INDUCTION, 259 
 
 ever dies except during the ebbing of the tide. Several cen- 
 turies later, Pliny, the greatest naturalist of an empire that 
 was washed by many tidal seas, directed his attention to this 
 statement. He declared that after careful observations which 
 had been made in Gaul, it had been found to be inaccurate, 
 for what Aristotle stated of all animals, was in fact only true 
 of man. It was in 1727 and the two following years, that 
 scientific observations made at Rochefort and at Brest finally 
 dissipated the delusion.' 
 
 We add one more instance, showing the extraordinary 
 readiness with which men, even of remarkable acuteness 
 and erudition, will accept the strangest fancies, though 
 absolutely unsupported by evidence. It is taken from 
 GlanvilFs Scepsis Scientifica, published in 1665^^: — 
 
 ^Besides this there is another way of secret conveyance 
 that's whisper'd about the World, the truth of which I vouch 
 not, but the possibility : it is conference at distance by sym- 
 pathized handes. For say the relatours of this strange secret : 
 The hands of two friends being allyed by the transferring of 
 Flesh from one into another, and the place of the Letters 
 mutually agreed on ; the least prick in the hand of one, the 
 other will be sensible of, and that in the same part of his own. 
 And thus the distant friend, by a new kind of Chiromancy, 
 may read in his own hand what his correspondent had set 
 down in his. For instance, would I in London acquaint my 
 intimate in Paris, that I am well: I would then prick that 
 part where I had appointed the letter [I] and doing so in 
 another place to signifie that word was done, proceed to [A], 
 thence to [M], and so on, till I had finisht what I intended to 
 make known.* 
 
 ^® Scepsis Scientijica, ch. 24. 
 S 2 
 
25o FALLACIES INCIDENT 
 
 The influence of some strong passion or affection in 
 causing men to accept theories without any support from 
 observation or experiment, and often in direct defiance 
 of them, may be illustrated from almost all the more 
 powerful feelings of human nature. The mythologies of 
 every nation are full of the wildest and most improbable 
 stories, originating partly in the strength of the religious 
 sentiment, partly in that love of the marvellous which 
 seems to be connatural to every race of mankind, partly 
 in later misinterpretations of that poetical language in 
 which early races are wont to clothe their ideas. Thus, 
 stories of the transformation of men into beasts, of 
 rivers flowing backwards, of images falling down from 
 heaven, besides other tales still more fantastic, have been 
 greedily received by generation after generation, in spite 
 of all the analogies of nature and without one single 
 instance to confirm them. The beliefs in ghosts, spirit- 
 rapping, and similar phenomena, seem to have their 
 origin in man's insatiable craving for the marvellous, 
 acting often in combination with the feelings of fear, 
 hope, or curiosity. One of the most powerful agents 
 in human affairs is the passion of avarice or the insa- 
 tiable desire for the accumulation of wealth. In the 
 middle ages, this passion led the alchemists, contrary to 
 all experience, to the belief that it was open to men to 
 become suddenly and enormously rich by discovering the 
 secret of transmuting other metals into gold. In modern 
 times it has frequendy led, and still leads, men to embark 
 in the most desperate speculations, which no scientific 
 
TO INDUCTION. 26 1 
 
 calculation of chances would justify. In a lottery, for 
 instance (which is a comparatively innocuous form of 
 speculation), the value of the chance is, owing to the 
 expenses of management and the profit required by the 
 projectors, invariably much less than the price paid for 
 the ticket. But, perhaps, the most remarkable exempli- 
 fication of the unreasoning desire for sudden accessions 
 of wealth is to be found in the pertinacity with which, 
 in spite of every warning, men would, till within the 
 last few years, expend large fortunes in sinking shafts 
 for coal and other minerals in strata in which the uni- 
 versal experience of geologists and miners testified against 
 their occurrence. In this, as in many other cases, the 
 observations of competent authorities went for nothing; 
 the passion was so absorbing that it alone determined 
 action. 
 
 The fallacies due to non-observation of instances may 
 be further exemplified by the tendency of the mind to 
 acquiesce in the first instances which offer themselves ^^ 
 especially if they be of a striking kind ^^, instead of care- 
 
 " ' Axiomata, quae in usu sunt, ex tenui et manipulari cxperientia, et 
 paucis particularibus, quae ut plurimum occurrunt, fluxere ; et sunt fere 
 ad mensuram eorum facta et extensa.' — Novum Organum, Lib. I. 
 Aph. xxy. 
 
 ^* • Intellectus humanus illis, quae simul et subito mentem ferire et 
 subire possunt, maxime movetur ; a quibus phantasia impleri et inflari 
 consuevit : reliqua vero modo quodam, licet imperceptibili, ita se habere 
 fingit et supponit, quomodo se habent pauca ilia quibus mens obsidetur ; 
 ad ilium vero transcursum ad instantias remotas et heterogeneas, per 
 quas axiomata tanquam igne probantur, tardus omnino intellectus est et 
 
262 FALLACIES INCIDENT 
 
 fully searching for other instances of a similar nature 
 with which to compare and by means of which to in- 
 terpret them. Thus, the phenomena of thunder and 
 lightning would probably have received a much earlier 
 explanation, had the attention of men been sooner di- 
 rected to the instances of electricity which nature presents 
 of a less striking kind and on a smaller scale. Again, the 
 difficulties presented to early speculators by volcanoes 
 and earthquakes would have been considerably dimi- 
 nished, had they been aware of the fact that there is 
 hardly any portion of the earth's surface which is not 
 undergoing a constant change of level by the process 
 either of elevation or of subsidence, though such change 
 is usually imperceptible to each single generation. The 
 mistakes originating in this source of error are count- 
 less. We observe certain peculiarities in some particular 
 representative of a class, profession, or nation, and then 
 proceed to argue as if all the members of the class, 
 profession, or nation were like him. Or, a person on 
 his travels in some country is unfavourably impressed 
 with the hotel-keepers, porters, and carriage-drivers, and 
 then proceeds to denounce the whole nation to which 
 they belong, as if the characteristics of a few exceptional 
 classes were the characteristics of a nationality *^. 
 
 inhabilis, nisi hoc illi per duras leges et violentum imperium imponatur.' — 
 Novum Organum, Lib. I. Aph. xlvii. 
 
 1^ The history of the French language furnishes a striking instance 
 ot non- observation and of the curious and baseless theories to which it 
 may lead : ' It is well known that before certain feminine substantives. 
 
TO INDUCTION, 263 
 
 The student must have already perceived that we are 
 trenching on Fallacies of GeneraHsation. When we 
 proceed to treat insufficient evidence, or the absence of 
 evidence, or popular beliefs which run counter to all 
 the evidence available, as if they afforded perfectly suf- 
 ficient evidence, the fallacy is one of inference, and, if 
 
 such as messe, mere, soif, faim, peur^ &c., the adjective grand keeps 
 its masculine termination, grancTmessey grand'mere, &c. Why so? 
 Grammarians, who are puzzled by nothing, tell us without hesitation 
 that grand is here put for grande, and that the apostrophe marks the 
 suppression of the final e. But the good sense of every scholar protests 
 against this ; after having learnt in childhood that e mute is cut off 
 before a vowel, and never before a consonant, he is told that the e 
 is here cut off without the slightest reason in such phrases as grand'- 
 route, &c. The real explanation is in fact a very different one. In its 
 beginning, French grammar was simply the continuation and prolonga- 
 tion of Latin grammar ; consequently the Old French adjectives followed 
 in all points the Latin adjective ; those adjectives which had two termi- 
 nations for masculine and feminine in Latin (as bonus^ bona) had two in 
 Old French, whereas those Latin adjectives which had but one (as grandis, 
 fortis, &c.), had only one in French. In the thirteenth century men 
 said ufie grand femme, grandis femina ; une dme mortel, mortalis anima ; 
 une coutume cruel, crudelis ; une plaine vert^ viridis planities, &c. In 
 the fourteenth century the meaning of this distinction was no longer 
 understood ; and men, deeming it a mere irregularity, altered the form 
 of the second to that of the first class of adjectives, and wrote grande, 
 ve7'te, forte, &c., after the pattern of bonne, &c. A trace of the older 
 and more correct form survives in such expressions as grana'mere^ 
 grand'route, grand'faim, grand'garde, &c., which are the debris of the 
 older language. In the seventeenth century, Vaugelas and the gram- 
 marians of the age, in their ignorance of the historic reason of this usage, 
 pompously decreed that the form of these words arose from an euphonic 
 suppression of the e mute, which must be indicated by an apostrophe.' — 
 Brachet's Historical Grammar of the French Tongue, Mr. Kitchin's 
 Transly Preface, p. vi. 
 
264 FALLACIES INCIDENT 
 
 the simulated inference be inductive, it is a Fallacy of 
 Generalisation. But the absence or insufficiency of the 
 evidence, if due to our not having kept our minds 
 sufficiently open to facts or not having taken sufficient 
 pains to collect all the facts pertinent to the question, 
 is a Fallacy of Non-observation, and is a defect in the 
 preliminary process rather than in the inductive in- 
 ference itself It is believed that all the instances de- 
 scribed above fall under this head, though the inferences 
 founded upon them, where they possess any show of 
 justification at all, are cases of unwarranted Inductio per 
 Simplicem Enumerationem, and so afford illustrations of 
 Fallacies of Generalisation. 
 
 (2) The second division of the Fallacies of Non-obser- 
 vation is the fallacy which arises from overlooking some 
 of the material circumstances attendant on a given in- 
 stance. Here the defect is not in the number or per- 
 tinency of the instances, but in their character; the 
 description of the instances themselves is untrustworthy. 
 Till we have ascertained that we are fully acquainted with 
 all the material circumstances of the cases examined, we 
 cannot rely upon our facts, and, consequently, we have 
 no right to proceed to ground any inference upon them. 
 ' The circumstances,' says Sir John Herschel ^S ^ which 
 accompany any observed fact, are main features in its 
 observation, at least until it is ascertained by sufficient 
 experience what circumstances have nothing to do with 
 
 ^* Herschers Discourse on the Study of Natural Philosophy, § ill. 
 
TO INDUCTION. 265 
 
 it, and might therefore have been left unobserved without 
 sacrificing the fact. In observing and recording a fact, 
 therefore, altogether new, we ought not to omit any cir- 
 cumstance capable of being noted, lest some one of the 
 omitted circumstances should be essentially connected 
 with the fact. . . . For instance, in the fall of meteoric 
 stones, flashes of fire are seen proceeding from a cloud, 
 and a loud rattling noise like thunder is heard. These 
 circumstances, and the sudden stroke and destruction 
 ensuing, long caused them to be confounded with an 
 effect of lightning, and called thunderbolts. But one 
 circumstance is enough to mark the difference : the flash 
 and sound have been perceived occasionally to emanate 
 from a very small cloud insulated in a clear sky ; a com- 
 bination of circumstances which never happens in a 
 thunder storm, but which is undoubtedly intimately con- 
 nected with their real origin.' 
 
 The extreme difficulty of obtaining, by means of the 
 thermometer, a correct measure of the temperature of 
 the atmosphere, owing to the conduction of heat by the 
 stand and its radiation from surrounding objects, and the 
 consequent errors frequently made by observers from not 
 sufficiently providing against, or allowing for, these 
 sources of interference, will serve to every one as a 
 familiar illustration of the great importance of the caution 
 which it is here intended to furnish. 
 
 The following examples, adduced by Mr, MilP^ are 
 
 ^ System of Logic, Bk. V. ch. iv. § 4, 
 
266 FALLACIES INCIDENT 
 
 SO interesting and appropriate, that I take the Hberty 
 of transcribing them : — 
 
 * Such, for instance [namely, the imperfect observation of 
 particular facts], was one of the mistakes committed in the 
 celebrated phlogistic theory ; a doctrine which accounted for 
 combustion by the extrication of a substance called phlogiston, 
 supposed to be contained in all combustible matter. The 
 hypothesis accorded tolerably well with superficial appear- 
 ances ; the ascent of flame naturally suggests the escape of 
 a substance; and the visible residuum of ashes, in bulk and 
 weight, generally falls extremely short of the combustible 
 material. The error was, non-observation of an important 
 portion of the actual residue, namely, the gaseous products 
 of combustion. When these were at last noticed and brought 
 into account, it appeared to be an universal law, that all 
 substances gain instead of losing weight by undergoing com- 
 bustion ; and, after the usual attempt to accommodate the old 
 theory to the new fact by means of an arbitrary hypothesis 
 (that phlogiston had the quality of positive levity instead of 
 gravity), chemists were conducted to the true explanation, 
 namely, that instead of a substance separated, there was on 
 the contrary a substance absorbed. 
 
 ^ Many of the absurd practices which have been deemed 
 to possess medicinal efficacy, have been indebted for their 
 reputation to non-observance of some accompanying circum- 
 stance which was the real agent in the cures ascribed to them. 
 Thus, of the sympathetic powder of Sir Kenelm Digby : 
 " Whenever any wound had been inflicted, this powder was 
 applied to the weapon that had inflicted it, which was, more- 
 over, covered with ointment, and dressed two or three times 
 a day. The wound itself, in the meantime, was directed 
 to be brought together, and carefully bound up with clean 
 linen rags, but abo've ally to be let alone for seven days, at the 
 end of which period the bandages were removed, when the 
 
TO INDUCTION. 267 
 
 wound was generally found perfectly united. The triumph 
 of the cure was decreed to the mysterious agency of the 
 sympathetic powder which had been so assiduously applied 
 to the weapon, whereas it is hardly necessary to observe that 
 the promptness of the cure depended upon the total ex- 
 clusion of air from the wound, and upon the sanative opera- 
 tions of nature not having received any disturbance from the 
 officious interference of art. The result, beyond all doubt, 
 furnished the first hint which led surgeons to the improved 
 practice of healing wounds by what is technically called the 
 Jirst intention ^^" ' 
 
 The next example I extract from Bp. Wilkins' very 
 curious tractate, entitled A Discovery of a Neiv World, 
 or a Discourse tending to prove that 'tis probable there may 
 be afiother Habitable World in the Moon : — 
 
 * He [that is, ' a late reverend and learned Bishop,' 
 writing * under the feigned name of Domingo Gonsales,' ^''] 
 supposeth that there is a natural and usual passage for many 
 creatures betwixt our earth and this planet. Thus, he says, 
 those great multitude of locusts wherewith divers countries 
 have been destroyed, do proceed from thence. And if we 
 peruse the authors who treat of them, we shall find that many 
 times they fly in numberless troops or swarms, and for sundry 
 days together before they fall are seen over those places in 
 great high clouds, such as coming nearer, are of extension 
 enough to obscure the day, and hinder the light of the sun. 
 From which, together with divers other such relations, he 
 
 ^* Dr. Paris' Pharmacologia, pp. 23-24. 
 
 ^^ The small tract here referred to is republished in vol. viii. of the 
 Harleian Miscellanies (Park's Edition). The author was Francis God- 
 win, afterwards Bishop of Hereford, and author of the well-known book 
 Be PrcBSiilibus Anglice Commentarius, 
 
268 FALLACIES INCIDENT 
 
 concludes that *tis not altogether improbable they should 
 proceed from the moon. Thus, likewise, he supposes the 
 swallows, cuckoos, nightingales, with divers other fow^l, which 
 are with us only half a year, to fly up thither when they go 
 from us. Amongst which kind, there is a wild swan in the 
 East Indies, which at certain seasons of the year do constantly 
 take their flight thither. Now, this bird being of a great 
 strength, able to continue for a long flight, as also going 
 usually in flocks like our wild geese, he supposeth that 
 many of them together might be thought to carry the weight 
 of a man; especially if an engine were so contrived (as he 
 thinks it might) that each of them should bear an equal share 
 in the burden. So that by this means, 'tis easily conceivable, 
 how once a year a man might finish such a voyage; going 
 along with these birds at the beginning of winter, and again 
 returning with them in the spring ^^.' 
 
 A more accurate and extended series of observations 
 would, of course, have shown that the birds and locusts 
 migrated from other parts of the earth's surface. 
 
 It is not necessary to multiply examples of the errors 
 arising from slovenhness and inattention in the collec- 
 tion or examination of our instances. The necessity 
 of maintaining the strictest caution and accuracy in 
 the conduct of our observations and experiments has 
 already been insisted upon in the Second Chapter of 
 this work. 
 
 11. Besides the errors which originate in the neglect of 
 instances or of some of the circumstances which are con- 
 nected with a given instance, there is another class of 
 errors derived from mistaking for observation that which 
 
 ^* Wilkins' Discovery of a New World, Fifth Edition, p. i6o. 
 
TO INDUCTION, 269 
 
 is not observation at all, but inference. To this class of 
 errors Mr. Mill gives the name of Fallacies of Mal- 
 Observation. That which is strictly matter of perception 
 does not admit of being called in question; it is the 
 ultimate basis of all our reasoning, and, if v^e are 
 to repose any confidence whatever in the exercise of 
 our faculties, must be taken for granted. But there are 
 few of our perceptions, even of those which to the un- 
 philosophical observer appear to be the simplest, which 
 are not inextricably blended with inference. Thus, as 
 is well known to every student of psychology, in what 
 are familiarly called the perceptions of distance and of 
 form, the only perception proper is that of the various 
 tints of colour reflected on the retina of the eye, and it is 
 by a combination of this with perceptions of touch, and 
 of the muscular sense, that the mind gains its power of 
 determining form and distance. Now, a judgment of this 
 kind, which is really due to inference, is, especially by 
 the uneducated and unreflecting, perpetually mistaken for 
 that which is due to direct observation ; and thus what is 
 really only an inference from facts is often emphatically 
 asserted to be itself a matter of fact. * In proportion,' 
 says Mr. Mill ^^, ' to any person's deficiency of knowledge 
 and mental cultivation, is generally his inability to dis- 
 criminate between his inferences and the perceptions on 
 which they were grounded. Many a marvellous tale, 
 many a scandalous anecdote, owes its origin to this in- 
 capacity. The narrator relates, not what he saw or heard, 
 
 i» Mill's Logic, Bk. V. ch. iv. § 5. 
 
270 FALLACIES INCIDENT 
 
 but the impression which he derived from what he saw or 
 heard, and of which perhaps the greater part consisted 
 of inference, though the whole is related not as inference 
 but as matter-of-fact. The difficulty of inducing wit- 
 nesses to restrain within any moderate limits the inter- 
 mixture of their inferences with the narrative of their 
 perceptions, is well known to experienced cross-ex- 
 aminers; and still more is this the case when ignorant 
 persons attempt to describe any natural phenomenon. 
 " The simplest narrative," says Dugald Stewart, " of the 
 most illiterate obsei:ver involves more or less of hypo- 
 thesis ; nay, in general, it will be found that, in pro- 
 portion to his ignorance, the greater is the number of 
 conjectural principles involved in his statements. A 
 village apothecary (and, if possible, in a still greater 
 degree, an experienced nurse) is seldom able to describe 
 the plainest case, without employing a phraseology of 
 which every word is a theory : whereas a simple and 
 genuine specification of the phenomena which mark a 
 particular disease; a specification unsophisticated by 
 fancy, or by preconceived opinions, may be regarded as 
 unequivocal evidence of a mind trained by long and 
 successful study to the most difficult of all arts, that of 
 the faithful interpretation of nature/' ' 
 
 No better instance of the Fallacy of Mal-observation 
 can be given than that adduced by Mr. Mill and many 
 other authors of the confusion between observation and 
 inference, namely, what was called the common-sense 
 argument against the truth of the Copernican System. 
 
TO INDUCTION. 27 1 
 
 That the earth should move round the sun, men said, was 
 impossible ; for, every day, they saw the sun rise and set 
 and perform his course in the heavens. They felt the 
 earth at rest, they saw the sun in motion, and it was 
 absurd to call upon them to disbelieve the direct evidence 
 of their senses. It need hardly be said that what they 
 mistook for the direct evidence of their senses was really 
 an inference. What they saw was consistent with one 
 or other of two hypotheses, that the sun moved, or that 
 the earth moved ; and, neglecting to take any account of 
 the latter, they assumed the former. If it were not for 
 the impressions of a contrary kind derived from the 
 actual motion of the carriage, a man, whirled along in 
 a railway train, might with equal justice maintain, by an 
 appeal to the evidence of his eyesight, that the trees and 
 the houses were running past him. 
 
 Ventriloquism supplies another familiar instance of the 
 same error. A man who had never before been imposed 
 upon by the tricks of a ventriloquist, and who was not 
 aware of the character of the deception, would be positive 
 in maintaining that he had the direct evidence of the 
 sense of hearing in support of his belief that the sound 
 he heard proceeded from a particular person or a par- 
 ticular part of the building other than that from which it 
 really came. The fact, of course, is that the sound itself is 
 all that is directly perceived by the sense of hearing ; the 
 reference of it to a particular person or a particular place 
 is an act of inference grounded upon constant, or at 
 least frequent, association. What is done by the ven- 
 
2"]% FALLACIES INCIDENT 
 
 triloquist is not to deceive the sense of hearing, but to 
 mislead the faculty of judgment. 
 
 What are called * delusions ' and ' hallucinations ' fur- 
 nish a further instance of Mal-observation. It seems to 
 be now pretty generally agreed that these are due to 
 morbid affections of the sensory ganglia. ^ The patient's 
 senses/ says Dr. Maudsley^^, speaking of what he calls 
 sensorial insanity, ' are possessed with hallucinations, their 
 ganglionic central cells being in a state of convulsive 
 action; before the eyes are blood-red flames of fire, amidst 
 which whosoever happens to present himself, appears as 
 a devil, or otherwise horribly transformed ; the ears are 
 filled with a terrible roaring noise, or resound with a voice 
 imperatively commanding him to save himself; the smell 
 is perhaps one of sulphurous stifling ; and the desperate 
 and violent actions are, like the furious acts of the ele- 
 phant, the convulsive reactions to such fearful halluci- 
 nations. The individual in such a state is a machine set 
 in destructive motion, and he perpetrates the extreme st 
 violence or the most desperate murder without conscious- 
 ness at the time, and without memory of it afterwards.' 
 What is here said of delusions in that extreme form in 
 which they assume unmistakeably the character of mad- 
 ness applies equally, as an explanation, to those less 
 obtrusive, though far more frequent, forms in which they 
 produce semi-insanity, monomania, melancholy, or par- 
 tial and temporary deception. In all these cases, the 
 sensations are really experienced; the error consists in 
 
 ^^ Maudsley, The Physiology and Pathology of Mind ^ ch. iv. p. loi. 
 
TO INDUCTION. 2 7 3 
 
 referring the cause of the sensations to external objects 
 rather than to the morbid condition or action of the 
 brain itself. The testimony of others, or the inherent 
 improbability of the things perceived, ought to be re- 
 garded, though they seldom are, as sufficient proof that 
 the evidence of the senses is given under abnormal and 
 untrustworthy conditions. 
 
 The description here given of the errors originating 
 in Non-observation or Mal-observation, includes, as will 
 already have been perceived, the errors incident to arti- 
 ficial as well as to natural observation, that is, to experi- 
 ment as well as to observation proper. 
 
 III. The errors incidental to the other operations 
 preliminary to induction, namely, classification, nomen- 
 clature, terminology, and hypothesis, will be sufficiently 
 apparent on a perusal of the sections appropriated to 
 the discussion of those processes. In the steps inter- 
 mediate between the observation of individual facts and 
 the inductive inference itself, it is in the employment 
 of artificial instead of natural classifications, and in 
 the neglect of the rules designed to guard against the 
 formation of illegitimate hypotheses, that the danger of 
 error mainly lies. 
 
 B. The fallacies incidental to the performance of the in- 
 ductive process itself may be called Fallacies of General- 
 isation. An error of this class is committed whenever, 
 in arguments grounded on experience, we overrate the 
 
 T 
 
274 FALLACIES INCIDENT 
 
 value of the evidence before us; that is, whenever we 
 accept an imperfect induction as a perfect one, or when- 
 ever, in an induction confessedly imperfect, we under- 
 estimate the amount of imperfection. 
 
 Of the imperfect inductions, the argument from analogy 
 is little likely to be mistaken for a perfect induction. The 
 strength of the analogy is often grossly exaggerated, and 
 an argument which possesses litde or no probability is 
 often adduced as affording highly probable evidence; but, 
 as this kind of argument is very seldom ^^ treated as 
 affording absolute certainty, the discussion of false ana- 
 logies may be reserved till we have completed the treat- 
 ment of those errors which consist in regarding imperfect 
 as perfect inductions. 
 
 Excluding analogy, there are, as we have seen, two 
 forms of imperfect induction, that which employs the 
 incomplete Inductio per Simplicem Enumerationem and 
 that which consists in an imperfect fulfilment of the 
 conditions of the inductive methods. An argument of 
 either of these classes may be, and frequently is, mis- 
 taken for a perfect induction. We shall first notice the 
 case in which scientific induction is simulated by the 
 incomplete Inductio per Simplicem Enumerationem 2^. 
 
 ^^ The geological example on p. 230 may perhaps be an instance of 
 an analogical argument thus regarded. Many writers have certainly 
 treated the inference as if its certainty admitted of no doubt. 
 
 ^ The student who has read the first and fourth Chapters hardly 
 needs to be reminded that there are cases, however, in which the method 
 of Inductio per Enumerationem Simplicem may, or even must, be em- 
 
TO INDUCTION, 275 
 
 IV. When men first begin to argue from their experience 
 of the past to their expectation of the future, or from 
 the observation of what immediately surrounds them to 
 the properties of distant objects, they seem naturally to 
 fall into this unscientific and unreflective mode of reason- 
 ing. They have constantly seen two phenomena in con- 
 junction, and, consequently, they cannot imagine them 
 to be dissevered, or they have never seen two phenomena 
 in conjunction, and, consequently, they cannot imagine 
 them to be associated. The difficulties experienced by 
 children in accommodating their conceptions to the 
 wider experiences of men; the tendency of the unin- 
 structed, and frequently even of the instructed, to 
 invest with the peculiar circumstances of their own time 
 or country the men of a former generation or of another 
 land ; the prejudices entertained against those of another 
 creed, or party, or nationality, as if moral excellence 
 were never dissociated from particular opinions or a 
 particular lineage, — are all evidences of the limited 
 character of our first efforts at generalisation. It is 
 long before men learn to discriminate between the 
 material and immaterial circumstances attendant on 
 any given phenomenon, to perceive the irrelevancy of 
 the immaterial circumstances, and to recognise the 
 necessity of insisting on a repetition of all the mate- 
 rial circumstances before they anticipate a similar 
 effect. But not only is the Inductio per Simplicem 
 
 ployed. The fallacies here treated are due to the unnecessary or inju- 
 dicious employment of the method. 
 
276 FALLACIES INCIDENT 
 
 Enumerationem the mode of generalisation natural to 
 immature and uninstructed minds ; it is the method 
 which, till the time of Bacon ^^, or at least till the era 
 of those great discoveries which shortly preceded the 
 time of Bacon, was almost universal. Aristotle, it is 
 true, requires that an induction should be based on an 
 examination of all the instances; but this requirement 
 being in the vast majority of cases impossible of ful- 
 filment, he was obliged, whenever he had recourse to 
 experience, to content himself with an inspection of 
 those cases which were nearest at hand. Thus, in the 
 very passage ^^ in which he emphatically asserts that the 
 
 "^ Bacon seems to be never weary of condemning this unscientific 
 procedure. Thus, in addition to the aphorism already quoted (p. 123), 
 we have, amongst others, the following emphatic passages : * Axiomata 
 quae in usu sunt, ex tenui et manipulari experientia, et paucis particulari- 
 bus, quae ut plurimum occurrunt, fluxere; et sunt fere ad mensuram 
 eorum facta et extensa : ut nil mirum sit, si ad nova particularia non 
 ducant. Quod si forte instantia aliqua, non prius animadversa aut 
 cognita, se offerat, axioma distinctione aliqua frivola salvatur, ubi emen- 
 dari ipsum verius foret.' — Nov. Org. Lib. I. Aph. xxv. ' At philosophiae 
 genus empiricum placita magis deformia et monstrosa educit, quam 
 sopkisttcum aut rationale genus; quia non in luce notionum vulgarium 
 (quae licet tenuis sit et superficialis, tamen est quodammodo universalis, 
 et ad multa pertinens) sed in paucorum experimentorum angustiis et 
 
 obscuritate fundatum est Sed tamen circa hujusmodi philosophias 
 
 cautio nuUo modo praetermittenda erat ; quia mente jam praevidemus et 
 auguramur, si quando homines, nostris monitis excitati, ad experientiam 
 se serio contulerint (valere jussis doctrinis sophisticis) tum demum, 
 propter praematuram et praeproperam intellectus festinationem et saltum 
 sive volatum ad generalia et rerum principia, fore ut magnum ab hujus- 
 modi philosophiis periculum immineat ; cui malo etiam nunc obviam ire 
 debemus.' — Aph. Ixiv. . ^* Analytica Priora, ii. 25. 
 
TO INDUCTION, I^J 
 
 minor premiss of the inductive syllogism (for he repre- 
 sents induction under the syllogistic form) should include 
 all the instances, he argues that all animals which are 
 deficient in bile are long-lived, because he finds this to 
 be the case with the man, the horse, and the mule. 
 Aristotle's works, and especially those on Natural His- 
 tory, abound in rash generalisations of this kind. * It 
 is a fact,' says Mr. Lewes ^^ ' that normally in turtles, 
 and exceptionally in elephants, horses, and oxen, there 
 is an ossification of the septum of the heart. Aristotle 
 saw or heard of one of these " bones " in the hearts of 
 a horse and an ox, and forthwith generalised the obser- 
 vation thus : " The heart is destitute of bones except in 
 horses and in a species of ox; these, however, in con- 
 sequence of their size, have something bony as a support, 
 just as we find throughout the whole body^^." His 
 Spanish follower Funes Y Mendo9a improves on this 
 by saying that the bone acts Hke a stick to support the 
 weight of the heart, which is very great.' 
 
 There is another passage in which Aristotle tells us 
 that the cranium of a dog consists of a single bone^l 
 * It is probable,' says the author of the review previously 
 quoted ^^, '■ that Aristotle had got hold of the cranium 
 of an old individual in which the sutures had become 
 obliterated/ J^' 
 
 ^^ Lewes' Aristotle, ch. xvi. § 399. // > '^ / 
 
 2« De Partihus Animalium, Bk. III. ch. ivj" A^ // 
 
 ^■^ TcL fiev yap Ix^t iiovoanov to Kpavi^^ cuatrtp 6 K/caVy^Ta Se atf-^ 
 eifievov, wa-n^p dvOpomos. — Hisioria AnimdiiumCBk. Ill, chy^L ^/ 
 
 uei^evov, (jjCTT€p dvOpomos. — Hisioria Animdliutr^Bk. Ill, chy^L ^ 
 
 Qwor/^/y /^m^M/, No. 233, Art. ii. ^i/ ^A' 
 
 ri> 
 
-ay 8 FALLACIES INCIDENT 
 
 The employment of the Inductio per Simplicem Enu- 
 merationem prevailed so universally from the time of 
 Aristode to the rise of modern science that it seems 
 unnecessary to multiply instances of it during that period. 
 But it may be instructive to illustrate from the history 
 of more recent times the peculiar facility with which 
 some even of the greatest discoverers have lapsed into 
 this erroneous form of reasoning. 
 
 *Bichat/ says Mr. Lewes ^^, 'tried to establish a gene- 
 ralisation which has been much admired, namely, that all the 
 organs of Animal life are double and symmetrical, while all 
 the organs of Vegetal life are single and asymmetrical. Un- 
 happily the facts do not fit. In the commencement almost 
 e'very organ is double and symmetrical ; and only in the later 
 stages of development do the differences appear. Even in the 
 matured organism we find many striking exceptions to Bichat's 
 generalisation. Thus the parotid, sublingual, and mammary 
 glands, the lungs, the kidneys, ovaries, and testes, are all 
 vegetal organs, and all generally double. And if the heart 
 and uterus are classed as single organs, then must the brain 
 and spinal cord be classed thus. While in birds the liver is 
 double and symmetrical.' 
 
 * It is in a great degree true,' we are informed by Dr. 
 Paris ^^, * that the sensible qualities of plants, such as coloury 
 taste, and smell, have an intimate relation to their properties, 
 and may often lead by analogy to an indication of their 
 powers ; we have an example of this in the dark and gloomy 
 aspect of the Luridce, which is indicative of their narcotic and 
 very dangerous qualities, as Datura, Hyoscyamus, Atropa, and 
 
 2^ Lewes' Aristotle, ch. xvi. § 399 d. 
 
 ^ Pharmacologia, ninth ed. pp. 110, 1 11. 
 
TO INDUCTION. 279 
 
 Nicotiana, Colour is certainly in many cases a test of activity ; 
 the deepest of coloured flowers, the Digitalis, for example, 
 are the most active, and v^^hen the leaves of powerful plants 
 lose their green hue, we may conclude that a corresponding 
 deterioration has taken place with respect to their virtues ; 
 but Linnaeus ascribed too much importance to such an indica- 
 tion, and his aphorisms are unsupported by facts; for in- 
 stance, he says, " Color pallidus insipidum, viridis crudum, 
 luteus amarum, ruber acidum, albus dulce, niger ingratuniy 
 indicat." * 
 
 The early history of Geology presents, in the con- 
 troversy which was long carried on between the Nep- 
 tunians and Vulcanians, a remarkable instance of the 
 errors arising from a partial induction, as well as of the 
 tenacity with which men will cling to views to which they 
 have once committed themselves. The Neptunians, the 
 student need hardly be told, referred all geological phe- 
 nomena to the influence of water, while the Vulcanians 
 greatly exaggerated the action of heat in the past his- 
 tory of the globe, and multiplied to an excess the number 
 of formations to be ascribed to an igneous origin. Of 
 the Neptunians, the great Saxon geologist Werner was 
 the chief. 
 
 * Werner,' says Sir Charles LyelP^, *had not travelled to 
 distant countries; he had merely explored a small portion 
 of Germany, and conceived, and persuaded others to believe, 
 that the whole surface of our planet, and all the mountain 
 chains in the world, were made after the model of his own 
 province. It became a ruling object of ambition in the minds 
 
 ^^ Lyell's Principles of Geology, Bk. I. ch. iv. 
 
28o FALLACIES INCIDENT 
 
 of his pupils to confirm the generalisations of their great 
 master, and to discover in the most distant parts of the globe 
 his " universal formations," which he supposed had been each 
 in succession simultaneously precipitated over the whole earth 
 from a common menstruum or " chaotic fluid." It now 
 appears that the Saxon professor had misinterpreted many 
 of the most important appearances even in the immediate 
 neighbourhood of Freyberg. Thus, for example, within a 
 day's journey of his school, the porphyry, called by him 
 primitive, has been found not only to send forth veins or 
 dikes through strata of the coal formation, but to overlie 
 them in mass.* 
 
 *In regard to basalt and other igneous rocks, Werner's 
 theory was original, but it was also extremely erroneous. 
 The basalts of Saxony and Hesse, to which his observations 
 were chiefly confined, consisted of tabular masses capping the 
 hills, and not connected with the levels of existing valleys, 
 like many in Auvergne and the Vivarais. These basalts, and 
 all other rocks of the same family in other countries, were, 
 according to him, chemical precipitates from water. He 
 denied that they were the products of submarine volcanoes ; 
 and even taught that, in the primeval ages of the world, there 
 were no volcanoes.' 
 
 After describing the complete demolition of this theory 
 by some of Werner's contemporaries, Sir Charles Lyell 
 adds : — 
 
 'Notwithstanding this mass of evidence, the scholars of 
 Werner were prepared to support his opinions to their utmost 
 extent; maintaining, in the fulness of their faith, that even 
 obsidian was an aqueous precipitate. As they were blinded 
 by their veneration for the great teacher, they were impatient 
 of opposition, and soon imbibed the spirit of a faction ; and 
 
TO INDUCTION, 28 1 
 
 their opponents, the Vulcanists, were not long in becoming 
 contaminated with the same intemperate zeal. Ridicule and 
 irony were weapons more frequently employed than argument 
 by the rival sects, till at last the controversy was carried on 
 with a degree of bitterness almost unprecedented in questions 
 of physical science. Desmarest alone, who had long before 
 provided ample materials for refuting such a theory, kept 
 aloof from the strife; and whenever a zealous Neptunist 
 wished to draw the old man into an argument, he was satisfied 
 with replying " Go and see." ' 
 
 In the Science of Probability, there is an interesting 
 example of the unreflecting application of the Inductio 
 per Simplicem Enumerationem. Averages of a suffi- 
 ciently trustworthy character can often be struck as to 
 the frequency of such events as the number of deaths, 
 the number of suicides, the number of lost letters which 
 occur in a year. But the least reflection, ought to show 
 that the accuracy of these calculations depends on the 
 assumption that the causes in operation, so far as they 
 aifect these events, will continue to be much the same 
 as at present. This, however, is a consideration which 
 is frequently lost sight of, and thus averages, which may 
 be perfectly true within certain limits and on certain 
 hypotheses, are extended, as if they were true universally 
 and unconditionally. Mr. Venn, in his recent work on 
 the Logic of Chance^'^, has drawn especial attention to 
 this source of error. The following passage selected 
 from that work will, perhaps, afford a sufficient illustration 
 of the point in question : — 
 
 S2 
 
 Venn's Logic of Chance, chap. i. 
 
zSa FALLACIES INCIDENT 
 
 'Let us take, for example, the average duration of life. 
 This, provided our data are sufficiently extensive, is known 
 to be tolerably regular and uniform. But a very little con- 
 sideration will show that there may be a superior as well 
 as an inferior limit to the extent within which this uniformity 
 can be observed. At the present time the average duration 
 of life in England may be, say thirty ; but a century ago it 
 was decidedly less ; several centuries ago it was very much 
 less; whilst if we possessed statistics referring to our early 
 British ancestors we should probably find that there has been 
 since that time a still more marked improvement. What 
 may be the future tendency no man can say for certain. It 
 may be, and we hope will be the case, that owing to sanitary 
 and other improvements, the duration of life will go on 
 increasing steadily; it is quite conceivable that it should do 
 so without limit. On the other hand, this duration might 
 gradually tend towards some fixed length. Or, again, it is 
 perfectly possible that future generations might prefer a short 
 and a merry lifp, and therefore reduce their average. All 
 that I am concerned to indicate is, that this uniformity (as 
 we have hitherto called it) has varied, and, under the influence 
 of future eddies in opinion and practice, may vary still ; and 
 this to any extent, and with any degree of irregularity. To 
 borrow a term from Astronomy, we find our uniformity 
 subject to what might be called an irregular secular variation. 
 
 'The above is a fair typical instance. If we had taken 
 a less simple feature than the length of life, or one less closely 
 connected with what may be called the great permanent 
 uniformities of nature, we should have found the peculiarity 
 under notice exhibited in a far more striking degree. The 
 deaths from small-pox, for example, or the instances of 
 duelling or accusations of witchcraft, if examined during 
 a few successive years, would have shown a very tolerable 
 degree of uniformity. But this uniformity has risen probably 
 from zero; after various and very great fluctuations seems 
 
TO INDUCTION. 283 
 
 tending towards zero again ; and may, for anything we know, 
 undergo still greater fluctuations in future. Now these 
 examples I consider to be only extreme ones, and not such 
 very extreme ones, of what is the almost universal rule in 
 nature. I shall endeavour to shew that even the few apparent 
 exceptions, such as the proportions between male and female 
 births, &c., may not be, and probably in reality are not, 
 exceptions. A type that is persistent and invariable is scarcely 
 to be found in nature ^^.' 
 
 In these and similar cases, the fallacy arises from 
 supposing that mere frequency of occurrence affords a 
 sufficient guide to inference, without reflecting that the 
 events depend on causes, and that, if the causes vary, 
 the character of the events must vary with them. 
 
 Sometimes, frequency of occurrence, instead of furnish- 
 ing an argument for the recurrence of an event, ought, 
 if we duly reflect on the natural action of causes, 
 actually to furnish an argument against it. Thus, a 
 miner, instead of trusting to his rope, because it has 
 served him so often, ought actually to distrust it, because 
 it has been strained so much ; a prodigal, who has 
 frequently succeeded in borrowing from his friends, ought 
 to begin to suspect that their patience may be exhausted ; 
 a timid man, who has on one or two occasions aroused 
 his neighbours by a false alarm, instead of arguing from 
 experience that they will come to his rescue again, ought 
 rather to expect that, warned by the past, they will 
 remain comfortably in their beds. It cannot be too often 
 
 ^ Venn's Logic of Chance, ch. i. sect. 10, 11. 
 
S&84 FALLACIES INCIDENT 
 
 repeated, that we ought never to depend on frequency 
 of occurrence, wherever it is possible to have recourse 
 to facts of causation. 
 
 It is remarked by Mr. Mill that the Method of Simple 
 Enumeration, though almost banished from th6 physical 
 sciences, is still the common and received method of 
 induction in whatever relates to man and society. The 
 reason of this is to be sought in the extraordinary dif- 
 ficulty of subjecting this class of speculations to the 
 more scientific methods. Moral and social phenomena 
 are so complex that it is often next to impossible 
 to discover by elimination the true connection between 
 any two events or sets of facts. Take, for instance, such 
 questions as the influence of any particular form of 
 government upon the welfare of the people among whom 
 it is established, the effects of religion, or of any particular 
 form of religion, upon morals, the social and political 
 conditions most favourable to the development of art 
 or literature or science or commerce. Here, if it be re- 
 quired to discover the cause of a given effect, our ma- 
 terials are a set of consequents constantly varying in their 
 character and intensity, and a set of antecedents, often 
 very numerous, any one of which may have an appreci- 
 able influence in the production of the effect in ques- 
 tion ; and it is obvious that to detect the precise degree 
 in which the effect is due to any one of these antecedents, 
 even supposing the task to be possible, will require the 
 utmost skill, patience, and dispassionateness in the 
 selection and comparison of instances. Nor, if it be 
 
TO INDUCTION. 285 
 
 required to discover the effect of a given cause, will the 
 task be much simplified ; for, though it may be possible 
 to fix the precise time at which a new cause — say a new 
 form of religion, a new form of government, or a new 
 commercial tariff — was introduced, yet, before it can be 
 argued that any novel event which may appear to have 
 resulted from it, is really due to it, as an effect to a cause, 
 the enquirer is bound to satisfy himself (i) that the intro- 
 duction of the new cause was not accompanied by other 
 causes which may have wholly or partially produced the 
 supposed effect, (2) that the new cause and the supposed 
 effect are not joint effects of some common cause which 
 he may have overlooked. It is the extreme difficulty of 
 bringing this class of questions within the requirements 
 of scientific induction, that has led, on the one hand, to 
 the employment of the loose Method of Inductio per 
 Simplicem Enumerationem, or of a mere appeal to un- 
 sifted experience, and on the other to the disbelief in the 
 possibility of arriving at any satisfactory conclusions upon 
 them. At the same time, there can be litde doubt that 
 moral and social enquiries are beginning to emerge from 
 the chaotic state of confusion in which they have hitherto 
 been sunk, and that what are now dignified with the titles 
 of the moral and political sciences, however imperfect 
 they may be, are beginning to be something more than 
 mere collections of random guesses, or conclusions drawn 
 from the first undisciplined impressions of the teaching of 
 experience. 
 
 To the class of fallacies originating in the employment 
 
0,86 FALLACIES INCIDENT 
 
 of the incomplete Inductio per Simplicem Enumerationem 
 may perhaps be referred the illegitimate use of the Argu- 
 ment from Authority. The opinions or predictions of a 
 certain man or of a certain class of men upon some parti- 
 cular question or questions have been subsequently found 
 to be verified by the issue of events or an examination of 
 the facts. From this it is sufficiently rash to infer, without 
 further warrant, that the correspondence between these 
 predictions or opinions and the subsequent events or 
 ascertained facts is the result of knowledge, and not of 
 what we call accident ; but, not content even with this, 
 men are apt to draw the far more unwarrantable in- 
 ference that this person or class of persons is to be 
 accepted as an authority on all matters, or at least on 
 all matters of the same or of an analogous kind. It is 
 on this principle that a savage, or even an uneducated man 
 in a civilised community, will trust implicitly any person 
 for whom he has conceived a general respect. In nine 
 cases out of ten he probably acts more wisely in trust- 
 ing to such a person than in trusting to himself. But 
 the same habit of mind, which is a virtue among un- 
 educated men and in primitive states of society, be- 
 comes one of the most serious obstacles to progress 
 and knowledge when men, either individually or col- 
 lectively, have attained that stage at which they are 
 able to enquire for themselves. We have to learn not 
 only that men are to be trusted exclusively within the 
 limits of their own experience, in their own profession 
 or pursuit, but that even within those limits their authority 
 
TO INDUCTION. 28/ 
 
 is apt to become tyrannical and irrational unless it is 
 constantly confronted with facts and subjected to the 
 criticism of others. 
 
 , But an undiscriminating submission to the authority 
 of contemporaries, of which we have hitherto exclusively 
 spoken, has been but a slight source of error when com- 
 pared with undiscriminating submission to the authority 
 of past generations^*. The latter involves a kind of com- 
 pound fallacy. The authority of an Aristotle or a Galen 
 has come, by the process already described, to be re- 
 ceived without question and without limit by his own or 
 by the succeeding generation; and then, by the con- 
 stant repetition of a similar process, it is received from 
 that generation by the leading minds of the next, from 
 them by their contemporaries, and so on, respect for 
 tradition being blended with respect for a great name, 
 and both these resting for their support on the de- 
 ference paid to established authority. Many of the 
 propositions accepted without the slightest hesitation 
 by previous generations on this kind of authority now 
 
 ^^ Of this tendency we have many ' glaring instances/ as Bacon would 
 call them. The error has been, so to say, canonised in the proverb 
 *Mallem cum Platone errare.' There is a characteristic anecdote of 
 Scheiner, who contests with Galileo the honour of having been the first 
 to observe the spots in the sun. ' Scheiner was a monk ; and, on commu- 
 nicating to the superior of his order the account of the spots, he received 
 in reply from that learned father a solemn admonition against such 
 heretical notions : — " I have searched through Aristotle," he said, " and 
 can find nothing of the kind mentioned : be assured, therefore, that it 
 is a deception of your senses, or of your glasses."* — Baden Powell's 
 History of Natural Philosophy, p. 1 71. 
 
288 FALLACIES INCIDENT 
 
 appear to us patently absurd, nor is it without' effort 
 that we can realise the universality of their former re- 
 ception^^ Instances of such propositions have already 
 been given under the head of the Fallacies of Non- 
 Observation, to the production of which class of fallacies 
 the undue devotion to authority has, perhaps, contributed 
 more than any other cause ^^ But in subjects lying 
 
 2^ The increasing unwillingness of men to accept a proposition on 
 mere authority is thus forcibly put by Bentham, Booh of Fallacies, 
 Part I. ch. i., first published in French by M. Dumont, in 1815, and in 
 English by * A Friend,' in 1824. 
 
 ' As the world grows older, if at the same time it grows wiser (which 
 it will do, unless the period shall have arrived at which experience, the 
 mother of wisdom, shall have become barren), the influence of authority 
 will in each situation, and particularly in parliament, become less and 
 less.' 
 
 ' Take any part of the field of moral science, private morality, consti- 
 tutional law, private law ; go back a few centuries, and you will find 
 argument consisting of reference to authority, not exclusively, but in as 
 large a proportion as possible. As experience has increased, authority 
 has been gradually set aside, and reasoning, drawn from facts, and guided 
 by reference to the end in view, true or false, has taken its place. 
 ***** -x- 
 
 ' In mechanics, in astronomy, in mathematics, in the new-born science 
 of chemistry — no one has at this time of day either effrontery or folly 
 enough to avow, or so much as to insinuate, that the most desirable state 
 of these branches of useful knowledge, the most rational and eligible 
 course, is to substitute decision on the ground of authority to decision 
 on the ground of direct and specific evidence.' 
 
 2^ It might appear that the illegitimate use of the Argument from 
 Authority should be classed amongst the Fallacies of Non-Observation ; 
 but, though a blind devotion to authority is one of the most powerful 
 influences in leading men to neglect observation and experiment, the 
 disposition to bow thus unduly to it is itself a fact which requires 
 explanation, and one which it is here attempted to explain. 
 
TO INDUCTION, 289 
 
 remote from ordinary observation, propositions almost 
 equally absurd have held their ground till quite recendy ; 
 some continue to maintain themselves, and others no 
 doubt will be propounded to take advantage of the 
 credulity of mankind. 
 
 ' To give a general currency,' says Dr. Paris ^^, *to a hypo- 
 thetical opinion, or medicinal reputation to an inert substance, 
 nothing more is required than the talismanic aid of a few 
 great names ; when once established upon such a basis, inge- 
 nuity, argument, and even experiment, may open their inef- 
 fectual batteries ; the laconic sentiment of the Roman satirist 
 is ever opposed to remonstrance: — ^^ Marcus dixit f ita estT 
 A physician cannot err in the opinion of the public, if he 
 implicitly obeys the dogmas of authority. In the most bar- 
 barous ages of ancient Egypt, he was punished or rewarded 
 according to the extent of his success; but to escape the 
 former it was only necessary to show that an orthodox plan 
 of cure had been followed, such as was prescribed in the 
 acknowledged writings of Hermes. It is an instinct in our 
 nature to follow the track pointed out by a few leaders ; 
 we are gregarious animals, in a moral as well as a physical 
 sense, and we are addicted to routine because it is always 
 easier to follow the opinions of others than to reason and 
 judge for ourselves ; and thus do one half of the world live 
 as alms-folk on the opinions of the other half. What but 
 such a temper could have upheld the preposterous system of 
 Galen for more than thirteen centuries, and have enabled 
 it to give universal laws in medicine to Europe, Africa, and 
 part of Asia ? What, but the spell of authority, could have 
 inspired a general belief that the sooty washings of resin could 
 act as a universal remedy? What, but a blind devotion to 
 authority, or an insuperable attachment to established custom 
 
 "^ Dr. Paris' Pharmacologia, Introduction, p. 76, &c. 
 U 
 
290 FALLACIES INCIDENT 
 
 and routine, could have so long preserved from oblivion the 
 absurd medicines which abound in our earlier dispensatories ? 
 for example, the " Decoctum ad Ictericos " of the Edinburgh 
 College, which never had any foundation but that of the 
 doctrine of signatures in favour of the Curcuma and Cheli- 
 donium majus ; and it is only within a few years that the 
 Theriaca Andromachi, in its ancient form, has been dismissed 
 from our Pharmacopoeia. The Codex Medicamentarius 
 of Paris still cherishes the many-headed monster of phar- 
 macy, under the appropriate title of ^^ Electuarium Opiatum 
 Polupharmacumy * 
 
 * The same devotion to authority which induces us to re- 
 tain an accustomed remedy with pertinacity, will frequently 
 oppose the introduction of a novel practice with asperity, 
 unless indeed it be supported by authority of still greater 
 weight and consideration. The history of various articles 
 of diet and medicine will prove in a striking manner how 
 greatly their reputation and fate have depended upon 
 authority. It was not until many years after Ipecacuan 
 had been imported into Europe, that Helvetius, under the 
 patronage of Louis XIV, succeeded in introducing it into 
 practice : and to the eulogy of Katharine, queen of Charles 
 II, we are indebted for the general introduction of tea into 
 England.' 
 
 *The history of the warm bath presents us with another 
 curious instance of the vicissitudes to which the reputation 
 of our valuable resources is so universally exposed; that 
 which for so many ages was esteemed the greatest luxury 
 in health, and the most efficacious remedy in disease, fell into 
 total disrepute in the reign of Augustus, for no other reason 
 than because Antonius Musa had cured the emperor of a 
 dangerous malady by the use of the cold bath. The most 
 frigid water that could be procured was, in consequence, 
 
TO INDUCTION. 29 1 
 
 recommended on every occasion : thus Horace, in his epistle 
 to Vala, exclaims — 
 
 ** Caput ac stomachum supponerc fontibus audent 
 Clusinis, Gabiosque petunt, et frigida rura." — Epist. xv. lib. i. 
 
 * This practice, however, was doomed but to an ephemeral 
 popularity, for although it had restored the emperor to health, 
 it shortly afterwards killed his nephew and son-in-law, Mar- 
 cellus; an event which at once deprived the remedy of its 
 credit and the physician of his popularity. 
 
 ^ The history of the Peruvian bark would furnish a very 
 curious illustration of the overbearing influence of authority 
 in giving celebrity to a medicine, or in depriving it of that 
 reputation to which its virtues entitle it. This heroic remedy 
 was first brought to Spain in the year 1632, and we learn 
 from Villerobel that it remained for seven years in that 
 country before any trial was made of its powers, a certain 
 ecclesiastic of Alcala being the first person in Spain to whom 
 it was administered in the year 1639 ; but even at this period 
 its use was limited, and it would have sunk into obhvion but 
 for the supreme power of the Roman church, by whose 
 auspices it was enabled to gain a temporary triumph over 
 the passions and prejudices which opposed its introduction. 
 Innocent the Tenth, at the intercession of Cardinal de Lugo, 
 who was formerly a Spanish Jesuit, ordered that the nature 
 and effects of it should be duly examined, and upon being 
 reported as both innocent and salutary, it immediately rose 
 into public notice ; its career, however, was suddenly stopped 
 by its having unfortunately failed, in the autumn of 1652, to 
 cure Leopold, Archduke of Austria, of a quartan intermittent; 
 this disappointment kindled the resentment of the prince's 
 principal physician, Ghifletius, who published a violent philippic 
 against the virtues of Peruvian bark, which so fomented the 
 prejudices against its use, that it had nearly fallen into total 
 neglect and disrepute.' 
 
 u 2 
 
2^2, FALLACIES INCIDENT 
 
 In discussing the Argument from Authority^ we have 
 already touched on the Argument from Universal Consent, 
 ' This is a proposition to which we cannot refuse our 
 assent, for it is accepted by all mankind/ In dealing 
 with this argument, we must always ask, first of all, 
 whether the proposition assented to expresses an im- 
 mediate perception or an inference. If it expresses the 
 former, we cannot call it in question, for the immediate 
 perceptions of men are ultimate facts, true, at all events, 
 to us, and admitting of no further test. But if the pro- 
 position expresses an inference, as, for instance, in the 
 case of the belief in the motion of the sun round the 
 earth, or the non-existence of antipodes, we must pro- 
 ceed to ask further what are the grounds of the inference, 
 and, unless the grounds of the inference approve them- 
 selves to us, we are at liberty to doubt or reject it. At 
 the same time, this argument, even though the proposi- 
 tion only express an inference, may possess considerable, 
 if not overwhelming, force, provided that the conclusion 
 has been arrived at by a number of competent persons 
 after due examination, and as a result of independent 
 investigation. Even here, however, the true authority is 
 that of the competent investigators, not that of their 
 credulous or incompetent followers ^l The latter, as was 
 
 ^^ ' Verus enim consensus is est, qui ex libertate judicii (re prius ex- 
 plorata) in idem conveniente consistit. At Humerus longe maximus 
 eorum, qui in Aristotelis philosophiam consenserunt, ex praejudicio et 
 auctoritate aliorum se illi mancipavit ; ut sequacitas sit potius et coitio, 
 quam consensus.* — Bacon, Nov. Org., Lib. I. Aph. Ixxvii. 
 
TO INDUCTION, 293 
 
 once said by the late Bi§hop Thirlwall, may be regarded 
 as the ciphers after a decimal point^^ 
 
 V. The errors incident to the employment of the 
 various Inductive Methods have already been pointed out 
 in our detailed description of each of these Methods, but 
 it may be useful in this place to take note of certain forms 
 of fallacy which appear to be common to them all. 
 
 The Inductive Methods may all be regarded as de- 
 vices for the elimination of extraneous circumstances and 
 for the establishment of a causal connection between some 
 two phenomena, a and 5, the connection which it is sought 
 to establish being generally that of cause and effect. 
 Now, in our investigation, we may either have mistaken 
 the precise relation between a and d, or we may have 
 overlooked some other material circumstance or group 
 of circumstances, c. In the former case, the most 
 common sources of error are either the inversion of 
 cause and effect or the neglect of their reciprocal action, 
 the ' mutuality of cause and effect,' as it is called by 
 Sir G. C. Lewis. In the latter case (supposing a to 
 be the presumed cause, and d the presumed effect), it 
 seems open to us to have committed any of the following 
 errors: (i) to have mistaken a for the cause, when the 
 real cause is ^ ; (2) to have mistaken a for the sole cause, 
 when a and c are the joint causes, either (a) as both 
 
 3^ Cp. Glanvill's Scepsis Scientijica, ch. xvii. : ' Authorities alone with 
 me make no number, unless Evidence of Reason stand before them : for 
 all the Ciphers of Arithmetic are no better than a single nothing.' 
 
294 FALLACIES INCIDENT 
 
 contributing to the /ofal effect, or (/3) as being both essen- 
 tial to the production of any effect whatever*^; (3) to 
 have mistaken a for the cause of d, when they are really 
 both of them effects of c; (4) to have mistaken a for 
 the proximate cause of <5, when it is really only the re- 
 mote cause, Cj which has escaped our attention, being 
 the proximate cause. 
 
 To begin with the latter class of errors, 
 
 (i) The following extract from Mr. Lewes' Physiology 
 of Common Life^^ may serve as an illustration of the first 
 subdivision : — 
 
 ' One very general, indeed almost universal, misconception 
 on this subject (asphyxia or suffocation) is, that carbonic acid 
 is poisonous in the blood ; but the truth seems to be that the 
 carbonic acid is noxious only when it prevents the access 
 of oxygen. There is always carbonic acid in the blood, both 
 venous and arterial. Its accumulation in the blood is only 
 fatal when there is such an accumulation in the atmosphere 
 as will prevent its exhalation ; its mere presence in the blood 
 seems to be quite harmless, even in large quantities, provided 
 always that it be not retained there to the exclusion of 
 oxygen. Carbonic acid, when absorbed into the blood, which 
 is alkaline, cannot there exert its irritant action as an acid, 
 because it will either be transformed into a carbonate or be 
 dissolved. Bernard has injected large quantities into the 
 veins and arteries, and under the skin of rabbits, and found 
 
 ''^ The distinction may be illustrated by a familiar example. If a 
 cistern is filled by two pipes, the water passing through each contributes 
 to the total amount of water in the cistern. But, if the cistern is filled 
 by one pipe having two taps, one above the other, both taps must be 
 turned in order that the cistern may receive any water whatever. 
 
 " Vol. i. p. 383. 
 
TO INDUCTION. ^()^ 
 
 no noxious effect ensue. The more carbonic acid there is 
 in the blood, the more will be exhaled, provided always that 
 the air be not already so charged with it as to prevent this 
 exhalation/ 
 
 Here there are really two antecedents, the presence 
 of carbonic acid and the exclusion of oxygen, and the 
 noxious effects, which are erroneously ascribed to the 
 former cause, ought properly to be referred to the 
 latter. 
 
 The above extract exempKfies this error as vitiating 
 an application of the Method of Agreement. In the 
 following extracts from Dr. Paris' Pharmacologia, it will 
 be seen also to vitiate applications of the Method of 
 Difference : — 
 
 ' Soranus, who was contemporary with Galen, and wrote 
 the life of Hippocrates, tells us that honey proved an easy 
 remedy for the aphthae of children ; but instead of at once 
 referring the fact to the medical qualities of the honey, he 
 very gravely explains it, from its having been taken from 
 bees that hived near the tomb of Hippocrates *^ ! ' 
 
 *In my life of Sir Humphry Davy, I have published an 
 anecdote which was communicated to me by the late Mr. 
 Coleridge, and which bears so strikingly upon the present 
 subject that I must be excused for repeating it. As soon 
 as the powers of nitrous oxide were discovered. Dr. Beddoes 
 at once concluded that it must necessarily be a specific for 
 paralysis: a patient was selected for the trial, and the 
 management of it was entrusted to Davy. Previous to the 
 administration of the gas, he inserted a small pocket thermo- 
 meter under the tongue of the patient, as he was accustomed 
 
 ^"^ Pharmacologia, p. 20. 
 
2,g6 FALLACIES INCIDENT 
 
 to do upon such occasions, to ascertain the degree of animal 
 temperature, with a view to future comparison. The paralytic 
 man, wholly ignorant of the nature of the process to which 
 he was to submit, but deeply impressed, from the representa- 
 tions of Dr. Beddoes, with the certainty of its success, no 
 sooner felt the thermometer under his tongue, than he con- 
 cluded the talisman was in full operation, and in a burst of 
 , enthusiasm declared that he already experienced the effect 
 of its benign influence throughout his whole body: the 
 opportunity was too tempting to be lost; Davy cast an 
 intelligent glance at Mr. Coleridge, and desired his patient 
 to renew his visit on the following day, when the same 
 ceremony was performed, and repeated every succeeding day 
 for a fortnight, the patient gradually improving during that 
 period, when he was dismissed as cured, no other application 
 having been used *'\* 
 
 * Amongst the numerous instances which have been cited 
 to show the power of faith over disease, or of the mind over 
 the bodily organs, the cures performed by royal touch have been 
 considered the most extraordinary : but it would appear, upon 
 the authority of Wiseman, that the cures which were thus 
 effected were in reality produced by "a very different cause; 
 for he states that part of the duty of the royal physicians and 
 Serjeant surgeons was to select such patients afflicted with 
 scrofula as evinced a tendency towards recovery, and that 
 they took especial care to choose those who approached the 
 age of puberty. In short, those only were produced whom 
 Nature had shown a disposition to cure ; and as the touch of 
 the king, like the sympathetic powder of Digby, secured the 
 patient from the mischievous importunities of art, so were the 
 effbrts of Nature left free and uncontrolled, and the cure of 
 the disease was not retarded or opposed by the administration 
 of adverse remedies. The wonderful cures of Valentine 
 
 *^ Pharmacologia, p. 28. 
 
TO INDUCTION, 297 
 
 Greatricks, performed in 1666, which^fcre witnessed by 
 contemporary prelates, members of pa^rament, and fellows 
 of the Royal Society, amongst whom was the celebrated 
 Mr. Boyle, would probably, upon investigation, admit of a 
 similar explanation. It deserves, however, to be noticed, 
 that in all records of extraordinary cures performed by 
 mysterious agents, there has always been a desire to conceal 
 the remedies and other curative means which might have 
 been simultaneously administered. Thus Oribasius com- 
 mends, in high terms, a necklace of peony-root for the cure 
 of epilepsy ; but w^e learn that he always took care to accom- 
 pany its use with copious evacuations, although he assigns 
 to them not the least share of credit in the cure. In later 
 times, we have an excellent specimen of this species of 
 deception, presented to us in a work on scrofula by Mr. 
 Morley, written, as we were informed, for the sole purpose 
 of restoring the much-injured character and use of the 
 wervain; in which the author directs the root of that plant 
 to be tied with a yard of ivhite satin riband around the neck ; 
 —but mark— during the period of its application, he calls 
 to his aid the most active medicines in the materia medica. 
 " It is unquestionable," says Voltaire, speaking of sorceries, 
 " that certain words and ceremonies will effectually destroy 
 a flock of sheep, if administered with a sufficient portion of 
 
 ' Our inability upon all occasions to appreciate the efforts 
 of nature in the cure of disease, must necessarily render our 
 notions, with respect to the powers of art, liable to numerous 
 errors and deceptions. Hence protracted or <ivire-dra<wn 
 cures ought to be very cautiously received as evidences of the 
 success of medical treatment. Many diseases require only 
 time to enable nature to remove them. All the long train 
 connected with hysteria are cured by time; the solution of 
 
 ** Pharmacologia, p. 30. 
 
298 FALLACIES INCIDENT 
 
 which, as Mr. Travers has observed, is to be found in the 
 fact, that the hysteric period wanes, and the restlessness of 
 the temperament undergoes a slow but salutary change. 
 Nothing, certainly, is more natural, although it may be very 
 erroneous, than to attribute the cure of a disease to the last 
 medicine that had been administered ; the advocates even of 
 amulets and charms have been thus enabled to appeal to 
 the testimony of what they call experience, in justification of 
 their superstition *^.' 
 
 Of a similar character was the old superstition, noticed 
 by Sir Thomas Browne ^^ and many other authors, that 
 the hardest stone could be broken by goat's blood : — 
 
 ' And, first, we hear it in every mouth, and in many good 
 authors read it, that a diamond, which is the hardest of 
 stones, not yielding unto steel, emery, or any thing but its 
 own powder, is yet made soft, or broke by the blood of a 
 goat. . . . But this, I perceive, is easier affirmed than 
 proved. For lapidaries, and such as profess the art of cutting 
 this stone, do generally deny it; and they that seem to 
 countenance it have in their deliveries so qualified it, that 
 little from thence of moment can be inferred for it. For 
 first, the holy fathers, without a further enquiry, did take it 
 for granted, and rested upon the authority of the first de- 
 liverers. . . . But the words of Pliny, from whom most likely 
 the rest at first derived it, if strictly considered, do rather 
 overthrow, than any way advantage this effect. His words 
 are these : Hircino rumpitur sanguine^ nee aliter quam recenti^ 
 calidoque maeerata^ et sic quoque multis ictibus, tune etiam prcBter- 
 quam eximias incudes malleosque ferreos frangens. That is, it is 
 broken with goat's blood, but not except it be fresh and warm, 
 
 *' Pharmacologia, p. 88. 
 
 ^ Enquiry into Vulgar and Common Errors^ Bk. II, ch. v. Collected 
 Works, vol. ii. pp. 334, 335. 
 
TO INDUCTION. 299 
 
 and that not without many blows, and then also it will break 
 the best anvils and hammers of iron.' 
 
 The example of Sir Kenelm Digby's sympathetic 
 powder (already quoted p. 266) also illustrates this class 
 of fallacies*'^. 
 
 It should be noticed that, when we attribute a pheno- 
 menon to a wrong cause, it does not always follow that this 
 cause, had it been in action, might not have produced the 
 event. Thus, we may wrongly attribute death in some 
 given case to poison, or infection to actual contact with 
 a diseased person, or ignition to friction, because these 
 causes were not then and there in action, though, had 
 they been actually operating, they would have been per- 
 fectly competent to produce the effect. When we make 
 a mistake of this kind, it frequently arises from our 
 concentrating our attention exclusively on some one or 
 
 *^ These instances, together with many others in this chapter, illus- 
 trate the ancient fallacies * Non causa pro causa ' and ' Post hoc, ergo 
 propter hoc' It will probably have already occurred to the student that 
 some of the examples just cited might have been equally well adduced as 
 examples of the fallacy of non-observation. It, in fact, frequently happens 
 that the same error may be assigned indifferently to two or more sources 
 of deception. * From the elliptical form/ says Archbishop Whately 
 (Elements of Logic ^ Bk. iii. § l), * in which all reasoning is usually ex- 
 pressed, and the peculiarly involved and oblique form in which fallacy is 
 for the most part conveyed, it must of course be often a matter of doubt, 
 or rather of arbitrary choice, not only to which genus each kind of fallacy 
 should be referred, but even to which kind to refer any one individual 
 fallacy.' Thus, so intimately are our intellectual operations blended, that 
 it is often extremely difficult to decide whether a mistake be mainly due 
 to defective observation or erroneous reasoning. 
 
300 FALLACIES INCIDENT 
 
 a few of the possible causes which may produce a given 
 effect, thus neglecting the consideration of the Plurality 
 of Causes, to which attention has repeatedly been drawn 
 in the previous pages ^^. 
 
 (2) When an effect is the joint result of two or more 
 causes, the causes may either simply contribute towards 
 the production of the total result, though one only would 
 produce some portion of it, or they may all be essential 
 to the production of any result whatever. It would be 
 convenient if, in the former case, we could speak of the 
 causes as joint causes^ in the latter as joint conditions, but 
 to do so w^ould perhaps be too great an innovation on 
 established language. 
 
 (a) An instance of supposing that a phenomenon is en- 
 tirely due to one cause, when it seems in reality to be only 
 partially due to it, is furnished by the prevalent notion 
 that the heart is the sole cause of the circulation of the 
 blood. 
 
 ' What is it,' says Mr. Lewes *^, * which causes the blood to 
 circulate ? " The heart," answers an unhesitating reader. 
 That the heart pumps blood incessantly into the arteries, and 
 that this pumping must drive the stream onwards with great 
 force, there is no doubt; but although the most powerful 
 agent in the circulation, the heart is not the sole agent ; and 
 the more we study this difficult question, the more our doubts 
 gather round the explanation.' 
 
 * Let a few of the difficulties be stated. There have been 
 
 ^ See pp. 6, 125, 127-130. 
 
 ** Physiology of Common Life, vol. i. p. 322. 
 
TO INDUCTION. 3OI 
 
 cases of men and animals born without a heart ; these " acar- 
 diac monsters " did not live, indeed could not live ; but they 
 had grown and developed in the womb, and consequently 
 their blood must have circulated. In most of these cases 
 there has been a twin embryo, which was perfect ; and the 
 circulation in both was formerly attributed to the heart of 
 the one ; but it has been fully established that this is not the 
 case. Further, Dr. Carpenter reminds us that " it has occa- 
 sionally been noticed that a degeneration in the structure of 
 the heart has taken place, during life, to such an extent that 
 scarcely any muscular tissue could at last be detected in it, 
 but without any such interruption to the circulation as must 
 have been anticipated if this organ furnishes the sole impelling 
 force." On the other hand, an influence acting on the capil- 
 laries will give a complete check to the action of the heart, 
 although that organ is itself perfectly healthy and vigorous.' 
 
 Mr. Lewes then proceeds to discuss the subject at 
 greater length, but the above quotation will be sufficient 
 for our purpose. 
 
 A familiar instance of this error occurs in the vulgar 
 notion that the mean annual temperature of a place is 
 exclusively determined by its latitude. The reader need 
 hardly be told that in this case there are many other 
 causes at work, namely, elevation, distance from the sea, 
 proximity of mountain chains, and the like. 
 
 When a number of causes contribute towards the total 
 effect, it is plain that, as in the last instance, they may 
 operate in the way of modifying, counteracting, or even 
 frustrating^^ each other's influence. This is a considera- 
 
 ^ We sometimes speak of causes * wholly or partially counteracting 
 each other.* It would be an advantage if we could appropriate the 
 word frustration to express complete counteraction. 
 
30a FALLACIES INCIDENT 
 
 tion which it is often of the utmost importance to bear 
 in mind, as will be obvious from the following examples, 
 extracted, the former from Dr. Paris' Pharmacologia^'^, the 
 latter from Sir G. C. Lewis' Methods of Observation and 
 Reasoning in Politics'^'^, 
 
 * In ordering saline draughts as vehicles for active medicines, 
 it is very important that they should be rendered perfectly 
 neutral; the effect of a predominating acid or alkali may 
 produce decompositions fatal to the efficacy of the remedy, 
 as the practitioner will fully understand by a reference to the 
 Acetate of Ammonia^ and other preparations in the Table of 
 Incompatibles. In prescribing them to be taken in a state of 
 effervescence, we must consider whether the disengaged car- 
 bonic acid may not invalidate the powers of the remedies 
 simultaneously given with them. I should certainly recom- 
 mend such a form to be avoided, in all cases where a salt of 
 lead had been administered, for the carbonic acid retained 
 in the stomach might probably convert it into a carbonated 
 
 ' But it is to be borne in mind that, in estimating negative 
 instances, due allowance must be made for the occasional 
 
 frustration of causes For example : it might be 
 
 argued, from the occurrence of several cases in which the 
 absence of high import duties and of commercial restrictions 
 was accompanied with abundance and cheapness of com- 
 modities, that the former was the cause of the latter. Certain 
 instances might then occur, in which the former existed with- 
 out the latter; but each of these exceptional cases might 
 be accounted for, by showing that there was a special circum- 
 stance, such as a deficient supply, or interruption of inter- 
 course by war or blockade, which partially obstructed, and for 
 
 " P. 498. 52 Vol. i. p. 386. 
 
TO INDUCTION. 3O3 
 
 a time suspended, the operation of the former cause. Again : 
 it might be shown, by the evidence of facts, that the operation 
 of a new law had been generally beneficial, with the exception 
 of certain districts, where its enforcement had been prevented 
 or retarded by certain peculiar and accidental circumstances. 
 Exceptions of this kind, which admit of an adequate special 
 explanation, serve rather to confirm the general inference 
 than to weaken it ; inasmuch as they raise the presumption 
 that, but for the partial obstruction to the cause, it would 
 have operated in these as in the other instances where no 
 obstructions existed ^^.' 
 
 Mt is probably from observing this case of the problem 
 of causation, that the popular error has arisen of supposing 
 that a rule is sometimes proved by its exceptions. Every 
 exception to a general proposition must, in so far as it is 
 an exception, detract from the application of the proposition, 
 and consequently disprove [or rather go towards disproving] 
 it. Thus, if it were asserted that all cloven-footed animals 
 ruminate, this assertion certainly would receive no confirma- 
 tion from the fact, that certain cloven-footed animals — such 
 as the hog — do not ruminate. If, however, the exception, 
 as in the case which we have been examining, admitted 
 of a peculiar explanation, and it could be shown that the 
 nisus or tendency of the cause was the same in the excep- 
 tional as in the other instances, but that in the former it 
 was counteracted and overcome, while in the latter it was 
 not — then the exception may be said not to invalidate, but 
 rather to confirm the rule.* 
 
 The above passage is noteworthy, as furnishing a good 
 comment on the maxim, Exceptio prohai regulam, a 
 
 *^ Sir G. C. Lewis' Methods of Observation and Reasoning in Politics, 
 vol. i. p. 386. 
 
304 FALLACIES INCIDENT 
 
 maxim which is, of course, only applicable where the 
 exceptions are apparent, and where they admit of ex- 
 planation in conformity with the rule. 
 
 (^) That every event depends upon the concurrence 
 of a number of causes, positive and negative, or, as they 
 are often called, conditions, has already been pointed 
 out (Chap. I. pp. 13-15). Thus, the burning of a 
 fire depends not only on the application of a lighted 
 match and the supply of fuel, but also on the presence 
 of atmospheric air, or rather of the oxygen which it 
 contains, though, from the universal presence of air, we 
 are less apt to think of the latter cause than of the former 
 ones. The importance, however, of not overlooking this 
 consideration is shewn by the extent to which we can 
 augment the temperature by constantly bringing fresh 
 currents of air into contact with any heated mass, as well 
 as by the familiar phenomenon of the increased bright- 
 ness with which a fire burns on a frosty day, when the 
 atmosphere is more than ordinarily dry or free from 
 aqueous vapour. 
 
 The importance of bearing in mind that an event 
 depends upon a concurrence of causes may be further 
 illustrated by the boiling-point of water. The point at 
 which water boils depends upon two causes or con- 
 ditions, the temperature of the water and the pressure 
 of the atmosphere. Now, as the latter varies at diff"erent 
 heights and in different states of weather, water does not 
 always boil at the same temperature, the boiling-point 
 being, as a rule, diminished by 1° for every 590 feet that 
 
TO INDUCTION, 305 
 
 we ascend, so that, whereas at the sea level water boils 
 at about 212° Fahrenheit, on the top of Mont Blanc it 
 boils at about 185°. It is obvious that any one, not bear- 
 ing in mind this fact, might be exposed to the greatest 
 practical inconveniences. 
 
 The following quotations from Dr. Paris' Pharmaco- 
 logia will furnish a sufficient illustration of the importance 
 of this consideration and of the errors which may result 
 from neglecting it. 
 
 * In some cases of irritability of stomach, the addition of a 
 small quantity of opium will impart efficacy to a remedy 
 otherwise inert ; an emetic will often thus be rendered more 
 active, as I have frequently witnessed in my practice. In 
 some states of mania, and affections of the brain, emetics will 
 wholly fail, unless the stomach be previously influenced and 
 prepared by a narcotic. I have often also found that the 
 system has been rendered more susceptible of the influence 
 of mercury by its combination with antimony and opium. 
 So, again, when the system is in that condition which is 
 indicated by a hot and dry skin, squill will fail in exciting 
 expectoration; but administer it in conjunction with am- 
 monia, and in some cases with Antimonial Wine and a saline 
 draught, and its operation will be promoted. As a diuretic, 
 Squill is by no means active, when singly administered, but 
 Calomel, or some mercurial, when in combination with it, 
 appears to direct its influence to the kidneys, and in some 
 unknown manner to render these organs more susceptible of 
 its influence ^*.' 
 
 * It has been determined by the most ample experience, 
 that substances will produce effects upon the living system, 
 
 ** Pharmacologia^ p. 388. 
 X 
 
3o6 FALLACIES INCIDENT 
 
 when presented in a state of simple mechanical mixture, 
 very different from those which the same medicinal ingre- 
 dients will occasion when they are combined by the agency 
 of chemical affinity. To illustrate this by a simple case, — a 
 body suspended in a mixture in the form of a powder, will 
 act very differently if held in solution by a fluid. The rela- 
 tive effects of alcohol in the form of what is termed " j/»ir/V," 
 and in that of wine, may be explained upon the same prin- 
 ciple ; in the former case it is in a state of mixture, in the 
 latter in that of combination. It has been demonstrated 
 beyond all doubt, that a bottle of port, madeira, or sherry, 
 actually contains as much alcohol as exists in a pint of 
 brandy; and yet how different the effect! — a fact which 
 affords a very striking illustration of the extraordinary 
 powers of chemical combination in modifying the activity 
 of substances upon the living system ^^.' 
 
 * It has been very generally supposed that substances, 
 whose application does not produce any sensible action upon 
 the healthy system cannot possess medicinal energy ; and, on 
 the contrary, that those which occasion an obvious effect 
 must necessarily prove active in the cure or palliation of 
 disease. To this general proposition, under certain limita- 
 tions and restrictions, we may perhaps venture to yield our 
 assent ; but it cannot be too early, nor too forcibly impressed 
 upon the mind of the young practitioner, that medicines are, 
 for the most part, but relati've agents, producing their effects in 
 reference only to the state of the li'ving frame. We must, there- 
 fore, concur with Sir Gilbert Blane in stating that the virtues 
 of medicines cannot be fairly essayed, nor beneficially ascer- 
 tained, by trying their effects on sound subjects, because that 
 particular morbid condition does not exist which they may be 
 exclusively calculated to remove; thus, in a robust state of 
 the body, the effects of steel, in commendation of which, in 
 
 ^ Pharmacologia, pp. 426, 427. 
 
TO INDUCTION. 307 
 
 certain diseases, professional opinion is unanimous, may be 
 wholly imperceptible. Bitter tonics, also, may either prove 
 entirely inert, or they may give strength, relax the bowels, or 
 induce constipation, according to the particular condition of 
 the patient to whom they are administered; so again in a 
 healthy state of the stomach, a few grains of soda or magnesia 
 will not occasion the least sensible effect, but where that 
 organ is infested with a morbid acid, immediate relief will 
 follow the ingestion of the one, and purgation that of the 
 other. By not reasoning upon such facts, physicians have, in 
 my opinion, very unphilosophically advanced to conclusions 
 respecting the inefficacy of certajn agents. They have ad- 
 ministered particular preparations in large doses, and not 
 having observed any visible effects, have at once denounced 
 them as inert. I might allude, for instance, to the iris-nitrate 
 of bismuth, a substance which, however powerless in health, I 
 am well satisfied, from ample experience, is highly effica- 
 cious in controlling certain morbid states of the stomach. 
 Dr. Robertson has well observed, that disease calls forth 
 the powers, and modifies the influence of medicines. That 
 which agitates the calm of health may soothe the irritation 
 of illness, and that which without opposition is inert, may 
 act powerfully where it meets with an opponent. Experi- 
 ments should be made on the sick, in order to determine how 
 the sick will be affected, and nothing should be pronounced 
 feeble, merely because it has done nothing where there was 
 nothing to be done^^.' 
 
 To adduce one more illustration : insanity, though 
 sometimes due to a number of causes, each one of 
 which simply contributes to and augments the affection, 
 which would still exist, though in a weaker degree, 
 even if some of them were absent, appears at other 
 
 *• Pharmacologia, pp. 133, 134. 
 X 2 
 
308 FALLACIES INCIDENT 
 
 times to be the joint result of a number of causes, the 
 presence of every one of which seems to be essential to 
 the production of any effect so definite as to deserve the 
 name of mental derangement. The train, in these cases, 
 appears to be laid by a number of precedent circum- 
 stances, and the addition of some one other circumstance 
 seems to be the spark which produces the conflagration. 
 
 * When we are told,' says Dr. Maudsley ^^, ' that a man 
 has become deranged from anxiety or grief, we have 
 learned very little if we rest content with that. How does it 
 happen that another man, subjected to an exactly similar 
 cause of grief, does not go mad ? It is certain that the entire 
 causes cannot be the same where the effects are so different ; 
 and what we want to have laid bare is the conspiracy of 
 conditions, internal and external, by which a mental shock, 
 inoperative in one case, has had such serious consequences 
 in another. A complete biographical account of the indi- 
 vidual, not neglecting the consideration of his hereditary 
 antecedents, would alone suffice to set forth distinctly the 
 causation of his insanity. If all the circumstances, internal 
 and external, were duly scanned and weighed, it would be 
 found that there is no accident in madness; the disease, 
 whatever form it might take, by whatsoever complex con- 
 currence of conditions, or by how many successive links of 
 causation, it might be generated, would be traceable as the 
 inevitable consequence of certain antecedents, as plainly as 
 the explosion of gunpowder may be traced to its causes, 
 whether the train of events of which it is the issue be long 
 or short. The germs of insanity are sometimes latent in 
 the foundations of the character, and the final outbreak 
 is perhaps the explosion of a long train of antecedent 
 preparations.' 
 
 ^^ Physiology and Pathology of Mind, Part II. ch. i. p. 225. 
 
TO INDUCTION. 309 
 
 (3) The phenomena of insanity also furnish a good 
 illustration of the next source of error, the mistaking of 
 joint effects for cause and effect. In this, as in many other 
 diseases, symptoms are often mistaken for causes. Thus, 
 it is not uncommon to hear violent religious excitement 
 or inordinate grief adduced as causes of insanity, whereas 
 these are probably merely incipient symptoms, due, in the 
 vast majority of cases, to precisely the same combination 
 of physical and mental causes, which, when they operate 
 with greater intensity, ultimately issue in definite and 
 unmistakable insanity. 
 
 We have an instructive instance of the same error 
 in some of the speculations respecting the origin of 
 fevers. In Abdominal Typhus (the so-called Typhoid 
 or Enteric Fever of the English Physicians) the febrile 
 symptoms (Pyrexia, Erethism, &c.) have been ascribed 
 to certain lesions of the glandular structures of the 
 intestines; but a wider observation has shown that 
 the other symptoms often precede by some time the 
 formation of the lesions, and that the fever may even 
 run a fatal course, though it may be impossible, in a 
 post-mortem examination, to detect the specific lesions 
 in question. Practically, the correction of this and 
 similar errors is of great importance, as much mischief 
 may be done, and much time may be lost, by a mode 
 of treatment which, through mistaking symptoms for 
 causes, or co-effects for cause and effect, addresses 
 itself only to the consequences of the malady, and leaves 
 the real source of evil unattacked. 
 
3IO FALLACIES INCIDENT 
 
 The following anecdote, told by Dr. Paris, affords an 
 amusing illustration of the extent to which the ignorant, 
 in reasoning on cause and effect, may be deceived by an 
 invariable, or even frequent, concurrence of events. 
 
 * It should,' says he °^, * be kept in mind, that two events 
 may arise from a common cause, and be co-existent, and yet 
 have not the most remote analogy to, or dependence upon, 
 each other. It was a general belief at St. Kilda, that the 
 arrival of a ship gave all the inhabitants colds. Dr. John 
 Campbell took a great deal of pains to ascertain the fact, 
 and to explain it as the effect of effluvia arising from human 
 bodies ; the simple truth, however, was, that the situation of 
 St. Kilda renders a north-east wind indispensably necessary 
 before a stranger can land, — the wind, not the stranger, 
 occasioned the epidemic' 
 
 In speculations on the history of language, languages, 
 which recent investigation has shown to be related col- 
 laterally, were by older philologers erroneously regarded 
 as standing to each other in the relation of parent and 
 child. I extract from Professor Max Miiller's Lectures on 
 the Science of Language^^ the following illustration, which 
 will already be famihar to many of my readers : — 
 
 * A glance at the modern history of language will make 
 this clearer. There never could be any doubt that the so- 
 called Romance languages, Italian, Wallachian, Provencal ^^, 
 
 ^' Pharmacologia, p. 89. 
 
 ^* First Series. Lecture V. 
 
 ^ The exact relationship of French to Proven9al may be represented 
 thus : the Peasant Latin became in the South of France the Langue d'Oc 
 (or Provenjal), and in the North the Langue d'Oil, of which the French 
 
TO INDUCTION, 31I 
 
 French, Spanish, and Portuguese, were closely related to each 
 other. Everybody could see that they were all derived from 
 Latin. But one of the most distinguished French scholars, 
 Raynouard, who has done more for the history of the Romance 
 languages and literature than any one else, maintained that 
 Provenyal only was the daughter of Latin ; whereas French, 
 Italian, Spanish, and Portuguese were the daughters of 
 Proven9al. He maintained that Latin passed, from the 
 seventh to the ninth century, 'through an intermediate stage, 
 which he called Langue Romane, and which he endeavoured 
 to prove was the same as the Proven9al of Southern France, 
 the language of the Troubadours. According to him, it was 
 only after Latin had passed through this uniform metamor- 
 phosis, represented by the Langue Romane or Proven9al, 
 that it became broken up into the various Romance dialects 
 of Italy, France, Spain, and Portugal. This theory, which 
 was vigorously attacked by August Wilhelm von Schlegel, 
 and afterwards minutely criticised by Sir Gornewall Lewis, 
 can only be refuted by a comparison of the Provencal 
 grammar with that of the other Romance dialects. And here, 
 if you take the auxiliary verb to be, and compare its forms 
 in Provencal and French, you will see at once that, on 
 several points, French has preserved the original Latin forms 
 in a more primitive state than Proven9al, and that, therefore, 
 it is impossible to classify French as the daughter of Pro- 
 vengal, and as the granddaughter of Latin. We have in 
 Provenyal : — 
 
 jetTiy corresponding to the French nous sommes, 
 et% „ 'vous etes, 
 
 son „ Us sontf 
 
 and it would be a grammatical miracle if crippled forms, such 
 
 (or the dialect of the Isle de France) was the principal dialect, and has in 
 its modern form become the language of the nation. See Brachet's 
 Historical Grammar (Mr. Kitchin's Translation), p. 18. 
 
312 FALLACIES INCIDENT 
 
 as sffrif etz, and jo«, had been changed back again into the 
 more healthy, more primitive, more Latin, sommes^ etej, sont ; 
 jumuSj estis, sunt. 
 
 Let us apply the same test to Sanskrit, Greek, and Latin; 
 and we shall see how their mutual genealogical position is 
 equally determined by a comparison of their grammatical 
 forms. It is as impossible to derive Latin from Greek, or 
 Greek from Sanskrit, as it is to treat French as a modification 
 of Provencal. Keeping to the auxiliary verb to be, we find 
 that / am is in 
 
 Sanskrit Greek Lithuanian 
 
 ajmi esmi esmi. 
 
 The root is as, the termination mi. 
 
 Now, the termination of the second person is si, which 
 together with as, or es, would make 
 
 as'si es-si es-si. 
 
 But here Sanskrit, as far back as its history can be traced, 
 has reduced assi to asi ; and it would be impossible to suppose 
 that the perfect, or, as they are sometimes called, organic, 
 forms in Greek and Lithuanian, es-si, could first have passed 
 through the mutilated state of the Sanskrit asi. 
 
 The third person is the same in Sanskrit, Greek, and 
 Lithuanian, as-ti or es-ti ; and, with the loss of the final /, we 
 recognise the Latin est, Gothic ist, and Russian est\ 
 
 The same auxiliary verb can be made to furnish sufficient 
 proof that Latin never could have passed through the Greek, 
 or what used to be called the Pelasgic stage, but that both 
 are independent modifications of the same original language. 
 In the singuliar, Latin is less primitive than Greek ; for sum 
 stands for es-um, es for es-is, est for es-ti. In the first person 
 plural, too, sumus stands for es-umus, the Greek es-mes, the 
 Sanskrit ^smas. The second person es-tis, is equal to Greek 
 es-te, and more primitive than Sanskrit stha. But in the third 
 person plural Latin is more primitive than Greek. The 
 
TO INDUCTION. 313 
 
 regular form would be as-anti; this, in Sanskrit, is changed 
 into santL In Greek, the initial s is dropped, and the iEolic 
 enti is finally reduced to eisi. The Latin, on the contrary, 
 has kept the radical j, and it would be perfectly impossible 
 to derive the Latin sunt from the Greek eisi' 
 
 (4) A not uncommon source of error is the confusion 
 of the proximate with the primary or remote cause of 
 a phenomenon. To be on our guard against this error 
 is often of the utmost practical importance; for the re- 
 moval of the proximate cause may only temporarily 
 remove the effect, and the primary cause may, after a 
 time, reproduce it ; or, again, the removal of the primary 
 cause may still leave the proximate cause in full action. 
 This is well exemplified in Mr. Lewes' account of Thirst. 
 
 * The sensation of Thirst is not merely a sensation depen- 
 dent on a deficiency of liquid in the system, but a local sensa- 
 tion dependent on a local disturbance : the more water these 
 men (the prisoners confined in the Black Hole at Calcutta) 
 drank, the more dreadful seemed their thirst ; and the mere 
 sight of water rendered the sensation, which before was 
 endurable, quite intolerable. The increase of the sensation 
 following a supply of water, would be wholly inexplicable to 
 those who maintain that the proximate cause of Thirst is 
 deficiency of liquid; but is not wholly inexplicable, if we 
 regard the deficiency as the primary, not the proximate 
 cause ; for this primary cause having set up a feverish con- 
 dition in the mouth and throat, that condition would continue 
 after the original cause had ceased to exist. The stimulus 
 of cold water is only a momentary relief in this case, and 
 exaggerates the sensation by stimulating a greater flow of 
 blood to the parts. If, instead of cold water, a little luke- 
 warm tea, or milk-and-water, had been drunk, permanent 
 
314 FALLACIES INCIDENT 
 
 relief would have been attained ; or if, instead of cold water, 
 a lump of ice had been taken into the mouth, and allowed 
 to melt there, the effect would have been very different — 
 a transitory application of cold increasing the flow of blood, 
 a continuous application driving it away. 
 
 'We must not, however, forget that although, where a 
 deficiency of liquid has occasioned a feverish condition of the 
 mouth and throat, no supply of cold liquid will at once re- 
 move that condition, the relief of the Systemic sensation 
 not immediately producing relief of the local sensation, never- 
 theless, so long as the system is in need of liquid, the feeling 
 of thirst must continue. Claude Bernard observed that a 
 dog which had an opening in its stomach drank unceasingly 
 because the water ran out as fast as it was swallowed; in 
 vain the water moistened mouth and throat on its way to 
 the stomach. Thirst was not appeased because the water 
 was not absorbed. The dog drank till fatigue forced it to 
 pause, and a few minutes afterwards recommenced the same 
 hopeless toil ; but no sooner was the opening closed, and the 
 water retained in the stomach, from whence it was absorbed 
 into the system, than thirst quickly vanished ^\' 
 
 In studying the history of a language, it is often 
 most important to bear in mind that words ultimately 
 derived from one language are proximately derived 
 through the medium of another. Thus, there will occur 
 to the reader numberless EngUsh words which have been 
 derived from the Latin through the French, as, for in- 
 stance, Judge, noble, emperor, governor, prince. And, to 
 quote M. Brachet: — 
 
 *• When Jerome translated the Old Testament into Latin, 
 he incorporated into his version certain Hebrew words which 
 
 ^^ Lewes' Physiology of Common Life^ vol. i. pp. 45-47. 
 
TO INDUCTION, 315 
 
 had no Latin equivalents, as seraphim, Gehenna, pascha, &c. ; 
 from Latin they passed at a later time into French {seraphin, 
 gene^pdque). But they entered French from the Latin, not 
 from the Hebrew. The same is the case with the Arabic ; 
 its relations with French have been purely accidental. To 
 say nothing of those words which express oriental things, 
 such as Alcoran, hey, cadi, cara'vane, dewiche, firman, janissaire, 
 &c., which were brought into the west by travellers, the 
 French language received, in the middle ages, many Arabic 
 words from another source : the Crusades, the scientific 
 greatness of the Arabians, the study of oriental philosophies, 
 much followed in France between the twelfth and fourteenth 
 centuries, enriched the vocabulary of the language with many 
 words belonging to the three sciences which the Arabians 
 cultivated successfully : in astronomy it gave such words as 
 azimuth, nadir, zenith j in alchemy, alcali, alcool, alambic, 
 alchimie, elixir, strop', in mathematics, algebre, zero, chiffre. 
 But even so these words did not come directly from Arabic 
 to French; they passed through the hands of the scientific 
 Latin of the middle ages. In fact, the oriental languages 
 have had little or no popular or direct influence on French ^^.* 
 
 The non-recognition of these intermediate channels 
 through which the words of one language have been 
 introduced into another, has often led to the most erro- 
 neous theories as to the connection of languages or the 
 relations subsisting between the people speaking them. 
 Thus, it was once a favourite theory that all languages 
 are derived from Hebrew, and the occurrence in dif- 
 ferent languages of the same words has often, without 
 any other ground, been regarded as a proof of the con- 
 nection of the most diverse races. 
 
 ^ Historical Grammar, p. 22, note a. 
 
3l6 FALLACIES INCIDENT 
 
 We add an example from the science of Political 
 Economy. It has often been supposed that high prices 
 produce high wages. A sudden rise in the price of any- 
 particular class of commodities may lead, by a desire 
 on the part of the producers to increase the supply, and 
 by a consequent increase in the demand for labour in 
 that particular department, to a temporary rise in wages. 
 But a rise in prices produces no permanent rise in wages, 
 unless it leads to an increased accumulation of capital, 
 that is, an augmentation of the fund available for the 
 further production of wealth and, consequently, for the 
 payment of wages ^^. Here the rise in prices is the 
 remote or primary, and the increased accumulation of 
 capital is the proximate, cause of the phenomenon ; but, 
 as counteracting causes, such as reckless speculation or 
 the adoption of a more luxurious style of living on the 
 part of the capitalists, may prevent the rise in prices 
 from being followed by an increased accumulation of 
 capital, it is often of great importance to distinguish the 
 two. 
 
 We have, thus far, discussed those errors which ori- 
 ginate in overlooking the presence of some third circum- 
 stance. But, even when all the circumstances except the 
 cause and effect (or what we suppose to be such) have 
 been eliminated, we may still commit an error, either 
 from mistaking the cause for the effect, or from neglect- 
 ing to take account of their mutual action and reaction, 
 
 ®^ See Mill's Political Economy, Bk. II. ch. xi. § 2. 
 
TO INDUCTION. 317 
 
 and being thus led erroneously to assign to one of the 
 two exclusively the whole share in the production of the 
 ultimate effect. 
 
 (5) The importance of not overlooking this latter source 
 of error is well illustrated by the following remarks of 
 Sir G. C. Lewis«*:— 
 
 'An additional source of error in determining political 
 causation is likewise to be found in the mutuality of cause 
 and effect. It happens sometimes that when a relation of 
 causation is established between two facts, it is hard to 
 decide which, in the given case, is the cause and which the 
 effect, because they act and re-act upon each other, each 
 phenomenon being in turn cause and effect. Thus, habits 
 of industry may produce wealth; while the acquisition of 
 wealth may promote industry : again, habits of study may 
 sharpen the understanding, and the increased acuetness of 
 the understanding may afterwards increase the appetite for 
 study. So an excess of population may, by impoverishing the 
 labouring classes, be the cause of their living in bad dwellings ; 
 and, again, bad dwellings, by deteriorating the moral habits 
 of the poor, may stimulate population. The general intelli- 
 gence and good sense of the people may promote its good 
 government, and the goodness of the government may, in its 
 turn, increase the intelligence of the people, and contribute 
 to the formation of sound opinions among them. Drunken- 
 ness is in general the consequence of a low degree of intelli- 
 gence, as may be observed both among savages and in civilized 
 countries. But, in return, a habit of drunkenness prevents 
 the cultivation of the intellect, and strengthens the cause 
 out of which it grows. As Plato remarks, education im- 
 proves nature, and nature facilitates education. National 
 
 ^* On Methods of Observation and Reasoning in Politics^ vol. i. 
 p. 375. 
 
3l8 FALLACIES INCIDENT 
 
 character, again, is both effect and cause : it re-acts on the 
 circumstances from which it arises. The national peculiarities 
 of a people, its race, physical structure, climate, territory, 
 &c., form originally a certain character, which tends to 
 create certain institutions, political and domestic, in harmony 
 with that character. These institutions strengthen, per- 
 petuate, and reproduce the character out of which they 
 grew, and so on in succession, each new effect becoming, 
 in its turn, a new cause. Thus a brave, energetic, restless 
 nation, exposed to attack from neighbours, organises military 
 institutions : these institutions promote and maintain a war- 
 like spirit : this warlike spirit, again, assists the development 
 of the military organisation, and it is further promoted by 
 territorial conquests and success in war, which may be its 
 result — each successive effect thus adding to the cause out 
 of which it sprung.' 
 
 The difference between the calculated and observed 
 velocities of sound (already noticed ^^) furnishes another 
 illustration of the importance of attending to the mutual 
 action of cause and effect. The wave of sound, in its 
 passage through the air, developes heat by compression, 
 and this heat, by augmenting the elasticity of the air, 
 increases, in turn, the velocity with which the sound 
 is transmitted. Thus the effect re-acts upon, and pro- 
 motes the operation of, the original cause. It was from 
 overlooking this fact that Newton's calculation of the 
 velocity of sound fell short of the observed velocity by 
 about one-sixth of the actual rate. 
 
 Malthus' speculations on the increase of population 
 illustrate another form of the same error. He found 
 
 «5 Pp. 177, 178. 
 
TO INDUCTION. 319 
 
 that, in many cases, population increased faster than 
 food increased. He inferred that this increase of popu- 
 lation once begun would continue under all circum- 
 stances ; and that therefore a time was at hand, in many 
 countries, when the bulk of the people would be reduced 
 almost to a state of starvation. He did not observe 
 that in this case, the effect re-acts upon the cause ; not, 
 however, in the way of promoting but of retarding its 
 operation. The tendency of an increase of population 
 is certainly to diminish the supply of food; but, in 
 attempting to forecast the ultimate result of this ten- 
 dency, Malthus did not take sufficient account of the 
 fact that the diminution in the supply of food has, 
 in its turn, a tendency to arrest the increase of popu- 
 lation. 
 
 Instances of the tendency of an effect to re-act upon 
 its cause, in the way of diminishing its intensity, are very 
 frequent in human affairs. Thus, when a man discovers 
 that he is labouring under a disease, the additional 
 prudence which he is induced to exercise will often 
 not only arrest or retard the progress of the disease, 
 but lead to the prolongation of his Hfe beyond the usual 
 term. Again, when a deficiency of sanitary arrange- 
 ments has led to an increased mortality or the outbreak 
 of a pestilence, the attention thus directed to the noxious 
 influences at work will often result in their removal, or, 
 at least, in some considerable alleviation of them. It is 
 plain that, in speculating on the future, these are con- 
 siderations which ousfht not to be left out of account. 
 
3^0 FALLACIES INCIDENT 
 
 (6) We may invert cause and effect, mistaking one 
 for the other. This error is not infrequent in historical 
 speculations, as, for instance, when some great event, 
 such as the religious reformation of the sixteenth cen- 
 tury, or the French Revolution, is assigned as the cause 
 of a general change of opinion or of certain mental 
 and social habits, whereas, in reality, the gradual, and 
 often unobserved, operation of this change has been the 
 cause, and not the effect, of the historical event. In 
 a case of this kind, however, the event may, in turn, 
 have intensified, and, perhaps, given the sanction of 
 authority to, the causes which produced it. 
 
 Again, a particular form of government, monarchical, 
 aristocratical, democratical, or the like, is often assigned 
 as the cause of certain peculiarities of social feeling or 
 national character, whereas it would probably be far 
 more correct to regard the form of government as due, 
 in the first instance, to these peculiarities, though it, in 
 turn, may have intensified the causes to which it was 
 originally due. 
 
 In meteorological speculations it has been questioned 
 whether the electrical phenomenon of lightning is the 
 cause or effect of the sudden precipitations of rain and 
 hail which it generally accompanies. Sir John Herschel 
 (in opposition to the ordinary opinion ^^) maintains that 
 it is the effect, and argues thus : — 
 
 * Whatever may be the state of the ultimate molecules of 
 ^ Herschel's Meteorology, §§ 135, 137. 
 
TO INDUCTION. 32 1 
 
 vapour, it seems impossible but that when a great multitude 
 of them lose their vaporous state by cold, and coalesce into 
 a drop or snow spangle, however minute, that drop will have 
 collected and retained on its surface (according to the laws 
 of electric equilibrium) the whole electricity of its con- 
 stituent molecules, which will therefore have some finite, 
 though very feeble tension. Now, suppose any number (1000 
 for instance) of such globules to coalesce, or that by successive 
 deposition one should gradually grow to 1000 times its original 
 nyolume. The diameter will be only 10, and the surface 100 
 times increased. But the electric contents being the sum 
 of those of the elementary globules, will be increased one 
 thousandfold, and being spread entirely over the surface, will 
 have a tenfold density (J»e, tension). 
 
 * It will easily be seen, that when thousands of these electri- 
 ferous globules again further coalesce into rain drops, a great 
 and sudden increase of tension at their surface must take 
 place. Their electricity, then, is enabled to spring from drop 
 to drop, and rushing in an instant of time from all parts of 
 the cloud to the surface, a flash is produced. Accordingly, 
 in thunder-storms, it is the commonest of all phenomena to 
 find each great flash succeeded by a sudden rush of rain at 
 such an interval of time as may be supposed to have been 
 occupied in its descent. The sudden precipitation of large 
 quantities of rain, and especially of hail, which is formed in 
 a cold region where the insulating power of the air is great, 
 is almost sure to be accompanied with lightning, which the 
 usual perversity of meteorologists, where electricity is in ques- 
 tion, long persisted, and even yet persists, with few exceptions, 
 in regarding as the cause, and not the consequence, of the 
 precipitation.' 
 
 A question has also been raised whether the copious 
 precipitation of rain which usually takes place in the 
 
 Y 
 
^0,2, FALLACIES INCIDENT 
 
 centre of a cyclone is the cause or the effect of the 
 cyclone. The more probable view is that the partial 
 vacuum produced by the rain-fall, and the consequent 
 inrush of the surrounding atmosphere, is the cause of 
 the cyclone. 
 
 Mr. M'Lennan, in his Primitive Marriage, conceives 
 that marriage by capture arose from the custom of 
 exogamy, that is to say, from the custom which forbad 
 marriage within the tribe. Sir John Lubbock ^^, on the 
 other hand, opposes this opinion, and regards exogamy 
 as arising from marriage by capture, not marriage by 
 capture from exogamy. 'Mr. M'Lennan's theory,' 
 says he, * seems to me quite inconsistent with the exist- 
 ence of tribes which have marriage by capture and yet 
 are endogamous. The Bedouins, for instance, have 
 unmistakeably marriage by capture, and yet the man has 
 a right to marry his cousin, if only he be willing to give 
 the price demanded for her.' 
 
 Professor Rogers, in his recently published Manual of 
 Political Economy ^^, calls in question the received opinion 
 on the relation between the increase of population and 
 the cultivation of inferior soils. Though I cannot accept 
 his position, the passage will serve as an instance of 
 the difficulty frequently experienced in determining which 
 of two phenomena or events is cause and which is 
 effect. 
 
 «^ Origin of Civilization and Primitive Condition of Man, ch. 3. 
 *' p. 153. 
 
TO INDUCTION. 323 
 
 * There is not a shadow of evidence in support of the state- 
 ment that inferior lands have been occupied and cultivated as 
 population increases. The increase of population has not 
 preceded but followed this occupation and cultivation. It is 
 not the pressure of population on the means of subsistence 
 which has led men to cultivate inferior soils, but the fact that 
 these soils being cultivated in another way, or taken into 
 cultivation, an increased population became possible. How 
 could an increased population have stimulated greater labour 
 in agriculture, when agriculture must have supplied the means 
 on which that increased population could have existed ^'^ ? To 
 make increased population the cause of improved agriculture 
 is to commit the absurd blunder of confounding cause and 
 eflfect.' 
 
 While agreeing with the ordinary theory that the 
 pressure of population leads, in the first instance, to 
 the cultivation of inferior lands, I should admit that the 
 greater area of land under cultivation, by rendering 
 possible a larger population, reacts upon and intensifies 
 the original cause, an increased population leading to the 
 cultivation of fresh lands, that rendering possible a still 
 larger population, this in turn leading to the cultivation 
 of fresh lands, and so on, till the process is arrested 
 by counteracting causes. If this view be correct, the 
 ordinary theory is more justly open to the charge of 
 neglecting to take into account the 'mutuahty' of cause 
 and effect, noticed a few pages back, than of inverting 
 their relation. 
 
 *® This question appears to ignore the fact that a population may have 
 an insufficient supply of food, though what it does possess may be just 
 competent to sustain life. 
 
 Y 2 
 
3^4 FALLACIES INCIDENT 
 
 VI. The Argument from Analogy, as has already been 
 stated, consists in drawing the conclusion that, because 
 two phenomena resemble each other in certain observed 
 points, they also resemble each other in certain other 
 points beyond the range of our observation. The con- 
 ditions to which such an inference, in order to be legi- 
 timate, must conform, need not be here repeated. If 
 the conditions be not fulfilled, we may commit the error 
 either of over-estimating the force of the analogy; of 
 mistaking the direction in which it points, so as to regard 
 an analogy which makes against a certain position as 
 making for it, or the reverse; or, lastly, of supposing 
 grounds of analogy to subsist where there are really 
 none. The two former errors have been sufficiently ex- 
 emplified in the chapter on Imperfect Inductions. 
 
 When we exaggerate the value of analogical evidence, 
 or mistake the conclusion to be drawn from it, we may 
 be led to do so either by over-rating the number of 
 ascertained points of resemblance as compared with 
 ascertained points of difference, or the reverse, or by 
 miscalculating the extent of our knowledge of the pheno^ 
 mena. The examples referred to illustrate both sources 
 of error. Thus, for instance, the points in which elec- 
 tricity resembles a fluid are obvious, while the points of 
 difference are far less obtrusive, and, moreover, the un- 
 known properties of electricity are probably out of all 
 proportion to those which we know. In this case, too, 
 when we include the consideration of heat, light, and 
 similar agencies, the argument from analogy may be 
 
TO INDUCTION, 325 
 
 used againsiy rather than in favour of, the identification 
 of electricity with a fluid. 
 
 The student need, however, hardly be reminded that 
 an analogy which in one state of knowledge appears, 
 to be a strong one may, as knowledge advances, become 
 extremely faint, worthless, or even positively unfavourable 
 to the position which it was originally adduced to support. 
 
 The term False Analogy is, strictly speaking, applied 
 not to those cases in which we over-estimate the value 
 of the analogy, or mistake the direction in which the 
 argument points, but to those cases of analogical in- 
 ference in which there exists no ground for any analogy 
 whatever. Two phenomena. A, B, resemble each other 
 in the possession of the properties a, b, c. The pheno- 
 menon A is observed also to present the property d, and 
 hence it is inferred as probable that the same property 
 is to be found also in B. Now it has already been pointed 
 out that if we have any special reason for supposing d to 
 be causally connected with any of the properties a, by c, 
 the argument ceases to be analogical, and becomes in- 
 ductive. But if, on the other hand, we have any special 
 reason for supposing that d is causally connected with 
 none of the properties <2, 3, Cj there is no room for any 
 inference whatever. The whole force of the Argument 
 from Analogy consists in the chance ^o^ d being causally 
 connected with a, 3, 01 c; if we have reason to believe 
 that this is the case, the argument becomes more than 
 analogical; if we have reason to beheve that it is not 
 the case, we are debarred from employing the argument 
 
3^6 FALLACIES INCIDENT 
 
 altogether. Thus, in a certain sense, the Argument from 
 Analogy is based on our ignorance ; it is the result of 
 a calculation of chances, which an accession of know- 
 ledge may invalidate, by either augmenting, diminishing, 
 or annihilating it. Of False Analogy, in its strict sense, 
 that is to say, the error of supposing that similarity or 
 dissimilarity in certain points is an evidence of similarity 
 or dissimilarity in other points, when more careful re- 
 flection or observation would lead to the belief that there 
 is probably no connection whatever between the ob- 
 served points from which the Analogy proceeds, and the 
 unobserved points to which it argues, instances are 
 extremely numerous in almost every branch of knowledge. 
 As this form of Fallacy is so common, we shall subjoin 
 several examples of it. 
 
 The following excellent illustration is quoted by Mr. 
 Mill from Archbishop Whately's Rhetoric^^'. 
 
 * It would be admitted that a great and permanent diminu- 
 tion in the quantity of some useful commodity, such as corn, 
 or coal, or iron, throughout the world, would be a serious 
 and lasting loss ; and again, that if the fields and coal mines 
 yielded regularly double quantities with the same labour, we 
 should be so much the richer ; hence it might be inferred, that 
 if the quantity of gold and silver in the world were diminished 
 one half, or were doubled, like results would follow; the 
 utility of these metals, for the purposes of coin, being very 
 great. Now there are many points of resemblance and many 
 
 ^•^ Mill's Logic, Bk. V. ch. v. § 6; Whately*s Rhetoric, Part I. ch. ii. 
 § 7. The passage does not occur in the earlier editions of Whately's 
 Rhetoric. 
 
TO INDUCTION. 327 
 
 of difference, between the precious metals on the one hand, 
 and corn, coal, &c. on the other ; but the important circum- 
 stance to the supposed argument is, that the utility of gold 
 and silver (as coin, which is far the chief) depends on their 
 valtiey which is regulated by their scarcity; or rather, to 
 speak strictly, by the difficulty of obtaining them ; whereas, 
 if corn and coal were ten times as abundant (i. e. more easily 
 obtained), a bushel of either would still be as useful as now. 
 But if it were twice as easy to procure gold as it is, a sove- 
 reign would be twice as large ; if only half as easy, it would 
 be of the size of a half-sovereign, and this (besides the trifling 
 circumstance of the cheapness or dearness of gold ornaments) 
 would be all the difference. The analogy, therefore, fails in 
 the point essential to the argument.' 
 
 Respect for antiquity is often urged by an argument 
 so sweeping as to assume the form of a False Analogy. 
 *Who are we,' it is said, Uhat we should presume to 
 think that we know better than previous generations?' 
 Now, on many matters of fact, there can be no question 
 that the beHef of previous generations, when properly 
 examined and sifted, must be accepted as final, inasmuch 
 as they were contemporary, or nearly contemporary, 
 with the original sources of information. To infer from 
 this just and limited deference the necessity of an undis- 
 criminating submission to the opinions of our ancestors, 
 would be an instance of the fallacy of Inductio per 
 simpHcem enumerationem. But this, at least in many 
 cases, seems not to be the nature of the argument, which 
 appears rather to proceed on some such grounds as 
 these: we reverence the opinions of the aged, because 
 they have had more experience than we have had, and 
 
3^8 FALLACIES INCIDENT 
 
 therefore, surely, on the same principle, we ought to 
 accept the opinions of our ancestors, who lived in bygone 
 generations. The point of resemblance is the fact of 
 having been born at a period prior to ourselves, and 
 hence it is inferred that the greater experience and the 
 greater wisdom which are found to be concomitants of 
 this fact in the case of many of our senior contemporaries 
 may also be presumed in the case of those who have 
 long since been dead. It, of course, escapes the notice 
 of those who have recourse to this argument, that the 
 average age of the persons living at any one time is 
 about the same as that of those living at any other, and 
 that superior wisdom is the consequence not of priority 
 of birth but of greater experience. Thus far, the fallacy 
 may be regarded as one of False Analogy, strictly so 
 called. But there is another consideration which turns 
 the edge of the argument. Experience grows with time, 
 each generation not only inheriting the accumulated 
 experience of previous generations, but adding to the 
 stock its own acquisitions. * Recte enim,' says Bacon ''^ 
 
 ''^ Novum Organum, Lib. I. Aph. Ixxxiv. In the first edition of this 
 work I suggested that the reference might possibly be to iEschylus, 
 Prometheus Vinctus, 1. 981 : aXK k/chdd(rK€i vavO^ 6 y7]pd(TK(uv xp6vos. 
 Through the courtesy of the Rev. E. Marshall, of Sandford, near Steeple 
 Aston, I am now enabled to supply the true reference, which is to Aulus 
 Gellius, Nodes Atdcce, Lib. XIL cap. 1 1 : ^ Alius quidam veterum poetarum, 
 cujus nomen mihi nunc memoriae non est, veritatem temporis filiam 
 esse dixit.' Compare the following sentences in the same Aphorism of 
 the Novum Organum : ' De antiquate autem opinio, quam homines de 
 ipsa fovent, negligens omnino est, et vix verbo ipsi congrua. Mundi enirn 
 senium et grandaevitas pro antiquitate vere habenda sunt ; quae temporibus 
 
TO INDUCTION. 329 
 
 'Veritas temporis filia dicitur, non auctoritatis/ 'Anti- 
 quitas sseculi juventus mundi'^'^/ 
 
 nostris tribui debent, non juniori aetati mundi, qualis apud antiques fuit. 
 Ilia enim aetas, respectu nostri, antiqua et major; respectu mundi ipsius, 
 nova et minor fuit. Atque revera quemadmodum majorem rerum huma- 
 narum notitiam, et maturius judicium, ab homine sene expectamus, quam 
 a juvene, propter experientiam, et rerum, quas vidit, et audivit, et 
 cogitavit, varietatem et copiam ; eodem modo et a nostra setate (si vires 
 suas nosset, et experiri et intendere vellet) majora multo quam a priscis 
 temporit^us expectari par est ; utpote aetate mundi grandiore, et infinitis 
 experimentis et observationibus aucta et cumulata.' Bentham in his 
 Booh of Fallacies, Part I. ch. ii., and Sydney Smith in his review of that 
 work {Edmburgh Review, No. Ixxxiv, reprinted in his Collected Works), 
 have some very apposite and amusing remarks on this subject. 
 
 "^^ De Augmentis Scientiarum, Lib. I. Dr. Whewell in his Philosophy 
 of Discovery (chap. xiii. § 4) appears to think that this celebrated Apho- 
 rism may be traced to Giordano Bruno. * It is worthy of remark that 
 a thought which is often quoted from Francis Bacon, occurs in Bruno's 
 Cena di Cenere, published in 1584; I mean, the notion that the later 
 times are more aged than the earlier. In the course of the dialogue, the 
 Pedant, who is one of the interlocutors, says, " In antiquity is wisdom ; " 
 to which the Philosophical Character replies, " If you knew what you 
 were talking about, you would see that your principle leads to the 
 opposite result of that which you wish to infer ; — I mean, that tve are 
 older, and have lived longer, than our predecessors." He then proceeds 
 to apply this thought, by tracing the course of astronomy through the 
 earlier astronomers up to Copernicus.* See Wagner's edition of Giordano 
 Bruno* s Works, vol. i. p. 132. In the original the passage runs thus: — 
 * Prudenzio. Sii come la si vuole, io non voglio discostarmi dal parer 
 de gli antichi ; per che dice il saggio : Ne I'antiquita e la sapienza. 
 Teofilo. E soggiunge : In molti anni la prudenza. Se voi intendeste 
 bene quel che dite, vedreste, che dal vostro fondamento s* inferisce il 
 contrario di quel che pensate : voglio dire, che noi siamo piu vecchi et 
 abbiamo piti lunga eta, che i nostri predecessori.' Mr. Spedding, how- 
 ever, in his edition of Bacon, questions whether Bacon intended the 
 aphorism as a quotation, and thinks it probable that he did not derive it 
 
330 FALLACIES INCIDENT 
 
 Bishop Wilkins' Discovery of a New World contains 
 the following curious extract, translated from the work 
 of Cardinal Nicolo de Cusa De doctd Ignorantid'^^ : 
 
 * We may conjecture the inhabitants of the sun are like to 
 the nature of that planet, more clear and bright, more intel- 
 lectual than those in the moon where they are nearer to the 
 nature of that duller planet, and those of the earth being 
 more gross and material than either, so that these intellectual 
 natures in the sun are more form than matter, those in the 
 earth more matter than form, and those in the moon 'betwixt 
 both. This we may guess from the fiery influence of the sun, 
 the watery and aerous influence of the moon, so also the 
 material heaviness of the earth. In some such manner like- 
 wise is it with the regions of the other stars ; for we con- 
 jecture that none of them are without inhabitants, but that 
 there are so many particular worlds and parts of this one 
 universe, as there are stars, which are innumerable, unless 
 it be to Him who created all things in number.' 
 
 The analogy in this case is founded not, as in the 
 previous instances, on points of resemblance but on 
 points of dissimilarity. The sun, the moon, and the 
 earth are formed of different materials, and, therefore, 
 it is argued, their inhabitants differ in their intellectual 
 capacities, the exaltation of intelligence rising in pro- 
 portion to the ^ clearness and brightness ' of the globe 
 which they inhabit. Waiving the assumptions as to the 
 materials of which the three bodies are composed and 
 
 from any earlier writer. — See Ellis and Spedding's edition of Bacon, vol. i. 
 p. 458, n. 4. 
 
 ■^^ Wilkins* Discovery of a New World in the Moon, p. 128 ; Cusanus, 
 De doctd Ignorantidj Lib. II. ch. xii. 
 
TO INDUCTION. 33 1 
 
 the habitation of them all by intelligent beings, it is 
 plain that there is no presumption in favour of the 
 theory that the intelligence of the inhabitants stands in 
 any relation to the material of the globe on which they 
 live ; by parity of reasoning, birds ought to be far more 
 intelligent than men. 
 
 The following passage from Bacon's Novum Organum'^^ 
 furnishes a remarkable example of a combination of 
 Confusion of Language with False Analogy : ' Sed 
 temporibus insequentibus, ex inundatione Barbarorum in 
 imperium Romanum, postquam doctrina humana velut 
 naufragium perpessa esset; tum demum philosophise 
 Aristotelis et Platonis, tanquam tabulae ex materia leviore 
 et minus solida, per fluctus temporum servatae sunt/ 
 The student may exercise his sagacity in assigning its 
 due share to each source of deception. 
 
 The arguments for or against the independence of 
 colonies will often be found to rest on a False Analogy. 
 Sometimes it is said that, under no circumstances, ought 
 a colony to rebel against the authority of the mother- 
 country ; at other times, that, the colony having come to 
 maturity, the time for its emancipation has arrived. In 
 each of these cases the argument is suggested by the 
 term * mother-country/ Now the relations of the child 
 to the parent are mainly determined by natural affection, 
 by early associations, by gratitude for favours received, 
 and frequently by the fact that, while the child is gra- 
 dually approaching to the prime of life, the parent 
 ^* Lib. I. Aph. Ixxvii. 
 
33^ FALLACIES INCIDENT 
 
 is gradually receding from it. Similar circumstances, 
 though to a far weaker degree, may undoubtedly de- 
 termine the relations of a colony to its ^ mother-country/ 
 as, for instance, sympathy of race, the associations of 
 many of the colonists with their early home, gratitude 
 for assistance received at the foundation of the colony 
 or during the earlier years of its existence, the growing 
 prosperity of the colony or the waning power of the 
 * mother-country/ But, in addition to the fact that there 
 are many cases in which these circumstances or some 
 of them do not exist, or in which they exist only to 
 the slightest extent, it must be plain, on reflection, that 
 the justice or injustice, the expediency or inexpediency, 
 of separation from the mother-country or of repudia- 
 tion by it must often be settled by considerations totally 
 distinct from these, and such as receive no elucidation 
 whatever from the relations between parent and child. 
 
 The illusion, originating in a false analogy, that every 
 community must, like every individual man, pass through 
 the three stages of growth, vigour, and decay, is thus 
 exposed by Sir G. C. Lewis "^^i 
 
 ^^ Methods of Observation and Reasoning in Politics, vol. ii. p. 438. 
 The Rev. E. H. Hansell has pointed out to me a striking passage in 
 Burke's ' Letters on a Regicide Peace,' in which Sir G. C. Lewis' notice of 
 this fallacy is anticipated. The passage appears to me to be worth 
 appending : ' I am not quite of the mind of those speculators who seem 
 assured that necessarily, and by the constitution of things, all states have 
 the same periods of infancy, manhood, and decrepitude, that are found 
 in the individuals who compose them. Parallels of this sort rather 
 furnish similitudes to illustrate or to adorn, than supply analogies 
 from whence to reason. The objects which are attempted to be forced 
 
TO INDUCTION. 333 
 
 * From what has been already said, it follows that the com- 
 parison which is sometimes instituted between the progress 
 of a community and the life of a man fails in essentials, and is 
 therefore misleading. Both a man and a community, indeed, 
 advance from small beginnings to a state of maturity ; but a 
 man has an allotted term of life, and a culminating point from 
 which he descends; whereas a community has no limited 
 course to run; it has no necessary period of decline and 
 decay, similar to the old age of a man ; its national existence 
 does not necessarily cease within a certain time. Nations, as 
 compared with other nations, have periods of prosperity and 
 power ; but even these periods often ebb and flow, and when 
 a civilised nation loses its pre-eminence — as Italy in the nine- 
 teenth, as compared with Italy in the fourteenth and six- 
 teenth centuries — it does not necessarily lose its civihsation. 
 A political community is renewed by the perpetual succession 
 of its members ; new births, immigrations, and new adoptions 
 of citizens, keep the political body in a state of continuous 
 youth. No such process as this takes place in an individual 
 man. If he loses a limb, it is not replaced by a fresh growth. 
 The effects of disease are but partially repaired ; all the 
 bodily and mental functions are gradually enfeebled, as life 
 is prolonged, till at last decay inevitably ends in death; 
 whereas a community might, consistently with the laws of 
 human nature, have a duration co-extensive with that of 
 mankind. 
 
 into an analogy are not found in the same classes of existence. Indi- 
 viduals are physical beings, subject to laws universal and invariable. The 
 immediate cause acting in these laws may be obscure : the general results 
 are subjects of certain calculation. But commonwealths are not physical 
 but moral essences. They are artificial combinations, and, in their 
 proximate efficient cause, the arbitrary productions of the human mind. 
 We are not yet acquainted with the laws which necessarily influence the 
 stability of that kind of work made by that kind of agent.' — Works^ 
 vol. viii. pp. 78, 79. 
 
334 FALLACIES INCIDENT 
 
 *The supposed analogy between the existence of a poli- 
 tical community and the life of a man seems to have con- 
 tributed to the formation of the belief in a liability to 
 corruption, inherent in every society. It was a favourite 
 doctrine among some writers of the last century, that every 
 civilised community is fated to reach a period of corruption, 
 when its healthy and natural action ceases, and it undergoes 
 some great deterioration. The notion of an inevitable stage 
 of corruption in a nation was, indeed, partly suggested by the 
 commonplaces condemnatory of luxury, derived both from 
 the classical and ecclesiastical writers ; and by the more 
 modern eulogies of savage life. So far, however, as it was 
 founded on the inevitable periods of decay in animal and 
 vegetable life, the comparison was delusive; for the two 
 relations which are brought together do not correspond. The 
 death of individuals may, indeed, be considered a necessary 
 condition for the progress of the society, into which they 
 enter as temporary elements. It is by the substitution of new 
 intelligences, and of natures not hardened to old customs, 
 for minds whose thoughts and habits have learnt to move 
 uniformly in the same groove, that progressive changes in 
 human affairs are effected. The decay and death of the indi- 
 vidual, therefore, tends not only to prevent the deterioration 
 of the society, but to promote its improvement.' 
 
 Ancient medicine was full of false analogies. We may 
 take the following example from Dr. Paris "^^i 
 
 *An example of reasoning by false analogy is presented 
 to us by Paracelsus, in his work de 'vitd longd, wherein, 
 speaking of antimony, he exclaims, ^'Sicut antimonium finit 
 aurum, sic, eadem ratione et forma, corpus humanum purum 
 reddit."' 
 
 ^* Pkarmacologia, p. 64. 
 
TO INDUCTION. 335 
 
 The alchemists, or some of them, appear to have 
 imagined that the same preparation by which they hoped 
 to convert the baser metals into gold (called metaphori- 
 cally 'the healthy man') would also be effective in re- 
 moving the sources of all bodily diseases. Why should 
 not the impurities of the human body be removable by 
 the same means as the impurities of the metals? 
 
 * They [that is, the Arabian physicians] conceived,' says the 
 same author "^"^j 'that gold was the metallic element in a state 
 of perfect purity, and that all the other metals differed from 
 it in proportion only to the extent of their individual con- 
 tamination ; and hence the origin of the epithet base, as 
 applied to such metals. This hypothesis explains the origin 
 of alchemy ; but in every history we are informed that the 
 earlier alchemists expected, by the same means that they 
 hoped to convert the baser metals into gold, to produce an 
 universal remedy, calculated to prolong indefinitely the span 
 of human existence. 
 
 ' It is difficult to imagine what connexion could exist in 
 their ideas between the " Philosopher's Stone" which was to 
 transmute metals, and a remedy which could arrest the pro- 
 gress of bodily infirmity : upon searching, however, into the 
 writings of these times, it appears probable that this conceit 
 may have originated with the alchemists from the applica- 
 tion of false analogies, and that the error was subsequently 
 diffused and exaggerated by a misconstruction of alchemical 
 metaphors.' 
 
 The old maxim that 'Nature abhors a vacuum,' the 
 curious behef, still prevalent even amongst persons of 
 intelligence, that the weather changes with the ' changes ' 
 
 • "" Pharmacologia^ p. 64. 
 
33^ FALLACIES INCIDENT 
 
 of the moon, the once fashionable doctrine of the ' Social 
 Contract ' or ^ Original Compact,' the explanation of 
 moral and physical facts by applying to them the con- 
 ceptions of * perfect numbers ' and ' regular solids ''^,' the 
 Pythagorean theory of the Harmony of the Spheres, the 
 Aristotelian doctrine of the Mean, and innumerable 
 other instances with which the student will meet in his 
 reading, will abundandy illustrate the nature of False 
 Analogy and its frequency in the reasoning of early 
 speculators. 
 
 The Argument from Final Causes ^^, at least that 
 
 ■^^ On this subject the reader will find some very curious information 
 in Mill's Logic, Bk. V. ch. v. § 6, and Whewell's History of the Inductive 
 Sciences, Bk. IV. ch. iii. § 2. 
 
 '^ * Tum vero, ad ulteriora tendens [intellectus humanus], ad proximiora 
 recidit, videlicet ad causas finales, quae sunt plane ex natura hominis, 
 potius quam universi : atque ex hoc fonte philosophiam miris modis 
 corruperunt.' — Bacon, Nov. Org. Lib. I. Aph. xlviii. To prevent mis- 
 conception, I may state that I am far from denying that the Argument 
 from Final Causes, if it take sufficient account of the evolution of or- 
 ganisms and their power of adapting themselves to external circum- 
 stances, and if it be based on the contemplation of Nature as a whole, 
 instead of on that of individual objects, may not admit of being stated 
 in such a form as to occupy once more an important position in any 
 ' scheme of Natural Theology. Bearing in mind these qualifications, it 
 may be perfectly legitimate to speak, with reference to the universe at 
 large, of design and a designer, whatever may have been the agency, 
 and however mysterious and prolonged the process, by which an intel- 
 ligent Creator may have worked. Theories of evolution may be so 
 stated as not to impair, but indefinitely to exalt, our ideas of the power, 
 wisdom, and benevolence of the Being in whom Nature had its source. 
 The student will find a very temperate statement of the prevalent 
 
TO INDUCTION, 337 
 
 extreme form of it which assumes that every natural 
 organism was specially designed to subserve some special 
 object, and fashioned, once for all, in immediate reference 
 to that object, appears ultimately to repose on a False 
 Analogy. God or Nature (for both terms are used) is 
 assimilated to a human artificer, and the argument ap- 
 pears to rest on the assumption that the motives, con- 
 ceptions, and contrivances of the one may be regarded 
 as similar to those of the other. * Nature does nothing 
 in vain/ ' Nature always acts for the best.' ' Everything 
 is designed for some good purpose.' These and similar 
 maxims express the general principle on which the 
 argument rests. Of its application to special cases we 
 may take the following examples. 
 
 The instances given by Bacon, in the Advancement of 
 Learning and the De Augmentis ^^, when protesting against 
 
 theory, together with much useful information on the literature of the 
 subject, in Dr. Acland's Harveian Oration for 1865. On the other side 
 he may, with most advantage, consult the works of Mr. Herbert Spencer 
 and Mr. Darwin, 
 
 ^^ Advancement of Learning, Bk. II. (Ellis and Spedding's edition, 
 vol. iii. p. 358). Cf. De Augmentis, iii. 4. It should be noticed, how- 
 ever, that Bacon allows the use of Final Causes in what he calls ' Meta- 
 physic' Of the foregoing instances, * and the like,' he says that they 
 are ' well enquired and collected in Metaphysic ; but in Physic they are 
 impertinent.' And again : * Not because these final causes are not true, 
 and worthy to be enquired, being kept within their own province ; but 
 because their excursions into the limits of physical causes hath bred a 
 vastness and solitude in that track.' The rest of the paragraph may be 
 read with advantage. What Bacon appears to mean (and the distinc- 
 tion is important) is that we may argue in Theology or Metaphysics, 
 from an ascertained case of adaptation to the wisdom or goodness of the 
 
 Z 
 
338 FALLACIES INCIDENT 
 
 the employment of Final Causes in physical enquiries, 
 are the following : ' The hairs of the eye-lids are for a 
 quickset and fence about the sight; the firmness of the 
 skins and hides of living creatures is to defend them 
 from the extremities of heat or cold ; the bones are for 
 the columns or beams, whereupon the frames of the 
 bodies of living creatures are built ; the leaves of trees 
 are for protecting of the fruit ; the clouds are for water- 
 ing of the earth; the solidness of the earth is for the 
 station and mansion of living creatures/ 
 
 The absurd extent to which the argument may be 
 carried by speculators who attempt to find a Final 
 Cause for every phenomenon which falls under their 
 cognisance, will be plain from the examples which follow. 
 It would, however, be unjust to charge these absurdities 
 to the account of those writers of the past generation 
 who took a more sober, though, perhaps, an erroneous, 
 view of the argument. 
 
 Creator, but that we are not justified in assuming adaptation or design 
 as a datum in physical investigation. Those who defend this use of the 
 argument, would reply that many discoveries (such as, notably, Harvey's 
 discovery of the circulation of the blood, which set out from observing 
 the action of the valves in the veins of many parts of the body, and en- 
 quiring into their purpose) have been suggested by the idea of adapta- 
 tion (which, it may be noticed, does not necessarily include the idea of 
 design). See Acland's Harveian Oration, and Dugald Stewart's Philo- 
 sophy of the Human Mind, Part II. ch. xi. (Sir W. Hamilton's edition of 
 Stewart's Works, vol. iii. p. 335, &c.) This may be, and, in fact, must 
 be, admitted with respect to physiological enquiries (however the adapta- 
 tion may be accounted for), and hence Bacon's prohibition is certainly 
 too absolute. 
 
TO INDUCTION. 339 
 
 In the TimcEus of Plato ^\ the construction of the whole 
 universe, and specially of man, is explained on the 
 principle of Final Causes. The following extract from 
 Mr. Grote's Plaio^^ will serve as a specimen of the 
 method there employed : 
 
 *The Demiurgus, having constructed the entire Kosmos, 
 together with the generated Gods, as well as Necessity would 
 permit — imposed upon these Gods the task of constructing 
 Man : the second-best of the four varieties of animals whom 
 he considered it necessary to include in the Kosmos. He 
 furnished to them as a basis an immortal rational soul (di- 
 luted remnant from the soul of the Kosmos); with which 
 they were directed to combine two mortal souls and a body. 
 They executed their task as well as the conditions of the pro- 
 blem admitted. They were obliged to include in the mortal 
 souls pleasure and pain, audacity and fear, anger, hope, appe- 
 tite, sensation, &c., with all the concomitant mischiefs. By 
 such uncongenial adjuncts the immortal rational soul was 
 unavoidably defiled. The constructing Gods, however, took 
 care to defile it as little as possible. They reserved the head 
 as a separate abode for the immortal soul: planting the 
 mortal soul apart from it in the trunk, and establishing the 
 neck as an isthmus of separation between the two. Again 
 the mortal soul was itself not single but double: including 
 two divisions, a better and a worse. The Gods kept the two 
 parts separate ; placing the better portion in the thoracic 
 cavity nearer to the head, and the worse portion lower down, 
 in the abdominal cavity: the two being divided from each 
 other by the diaphragm, built across the body as a wall of 
 partition : just as in a dwelling-house, the apartments of the 
 
 *^ Of Plato, Bacon says truly, that he * ever anchoreth on that shore.* 
 ** Vol. iii. pp. 272-275. 
 
 Z 2 
 
340 FALLACIES INCIDENT 
 
 women are separated from those of the men. Above the 
 diaphragm and near to the neck, was planted the energetic, 
 courageous, contentious soul ; so placed as to receive orders 
 easily from the head, and to aid the rational soul in keeping 
 under constraint the mutinous soul of appetite which was 
 planted below the diaphragm. The immortal soul was fas- 
 tened or anchored in the brain, the two mortal souls in the 
 line of the spinal marrow continuous with the brain : which 
 line thus formed the thread of connection between the three. 
 The heart was established as an outer fortress for the exer- 
 cise of influence by the immortal soul over the other two. 
 It was at the same time made the initial point of the veins, 
 — the fountain from whence the current of blood proceeded 
 to pass forcibly through the veins round to all parts of the 
 body. The purpose of this arrangement is, that when the 
 rational soul denounces some proceeding as wrong (either 
 on the part of others without, or in the appetitive soul 
 within), it may stimulate an ebullition of anger in the heart, 
 and may transmit from thence its exhortations and threats 
 through the many small blood channels to all the sensitive 
 parts of the body ; which may thus be rendered obedient 
 everywhere to the orders of our better nature. 
 
 '■ In such ebullitions of anger, as well as in moments of 
 imminent danger, the heart leaps violently, becoming over- 
 heated and distended by excess of fire. The Gods foresaw 
 this, and provided a safeguard against it by placing the lungs 
 close at hand with the windpipe and trachea. The lungs 
 were constructed soft and full of internal pores and cavities 
 like a sponge; without any blood, — but receiving, instead 
 of blood, both the air inspired through the trachea, and the 
 water swallowed to quench thirst. Being thus always cool, 
 and soft like a cushion, the lungs received and deadened the 
 violent beating and leaping of the heart; at the same time 
 that they cooled down its excessive heat, and rendered it 
 a more equable minister for the orders of reason. 
 
TO INDUCTION. 34 1 
 
 * The third or lowest soul, of appetite and nutrition, was 
 placed between the diaphragm and the navel. This region 
 of the body was set apart like a manger for containing neces- 
 sary food ; and the appetitive soul was tied up to it like a wild 
 beast ; indispensable indeed for the continuance of the race, 
 yet a troublesome adjunct, and therefore placed afar off, in 
 order that its bellowings might disturb as little as possible 
 the deliberations of the rational soul in the cranium for 
 the good of the whole. The Gods knew that this appe- 
 titive soul would never listen to reason, and that it must 
 be kept under subjection altogether by the influence of 
 phantoms and imagery. They provided an agency for this 
 purpose in the liver, which they placed close upon the abode 
 of the appetitive soul. They made the liver compact, smooth, 
 and brilliant, like a mirror reflecting images: — moreover, 
 both sweet and bitter on occasions. The thoughts of the 
 rational soul were thus brought within view of the appetitive 
 soul, in the form of phantoms or images exhibited on the 
 mirror of the liver. When the rational soul is displeased, 
 not only images corresponding to this feeling are impressed, 
 but the bitter properties of the liver are all called forth. It 
 becomes crumbled, discoloured, dark, and rough; the gall 
 bladder is compressed ; the veins carrying the blood are 
 blocked up, and pain as well as sickness arise. On the con- 
 trary, when the rational soul is satisfied, so as to send forth 
 mild and complacent inspirations, — all this bitterness of the 
 liver is tranquillised, and all its native sweetness called forth. 
 The whole structure becomes straight and smooth ; and the 
 images impressed upon it are rendered propitious. It is 
 thus through the liver, and by means of these images, that 
 the rational soul maintains its ascendancy over the appeti- 
 tive soul; either to terrify and subdue, or to comfort and 
 encourage it. 
 
 . * Moreover, the liver was made to serve another purpose. 
 It was selected as the seat of the prophetic agency; w^hich 
 
342 FALLACIES INCIDENT 
 
 the Gods considered to be indispensable, as a refuge and aid 
 for the irrational department of man. Though this portion 
 of the soul had no concern with sense or reason, they would 
 not shut it out altogether from some glimpse of truth. The 
 revelations of prophecy were accordingly signified on the 
 liver, for the instruction and within the easy view of the 
 appetitive soul ; and chiefly at periods when the functions of 
 the rational soul are suspended — either during sleep, or 
 disease, or fits of temporary extasy. For no man in his 
 perfect senses comes under the influence of a genuine pro- 
 phetic inspiration. Sense and intelligence are often required 
 to interpret prophecies, and to determine what is meant by 
 dreams or signs or prognostics of other kinds, but such reve- 
 lations are received by men destitute of sense. To receive 
 them, is the business of one class of men : to interpret them, 
 that of another. It is a grave mistake, though often com- 
 mitted, to confound the two. It was in order to furnish 
 prophecy to man, therefore, that the Gods devised both the 
 structure and the place of the liver. During life, the pro- 
 phetic indications are clearly marked upon it : but after death 
 they become obscure and hard to decypher. 
 
 ^The spleen was placed near the liver, corresponding to 
 it on the left side, in order to take off" from it any impure or 
 excessive accretions or accumulations, and thus to preserve it 
 clean and pure.' 
 
 Aristotle constantly employs this method of reasoning. 
 Thus, in a famihar passage of the Ethics^"^^ he says 
 that ^ if it is better for men to attain happiness through 
 their own exertions than through chance, it is reason- 
 able to suppose that this will be the case, since every- 
 
 '^ Eth, Nic. i. 9 (5). El S' karlv ovtoj PikTiov ^ dia rvxrjv eifdai- 
 yLovuv, €v\oyou €X^^^ ovtojs, etirep to, Kara <pvaiv, d>s oJov re KaWicrra 
 
TO INDUCTION. 343 
 
 thing that depends on Nature*^"* is in the best possible 
 condition/ 
 
 From his physiological works (in which the argument 
 is most commonly employed) it will be sufficient to ad- 
 duce one or two examples, which will serve also to show 
 how a preconceived opinion may lead an author to invent 
 false facts for the purpose of supporting his theory. 
 
 Having fixed the seat of sensation in the heart, in- 
 asmuch as it is in the centre of the body, rather than 
 in the brain, as some philosophers had done, it was 
 necessary to discover a special function for the brain. 
 The necessity of discovering some function for it led 
 to the fiction of its * coldness,' which was supposed to 
 counteract the heat of the heart, and so to preserve 
 the body ' in a mean state ^^/ On this account, he sup- 
 posed, all animals which have blood are furnished with 
 
 ** The student will notice the transition from the Demiurgus and 
 inferior gods of Plato to the ' Nature ' of Aristotle. ' And in this,* says 
 Bacoa, ' Aristotle is more to be blamed than Plato, seeing that he left 
 out the fountain of final causes, namely God, and substituted Nature for 
 God ; and took in final causes themselves rather as the lover of logic 
 than of theology.' — The Dignity and Advancement of Learning (Trans- 
 lation of the De Augmentis), Bk. III. ch. iv. (Ellis and Spedding's Edition, 
 vol. iv. p. 364). 
 
 *5 Compare the extraordinary fancy (De Partihus Animalium, iii. 4) 
 that the reason why the heart, in man, inclines slightly towards the left 
 side is that it may temper the greater coldness of that side {irpos rd 
 dvKTovv rr]V Kardipv^iv rSiv dpiarfpouv fiaXiffra yap tcDi' dWojv ^(pcov 
 dvBpouTTOs €xct KaT€\f/vy/jL€va rd dpiarepd). It is needless to observe 
 that the left side of man is not colder than the right ; the fact is simply 
 assumed in order to account for the position of the heart in a manner 
 conformable to Aristotle's theories. 
 
344 FALLACIES INCIDENT 
 
 a brain, while bloodless animals, having little heat, re- 
 quire nothing to cool them, and are, therefore, without 
 one. Moreover, in order to temper the coldness of the 
 brain, blood is conveyed to the membrane which en- 
 velopes it by means of veins or channels. But, again, 
 lest the heat so conveyed should injure the brain, the 
 veins, instead of being large and few, are small and 
 many, and the blood conveyed, instead of being copious 
 and thick, is thin and pure^^ 
 
 * The viscera are formed out of the blood, and therefore 
 are only found in sanguineous animals, which necessarily have 
 a heart : for it is clear that, having blood, which is a fluid, 
 they must have a vessel to contain it, and hence also Nature 
 has created veins ; and for these veins the origin must neces- 
 sarily be one, since one, whenever possible, is better than 
 many. The heart is the origin of the veins : this is seen in 
 the fact that they spring from it, and do not go through it ; 
 also they resemble it in structure. The heart has the chief 
 position, namely, that of the centre, but more upwards than 
 downwards, and rather in front than behind : for Nature is 
 accustomed to seat the noblest in the noblest place, unless 
 any stronger reason prevails: ov ^rj tl KcaXveL jueZfoi/^^.' 
 
 The work of Bishop Wilkins, already quoted, furnishes 
 some curious examples of the arguments which, even 
 within the last two hundred years, have found favour with 
 men distinguished for their scientific attainments ^^. 
 
 ^^ Be Partibus Anitnalinm^ ii. ^. Cp. Lewes' Aristotle^ § 164, p. 180. 
 ^^ De Partibus Animalium, iii. 4. I here quote Mr. Lewes' summary, 
 • given in § 395, p. 31O, of his Aristotle. 
 
 ^^ Bishop Wilkins was one of the founders of the Royal Society, and 
 enjoyed one of the highest scientific reputations of his time. 
 
TO INDUCTION. 345 
 
 * But this [namely, a conceit of Philo's, in order to account 
 for the spots in the moon, that * in the fabrick of the world, 
 all things grow perfecter as they grow higher, and this is 
 the reason why the moon doth not consist of any pure simple 
 matter, but is mixed with air, which shows so darkly within 
 her body'] cannot be a sufficient reason ; for though it were 
 true, that nature did frame everything perfecter, as it was 
 higher, yet is it as true, that nature frames everything fully 
 perfect for that office to which she intends it. Now, had she 
 mtended the moon merely to reflect the sun-beams, and give 
 light, the spots then had not so much argued her providence, 
 as her unskilfulness and oversight, as if in the haste of her 
 work, she could not tell how to make that body exactly fit 
 for that office to which she intended it. 
 
 * It is likely, then, that she had some other end which 
 moved her to produce this variety, and this in all probability 
 was her intent to make it a fit body for habitation, with the 
 same conveniences of sea and land, as this inferior world doth 
 partake of. For since the moon is such a vast, such a solid 
 and opacous body, like our earth (as was above proved), why 
 may it not be probable, that those thinner and thicker parts 
 appearing in her do show the difference betwixt the sea and 
 land in that other world ? and Galilaeus doubts not, but that 
 if our earth were visible at the same distance, there would be 
 the like appearance of it. 
 
 Mf we consider the moon as another habitable earth, then 
 the appearances of it will be altogether exact, and beautiful, 
 and may argue unto that, it is fully accomplished for all those 
 ends to which Providence did appoint it. But consider it 
 barely as a star or light, and then there will appear in it much 
 imperfection and deformity, as being of an impure dark 
 substance, and so unfit for the office of that nature ^^.' 
 
 * Though there are some, who think mountains to be a 
 
 *^ A Discovery of a New World in the Moon, pp. 66, 67. 
 
34^ FALLACIES INCIDENT 
 
 deformity to the earth, as if they were either beat up by the 
 flood, or else cast up like so many heaps of rubbish left at the 
 Creation; yet, if well considered, they will be found as much 
 to conduce to the beauty and conveniency of the universe, as 
 any of the other parts. Nature (saith Pliny) purposely framed 
 them for many excellent uses : partly to tame the violence of 
 greater rivers, to strengthen certain joints within the veins 
 and bowels of the earth, to break the force of the sea's inun- 
 dation, and for the safety of the earth's inhabitants, whether 
 beasts or men^^' 
 
 ' I have now sufficiently proved that there are hills in the 
 moon, and hence it may seem likely that there is also a 
 world ; for since Providence hath some special end in all 
 its works, certainly then these mountains were not pro- 
 duced in vain; and what more probable meaning can we 
 conceive there should be, than to make that place convenient 
 for habitation ^^ ? ' 
 
 * It hath been before confirmed, that there was a sphere of 
 thick vaporous air encompassing the moon, as the first and 
 second regions do this earth. I have now showed, that thence 
 such exhalations may proceed as do produce the comets. 
 Now from hence it may probably follow, that there may be 
 wind also and rain, with such other meteors as are common 
 amongst us. This consequence is so dependent, that Fro- 
 mondus dares not deny it, though he would (as he confesses 
 himself), for if the sun be able to exhale from them such 
 fumes as may cause comets, why not such as may cause 
 winds, why not then such also as may cause rain, since I have 
 above showed that there is sea and land, as with us? Now 
 rain seems to be more especially requisite for them, since it 
 may allay the heat and scorchings of the sun, when he is over 
 
 ^^ A Discovery of a New World in the Moon, p. 77. 
 ^' Id.p.9X, 
 
TO INDUCTION. 347 
 
 their heads. And Nature hath thus provided for those in 
 Peru, with the other inhabitants under the line ®^.' 
 
 One of the most whimsical applications of the Argu- 
 ment from Final Causes is to be found in the ' Doctrine 
 of Signatures/ of which Dr. Paris thus speaks ^^. 
 
 * But the most absurd and preposterous hypothesis that has 
 disgraced the annals of medicine, and bestowed medicinal 
 reputation upon substances of no intrinsic worth, is that of 
 the " Doctrine of Signatures," as it has been called, which 
 is no less than a belief that e-very natural substance ivhich 
 possesses any medicinal 'virtues^ indicates by an ob'vious and <well' 
 marked external character^ the disease for nxihich it is a remedy^ 
 or the object for wuhich it should be employed. This extra- 
 ordinary monster of the fancy has been principally adopted 
 and cherished by Paracelsus, Baptista Porta, and CroUius, 
 although traces of its existence may certainly be discovered 
 in very ancient authors. 
 
 * * * « * 
 
 * The conceit, however, did not assume the importance of 
 a theory until the end of the fourteenth century, at which 
 period we find several authors engaged in the support of its 
 truth, and it will not be unamusing to offer a specimen of 
 their sophistry; they affirm that, since man is the lord of 
 the creation, all other creatures are designed for his use, and 
 therefore that their beneficial qualities and excellences must 
 be expressed by such characters as can be seen and under- 
 stood by every one ; and as man discovers his reason by 
 speech, and brutes their sensations by various sounds, motions, 
 and gestures, so the vast variety and diversity of figures, 
 colours, and consistencies, observable in inanimate creatures, 
 
 ®2 A Discovery of a New World in the Moon, p. I2l. 
 *^ Pharmacologia, pp. 47-50. 
 
348 FALLACIES INCIDENT 
 
 is certainly designed for some wise purpose. It must be, in 
 order to manifest those peculiar properties and excellences, 
 which could not be so effectually done in any other way, 
 not even by speech, since no language is universal. Thus, 
 the lungs of a fox must be a specific for asthma, because that 
 animal is remarkable for its strong powers of respiration. 
 Turmerkk has a brilliant yellow colour, which indicates that 
 it has the power of curing jaundice ; by the same rule. Poppies 
 must reheve diseases of the head; .... and the Euphrasia 
 (eye-bright) acquired fame as an application in complaints of 
 the eye, because it exhibits a black spot in its corolla resem- 
 bling the pupil. In the curious work of Chrysostom Magnenus 
 (Exercit. de Tabaco), we meet with a whimsical account of 
 the signature of tobacco. "In the first place," says he, "the 
 manner in which the flowers adhere to the head of the plant 
 indicates the infundibulum cerebri^ and pituitary gland ; in the 
 next place, the three membranes, of which its leaves are com- 
 posed, announce their value to the stomach, which has three 
 membranes." 
 
 ^ The blood-stone, the heliotropium of the ancients, from 
 the occasional small specks or points of a blood-red colour 
 exhibited on its green surface, is even at this day employed 
 in many parts of England and Scotland to stop a bleeding 
 from the nose; and nettle tea continues a popular remedy 
 for urticaria. 
 
 * It is also asserted that some substances bear the signa- 
 tures of the humours, as the petals of the red rose that of 
 the blood, and the roots of rhubarb, and the flowers of saffron, 
 that of the bile. 
 
 * I apprehend that John of Gaddesden, in the fourteenth 
 century, celebrated by Chaucer, must have been directed by 
 some remote analogy of this kind, when he ordered the son 
 of Edward I., who was dangerously ill with the small-pox, 
 
TO INDUCTION, 349 
 
 to be wrapped in scarlet cloth, as well as all those who 
 attended upon him, or came into his presence ; and even 
 the bed and room in which he was laid were covered with 
 the same drapery ; and so completely did it answer, say 
 the credulous historians of that day, that the prince was 
 cured without having so much as a single mark left upon 
 him/ 
 
 In these and similar instances, which might be multi- 
 plied to almost any extent^*, it is plain that much is 
 gained by the employment of the vague word Nature. 
 Presuming that the majority of at least the more modern 
 writers who have employed the Argument from Final 
 Causes, if pressed to attach a definite meaning to the 
 word Nature, would reply that they regard it, in this 
 connection, as only another name for God, the argument, 
 as employed in the above and similar examples (we are 
 not here discussing the more refined employment of it), 
 seems to rest on the three following assumptions : — 
 
 (i) That God [or Nature] acts, not by laws, governing 
 the evolution of natural objects, but after the manner of 
 a human artificer, having in view some special end in the 
 production of each object and of each separate part 
 of it. 
 
 ** The following example (taken from Plutarch, De Stoicorum Repug- 
 nantiisj p. 1042, by Mr. Lecky, in his History of European Morals, from 
 Augustus to Charlemagne, vol. ii. p. 174, note 2) is perhaps unsurpassed 
 in absurdity : * Chrysippus maintained that cock-fighting was the final 
 cause of cocks, these birds being made by Providence in order to inspire 
 us by the example of their courage.* 
 
359 FALLACIES INCIDENT 
 
 (2) That all objects are designed for the good of man, 
 or, at least, of sentient or intelligent beings. 
 
 (3) That we are so well acquainted with what is, on 
 the whole, good for ourselves, or others, or the world 
 at large, as well as with the general plan of the universe, 
 that we are able, in each case, to pronounce positively 
 on the ends which God [or Nature] proposed to himself 
 in his constructions ^^ 
 
 Of these three assumptions, the first and second are, 
 
 ®^ The • principle ' laid down by Descartes {De Principiis Philosophic, 
 i. 28) supplies an appropriate commentary on this assumption: 'Ita 
 denique nullas unquam rationes circa res naturales, a fine, quern Deus 
 aut natura in iis faciendis sibi proposuit, desumemus ; quia non tantum 
 nobis debemus arrogare, ut ejus consiliorum participes nos esse 
 putemus/ 
 
 It is interesting to compare the following extracts from Galileo's 
 Systema Cosmicuniy Dial. III. (Sir Thomas Salusbury's translation, 
 
 PP- 333» 334):— 
 
 * Salv. Methinks we arrogate too much to our selves, Simplicius, whilst 
 we will have it, that the onely care of us, is the adaequate work, and 
 bound, beyond which the Divine Wisdome and Power doth, or disposeth 
 
 of nothing If one should tell me, that an immense 
 
 space interposed between the Orbs of the Planets and the Starry Sphere, 
 deprived of stars and idle, would be vain and uselesse, as likewise that so 
 great an immensity for receipt of the fixed stars, as exceeds our utmost 
 comprehension would be superfluous, I would reply, that it is rashnesse to 
 go about to make our shallow reason judg of the Works of God, and to 
 call vain and superfluous, whatsoever thing in the Universe is not sub- 
 servient to us.' 
 
 * Sagr. Say rather, and I believe you would say better, that we know 
 not what is subservient to us ; and I hold it one of the greatest vanities, 
 yea follies, that can be in the World, to say, because I know not of what 
 use Jupiter or Saturn are to me, that therefore these Planets are super- 
 fluous, yea more, that there are no such things in rerum natura* 
 
TO INDUCTION. 35 1 
 
 as we conceive, based on false analogies, the first trans- 
 ferring to God [or Nature] the habit, observed in the 
 human artificer, of producing each object with reference 
 to some special end, and the second the motives which 
 usually guide the artificer in the selection of those ends. 
 The third assumption, it need hardly be added, in- 
 volves a generalisation from a very narrow range of ex- 
 perience to operations co-extensive with all space and 
 all time. 
 
 Even though these various errors have been avoided, 
 and the inductive process has been correctly performed, 
 it is still possible, either through confusion of language, 
 through mistaking the 'question at issue, or through 
 drawing erroneous inferences in our subsequent de- 
 ductions, to arrive at false conclusions. But these are 
 considerations which properly appertain to the other 
 branch of Logic, w^hich is concerned with deductive 
 reasoning. 
 
 , -^ ^ ^ ^' 4 /, 
 
INDEX. 
 
 Adsequata causa, why the expres- 
 sion is not here employed, 119. 
 
 Adequate hypotheses, 105-I10. 
 
 Affirmative instances, tendency of 
 the mind to notice, rather than 
 negative instances, 251-255. 
 
 Analogy, argument from, 221-232. 
 
 — dil!erent meanings of the word, 
 
 221, 222. 
 
 — false, fallacy of, 324-351. 
 Antiquitas saeculi juventus mundi, 
 
 origin of the apophthegm, 
 
 329, 330. 
 
 Antiquity, illegitimate use of the 
 argument from, 327-330. 
 
 Aristotle pointed out the depend- 
 ence of deduction on induc- 
 tion, 235. 
 
 — his constant employment of 
 
 inductio per simplicem enu- 
 merationem, 276, 277. 
 
 — his constant employment of the 
 
 argument from final causes, 
 
 342-344- 
 Astronomy, a science of observa- 
 tion, 41, 43. 
 
 — peculiarly rich in examples of 
 
 the Method of Residues, 171. 
 
 Authority, illegitimate use of the 
 argument from, 285-293. 
 
 Average of observations, 46, 47. 
 
 Averages, undue extension of con- 
 clusions based upon, 280-284. 
 
 Bacon, his condemnation of induc- 
 tio per simplicem enumera- 
 tionem, 123, 276. 
 
 — his instantice soli tart ce, 141. 
 
 — his instanticB crucisy 148-15 1. 
 
 — his approximation to the in- 
 
 ductive methods, 206-209. 
 
 — his notice of the tendency to take 
 
 account of affirmative rather 
 than negative instances, 251. 
 
 — his criticism of the argument 
 
 from final causes, 336-338. 
 Bain, Professor, referred to on uni- 
 formities of co-existence, 8, 9, 
 219. 
 
 — his view of the origin of uni- 
 
 versal beliefs, 33. 
 
 — quoted with reference to the 
 
 Intermixture of Effects, 204, 
 205. 
 Botany, reasons for the excellence 
 of iis classifications, 54. 
 
 A a 
 
354 
 
 INDEX. 
 
 Botany, nomenclature of, 88, 89. 
 
 — terminology of, 91, 92. 
 Brown, Dr. Thomas, his view of 
 
 the origin and nature of our 
 conception of cause, 23-25. 
 
 — his objection to one of Hume's 
 
 definitions of cause, 22. 
 
 Causal relations, various kinds of, 
 124-126. 
 
 Causation, can only be established 
 by the Experimental Methods, 
 7-9, 219, 232. 
 
 Cause, relation of, to the condi- 
 tions of a phenomenon, 13- 
 
 15- 
 
 — nature of our conception of, 
 
 17-29. 
 
 — origin of our conception of, 
 
 24-27. 
 
 — definition of, 22-24. 
 
 — error originating in mistaking 
 
 a joint cause for a sole cause, 
 300-308. 
 
 — error originating in mistaking 
 
 joint eflPects for cause and 
 effect, 309-313. 
 
 — error originating in the con- 
 
 fusion of the proximate with 
 the primary or remote cause 
 of a phenomenon, 313-316. 
 
 — error due to neglecting to take 
 
 into account the mutual ac- 
 tion and reaction (mutuality) 
 of cause and effect, 317-319- 
 
 — error due to the inversion of 
 
 cause and effect, 320-323. 
 Causes, exciting, 15. 
 
 Causes, predisposing, 15, ~ 
 
 — final, illegitimate employment 
 
 of the argument from, 336- 
 
 351- 
 
 Certainty, the question whether it 
 be predicable of inductive in- 
 ferences, xi-xxii. 
 
 Characteristick, 83, 84. 
 
 Chemistry, nomenclature of, 90. 
 
 — method of difference extensively 
 
 employed in, 151. 
 Classification, 50-87. 
 
 — scientific, distinguished from 
 
 that employed in the affairs 
 of ordinary Hfe, 51-54. 
 
 — scientific, regarded as subsidiary 
 
 to induction, definition of, 53. 
 
 — a natural system of, distin- 
 
 guished from an artificial sys- 
 tem of, 54-56. 
 
 — natural, rules for the right con- 
 
 duct of, 72-79. 
 Co-existence, Inductions of, 7-9, 
 
 53, 218, 219. 
 Colligation of facts, a hypothesis 
 
 serves for, 98. 
 Comparison, Method of, 196. 
 Conditions, relation of, to the 
 
 cause of a phenomenon, 13- 
 
 15- 
 Consent, Universal, argument from. 
 
 292, 293, 
 Consilience of inductions, 1 1 7- 1 1 9 . 
 Continuity, law of, 80-82. 
 Crucial instances, 1 48-1 51. 
 
 Darwin, Mr., quoted on the signi- 
 
INDEX. 
 
 355 
 
 fication of the word ' species,* 
 80. 
 
 Deduction, its relation to induc- 
 tion, 235-243. 
 
 Definition, are natural classes de- 
 termined by definition or 
 type, 84-87. 
 
 Descartes, his criticism of the argu- 
 ment from final causes, 350. 
 
 Diagnosis, 83, 84. 
 
 JKmpirical g eneralisations or laws, 
 219, 221. 
 Kxceptio probat regulam, the 
 
 maxim explained, 303, 304. 
 Exceptions to rules, 205. 
 P^xperiment, 38-50. 
 
 — how far employed by the 
 
 Greeks, 39. 
 
 — distinguished from observation, 
 
 38, 39. 
 
 — general superiority of, over ob- 
 
 servation, 39-41. 
 
 — not open to us in the attempt 
 
 to ascertain the cause of a 
 given effect, 41, 42. 
 
 — and observation, rules for the 
 
 right conduct of, 44-50. 
 Explanation, in the scientific sense, 
 what, 97. 
 
 Fallacies incident to induction, 
 
 250-351. 
 
 — of generalisation, 273-351. 
 
 — common to the employment of 
 
 the various inductive methods, 
 ^93-323- 
 
 — the same instance may often 
 
 A a 
 
 be indifi^erently ascribed to 
 several, 299. 
 . Falla,cy__of_non-obs ervati on, 250- 
 268. 
 
 — of non -observa tion of instances, 
 
 250-264. " ^ 
 
 — of non- obs ervation of circum- 
 
 stances attendant on a given 
 instance, 264-268. 
 
 — of inal-ob seryation, 268-27 3 • 
 
 — arising from treating the in- 
 
 ductio per simplicem enu- 
 merationem as if it were a 
 valid induction, 274-293. 
 
 — of * non causa pro causa,' 294- 
 
 300. 
 
 — due to the neglect of a joint 
 
 cause, 300-308. 
 
 — due to mistaking of joint effects 
 
 for cause and effect, 309- 
 
 313. 
 
 — due to the confusion of the 
 
 proximate with the primary 
 or remote cause of a phe- 
 nomenon, 313-316. 
 
 — due to neglecting to take into 
 
 account the mutual action 
 and reaction (mutuality) of 
 cause and effect, 317-319. 
 
 — due to the inversion of cause 
 
 and effect, 320-323. 
 
 — of false analogy, 324-351. 
 
 — due to the illegitimate employ- 
 
 ment of argument from final 
 causes, 336-351. 
 
 Final causes, fallacy due to the ille- 
 gitimate employment of the 
 argument from, 335-35 1. 
 
 2 
 
35^ 
 
 INDEX. 
 
 Frequency, confusion between ab- 
 solute and relative, 255. 
 
 — of occurrence does not always 
 furnish an argument for the 
 recurrence of an event, 283, 
 284. 
 
 Galileo, quoted on the theory of 
 Final Causes, 350. 
 
 Geology abounds in instances of 
 the employment of the method 
 ofconcomitant variations, 180. 
 
 Hamilton, Sir W., his criticism of 
 Hume's theory on the nature 
 of cause, 21. 
 
 Herschel, Sir John, distinctly recog- 
 nises the inductive methods, 
 206. 
 
 — quoted on our tendency to 
 
 notice affirmative rather than 
 negative instances, 252, 253. 
 
 Historical Method, 200-202, 245, 
 
 * 246. 
 
 Hume, his view of the nature of our 
 conception of cause, 17-29. 
 
 — injustice done to him by quoting 
 
 from his treatise of Human 
 Nature, 28, 29. 
 Hypothesis, 10-13, 95-121, 242, 
 
 — always suggested by facts 
 
 within our experience, xxi. 
 242. 
 
 — distinction between, and induc- 
 
 tion, 10-13, ITO-I13. 
 
 — description of, 96, 97. 
 
 Hypothesis, conditions of a legiti- 
 mate, 99-1 I I. 
 
 — difference between Mr. Mill 
 
 and Dr. Whewell as to the 
 functions of, 11 3-1 19. 
 
 — gratuitous, 120, 121. 
 Hypothetical, all reasoning is in a 
 
 sense, xvii-xix. 
 
 Inductio per simpHcem enumera- 
 tionem, 7-9, 122-124, 214- 
 221. 
 
 — complete, 123, 214. 
 
 — distinction between complete 
 
 and incomplete, 214, 215. 
 
 — distinguished from the Method 
 
 of Agreement, 217, 218. 
 
 — fallacy arising, in certain cases, 
 
 from its employment as if it 
 were a scientific induction, 
 274-293. 
 
 — its employment by Aristotle, 
 
 276, 277. 
 
 — instance of its employment in 
 
 the Science of Probability. 
 281-284. 
 
 — is still commonly employed in 
 
 social speculations, 284, 285. 
 Induction, ambiguous use of the 
 word, 3, 4. 
 
 — the nature of, 3-10, 122-124. 
 
 — defined, 9, 10. 
 
 — distinction between, and hypo- 
 
 thesis, 10-13. "" 
 
 — question whether it be from 
 
 the particuIarTl^'^the general, 
 orjrpm particulars to^djacent 
 particulars, 15-17- 
 
INDEX. 
 
 ?,S7 
 
 Induction, its relation to deduc- 
 tion, 235-243. 
 
 — fallacies incident to, 250-351. 
 Inductions of Co-existence, 7-9, 
 
 53, 218, 219. 
 
 — of Causation, 8, 9, 124, 219. 
 
 — of Equality, 8, 9. 
 
 — imperfect, 214-234. 
 
 — incomplete, 232-234. 
 Inductive Methods, 122-213, 217, 
 
 218. 
 
 — reducible to two only, 203. 
 
 — distinctly recognised by Sir John 
 J^erschel, though the import- 
 ^^nce now attached to them is 
 
 mainly due to Mr. Mill, 
 206. 
 
 — approximations to, in the No- 
 
 vum Organum, 206-209. 
 
 — defended against the attacks of 
 
 Dr. Whewell, 209-213. 
 
 — imperfect applications of, 232- 
 
 234- 
 
 — fallacies common to the em- 
 
 ployment of, 293-323. 
 
 Inverse Deductive Method, 201, 
 245, 246. 
 
 Intermixture of effects, 203-205. 
 
 Isolation of phenomena, import- 
 ance of, 48-50. 
 
 Jevons, Professor, referred to on 
 tlTe question whether induc- 
 tion be from the particular to 
 the general, or from particulars 
 to adjacent particulars, 1 7. 
 
 — on rules for legitimate hypo- 
 
 theses, 99. 
 
 Jevons p rofessor, on the uncertainty 
 attaching to inductive infer- 
 ence, iilltkxii. 
 
 — on the nature of inductive in- 
 
 ference, xi-xxii, 115. 
 
 Kant, his criticism of Hume's 
 account of causation, 25, 26. 
 
 L aw ofj miformity of nature, 5-9, 
 
 — of universal causation, 4-9, 29- 
 
 37. 
 
 Lewes, Mr., criticism of his state- 
 ments on the belief in the law 
 of universal causation, 29-31. 
 
 Locke, his account of the idea of 
 power, 18, 19. 
 
 Maine de Biran, M., his view of 
 the nature of our conception 
 of cause, 26. 
 
 Malebranche, his idea of causa- 
 tion, 18., 
 
 Mansel, Dr., his view of the na- 
 ture of our conception of 
 cause, 26, 27. 
 
 — his view of the origin of our 
 
 beliefs in the laws of universal 
 causation, and the uniformity 
 of nature, 35. 
 Method of Agreemen t. 126-144. 
 
 — of difference, 144-156. 
 
 — double, of agreement (or joint 
 
 method of agreement and dif- 
 ference), 156-169. 
 
 — of residues, 169-179. 
 
358 
 
 INDEX, 
 
 Method of concomitant variations, 
 179-201. .^ 
 
 — of concomitant vi^fctions, Jtfc". 
 
 Bain quoted on its application 
 in the case of Intermixture of 
 Effects, 204, 205. 
 
 — comparative, 196. 
 
 — historical, 200-202, 245, 246. 
 Methods, inductive or experi- 
 mental, 122-213. 
 
 Mill, James, quoted on the origin 
 of our belief in the law of 
 universal causation, 33, 34. 
 
 Mill, Mr., referred to on the rela- 
 tion between the cause and the 
 conditions of a phenomenon, 
 
 13-15. 
 
 — question between him and Dr. 
 
 Whewell, as to whether in- 
 ductive inference be from the 
 particular to the general, or 
 from particulars to adjacent 
 particulars, 15-17. 
 
 — his definition of cause criticised, 
 
 23» 
 
 — his answer ^o Reid's objection 
 
 to Hume's account of causa- 
 tion, 23, 24. 
 
 — his view of the origin of uni- 
 
 versal beliefs, 33-35. 
 
 — difference between him and 
 
 Dr. Whewell as to the func- 
 tion of hypotheses, 113-I19. 
 
 — importance now attached to 
 
 the inductive methods mainly 
 due to his influence, 206. 
 Mineralogy, mainly a classificatory 
 science, 54. 
 
 'V 
 
 Natural distinguished from artificial 
 classification, 54-56. 
 classification, rules for the right 
 conduct of, 72-79. 
 roups, arrangement of, in a 
 natural series, 76-79' 
 
 — groups, constant recognition of 
 
 new, 80-82. 
 Newton, his demonstration of a 
 central force, 111-113. 
 
 — his employment of the expres- 
 
 sion • Vera Causa,' 120. 
 Nomenclature, 87-90. 
 Non causa pro causa, 299. ^^ 
 
 Observation . 38-50. 
 
 — distinguished from experiment, 
 
 38. 39- 
 
 — general employment of, pre- 
 
 ceded that of experiment, 
 
 39- 
 
 — alone open to us in the attempt 
 
 to ascertain the cause of a 
 given effect, 41, 42. 
 
 — sciences wholly or mainly de- 
 
 pendent on, at a great disad- 
 vantage, as compared with 
 those in which we can largely 
 employ experiment, 42-44. 
 
 — and experiment, rules for the 
 
 right conduct of, 44-50, 
 Observ atio ns, importance of taking 
 an average of, 46, 47. 
 
 Physiology frequently employs the 
 method of concomitant varia- 
 tions, 191, 192. 
 
 Plato, his employment of the 
 
INDEX 
 
 argument from final causes 
 
 339-342. 
 ^ Plurality of caus es. 6, 22, 23, 125, 
 127-130. 
 
 — fallacy arising from neglectii 
 
 to take into account, 299, 
 
 300- 
 
 Post hoc, ergo propter hoc, 299. 
 
 Power, question whether the idea 
 of is involved in our concep- 
 tion of cause, 17-29. 
 
 Prediction, value to be attached 
 to, 115-119. 
 
 Re^Hiis criticism of Hume's ac- 
 count of causation, 21-24. 
 
 — his view of the nature of our 
 
 conception of cause, 26. 
 
 — his view of the origin of uni- 
 
 versal beliefs, 31, 32. 
 
 Social questions, the extreme dif- 
 ficulty attendant on their in- 
 vestigation, 284, 285. 
 
 Species, practice of naturalists in 
 stopping at, open to question, 
 79, 80. 
 
 — ind varieties^ constant recog- 
 
 nition of new, 80-82. 
 Spencer, Herbert, his view of the 
 origin of universal beliefs, 
 35, 36. 
 
 — referred to on the Theory of 
 
 Final Causes, 337. 
 Statisticsj conclusions based on, are 
 instances of the application of 
 the method of concomitant 
 variations, 200. 
 
 359 
 
 view of the 
 'ur conception of 
 
 bordination of characters, prin- 
 ciple of, 73, 74. 
 
 Terminology, 90-95. 
 Thermotics, Science of, furnishes 
 
 good examples of the Method 
 
 of Difference, 151. 
 Type, persistency of, 82. 
 
 — are natural classes determined 
 
 by definition or, 84-87. 
 
 Uniformity of nature, law o f. 5-9. 
 
 — converse does not hold true, 6. 
 
 — universality of the belief in, 29- 
 
 31. 
 
 — origin of the belief in, 7-9, 29- 
 
 37. 
 Universal beliefs, various theories 
 
 as to the origin of, 29-37. 
 Universal causation, law of, 4-9. 
 
 — universality of the belief in, 
 
 29-31. 
 
 — origin of the belief in, 29-37. 
 
 Variation of circumstances, im- 
 portance of, 48. 
 
 Venn, Mr., referred to on a com- 
 mon fallacy in the calculation 
 of probabilities, 281-283. 
 
 Vera causa, why the expression is 
 not here employed, 119, 120. 
 
 Verification, 243-249. 
 
 Veritas temporis filia dicitur, non 
 auctoritatis, origin of the 
 apophthegm, 314. 
 
360 
 
 INDEX. 
 
 Whewell, Dr., question between 
 him and Mr. Mill as to whether 
 inductive infeBJtoce be from 
 the particular to the general, 
 or from particulars to adjacent 
 particulars, 15-17. 
 
 — his view of the origin of uni- 
 
 versal beliefs, 32. 
 
 — his position that natural classes 
 
 are determined not by defini- 
 tion but by type, 84-87. 
 
 Whewell, Dr., his remarks on 
 terminology, 91-95. 
 
 — difference between him and 
 
 Mr. Mill as to the function 
 of hypotheses, 113-119. 
 
 — his criticism on the inductive 
 
 methods, 209-213. 
 
 Zoology, reasons for the excel- 
 lence of its classifications, 54. 
 
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