THE LIBRARY 
 
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 THE UNIVERSITY 
 
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 GIFT OF 
 
 Jake and Josephine 
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 LOGIC 
 
 DEDUCTIVE AND INDUCTIVE 
 
 THOMAS FOWLER, D.D. 
 
 President of Corpus Christi College 
 
 And sometime IVykeham Professor of Logic in the University of Oxford ; 
 Honorary Doctor of Laws in the University of Edinburgh 
 
 AT THE CLARENDON PRESS 
 
 M DCCC XCIII
 
 onion 
 HENRY FROWDE 
 
 OXFORD UNIVERSITY PRESS WAREHOUSE 
 AMEN CORNER, E.G. 
 
 MACMILLAN & CO. 
 ii3 FOURTH AVENUE
 
 *** IT has been suggested from many quarters that, 
 for the convenience of students, it is desirable to issue 
 an edition including the author's treatises on Logic 
 Inductive and Deductive in a single volume. Though, 
 in the order of reasoning, Induction precedes Deduction, 
 yet, as the Deductive branch of Logic is usually taught 
 before the Inductive, that order has been adopted for 
 practical considerations in the present edition of the 
 combined works.
 
 farendon 
 
 DEDUCTIVE LOGIC 
 
 FOWLER
 
 jJonbon 
 
 HENRY FROWDE 
 OXFORD UNIVERSITY PRESS WAREHOUSB 
 AMEN CORNER, E.C. . 
 
 Qtew ?)orft 
 
 na FOURTH AvtNut
 
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 /0 
 
 THE ELEMENTS f' 
 
 OF 
 
 DEDUCTIVE LOGIC 
 
 M^ 
 
 DESIGNED MAINLY 
 
 FOR THE USE OF JUNIOR STUDENTS 
 IN THE UNIVERSITIES 
 
 BY 
 
 THOMAS FOWLER, D.D. 
 
 President of Corpus Christi College 
 
 And formerly Professor of Logic in the University of Oxford 
 Honorary Doctor of Laws in the University of Edinburgh 
 
 TENTH EDITION, CORRECTED AND REVISED 
 
 Ojtforfc 
 
 AT THE CLARENDON PRESS 
 
 MDCCCXCII
 
 PRINTED AT THE CLARENDON PRESS 
 BY HORACE HART, PRINTER TO THE UNIVERSITY
 
 PREFACE 
 
 THE precise object of the following pages is (without 
 pre-supposing any technical acquaintance with logical 
 terminology) to enable a student of average intelligence 
 to acquire for himself an elementary knowledge of the 
 main problems, principles, and rules of Deductive Logic. 
 They are not designed to save him the trouble of after- 
 wards consulting more advanced text-books, either in 
 his own or other languages. The English student who 
 wishes to gain an exact and detailed knowledge of the 
 relations of Deduction to Induction, and consequently 
 of the true place and value of the former process in 
 any special science, must still have recourse to the works 
 of Mr. Mill ; or, if he wish to trace the history of logical 
 terms and doctrines (one of the most important chapters 
 in the history of both ancient and modern literature), 
 he must still consult Sir W. Hamilton's Lectures, and the 
 Appendices and Notes of Dr. Mansel to Aldrich's Logic. 
 
 To these works, as well as to Archbishop Whately's 
 luminous Chapter on Fallacies, and to the original and 
 suggestive work of Mr. James Mill on the Analysis of 
 the Phenomena of the Human Mind, the Author must, 
 once for all, express his obligations. He has, however, 
 endeavoured, on all disputed points, to reason out his
 
 VI PREFACE. 
 
 own conclusions, feeling assured that no manual, how- 
 ever elementary, can be of real service to the student, 
 unless it express what may be called the 'reasoned 
 opinions' of its author. 
 
 The great difficulty to be encountered by any writer 
 of an English Manual of Logic is the unsettled state 
 of our logical terminology. Many words have various 
 significations, or are used in different senses by different 
 writers, and often there are no recognised terms to 
 express some distinction which it is still incumbent on 
 the logician to notice. A fixed and sufficient terminology 
 can, however, only be created by the habit of teaching 
 Logic, and of carrying on our discussions on the science, 
 in our own language. But though, in some respects, 
 the I^atin terminology may be superior to our own, there 
 can be no question that the language in which men 
 habitually think must be the fittest medium for analysing 
 their thoughts. 
 
 The Notes appended to the Chapters (as distinguished 
 from the foot-notes) are designed to inform the student 
 of any divergences from the ordinary mode of treatment, 
 or to suggest to him further reading on topics which, 
 if noticed at all, are only alluded to in the text. They 
 may be omitted on the first reading. 
 
 Besides the Notes appended to the various Chapters, 
 it is perhaps desirable that the student, if he is entirely 
 unacquainted with logical and psychological discussions, 
 should omit, on the first reading, the Chapters on the 
 Relation of Logic to Psychology, on the various Kinds
 
 PREFACE. Vll 
 
 of Terms, on the Denotation and Connotation of Terms, 
 on the Relation of the Predicate to the Subject of a 
 Proposition, on Verbal and Real Propositions, on De- 
 finitions, and on Divisions and Classifications. Unfor- 
 tunately, the most difficult problems which the logician 
 has to solve occur at the outset of his task. 
 
 It is hoped that, independently of its bearing on 
 University studies, a Short English Manual of Logic may 
 be used with advantage in the Upper Forms of Schools, 
 and that it may not be without interest to the general 
 reader. 
 
 The Manuals of Sanderson, Wallis, Aldrich, &c., owing 
 to the peculiar circumstances of the period in which they 
 were written (a period, which, being transitional, retained 
 not only much of the scholastic terminology, but also 
 much of the Realistic doctrine), have ceased to be 
 adapted to modern instruction. The Author, with some 
 misgivings, and a keen sense of the difficulties of the 
 task, trusts that the present work may be found use- 
 fully to occupy their place. Its propositions cannot, 
 however, be presented in the same curt and dogmatic 
 shape, for we have learnt to regard many portions 
 of Logic, like many portions of the sciences whose 
 method it claims to analyse, as fairly open to differences 
 of opinion. 
 
 %* In the Table of Contents it will be observed that 
 the words Definitions, Divisions, Classifications, Infer- 
 ences, Oppositions, Conversions, Permutations, occur in
 
 viii PREFACE. 
 
 place of the more ordinary forms Definition, Division, 
 Classification, &c. The object of this change is to 
 suggest to the student the importance of distinguishing 
 the results from the processes by which they are gained. 
 Many words employed in Logic and Psychology admit 
 of both these meanings, and it is only by prefixing the 
 indefinite article or using the plural number, as when 
 we speak of ' a definition ' or ' definitions,' that we can 
 make it plain that we mean the result and not the 
 process. It would be very difficult in all cases to 
 mark the distinction, but I have endeavoured to do so 
 wherever it seemed to be of any importance J . 
 
 1 A similar confusion in many of the terms employed in Physics has 
 been noticed by Mr. [now Sir W. R.] Grove (Correlation of Forces, 
 fifth ed., p. 251). 'Another confusion of terms has arisen, and has, 
 indeed, much embarrassed me in enunciating the propositions put forth 
 in these pages on account of the imperfection of scientific language ; 
 an imperfection in great measure unavoidable, it is true, but not 
 the less embarrassing. Thus, the words light, heat, electricity, and 
 magnetism, are constantly used in two senses viz. that of the force 
 producing, or the subjective idea of force or power, and of the effect 
 produced, or the objective phenomenon. The word motion, indeed, 
 is only applied to the effect, and not to the force, and the term 
 chemical affinity is generally applied to the force, and not to the 
 effect ; but the other four terms are, for want of a distinct termin- 
 ology, applied indiscriminately to both.'
 
 PREFACE TO SUBSEQUENT EDITIONS 
 
 IN subsequent Editions several minor alterations and 
 additions have been introduced into the Text of some 
 of the Chapters. A few notes, as well as an Index and 
 a Collection of Examples, have also been added. In 
 making these alterations and additions, the Author has 
 gladly availed himself of suggestions kindly offered, from 
 time to time, by various correspondents and friends, 
 amongst whom he ought specially to mention Professor 
 Park, of Belfast. He has, however, endeavoured to pre- 
 vent the work from materially exceeding the limits of its 
 original size. 
 
 Several friends have suggested to the Author the intro- 
 duction of two new chapters, one on the Categories, the 
 other on the Formation of Terms. Influenced partly by 
 a desire not to increase the bulk of the volume, and partly 
 by still more important reasons, he has, after some hesi- 
 tation, decided against the introduction of these chapters. 
 The doctrine of Categories is important in the history of 
 Logic 1 , but it is not properly a branch of Logic, as that 
 
 1 On the categories of Aristotle the reader is referred to Hamilton's 
 Lectures on Logic, Lect. xi., and the Appendix to Mansel's Aldrich. 
 Note B. Both Sir W. Hamilton and Dr. Mansel, especially the 
 former, insist on their ' wholly extra-logical ' character.
 
 X PREFACE TO SUBSEQUENT EDITIONS. 
 
 word is now generally understood and as it has been 
 understood throughout this work. The Formation of 
 Terms is a subject which properly belongs to Psychology 
 and not to Logic, and moreover could not be adequately 
 treated in a small compass. It is true that some ques- 
 tions properly belonging to Psychology or the History of 
 Logic have been noticed in various parts of the book, 
 but they have only been casually alluded to, not treated 
 in distinct chapters. Logic has always been over-weighted 
 with extraneous matter, and, wherever it is possible, it is 
 desirable to relieve it of its superfluities, though much 
 discretion may be needed in the process, and though the 
 requirements of examinations have a constant tendency 
 to lead writers on Logic to consider not how little, but 
 how much they can introduce into their works. 
 
 In the Fifth and subsequent Editions, the Author has 
 added an Appendix on the Heads of Predicables. There 
 is no branch of elementary Logic so difficult to state in a 
 form at once satisfactory to the teacher and intelligible to 
 the learner. The attempt at a scientific treatment which 
 he has made in Pt. II. ch. v. is, he believes, usually found 
 too complicated for a beginner. As, however, he cannot 
 state his own view of the doctrine in a simpler form, he 
 has thought it the best course to add an Appendix, 
 which, without any attempt at an exhaustive treatment, 
 simply offers an explanation of the five words, Genus, 
 Species, Differentia, Property, Accident. This Appendix, 
 on the first reading of the book, may be substituted by the 
 student for Pt. II. ch. v., but should be combined with
 
 PREFACE TO SUBSEQUENT EDITIONS. xi 
 
 the formal definitions given on p. 46, of which, in fact, it 
 furnishes an explanation. 
 
 The principal changes in the eighth Edition were the 
 addition of notes to Pt. III. chs. i. and vii., and some 
 alterations in the text of the latter part of ch. vii. ; in the 
 ninth Edition, certain additions to the latter part of ch. 
 vii. and to the foot-note on p. 73 [now 75]. In the 
 present Edition, the principal changes are an addition 
 to note i on p. 19, the addition of a note on p. 21, 
 some changes of language on pp. 26, 27 and pp. 70, 
 71, an addition on the Law of Identity to note 3, p. 75, 
 and the addition of a new paragraph on the unsatisfactory 
 character of the Dilemma, as a practical argument, on 
 p. 123.
 
 CONTENTS 
 
 Introduction. 
 
 ::HAP. FACE 
 
 I. The Relation of Logic to Psychology . i 
 
 II. Definition of Logic 5 
 
 III. The Relation of Thought to Language ... 7 
 
 IV. Division of the Products of Thought .... 9 
 
 PART I. The Term. 
 
 I. The Various Kinds of Terms n 
 
 II. The Denotation and Connotation of Terms . . 19 
 
 PABT II. The Proposition. 
 
 I. The Subject and Predicate 24 
 
 II. The Copula 26 
 
 III. Division of Propositions according to their Quantity 
 
 and Quality 29 
 
 IV. Distribution of Terms 34 
 
 V. Relation of the Predicate to the Subject of a Proposition 
 
 (Heads of Predicates) 37
 
 XIV CONTENTS. 
 
 CHAP. 
 
 PAGE 
 
 VI. Verbal and Real Propositions 49 
 
 VII. Definitions 5 
 
 VIII. Divisions and Classifications 59 
 
 PART III. Inferences. 
 
 I. The Various Kinds of Inferences .... 69 
 
 II. Immediate Inferences 7* 
 
 i. Definition of an immediate Inference . . 78 
 
 2. Oppositions 78 
 
 3. Conversions 8 1 
 
 4. Permutations 83 
 
 III. Mediate Inference or Syllogism 85 
 
 i. Structure of the Syllogism .... 85 
 
 2. Moods and Figures < . . 89 
 3. Determination of the Legitimate Moods of 
 Syllogism, including the Syllogistic Rules, 
 Reduction, and the Special Rules of the 
 
 Figures 91 
 
 IV. Trains of Reasoning (the Sorites) . . . .no 
 V. Complex (Hypothetical) Propositions and Syllogisms . 113 
 
 5 i. Division of Complex Propositions into Con- 
 junctive and Disjunctive . . . .113 
 
 2. Conjunctive Syllogisms 115 
 
 3. Disjunctive Syllogisms 117 
 
 4. The Dilemma 120 
 
 VI. On the words 'Most,' 'Many,' &c., as expressing the 
 
 Quantity of Propositions 126 
 
 VII. Probable Reasoning, including Circumstantial Evidence 130
 
 CONTENTS. XV 
 
 CHAP. PAGE 
 
 VIII. Fallacies 142 
 
 i. Division of Fallacies 142 
 
 2. Fallacies due to the assumption of a False 
 
 Premiss 143 
 
 3. Fallacies due to the neglect of the Laws of 
 
 Deductive Inference ..... 144 
 4. Fallacies due to Irrelevancy . . .149 
 
 5. Fallacies due to Ambiguity of Language . 151 
 
 IX. On Method, as applied to the Arrangement of Syl- 
 logisms in a Train of Reasoning . . . .158 
 
 APPENDIX 162 
 
 EXAMPLES 167 
 
 INDEX 187
 
 INTRODUCTION. 
 
 CHAPTER I. 
 On the Relation of Logic to Psychology. 
 
 PSYCHOLOGY, or Mental Philosophy, may be de- 
 fined as the science which classifies and analyses the 
 phenomena of the human mind. It notes mental pheno- 
 mena, considers them in their mutual relations, and 
 investigates the mode of their generation. Of these 
 mental phenomena some are called emotional, others 
 intellectual. The intellectual phenomena may be re- 
 garded as the result, partly of Perception, partly of Im- 
 agination, partly of Comparison, Reflexion, or Thought. 
 Perception is the act or operation of apprehending some 
 present phenomenon. Imagination is the act or opera- 
 tion of representing to the mind some absent pheno- 
 menon. Comparison, Reflexion, or Thought, is the 
 act or operation of comparing phenomena, whether 
 present or absent, as well as of comparing, either with 
 these or with one another, the results themselves which 
 we derive from such comparisons. Thus I perceive this 
 particular rose before me, its colour, its smell, and the 
 
 * B
 
 2 RELATION OF LOGIC 
 
 pleasure I derive from seeing and smelling it. All these 
 perceptions I can recall to-morrow, even though the 
 rose be absent, by the act or operation of imagination. 
 Lastly, I may compare this particular rose with another 
 which lies on the table, or with one which I saw 
 yesterday, and I may express their similarity by calling 
 them both moss-roses, or their difference by calling one 
 a moss-rose and the other a Tudor rose. Again, moss- 
 rose and Tudor rose, which names are both results of 
 the act or operation of comparison, may themselves be 
 compared, and their points of similarity expressed by the 
 word ' rose.' So rose and dahlia may be compared, and 
 their points of similarity expressed by the word ' flower.' 
 Or I may compare the feeling with which I contemplate 
 the rose with similar feelings which 1 have previously 
 experienced, and call it ' pleasure ' ; or I may compare it 
 with the feeling which I experience when I prick my 
 finger with a thorn, and call one ' pleasure,' the other 
 ' pain ' ; or I may compare pleasure and pain themselves, 
 and call them both ' feelings.' The act of making com- 
 parisons, and of apprehending similarities and differences, 
 is usually called Thought or Thinking, and the results at 
 which it arrives Thought or Thoughts. The act or 
 operation itself, as distinguished from other mental acts 
 or operations, and the results which ensue from its cor- 
 rect or incorrect exercise, are alike legitimate subjects of 
 investigation for the psychologist or mental philosopher. 
 But the more detailed consideration of the latter, i. e. 
 Thoughts or the results of Thinking, becomes the subject
 
 TO PSYCHOLOGY. 
 
 of a science with a distinct name, Logic, which is thus 
 a subordinate branch of the wider science, Psychology. 
 
 Note i. The term Perception is here used in its or- 
 dinary sense. The distinctions between External and 
 Internal Perception, Perception Proper and Sensation 
 Proper, are foreign to the present subject. They are 
 discussed at great length in the works of Sir William 
 Hamilton and Dr. Mansel, as well as in those of the 
 Scottish school of metaphysicians generally, but, as in- 
 volving some of the most abstruse and disputed questions 
 in Psychology, it is not necessary or desirable that the 
 student should acquaint himself with them till he com- 
 mences the special study of that science. 
 
 Note 2. Imagination, as here defined, is what may be 
 called Simple, or Reproductive, as distinguished from 
 what may be called Complex, or Productive Imagination. 
 The former simply represents to the mind absent objects 
 of perception as they have already been perceived, the 
 latter combines phenomena or portions of phenomena, 
 whether absent or present, into a new whole. Thus the 
 notions of a particular man or a particular horse, if the 
 man and horse be absent, are products of simple or 
 reproductive imagination ; the notion of a centaur would 
 be a product of complex or productive imagination. 
 For further and more precise information on this distinc- 
 tion, which is here necessarily stated somewhat roughly, 
 
 B 2
 
 4 RELATION OF LOGIC TO PSYCHOLOGY. 
 
 see Sir W. Hamilton's Lectures on Metaphysics, Lect. xxxiii. 
 The creations of poetry and art are results of complex 
 imagination, or, in other words, of repeated processes of 
 simple imagination and comparison. Inasmuch as com- 
 plex imagination may be analysed into simple imagina- 
 tion and comparison, and is thus not one of the ultimate 
 acts or operations to which our mental phenomena are 
 traceable, it would have been beside my purpose to have 
 noticed it in the text. 
 
 Note 3. I have employed the expression ' act or 
 operation,' avoiding the expression 'power or faculty,' 
 as the latter implies a theory of mental phenomena which 
 would be rejected by many psychologists. It has been 
 necessary to speak of 'act or operation,' as the word 
 ' act,' like many other terms of logic or psychology, may 
 mean either the operation or the result. This is an in- 
 stance at the very outset of the ambiguity noticed in the 
 paragraph at the end of the preface.
 
 CHAPTER II. 
 
 Definition of Logic. 
 
 IT is the province of Logic to distinguish correct from 
 incorrect thoughts, i. e. to analyse those thoughts which 
 are accepted by mankind as indubitably correct, and to 
 point out wherein they differ from those which are re- 
 garded as doubtful or incorrect ; and, as a consequence 
 of this function, it is also its province to lay down rules 
 for the attainment of correct thoughts and for the avoid- 
 ance of incorrect thoughts. Thus Logic is both a Science 
 and an Art. It is a Science, inasmuch as it furnishes us 
 with a knowledge of what is, inasmuch as it is an analysis, 
 and determines the conditions on which valid thoughts 
 depend. It is an Art, inasmuch as it lays down^ru/es 
 for practice, and thus enables us to detect incorrect 
 thoughts in the reasonings of others, and to avoid them 
 in our own. 
 
 Logic may therefore be defined as the science of 
 the conditions on which correct thoughts depend, and 
 the art of attaining to correct and avoiding incorrect 
 thoughts. 
 
 Note. This definition is in substance that given by 
 Mr. Mill in his Examination of Sir W. Hamilton's
 
 6 DEFINITION OF LOGIC. 
 
 Philosophy, p. 391 (third ed., p. 448). ' Logic,' he says, 
 ' is the art of thinking, which means of correct thinking, 
 and the science of the conditions of correct thinking.' 
 The word ' thoughts ' is substituted for ' thinking,' in 
 order to bring more prominently before the student, what 
 Mr. Mill himself acknowledges, the fact that Logic is 
 concerned with the products or results rather than with 
 the process of thought, i.e. with thoughts rather than with 
 thinking, though, in estimating the conditions on which 
 correct thoughts depend, it is necessary, to some extent, 
 to take account of the processes by which they are 
 formed. It seems also desirable to introduce into the 
 definition of Logic some reference to ( incorrect thoughts,' 
 as bringing out more distinctly the character of Logic 
 as an art, and asserting for it the right of investigating 
 fallacies.
 
 CHAPTER III. 
 
 On the Relation of Thought to Language. 
 
 WHETHER it is possible to think without the aid 
 of language, is a question which has been a constant 
 source of dispute amongst logicians and psychologists. 
 It is not necessary, however, here to enter on this 
 discussion. As all logicians are agreed that we cannot 
 communicate our thoughts without the aid of language, 
 or of equivalent signs, and that practically we do always 
 think by means of language, by a sort of internal con- 
 verse, it will be safer to adopt the terminology of those 
 authors who regard our thoughts as expressed in lan- 
 guage rather than that of those who consider or attempt 
 to consider them in themselves as apart from their ex- 
 pression in words. I shall therefore speak of Terms and 
 Propositions, not of Concepts and Judgments. 
 
 Note. Sir W. Hamilton and his followers, regarding 
 Logic as primarily and essentially concerned with thought, 
 and only secondarily and accidentally with language, 
 attempt to mark the products of thought by words which 
 do not imply their expression in language. Thus, instead
 
 8 RELATION OF THOUGHT TO LANGUAGE. 
 
 of Terms and Propositions, they use respectively the 
 words Concepts and Judgments. The word Syllo- 
 gism, owing to the ambiguity of the Greek word \6yos, 
 stands either for the internal thought or the external 
 expression of it. (See Hamilton's Lectures on Logic, 
 Lecture i.)
 
 CHAPTER IV. 
 
 Division of the Products of Thought. 
 
 IT has been stated that thought is the act or operation 
 of comparison. Its simplest result is that which is ex- 
 pressed by the Term. Terms may be combined into 
 Propositions, and Propositions, either singly or in con- 
 junction with one or more other propositions, may lead 
 to Inferences. I shall treat in order of the Term, 
 of the Proposition, of Inferences. Before proceeding 
 further, it may perhaps be useful to the student to give 
 by anticipation instances of these products or results 
 of thought. Man, good, manliness, goodness, the good- 
 ness of man, the virtue of manliness, are all instances 
 of terms. 'This man is good,' 'All citizens of a state 
 are under an obligation to obey its laws,' are instances 
 of Propositions, and, according to logical phraseology, 
 ' good ' is said to be predicated of ' this man,' and ' under 
 an obligation to obey its laws ' is said to be predicated 
 of ' all citizens of a state.' The term predicated is called 
 the Predicate, and the term of which it is predicated is 
 called the Subject, the word ' is ' or ' are ' (or, in the case 
 of negative propositions, ' is not ' or ' are not '), which 
 connects the two, being called the Copula. Lastly, we 
 may take as instances of Inferences the following :
 
 10 DIVISION OF THE PRODUCTS OF THOUGHT. 
 
 No rectilineal figure is contained by less than three 
 
 lines ; 
 Therefore, no figure contained by less than three lines 
 
 is a rectilineal figure, 
 
 All Englishmen are of mixed descent, 
 This is an Englishman ; 
 Therefore, he is of mixed descent. 
 
 The last proposition (which is called the conclusion] 
 is said to be inferred from the proposition or pro- 
 positions which precede it (called the premiss or pre- 
 misses).
 
 <r 
 
 PART I. THE TERM. 
 
 CHAPTER I. 
 
 On the Various Kinds of Terms. 
 
 A TERM (so called from terminus, a boundary, be- 
 cause the terms are the two extremes or boundaries of 
 the proposition) is _a word or combination of words 
 which may stand by itself as the subject or predicate of 
 a Proposition ; it expresses either^ an individual, a group 
 of individuals, an attribute, or a group of attributes. This 
 definition obviously excludes all articles, adverbs, inter- 
 jections, conjunctions, prepositions, and oblique cases of 
 nouns. It also excludes verbs ; for though a verb ex- 
 presses attributes, and often serves at once for the copula 
 and the predicate (or part of the predicate), as in the pro- 
 positions ' John walks,' ' William fears Thomas,' it must, 
 in a logical proposition stated according to strict form, 
 always be analysed into the copula and participle : thus 
 the above propositions, when stated logically, become 
 'John is walking,' 'William is fearing Thomas 1 .' A 
 
 1 A proposition of which the verb is not analysed into the copula 
 and a participle is called by the older logicians ' secundi adjacentisj 
 in contradistinction to the form of proposition as ordinarily stated in 
 Logic, which is called ' tertii adjacentis? Thus vir currit is a pro- 
 position secundi atfjacenlis, vir est currens is a proposition tertii 
 adja entis.
 
 12 VARIOUS KINDS OF TERMS. 
 
 pronoun is only significant as standing in the place of a 
 substantive, and therefore we may limit ourselves to the 
 consideration of substantives, adjectives, and participles. 
 
 By the older logicians a term was defined as a Cate- 
 gorematic word (from Karrjyoprjfm ' something which can be 
 predicated '), i. e. a word or combination of words which 
 can stand by itself as the predicate of a proposition. All 
 words or combinations of words which require to be 
 joined with some other word or words in order to serve 
 this purpose were called Syncategorematic words. 
 
 It has been said that a term expresses an individual, 
 a group of individuals, an attribute, or a group of attri- 
 butes. If it expresses an individual, as Socrates, the 
 present Queen of England, the sea, hie, ille, hoc, illud, 
 &c., it is called a (i) Singular Term. If it expresses a 
 group of individuals, it may either be applicable to each 
 individual of the group severally as well as to the group 
 collectively, or to the group collectively but not to each 
 individual severally. Thus the terms, man, horse, flower, 
 are not only applicable to each individual of the groups 
 which they express, but also to the groups collectively ; 
 I can say, ' John is a man,' ' Thomas is a man,' ' this is 
 a horse,' ' that is a horse,' ' the rose is a flower,' ' the 
 dahlia is a flower,' &c. But I cannot say ' Caius is the 
 fourteenth legion,' 'Pompey is the Roman senate,' 
 though I can predicate ' fourteenth legion ' or ' the 
 Roman senate ' of the groups, taken collectively, which 
 these terms express. In the former case the term is 
 called a (2) Common Term, in the latter a (3) Collective
 
 VARIOUS KINDS OF TERMS. 13 
 
 Term. A collective term may by a slight change of 
 phraseology be expressed as a common term ; thus, 
 ' Roman senate ' may become ' Roman Senators,' or 
 ' fourteenth legion ' ' soldiers of the fourteenth legion.' 
 But, as it stands, a collective term is, in predication, as 
 will be noticed hereafter, equivalent to a singular term. 
 
 A common term is equally applicable to each indi- 
 vidual severally of the group which it expresses, and it is 
 so in virtue of certain points of similarity which all the 
 individuals possess in common. It is in fact because we 
 have observed that they all possess certain attributes in 
 common, that we are able to call them by a common 
 name. Thus a common term, like man, horse, &c., at 
 once suggests to me a certain group of individuals and 
 a certain group of attributes which is predicable of each 
 of these individuals severally. But there are other terms, 
 called (4) Attributives, and (5) Abstract Terms, which ex- 
 press attributes or groups of attributes only. Attribu- 
 tives may be distinguished from Abstract Terms by the 
 fact that they may form the predicate, but cannot, unless 
 joined with a singular, collective, common, or abstract 
 term, form the subject of a proposition. Grammatically, 
 they are represented by adjectives and participles, when 
 not used substantively. Of this class are the terms, 
 human, red, heavy, brave, willing, thinking, running, &c., 
 when not used substantively. Thus I may say, ' Socrates 
 is human,' but, when I wish to employ the term ' human ' 
 in the subject of a proposition, I must append to it some 
 such word as 'being,' and say 'this human being is
 
 14 VARIOUS KINDS OF TERMS. 
 
 Socrates 2 .' Such terms have, in fact, no signification, 
 unless used substantively, or in conjunction with a sub- 
 stantive, either as qualifying it or as predicated of it. 
 
 Abstract Terms, on the other hand, not only express 
 mere attributes or groups of attributes, but may be 
 thought of without any reference to the individuals of 
 which these attributes are predicable. Of this class are 
 such terms as humanity, colour, figure, fortitude, &c. To 
 it may be referred sentences employing the indicative 
 mood and introduced by the word ' that,' infinitive moods, 
 some instances of adjectives and participles used substan- 
 tively, and generally every term, being neither singular, 
 collective, nor common, which may be employed both as 
 the subject and as the predicate of a proposition. 
 
 All the terms discussed above may be employed as 
 predicates of propositions. Attributives alone cannot be 
 employed as subjects. 
 
 We have thus divided terms into singular, collective, 
 and common terms, attributives, and abstract terms. It 
 must however be borne in mind that many of those attri- 
 butives and abstract terms which are most frequently in 
 use, or which have been for a long time in use, have 
 come to be employed as common terms. Thus we some- 
 times speak of red, good, virtue, figure, number, pleasure, 
 
 2 It is perhaps hardly necessary to remark that in such phrases as 
 ' Great is Diana of the Ephesians,' ' Great is my rejoicing,' the places 
 of the subject and predicate are reversed, for the sake of laying 
 greater emphasis on the predicate. In a logical analysis of such 
 propositions, the subject and predicate must be restored to their 
 normal positions.
 
 VARIOUS KINDS OF TERMS. 1 5 
 
 colour, &c. (both in the singular and plural number), 
 exactly as if they were common terms, though they still 
 retain in other connexions their use as abstract terms 
 or attributives. This remark will be found of great 
 importance in some of the subsequent sections. 
 
 ffote i. Nothing has been said above of the com- 
 mon distinction between abstract and concrete terms. 
 An abstract term would be defined as a term expressive 
 of an attribute or group of attributes considered apart 
 from the individuals of which it is predicable; a con- 
 crete term as a term expressive of an attribute or group 
 of attributes considered in reference to the individuals 
 of which it is predicable, as well as of an individual or 
 group of individuals itself. The terms John, the tenth 
 legion, man, human, would all be called concrete ; 
 humanity would be called an abstract term 3 . It will 
 be noticed that I have availed myself of the expression 
 ' abstract term,' but avoided, as too wide to be of prac- 
 tical service, the contrasted expression ' concrete term.' 
 Concrete terms include what I have called attributives, 
 as well as singular, collective, and common terms. 
 
 3 Mr. Mill (Logic, bk. i. ch. ii. 4) states that Locke and several 
 later writers have applied the expression ' abstract name ' to all 
 general names, that is, attributives and common terms as well as 
 what I have called abstract terms. This statement, however, is not 
 uniformly true of Locke. See, for instance, Essay, bk. iii. ch. viii. 
 Mr. Mill himself, following the practice of the Schoolmen, takes the 
 expression in the same limited sense as in the text. By the older 
 logicians singular and collective terms were not regarded as concrete, 
 no account being taken of them in this distinction.
 
 1 6 VARIOUS KINDS OF TERMS. 
 
 Note 2. The term 'attributive' (which has already 
 been employed by Harris and James Mill) is used in 
 preference to the term 'adjective,' both because it in- 
 cludes participles, and because it seems undesirable in a 
 work on Logic to employ a technical term of Grammar. 
 Harris (Hermes, bk. i. ch. vi.) includes amongst ' attribu- 
 tives ' verbs ; but a verb, as has already been stated; is, in 
 Logic, always represented by the copula and a participle. 
 
 I have placed attributives before abstract terms, be- 
 cause they are more nearly allied to singular, collective, 
 and common terms, being, for the most part, either pre- 
 dicated of these terms or employed to qualify them. 
 They seem also as a rule to precede abstract terms in 
 their formation. Thus human, red, brave, good, willing, 
 must have been employed before the corresponding terms 
 humanity, redness, bravery, goodness, willingness. 
 
 Note 3. For the sake of completeness, I have 
 spoken of a term as expressing an attribute or a group 
 of attributes. There is however no distinct name for a 
 term expressing a single attribute incapable of analysis, 
 and the only peculiarity of such terms is, as will be 
 seen below, that they are incapable of definition. Locke 
 called attributes which were incapable of analysis ' simple 
 ideas,' but the expression 'simple term' would not be 
 applicable in a corresponding sense. 
 
 Note 4. That common terms, attributives, and ab- 
 stract terms are formed from a comparison of individual 
 objects or groups of objects, and that consequently they 
 are results of thought, is obvious. But it may not be so
 
 VARIOUS KINDS OF TERMS. 1 7 
 
 easy to perceive that this is the case with singular and 
 collective terms. These terms however are appropriated 
 to individual objects or groups of objects in order to 
 distinguish them from others, and the necessity for such 
 distinction can only arise after a comparison of this or 
 that individual or group with others, and a perception 
 of certain points of resemblance and difference between 
 them. Unless I had observed some difference between 
 John and Thomas, this table and that, the thirteenth 
 legion and the fourteenth, it would never have occurred 
 to me to distinguish them by separate names ; but this 
 very observation of a difference involves an act of com- 
 parison, and consequently an act of thought. 
 
 Note 5. It is important to notice that in a series of 
 terms, like man, human, humanity, all expressing the 
 same attributes, the later and more abstract terms can 
 hardly fail to suggest the earlier and more concrete, 
 and it is so because the earlier terms of the series have 
 been longer formed and are therefore, as a rule, more 
 familiar to us. Thus ' humanity ' can hardly fail to 
 suggest to us the word ' human,' from which it is formed, 
 and ' human ' will suggest the word ' man,' from the Latin 
 equivalent of which it is also formed, and whose attributes 
 it expresses. Nor can we use the word ' man ' without 
 thinking of this or that individual man with whom we are 
 familiar. A common term, in fact, expresses simply an 
 individual object divested of all its peculiar attributes, and 
 regarded as possessing only those attributes which it has 
 in common with all the other objects which are designated
 
 1 8 VARIOUS KINDS OF TERMS. 
 
 by the same name. But it is indifferent on which 
 object of the group the mind concentrates its attention, 
 and we are all along conscious that the particular object 
 selected is simply representative of the group. And hence 
 it is that a common name simultaneously suggests to 
 the mind a group of individual objects and a bundle 
 of attributes characteristic of that group. For a further 
 discussion of this subject, see Hamilton's Lectures on 
 Metaphysics, Lect. xxxv. and xxxvi. ; Mansel's Prolego- 
 mena Logica, ch. i. ; and Mill's Examination of Hamilton, 
 ch. xvii. 
 
 Note 6. Mr. Mill maintains that attributives, when 
 employed as predicates, are really common terms. Thus 
 the propositions ' All triangles are three-sided,' ' All wise 
 men are just,' are regarded by him as only abbreviated 
 modes of saying ' All triangles are three-sided figures,' 
 'All wise men are just men.' I should allow that the 
 attributive in the predicate, when taken in conjunction 
 with the subject, always suggests a common term which 
 may be substituted for it, as in the syllogism ' All wise 
 men are virtuous, All virtuous men are happy ; /. All wise 
 men are happy.' But, though the attributive may always 
 admit of being expressed as a common term, while it 
 continues to be expressed as an attributive there seem to 
 be present to the mind only attributes, whereas, when it 
 becomes a common term, there seems also to be present 
 a group of individuals possessing those attributes.
 
 CHAPTER II. 
 
 On tJu Denotation and Connotation of 
 Terms. 
 
 A_TERMjpay be said to denote or designate individuals 
 or groups of individuals, to connote or mean attributes -or 
 groups of attributes l . 
 
 1 It ought, perhaps, to have been stated in the earlier editions of 
 this work that the term connotation is here employed in a some- 
 what different sense from that which is attached to it either in the 
 scholastic logic or in the system of Mr. Mill. 
 
 In the scholastic logic, a connotative term is ' one which primarily 
 signifies an attribute, secondarily a subject,' as ' white,' the contrasted 
 term being called an ' absolute term,' as ' man ' or ' whiteness.' See 
 Mansel's Aldrich, cap. I, 3, note g. This distinction, though it 
 may have existed before, seems to have been first brought into 
 prominence by Occam. For good statements of it, see Prantl, 
 Geschichte der Logik, Vol. III. p. 364, n. 831 ; Vol. IV. pp. 109, 
 no, n. 459. Duns Scotus seems to have been the first logician 
 to employ connotation in this sense. See Prantl, Vol. III. p. 134, 
 n. 598. 
 
 According to Mr. Mill's nomenclature, a connotative term is one 
 which ' denotes a subject and implies an attribute.' 
 
 By Mr. Mill, not only singular and collective, but also abstract 
 terms are regarded as non-connotative. In the scholastic logic, 
 what I have called attributives are alone recognised as connotative 
 terms. See Mill's Logic, Bk. I. ch. ii. 5. 
 
 As the term is already employed with so much uncertainty, it 
 appears to me not inexcusable to claim still further licence, and to 
 appropriate the expressions ' denotation ' and ' connotation ' of 
 ' terms ' in a sense parallel to that which is expressed by the dis- 
 
 C 2
 
 20 DENOTATION AND 
 
 In the first place, a term may serve to denote or 
 point out an individual object or group of individuals. 
 Thus ' Socrates ' denotes or points out and distinguishes 
 from all others the individual man Socrates. The ex- 
 pression 'tenth legion' denotes or points out, and dis- 
 tinguishes from all other collections of men, the particular 
 group known as the tenth legion. Similarly, the word 
 ' man ' denotes or points out, and distinguishes from all 
 other groups, a certain group of individuals to each 
 member of which and to each member of which only 
 the word ' man ' may legitimately be applied. All terms 
 of this kind, therefore, viz. singular, collective, and 
 common terms, are denotative ; but terms like human, 
 white, humanity, whiteness, i. e. attributes and abstract 
 terms, are not denotative, except mediately, that is, so 
 far as they suggest the common terms ' human beings,' 
 ' white things.' 
 
 In the second place, a term may serve to connote 
 attributes or groups of attributes. Thus terms like 
 humanity, human, man, viz. abstract, attributive, and 
 common terms, are all connotative, that is, they at 
 once suggest or imply attributes. But singular and 
 
 tinction between the ' extension ' and the ' intension ' of a ' notion ' 
 or ' concept,' applying ' denotation ' simply to the objects, and 
 ' connotation ' simply to the attributes which are signified by a term. 
 This is a broad and exceedingly convenient distinction, and, notwith- 
 standing the apparent paradox involved in it, namely, that 'abstract 
 terms are not denotative," I believe that the general employment of 
 the expressions in this sense would considerably simplify the state- 
 ment and explanation of many logical difficulties.
 
 CONNOTATION OF TERMS. 21 
 
 collective terms like ' Socrates,' ' the tenth legion,' are 
 not connotative, except so far as they suggest common 
 terms. This remark requires some explanation. A col- 
 lective term like ' the tenth legion/ ' the House of 
 Commons,' at once suggests the corresponding common 
 term, 'soldiers of the tenth legion,' or 'members of 
 the House of Commons ' ; and this common term may 
 connote any number of attributes, but, as the attributes 
 are suggested mediately through the common term and 
 not directly by the collective term, the collective term is, 
 strictly speaking, non-connotative. The same is the case 
 with a singular term. A term like ' William ' may sug- 
 gest to me ' man,' ' male,' ' Englishman,' ' one of my 
 friends,' &c., and so may become connotative, but it is 
 in itself rightly regarded as non-connotative, inasmuch 
 as it suggests to me these attributes only through the 
 medium of the common terms to which it is referred. 
 
 It appears therefore that common terms are both 
 denotative and connotative ; that singular and collective 
 terms are denotative, but not connotative ; that abstract 
 terms and attributives are connotative 2 , but not denota- 
 tive ; and finally, that mediately, as suggesting common 
 terms, any non-connotative term may become connotative 
 and any non-denotative term denotative. 
 
 3 It must be borne in mind, however, that attributives and abstract 
 terms (both in the singular and plural number) are often employed 
 as common terms, as when we speak of a figure or figures, a colour 
 or colours, red or reds, good or goods. See pp. 14, 15. In that 
 case, they are, like common terms, both denotative and connotative.
 
 22 DENOTATION AND 
 
 distinction between the denotation and 
 connotation of a term is often otherwise expressed, as that , 
 between the extension and intension (or comprehension), or 
 the extensive and intensive (or comprehensive) capacity, 
 or the breadth and depth, of a notion. Having adopted 
 the phraseology which designates the simplest product of 
 thought as a term, instead of a notion, I shall speak 
 of the extensive and intensive (or comprehensive) ca- 
 pacity of a term. The extensive capacity of a term 
 is measured by . the number of individuals which it 
 designates (denotes), the intensive or comprehensive 
 capacity of a term by the number of attributes which it 
 includes, suggests or implies (connotes). It is plain that 
 in a series of common terms, standing to one another in 
 a relation of subordination, the denotation and connota- 
 tion, or the extensive and intensive capacities, of the term 
 are so related, that as the one increases the other de- 
 creases, and vice versa. Thus, if we arrange in order any 
 series of common terms, as flower, rose, moss-rose, we 
 see that ' flower,' which implies the smallest number of 
 attributes, is applicable to the largest number of indi- 
 viduals ; ' moss-rose,' which is applicable to the smallest 
 number of individuals, implies the largest number of 
 attributes : and generally in any series of common terms 
 arranged in subordination, the larger the denotation or 
 extensive capacity, the smaller is the connotation or 
 intensive capacity, and vice versa. In conformity with 
 this principle, the singular term which stands for the 
 individual, and is smallest in denotation, is, when we refer
 
 CONNOTATION OF TERMS. 2$ 
 
 it to the various common terms which may be predicated 
 of it, and so assign to it mediately an intensive capacity, 
 the largest in connotation. Thus the term Socrates, when 
 I regard it as expressing one who was a philosopher, a 
 teacher, a martyr, a soldier, an Athenian citizen, &c., &c., 
 suggests to me far more attributes than any one of these 
 common terms singly.
 
 PART II. THE PROPOSITION. 
 
 CHAPTER I. 
 On the Subject and Predicate. 
 
 A PROPOSITION asserts -or denies, as the result of 
 comparison, some word or combination of words of some 
 other word or combination of words, as e. g. ' James is 
 the man I saw yesterday ' ; ' No rectilineal figure is 
 confined by less than three lines'; 'Some stars are 
 not planets.' As before stated, the words or combina- 
 tions of words thus ' employed are called terms, the 
 term affirmed or denied is called the predicate, the term 
 of which it is affirmed or denied the subject, the con- 
 necting verb, whether qualified or not by the negative 
 particle, the copula, and the predicate is said to be 
 predicated of the subject. In the above examples, ' the 
 man I saw yesterday,' 'contained by less than three 
 straight lines,' and ' planets ' are predicates and are pre- 
 dicated respectively of ' James,' ' all rectilineal figures,' and 
 4 some stars,' as subjects. In the first case the predicate is 
 predicated affirmatively, a fact which is expressed by the 
 copula ' is ' ; in the two last negatively, a fact which is
 
 THE SUBJECT AND PREDICATE. 2$ 
 
 expressed by the copula ' is not.' These remarks may 
 appear inconsistent with the form of the second example, 
 but ' no rectilineal figure is, &c.' is really an abbreviated 
 and unambiguous mode of stating the longer and am- 
 biguous proposition ' All rectilineal figures are not, &c.' 
 
 The word ' predicated,' as equivalent to ' asserted or 
 denied,' is here used in a wider than its ordinary signifi- 
 cation. In common language, we say such and such 
 an attribute cannot be predicated of such and such a 
 term, using ' predicated ' as equivalent to ' asserted ' and 
 as opposed to ' denied.' All ambiguity may be avoided 
 by speaking of the predicate as predicated affirmatively 
 or predicated negatively of the subject.
 
 CHAPTER II. 
 
 On the Copula. 
 
 THE Logical Copula, its office being simply to serve 
 as a sign of predication, is limited to the present tense of 
 the verb ' to be,' with or without the addition of the nega- 
 tive particle, according as the proposition is negative or 
 affirmative. This limitation follows from the fact that it is 
 simply the office of the proposition to express my present 
 judgment as to the agreement or disagreement of two 
 terms. Hence all reference to time, past or future, and 
 even to time present, as respects the terms themselves, 
 and not my judgment as to their agreement, must be 
 expressed in the predicate and not in the copula. I may, 
 for brevity's sake, say ' fire burns,' ' Alexander was the son 
 of Philip,' ' The guns will be fired to-morrow,' and, in con- 
 versation or discussion, it would undoubtedly be pedantic 
 to express the propositions otherwise ; but formally, for 
 the purpose of being estimated logically, I must resolve 
 them into their logical elements, and say ' Fire is burning,' 
 ' Alexander is a person who was son of Philip,' The firing 
 of the guns is an event which will take place to-morrow.' 
 
 Not only does the logical copula convey no notion of 
 time with reference to the terms themselves (or, to speak 
 more accurately, the things signified by them), but it is
 
 THE COPULA. 27 
 
 also divested of the notion of existence. In other words, 
 it is employed simply as a connecting particle, not as a 
 substantive verb. Where the substantive verb is used in a 
 logical proposition, it must be expressed in the predicate. 
 Thus ' I am,' ' The king is not,' become ' I am existent,' 
 ' The king is non-existent.' That the copula implies no 
 notion of existence is evident from the fact that we can 
 use such propositions as these : ' The labours of Hercules 
 are a myth,' ' He is a nonentity.' 
 
 Can we modify the copula so as to express certainty, 
 probability, possibility, or other modes of connexion be- 
 tween the subject and the predicate ? This is the cele- 
 brated question of Modality, a question which has been 
 the source of much difference of opinion amongst logi- 
 cians. Even though it were granted that the proposition 
 simply expresses our present judgment on the agreement 
 or disagreement of two terms, it might be maintained 
 that it should express the nature of our judgment and 
 the degree of our assent or dissent, whether it be certain, 
 approximating to certainty, or faltering. Thus it might 
 be maintained that the following should be accepted as 
 instances of the ultimate analysis of a logical proposition : 
 'This is certainly the man I saw yesterday,' 'This is 
 probably the man I saw yesterday,' ' This is possibly the 
 man I saw yesterday.' That we use these forms in 
 conversation and discussion is unquestionable, but it is 
 one main object of Logic to analyse our abbreviated infer- 
 ences and statements into their full logical equivalents. In- 
 stead therefore of admitting various descriptions of copulae
 
 28 THE COPULA. 
 
 (other than the affirmative and negative), in order to adapt 
 Logic to ordinary language, it seems simpler, as well as 
 more scientific, to insist on the uniform character of the 
 copula, and to represent propositions like the foregoing 
 as predicating our degree of assent to or dissent from 
 the sentence in question. Thus, after asking myself the 
 question ' Is this the man I saw yesterday ? ' I may either 
 answer simply ' This is the man I saw yesterday,' or I may 
 describe the degree of my assent by stating ' That this is 
 the man I saw yesterday is certain, probable, possible,' &c. 
 In fact, such propositions seem to be the result of an act 
 of reflexion on the degree of our own conviction. 
 
 I shall therefore regard the form A is or is not B as the 
 ultimate and uniform logical analysis of all propositions, 
 though I shall occasionally, for the sake of brevity, avail 
 myself of the forms sanctioned by popular language. 
 
 Note. As regards the expression of time in the copula, 
 the student will find the opposite opinion to that taken in 
 the text adopted by Mr. Mill, Logic, vol. i. ch. iv. 2. In 
 support of my view, he may refer to Dr. Mansel's Prole- 
 gomena Logica, pp. 63, 64. On the question of expressing 
 in the copula the degrees of assurance with which a pro- 
 position is entertained ('certainly,' 'probably,' &c.), see 
 Sir W. Hamilton's Discussions, pp. 145-7, and, for a more 
 qualified view than that taken either by Sir W. Hamilton 
 or myself, Dr. Mansel's Prolegomena Logica, note G.
 
 CHAPTER III. 
 
 r Division of Propositions according to their 
 Qiiantity and Quality. 
 
 WE have already seen that propositions are either 
 affirmative or negative, according as the copula used is 
 of the form ' is ' or ' is not.' This is called a division of 
 propositions according to their Quality. 
 
 They are further divided, according to their Quantity, 
 into Universal and Particular. For, in affirming or 
 denying a predicate ofa "subject, it is obvious that I 
 may either affirm or deny the predicate of all the indi- 
 viduals denoted by the subject, or of part only. Thus 
 in affirming mortality of man, I may say ' All men are 
 mortal,' or 'Some men are mortal'; in denying wisdom 
 of man, I may deny it of all men or only of some 
 men, i. e. I may say ' No men are wise,' or ' Some 
 men are not wise.' When the predicate is affirmed or 
 denied of all the individuals denoted by the subject, the 
 proposition is called an Universal Proposition ; when 
 of part only, a Particular Proposition. A Singular Pro- 
 - position, i. e. a proposition of which the subject is a 
 singular term, ranks as an Universal, because the pre- 
 dicate is affirmed or denied of everything (i. e. in this
 
 30 DIVISION OF PROPOSITIONS. 
 
 case, the one thing) denoted by the subject. The same 
 remark holds good of a proposition in which the subject 
 is a collective term. An attributive, as we have already 
 seen, cannot, by itself, be used as the subject of a pro- 
 position. Abstract terms which have come to be used as 
 common terms, and admit of plurals, as figure, triangle, 
 virtue, pleasure, &c., have a denotative power, and 
 may, like common terms, form the subjects of either 
 universal or particular propositions. But those abstract 
 terms, like humanity, wisdom, &c., which retain their 
 original characteristic of being connotative only, and 
 admit of no plurals, simply express an attribute or group 
 of attributes with which, as a whole, it is asserted or 
 denied that the predicate is in agreement ; consequently, 
 a proposition, of which such a term is the subject, 
 ranks as an universal. 
 
 Thus such propositions as 'Ambition is aggressive,' 
 'Wisdom is a virtue,' 'The fourteenth legion is dis- 
 banded,' 'Socrates is an Athenian citizen,' are, on the 
 very face of them, universals. But propositions in which 
 the subject is a common term or an abstract term used 
 as a common term, must be quantified ; that is, we must 
 attach to the subject either an universal or a particular 
 designation. It is not sufficient to say, 'triangles are 
 figures,' 'horses are black'; we must state whether we 
 mean that ' all triangles ' or ' some triangles ' are ' figures,' 
 whether we mean that ' all horses ' or ' some horses ' are 
 black. ' Indefinite ' or ' indesignate ' propositions, as they 
 are called; i. e. propositions in which the subject, being
 
 QUANTITY AND QUALITY. 31 
 
 a common term, is not quantified, are inadmissible in 
 Logic. 
 
 By combining the division of propositions into uni- 
 versal and particular with that into affirmative and nega- 
 tive we obtain four forms, viz. 
 
 
 Universal Affirmative. All X is Y. J^r (A) 
 Universal Negative. No X is Y. (E) 
 
 Particular Affirmative. Some X is Y. - > 
 Particular Negative. Some X is not Y. (O) 
 
 I shall in future designate these forms of proposition 
 respectively as A, E, I, O l . 
 
 Note. Sir W. Hamilton 2 , followed by several other 
 logicians, maintains that in thought the predicate is 
 always quantified as well as the subject. He proposes to 
 reform the logical theory of the proposition accordingly, 
 
 1 It sometimes requires a little ingenuity to state a given proposi- 
 tion in one of the above forms. Thus the propositions ' None but 
 the brave deserve the fair,' ' The wise alone are good,' 'Not every 
 historian is worthy of credit,' ' All his acts are not defensible,' when 
 stated in strictly logical form, become respectively, No not-brave (or 
 None who are not brave) are deserving of the fair, No not-wise (or 
 None who are not wise) are good, Some historians are not worthy 
 of credit, Some of his acts are not defensible. The simplest equi- 
 valents of the two former propositions are, All who deserve the 
 fair are brave, All good men are wise ; but these are arrived at by 
 permutation and conversion, two forms of inference which have 
 not yet been explained. 
 
 3 Sir William Hamilton's theory was anticipated in a work now 
 little read, but full of original suggestions on logical questions, Mr. 
 George Bentham's Qutline of a New System of Logic, published in 
 1827.
 
 32 DIVISION OF PROPOSITIONS. 
 
 and in lieu of the four ordinary forms of proposition 
 substitutes the following : 
 
 All X is all Y. 
 All X is some Y. 
 All X is not any Y. 
 All X is not some Y. 
 
 Some X is all Y. 
 Some X is some Y. 
 Some X is not any Y. 
 Some X is not some Y. 
 
 This scheme, if adopted, would, as Sir W. Hamilton 
 shews, reduce all conversion to simple conversion, render 
 nugatory any discussion as to the distribution of terms, 
 and considerably simplify the forms of syllogism : see 
 the Appendices to Sir W. Hamilton's Discussions, and 
 to his Lectures on Logic. Amongst other criticisms may 
 be seen Mr. Mill's in his Examination of Hamilton's 
 Philosophy, ch. xxii. It would of course be undesirable 
 to enter here into any discussion as to the merits of 
 Sir W. Hamilton's theory, but, as reasons for not adopt- 
 ing the quantification of the predicate in the present 
 work, it may be sufficient to state (i) that, as to utility, 
 the trouble entailed by quantifying the predicate in every 
 proposition would probably far exceed that saved by 
 simplifying the forms of Conversion and Syllogism ; (2) 
 that the forms of expression given above are not merely- 
 unusual, but are such as we never do use; whereas, 
 though the analysis of our thoughts frequently leads to
 
 QUANTITY AND QUALITY'. 33 
 
 forms of expression which are unusual, this would, if 
 admitted, be the only case in which it led to forms 
 which are never used at all ; (3) that some of the above 
 propositions really contain in a compressed form two 
 ordinary propositions, as e. g. ' All A is all B ' contains 
 the two ordinary propositions ' All A is B ' and ' All 
 B is A,' the proposition ' Some A is all B ' contains the 
 two ordinary propositions ' Some A is B ' and ' All B is A, 
 whereas it is the object of Logic not to state, our thoughts 
 in a condensed form but to analyse them into their 
 simplest elements.
 
 CHAPTER IV. 
 
 Distribution of Terms. 
 
 A TERM is said to be distributed, when it is employed 
 in its entire extent, i. e. when it applies to all the indivi- 
 duals denoted by the name. Thus, when we say, ' all 
 men,' ' no men,' ' man ' is distributed ; when we say ' some 
 men,' it is undistributed. This phraseology of course 
 applies directly only to common terms ; but singular and 
 collective terms, as has already been explained, are always 
 taken in an universal acceptation, or, in other words, are 
 always distributed. The same is true of those abstract 
 terms which have not come to be used as common terms, 
 because they, as it were, personify the attribute or group 
 of attributes which they express ; so far as regards dis- 
 tribution, they are, in fact, virtually singular terms. In 
 such propositions as, 'This is wisdom/ 'Wisdom is jus- 
 tified of her children/ ' Warmth is essential to growth/ 
 ' Knowledge is power/ it is obvious that the abstract 
 terms are distributed precisely as if they were singular 
 terms, and that, for all logical purposes, these proposi- 
 tions rank as universal. Attributives, i. e. adjectives and 
 participles, have no meaning except in connexion with a 
 substantive. They must either be prefixed to a substantive 
 or predicated of it : we cannot say ' human ' alone ; we 
 must either speak of ' human being/ ' human nature/ &c.
 
 DISTRIBUTION OF TERMS. 35 
 
 or say, ' So and so is human.' Consequently the distri- 
 bution or non-distribution of an attributive, as ' human,' 
 ' red,' &c., follows that of the corresponding common 
 term, ' human being,' ' red thing,' &c. 
 
 Hence we perceive that a singular, collective, or abstract 
 term is distributed wherever it may occur in a proposition. 
 We have therefore only to enquire as to the distribution 
 of common terms and attributives. With regard to these, 
 the two following rules may be laid down. 
 
 1. All universal propositions distribute their subject, 
 whereas particular propositions do not. This rule is 
 obvious. The very word ' all ' or ' no ' shews that the 
 subject is distributed, whereas the word ' some ' shews 
 that it is undistributed. 
 
 2. All negative propositions distribute their predicate, 
 whereas affirmative propositions do not. For in every 
 negative proposition we necessarily exclude from the 
 subject every individual denoted by the predicate, but in 
 an affirmative proposition we do not necessarily include 
 in the subject every individual denoted by the predicate. 
 Thus, if I say, 'No crows are yellow/ 'Some cherries 
 are not red,' I exclude from the group ' crows ' every 
 individual object denoted by the term ' yellow things,' and 
 from the group ' some cherries ' every individual object 
 denoted by the term ' red things V But if I say, ' All 
 
 1 Here it will be noticed that the terms ' yellow ' and ' red,' though 
 not in themselves denotative, suggest the corresponding common 
 terms, 'yellow things' and 'red things,' and thus, through the medium 
 of the common terms, become denotative. 
 
 D 2
 
 36 DISTRIBUTION OF TERMS. 
 
 men are animals,' or ' Some Englishmen are poets,' I do 
 not include in the group ' men ' all animals, nor in the 
 group ' Englishmen ' all poets. It may of course happen 
 that the predicate in an A or I proposition is co-exten- 
 sive with the subject, as in the propositions 'All men 
 are rational animals,' ' Some men are poets,' but this fact 
 is accidental, and is not implied in the form of the pro- 
 position. 
 
 From these two rules we infer that, in the case of 
 common terms and attributives, an Ajproposition dis- 
 tributes its subject only, E both its subject and pre- 
 dicate, ^ neither, O its predicate only. If a term be 
 singular, collective, or abstract, it is invariably dis- 
 tributed.
 
 CHAPTER V. 
 
 tion of the Predicate to the Subject of a 
 'roposition (Heads of Predicables}. 
 
 N.B. For this Chapter, in the case of beginners, may be 
 substituted Appendix, pp. 162-4. See Preface, p. K. 
 
 FROM what has already been said, it is plain that a 
 singular, collective, or abstract term, inasmuch as it is 
 always distributed, cannot form the subject of an I or 
 
 proposition : on a little reflexion it will also be plain 
 that the predicate of a proposition cannot be singular, 
 collective, or abstract, unless the subject be the same. 
 
 1 have already noticed that an attributive can never 
 form the subject of any proposition. These considera- 
 tions will be found to simplify the problem before us. 
 
 This problem may be stated thus : How may the pre- 
 dicates of propositions be classified in relation to their 
 subjects ? or What are the heads of predicables (praedi- 
 cabilia, things or words that may be predicated) ? I 
 shall discuss the four forms of proposition in order. 
 
 To commence with A, and with the special case where 
 both subject and predicate are common terms, or abstract
 
 38 RELATION OF THE PREDICATE 
 
 terms which are used as common terms \ Here the pre- 
 dicate may either be (i) equivalent in extent to the sub- 
 ject, or (2) greater ; it cannot be less. We can say, for 
 instance, ' All men are animals,' or ' All men are rational 
 animals,' but we cannot say ' All animals are men.' Now, 
 if the predicate be (i) equivalent in extent to the subject, 
 it is either (a) a Synonym, as 'A wold is a down'; or 
 (/3) a Definition, as ' A plane triangle is a three-sided recti- 
 lineal figure ' ; or (y) a combination of a genus (a term 
 which will be explained immediately) with some attribute 
 which is peculiar to the term in question (called by 
 Aristotle an iSioi/ or ' peculiarity '}, as ' A plane triangle is 
 a rectilineal figure the sum of whose angles is equal to 
 two right angles.' A synonym, it need hardly be stated, 
 is an equivalent word, and a definition is an exposition 
 of the connotation of a term. Now it will be observed 
 that the definition of a plane triangle consists of two parts, 
 one in which it is designated as a 'rectilineal figure '- 
 a wider group, which includes not only triangles but 
 other rectilineal figures and the other part an attribu- 
 
 1 It may perhaps assist the student in following what, to be exhaus- 
 tive, must necessarily be a tedious disquisition, if I afford him some 
 clue to the order in which the cases will be discussed : 
 
 In the A proposition, (i) if the predicate be a common term, the 
 subject may be (a) a common, (/3) a singular or collective term ; 
 (2) if the predicate be a singular or collective term, the subject 
 must be the same ; (3) if the predicate be an abstract term, the 
 subject must be the same ; and (4) if the predicate be an 
 attributive, the subject may be (a) a common, (/3) a singular or 
 collective, (7) an abstract term. The discussion of the cases in 
 I, E, and O is much less elaborate.
 
 TO THE SUBJECT OF A PROPOSITION. 39 
 
 tive, 'three-sided,' which distinguishes triangles from all 
 other groups contained in the wider group to which 
 triangle has been referred. The former part of the 
 definition is called the genus, and with reference to it 
 ' plane triangles,' the group of figures defined, are called 
 a species ; the latter part of the definition, ' three-sided,' 
 which distinguishes triangles from squares, pentagons, 
 and other rectilineal figures which are designated by the 
 wider term, is called the differentia or ' differencing ' attri- 
 bute. It is obvious that there might be more than one 
 of these, and then they would be called the differentiae. 
 With reference to the third case, 'A plane triangle is 
 a rectilineal figure the sum of whose angles is equal to 
 two right angles,' 'rectilineal figure' is, as before, to be 
 regarded as a genus, but the attributive ' having the sum 
 of its angles equal to two right angles ' cannot be regarded 
 as a differentia, for it is not connoted by the term ' plane 
 triangle,' but requires to be proved of it ; at the same time 
 it is an attribute peculiar to the plane triangle, and hence, 
 retaining the Aristotelian term, we may call it an "idiov. 
 Lastly, there remains (2) the case in which the predicate 
 is of greater extent than the subject, both being com- 
 mon terms, as in the propositions ' All men are animals,' 
 'All triangles are figures.' Here the subject denotes a 
 smaller group of individuals included under the wider 
 group designated by the predicate; that is, according 
 to the nomenclature already explained, the predicate is 
 related to the subject as genus to species. This relation is 
 often spoken of as that of the containing to the contained.
 
 40 RELATION OF THE PREDICATE 
 
 When the predicate is a common term, and the sub- 
 ject a singular or collective term, as in the instances 
 ' Socrates is a philosopher,' ' Socrates is an Athenian 
 citizen,' 'The House of Commons is a branch of the 
 legislature,' the predicate is related to the subject as a 
 group of individuals to an individual, i. e. as a species to 
 an individual, for the word ' genus ' is only applicable to 
 a group containing other groups. The same account 
 must be given of those propositions in which the pre- 
 dicate is an abstract term employed as a common term, 
 and the subject is an abstract term employed strictly as 
 such, as e.g. 'Temperance is a virtue,' 'Heat is a mode 
 of motion.' 
 
 When the predicate is a singular or collective term, 
 the subject must, as we have already seen, be a similar 
 term. Moreover the predicate in these propositions is 
 always distributed as well as the subject, and conse- 
 quently the two terms are co-extensive. But, inasmuch 
 as singular and collective terms have, at least directly, no 
 connotation, the predicate cannot stand to the subject in 
 the relationof a definition, or of an iSioi/ 2 (i. e. an attribute 
 peculiar to the subject) combined with a genus. It can 
 only be (i) a synonym, or (2) a singular or collective 
 term designating the individual or the collective group. As 
 instances of these propositions we may take the following : 
 ' Cephas is Peter,' ' Socrates is the son of Sophroniscus,' 
 4 This is the man whom I saw yesterday, and whom I told 
 
 3 The English word ' characteristic ' might perhaps be employed 
 as the equivalent of the Greek tSioy.
 
 TO THE SUBJECT OF A PROPOSITION. 41 
 
 to come to me,' ' The fourteenth legion is the legion quar- 
 tered in Britain.' When the predicate is not a synonym, 
 it may perhaps be called a Designation. 
 
 When the predicate is an abstract term, the subject 
 must be abstract as well, and, as in the case of singular 
 and collective terms, the subject and predicate are both 
 distributed, and consequently are of equal extent. We 
 may take as instances of the various forms which propo- 
 sitions of this kind assume, ' Charity is love,' ' Honesty is 
 the best policy,' ' Definition is the exposition of the con- 
 notation of a term.' Now in the first example ' love ' is 
 intended as a synonym of ' charity,' in the second ' the best 
 policy ' is predicated of ' honesty ' as distinguishing it from 
 all other courses of conduct ; the third example is an ordi- 
 nary case of a definition. The case of two abstract terms 
 may therefore be regarded as identical, so far as concerns 
 the relation of the predicate to the subject, with that of 
 two common terms which are co-extensive. 
 
 Lastly, there remains the case in which the predicate is 
 an attributive. Supposing the subject to be a common term, 
 the predicate may, as we have seen, be (i) a differentia, as 
 in the proposition 'All triangles are three-sided,' or (2) an 
 Idiov, as in the proposition 'All plane triangles have the 
 sum of their angles equal to two right angles.' Or, though 
 neither a differentia nor an iSioi/, it may be (3) what, along 
 with the ibiov, modern logicians would call a Property, viz. 
 an attribute which, though not connoted by the subject, 
 nor even peculiar to it, follows from something connoted 
 by the subject, either (a) as effect from cause or (/3) as
 
 42 RELATION OF THE PREDICATE 
 
 conclusion from premiss 3 . An instance of (a) a. property 
 which follows from the connotation of the subject by demon- 
 stration would be given in the proposition ' A parallelo- 
 gram has its opposite sides equal,' or in the proposition 
 ' A circle is a figure the ratio of whose circumference to its 
 diameter is approximately 3.14159 : i.' As instances of 
 propositions in which the predicate expresses () a pro- 
 perty following from the connotation of the subject by 
 causation, we may take ' Men are capable of combining for 
 purposes of joint action,' ' Water communicates pressure 
 equally in all directions.' The first property follows from 
 rationality, or that combined with the power of articulate 
 speech, which seems to be connoted by the very word 
 ' man ' ; the second property follows from the fluidity of 
 water. The last example of a property following by way 
 of demonstration and the first of a property following by 
 way of causation are tSta in the sense of Aristotle, as well 
 as propria in the sense of the later logicians. There is 
 (4) one other case, that in which the attributive, though 
 neither connoted by the subject nor following from any- 
 thing connoted by the subject, is predicable of everything 
 denoted by it. Such an attributive is called an Inseparable 
 Accident, and the common instance given by logicians is 
 the proposition ' All crows are black.' If the blackness of 
 crows could be connected by way of causation with any 
 
 3 The student must bear in mind that every i&iov is a Properly, 
 though every Property is not an iStov. The definition given above 
 applies only to those properties which are not iSta. The formal 
 definition of Property will be found on p. 46.
 
 TO THE SUBJECT OF A PROPOSITION. 43 
 
 attribute connoted by the name, it would be regarded as a 
 property ; if, on the other hand, a crow could be found 
 which was not black, blackness would be degraded to 
 the rank of a Separable Accident, a term which will be 
 explained below. 
 
 We have thus far considered attributives as predicates 
 in the special case where the subject is a common term. 
 Where the subject is a singular or collective term, and 
 consequently has no direct connotation, the attributive 
 forming the predicate can only be an inseparable accident 4 . 
 I may indeed say ' Socrates is rational,' but I predicate 
 rationality of him as man, not as Socrates. Where the 
 subject is an abstract term, the attributive which forms the 
 predicate may be a differentia or a property, but cannot 
 be an inseparable accident, for an abstract term denotes 
 no individuals. 
 
 In the I proposition we are not concerned with singular, 
 collective, or abstract terms. If the predicate be ( i ) a com- 
 mon term, it may be related to the common term in the 
 
 * Sometimes a distinction is drawn between the separable and in- 
 separable accidents of an individual. An inseparable accident of an 
 individual is regarded as one which is predicable of it at all times, 
 a separable accident as predicable only at certain times. Thus in the 
 propositions, 'John is tall,' 'John is sitting down,' ' tall' is regarded 
 as an inseparable, ' sitting down ' as a separable accident. But the 
 expressions separable and inseparable accident are here employed in 
 an entirely different sense from that in which they have been employed 
 above, and it seems preferable to regard all attributes which are 
 predicated of individuals, in their individual character, as inseparable 
 accidents inseparable, that is to say, from the individual under the 
 circumstances in which it is at present placed.
 
 44 RELATION OF THE PREDICATE 
 
 subject either (a) as species to genus, or (#) as species to 
 species, as e. g. ' Some men are poets,' or ' Some poets are 
 philosophers.' The latter relation is that of two groups, 
 which have some members in common overlapping 
 species, as they have been called. The relation may also 
 be (y) that of genus to species, as ' Some men are animals,' 
 ' Some poets are men,' but this form of proposition is 
 practically useless, as it stops at a particular assertion 
 when an universal assertion is legitimate. If the predi- 
 cate be (2) an attributive, it must, unless the proposition 
 state less than the truth, be a Separable Accident, i. e. 
 an attribute which is true only of some of the individuals 
 denoted by the subject, as e. g. ' Some men are black,' 
 ' Some triangles are equilateral.' 
 
 With regard to negative propositions, it is not necessary 
 to speak at any length. The negation of an attributive 
 in an E proposition implies that it is neither a differentia, 
 property, nor accident ; in an O proposition that it is 
 neither a differentia, property, nor inseparable accident, 
 though it may be a separable accident. All that has been 
 said of the relations of singular, collective, and abstract 
 terms, as subjects, either to similar terms or to common 
 terms and attributives, as predicates, in the case of an A 
 proposition, holds good also, mutatis mutandis, of similar 
 relations in E. It may perhaps be as well to give a few 
 instances of such propositions : ' Socrates is not a poet,' 
 ' Socrates is not the man I saw yesterday,' ' The fourteenth 
 legion is not engaged in the battle,' ' Charity is not obtru-
 
 TO THE SUBJECT OF A PROPOSITION. 45 
 
 sive,' ' Ambition is not a virtue.' Where a common term 
 is denied of a singular or collective term, it stands to the 
 subject in the relation of species to individual. Where 
 a common term is denied of a common term, there is 
 nothing to prevent the terms being extremely remote from 
 each other and hardly admitting of comparison ; but here 
 the most appropriate relation is in an E proposition, 
 that of co-ordinate though exclusive species, i. e. of species 
 which having many characteristics in common, and both 
 falling immediately under the same genus, still denote no 
 individuals in common, in an O proposition, that of 
 overlapping species. Thus we should be far more likely 
 to derive information from such propositions as these, 
 ' No sandstone is limestone,' ' Some astronomers are not 
 mathematicians,' than from such propositions as these, 
 ' No men are trees,' ' Some stones are not vipers.' 
 
 From what has been said we have derived the follow- 
 ing names for the predicate in its relation to the subject : 
 (i) synonym, (2) definition, (3) designation, (4) genus, (5) spe- 
 cies, (6) differentia, (7) i'Stov, (5*>) property (not being an iSioj/), 
 (9) inseparable accident, (10) separable accident. Of these, 
 logicians have neglected synonym and designation, the 
 former probably on account of its slight importance, the 
 latter perhaps because it applies only to singular and col- 
 lective terms. Definition is analysed into genus and dif- 
 ferentia ; no distinction is drawn by later logicians between 
 iSia and those properties which are not peculiar to the sub- 
 ject, both being alike designated by the word ' property ' ;
 
 46 RELATION OF THE PREDICATE 
 
 and the word ' accident ' serves alike for separable and 
 "inseparable accident. Genus, difference, species, property, 
 and accident, are known as the Jive heads of predicables. 
 These terms may be briefly defined as follows : 
 
 A Genus is a common term expressive of a wider 
 group of individuals including narrower groups. 
 
 A Species, in reference to a genus, is a common term 
 expressive of a narrower group included in the 
 genus ; in reference to an individual, of a group 
 including it. 
 
 A Differentia is an attributive which expresses part 
 of the connotation of some common term, and 
 which distinguishes that term from all other species 
 which fall under the same genus. 
 
 A Property is an attributive which does not express 
 any part of the connotation of the common term, 
 but which follows from some part of the connota- 
 tion of the term, either as an effect from a cause, 
 or as a conclusion from premisses. 
 
 An Accident is an attributive which may be predicated 
 of the whole or part of the individuals denoted 
 by a common term, or which may be predicated 
 of an individual, but which is neither connoted 
 by the common term nor to be inferred from 
 anything which is connoted thereby 5 . 
 
 5 In the above definitions, wherever the expression ' common term ' 
 occurs, it must be understood as including those abstract terms which 
 have come to be employed as common terms.
 
 TO THE SUBJECT OF A PROPOSITION. 47 
 
 Note i . Contrary to the practice of most logicians, I 
 have discussed the heads of predicables under the second 
 part of Logic. In taking this course, I have attempted to 
 restore to them their original significance in the works 
 of Aristotle, as a classification of the predicates in their 
 relation to the subjects of propositions. It is perhaps 
 needless to add, that I have not followed implicitly the 
 Aristotelian account, or in all cases adopted the Aristo- 
 telian phraseology. By Porphyry, the schoolmen, and 
 their successors of the seventeenth and eighteenth cen- 
 turies, the heads of predicables were regarded as a classi- 
 fication of universals in their relations to one another, 
 rather than with reference to their place in a proposition, 
 and consequently, from the time that Logic was divided 
 into parts, were discussed under the first part. Defini- 
 tion and division, as dependent on a knowledge of genus, 
 species, and differentia, are also here treated under the 
 second part of Logic, though they are ordinarily discussed 
 under the first. 
 
 Note 2. On the vexed and subtle question of the 
 Import of Propositions, or, as it is sometimes called, the 
 Theory of Predication, the student may be referred to 
 Hobbes' Computation or Logic, ch. iii., Mr. Mill's Logic, 
 Bk. I. ch. v., Dr. Mansel's Prolegomena Logica, ch. ii., 
 Sir W. Hamilton's Lectures on Logic, Lects. viii. and xiii., 
 and Mr. Mill's Examination of Sir W. Hamilton's Philo- 
 sophy, ch. xviii. The view I should adopt may be 
 briefly stated as follows : wherever the predicate is a 
 singular or collective term, or, though a common or
 
 48 RELATION OF THE PREDICATE, ETC. 
 
 abstract term, a synonym of the subject, the theory of 
 Hobbes, that the predicate is a name of the same things 
 of which the subject is a name, furnishes a sufficient 
 account ; in all other cases, Hobbes' theory is true, 
 though insufficient, for, where the predicate is an at- 
 tributive or an abstract term (not being a synonym), the 
 predicate also asserts or denies certain attributes of the 
 subject, and where it is a common term (not being a 
 synonym), not only are certain attributes asserted or 
 denied of the subject, but the latter is referred to or 
 excluded from the group of individuals denoted by the 
 predicate. Thus, in the proposition ' Socrates is the son 
 of Sophroniscus,' the predicate may be regarded as simply 
 another name for the subject ; but when we say ' Socrates 
 is human,' we imply more than this, namely, that certain 
 attributes connoted by the word ' human ' may be affirmed 
 of Socrates. Further, when we say ' Socrates is a man,' 
 we not only assign another name to the subject, and 
 predicate of it certain attributes, but we also include it in 
 a certain group. This peculiarity follows from the double 
 signification of common terms, by which they both de- 
 note a group of individuals and connote a group of attri- 
 butes, or, in other words, simultaneously suggest to the 
 mind a group of individual objects and a bundle of attri- 
 butes characteristic of that group. From what has been 
 said it will be seen that I do not agree with Mr. Mill 
 in regarding all predication, other than that of a singular 
 or collective term, as a predication merely of attributes.
 
 CHAPTER VI. 
 On Verbal and Real Propositions. 
 
 AFFIRMATIVE propositions in which the subject is 
 a common or abstract term may be divided into Verbal 
 and Real. A verbal proposition expresses merely the 
 connotation, or part of the connotation of the term; a 
 real proposition expresses either solely, or in conjunc- 
 tion with part of the connotation of the term, properties, 
 accidents, or both. Thus a verbal proposition simply 
 states what might be gathered from a due consideration 
 of the name, as ' All men are rational,' ( All triangles are 
 three-sided'; whereas a real proposition imparts know- 
 ledge which could not be gathered from the name alone, 
 as 'All plane triangles have the sum of their angles 
 equal to two right angles,' ' Some men are black.' It is 
 plain that all particular affirmative propositions are real. 
 
 Note. The distinction between verbal and real propo- 
 sitions is otherwise expressed by that between Analytical 
 and Synthetical judgments (Kant), Explicative and Ampli- 
 ative judgments (Sir W. Hamilton and Abp. Thomson), 
 Essential and Accidental propositions (the schoolmen). 
 Tautologous propositions (All A is A), and propositions 
 in which the predicate is a synonym of the subject (as 
 e. g. ' Charity is love '), should be referred to the head of 
 verbal propositions. 
 
 E
 
 CHAPTER VII. 
 
 On Definitions. 
 
 A DEFINITION is an exposition of the connotation 
 of a term. It may always be represented in the form of 
 a proposition, of which the term defined forms the subject 
 and the exposition the predicate 1 . 
 
 As a definition expounds or enumerates the attributes 
 which a term implies, it is plain that singular and collec- 
 tive terms, inasmuch as they do not in themselves con- 
 note any attributes, are incapable of definition. They may, 
 however, be described by means of the various common 
 terms which are predicable of them, as well as by desig- 
 nations which are peculiar to themselves. Thus I may 
 say ' John is a tall man of fair complexion, is by profes- 
 sion a London solicitor, and occupies such and such a 
 house in Bedford-row.' This may be called a Description 
 of a Singular or Collective Term, in order to distinguish it 
 from the Description of a common term, which is noticed 
 below, and which I shall call simply Description. Besides 
 singular and collective terms, a term expressing a single 
 attribute, which is incapable of analysis into other attri- 
 butes, is incapable of definition. Thus it has been main- 
 tained that it is useless to attempt to define such terms 
 as pleasure, pain, colour, thing, attribute, &c. 
 
 1 It is indifferent whether we speak of the entire proposition as the 
 definition, or merely the exposition which forms the predicate ; 
 similarly in the case of a description.
 
 DEFINITIONS. 51 
 
 In defining a term, it would of course be impossible, 
 in every case, to state the definition in terms expressive 
 of attributes which are themselves incapable of analysis, 
 even if we were agreed as to what are terms of this 
 character. The terms employed in the definition may 
 therefore express groups of attributes, provided that, 
 when taken together, they exhaust the connotation of 
 the term defined. Thus each of the terms ' under one 
 supreme head' and 'political government' expresses a 
 large group of attributes, but if, when taken together, 
 they exhaust the connotation of the word 'monarchy,' 
 the definition may be accepted as legitimate. 
 
 In seeking to define a term, I invariably contrast it 
 with some other term ; often, when I imagine it to be 
 difficult to exhaust the connotation, with a variety of 
 other terms, from which I seek to distinguish it. Thus 
 in seeking to define ' monarchy,' I contrast it with other 
 forms of government ; in seeking to define 'plane triangle,' 
 I contrast it not only with other rectilineal figures but with 
 spherical triangles ; in seeking to define ' light,' I contrast 
 it with heat, sound, electricity, and other impalpable 
 powers of nature. Now that portion of the definition 
 which is common to the term defined and to the other 
 terms with which it has been compared is called the 
 genus, the term defined standing to it in the relation of 
 a species, as has already been explained; that portion 
 which distinguishes the term defined from the terms with 
 which it has been compared is called the differentia, or 
 sometimes, when there is more than one distinguishing 
 E 2
 
 52 DEFINITIONS. 
 
 attribute, the differentiae. 2 . Thus, if we were distinguish- 
 ing rectilineal triangle from spherical triangle, 'three- 
 sided figure ' would be the genus ; if from other rectilineal 
 figures, the genus would be 'rectilineal figure'; if from 
 both spherical triangles and other rectilineal figures, the 
 genus would be simply ' figure.' It will be observed that 
 the genus is always expressed in the form of a common 
 term, or of an abstract term which is used as a common 
 term, and that it may be qualified by an attributive. 
 This is the case even in defining abstract terms, as e. g. 
 in the definitions, ' Justice is a virtue which respects our 
 relations to other men in society,' ' Temperance is a 
 virtue which respects the control of our own desires,' the 
 genus s is ' a virtue,' an abstract term which has come 
 to be used as a common term. 
 
 A Definition being an exposition of the meaning 
 of a term, it is obvious that all definitions must be 
 limited by the state of our knowledge at the time when 
 we frame them. But some terms have been expressly 
 framed or have been appropriated to express a small 
 number of attributes. Such terms are monarchy, anarchy, 
 
 * Some logicians simply use the word ' differentia ' for the purpose 
 of expressing the distinguishing attributes, whether one or many; 
 others, as Aristotle, would in the latter case speak of the ' differentiae.' 
 
 3 Whenever abstract terms are defined or divided, or occur as por- 
 tions of definitions or divisions, they seem invariably to be treated as 
 if "they were common terms, and hence in the definitions of abstract 
 terms, as in other definitions, the term defined may be regarded as a 
 species; for the same reason, when an abstract term is divided, its 
 relation to the dividing members may be described as that of genus 
 to species.
 
 DEFINITIONS. 53 
 
 triangle, square, school, monastery, &c. Our accepted 
 definitions of these terms we may be quite sure we shall 
 not be compelled to alter with advancing knowledge, 
 provided at least that they continue to denote the 
 same objects. But however full and adequate to our 
 present state of knowledge our definitions of man, animal, 
 vegetable, light, heat, &c., might be at the present time, 
 they might, two hundred years hence, become most in- 
 adequate and incomplete, if not incorrect, even although 
 the terms continued to denote the same objects or sen- 
 sations. We might, for instance, discover the mode 
 of transmission of light, or that the animal world was 
 not separated from the vegetable by the same character- 
 istics by which we now conceive it to be, and henceforth 
 these discoveries would become part of the connotation 
 of the words, or would materially alter the connotation. 
 In the greater number of cases, therefore, we must be 
 content to regard our definitions as provisional *. 
 
 But not only must we in most cases be content with 
 provisional definitions ; we must often be content with 
 definitions which, measured even by our present state 
 of knowledge, are incomplete. It would often be most 
 inconvenient, when it is required simply to distinguish 
 between two terms, to give the full connotation of each. 
 
 4 It would be a service to logicians if there were recognised names 
 by which to distinguish between these two different classes of defini- 
 tions, viz. the definitions of terms whose connotation is limited, and 
 whose definitions are therefore final, and the definitions of terms whose 
 connotation is unlimited, and whose definitions are therefore pro- 
 visional.
 
 54 DEFINITIONS. 
 
 In such cases, therefore, it is regarded as practically suffi- 
 cient, if we refer the terms contrasted to their common 
 genus, and specify a sufficient number of attributes to 
 distinguish each from the other. Thus in the often- 
 quoted example of definition, ' Man is a rational animal,' 
 it would be absurd to suppose that ' rational ' and ' animal ' 
 exhaust the connotation of ' man,' but the word ' rational ' 
 is sufficient, for popular purposes, roughly to distinguish 
 the human race from the lower animals with which it is 
 generally contrasted. When these incomplete definitions, 
 as they are called (i. e. definitions which do not give the 
 complete connotation of a term), are once admitted, it is 
 obvious that our definitions of the same term may vary 
 indefinitely according to the particular point of view from 
 which we make them, or the science which we happen to 
 be pursuing at the time. 
 
 An exposition of a term which gives no part of its 
 connotation, but in lieu of it an enumeration of pro- 
 perties and accidents, is called a Description. Thus 
 ' Man is a featherless biped 5 ' would be regarded as a 
 description, not as a definition of man. But the term 
 ' description ' is also extended to those cases in which 
 properties and accidents are combined with a portion 
 of the connotation, the latter being usually stated as 
 the genus. Thus we might describe horse as an animal 
 
 5 Here the attributive ' biped,' being used as a quasi-genus (i. e. a 
 property or accident which, for a special purpose, is employed as a 
 genus), is stated in the form of a substantive. This particular 
 example of a description is, of course, absurd, and simply serves the 
 purpose of roughly distinguishing men from birds.
 
 DEFINITIONS. 55 
 
 which is domesticated, which has a mane and a tail, 
 which has a high value attached to it, which is to be 
 found in Arabia and Europe, &c., &c. ; or we may 
 take as an instance of a description Cuvier's definition 
 of man, as a mammiferous animal having two hands. 
 The latter instance is sufficient to shew that a description 
 may often serve the purpose of distinguishing the term 
 described from all other terms, and may therefore be 
 quite adequate to fulfil the purposes of a definition for 
 any special object. 
 
 From what has been said it will be seen that definitions 
 and descriptions may be classified as follows : 
 
 (1) A definition complete and final. 
 
 (2) Complete (so far as we know), but provisional. 
 
 (3) Incomplete, but sufficient to distinguish the term 
 
 defined from all other terms. 
 
 (4) Incomplete, but sufficient to distinguish the term 
 
 defined for the special purpose in hand. 
 
 (5) A description only, but sufficient to distinguish the 
 
 term described from all other terms. 
 
 (6) A description only, but sufficient to distinguish the 
 
 term described for the special purpose in hand. 
 Any pretended definition or description which does not 
 fulfil one of these conditions must be rejected as having 
 no value whatever. In testing a definition or description, 
 we should at once reject it if it were applicable to any 
 other term, unless we were expressly told that it was 
 used only for the purposes of a particular science, and 
 we found on investigation that it was distinguishable
 
 56 DEFINITIONS. 
 
 from all other terms employed in that science. Thus, 
 in a discussion on politics, it would be sufficient to 
 define monarchy as the supreme government of one 
 man, but, if speaking generally, I must add ' in a state,' 
 for one man may be supreme governor in his family, in a 
 school, in a religious association, &c. 
 
 The rules for a legitimate definition must depend on 
 the kind of definition which we purpose or are compelled 
 to employ. The following rules are common to the three 
 first kinds of definition enumerated above : 
 
 1. The definition must be convertible with the term 
 
 defined, i. e. it must apply to every object denoted 
 by the term defined, and to no other objects. 
 
 2. The definition must consist of one common term 
 
 or abstract term employed as a common term 
 (the genus), and of one or more attributives (the 
 differentia or differentiae). 
 
 3. Each of these terms, constituting the definition, 
 
 must connote less than the term defined ; other- 
 wise, they afford no explication of it. 
 
 4. Each of these terms must have a connotation distinct 
 
 from that of the others ; otherwise, the definition 
 will be redundant. 
 
 Note i. It may have occurred to the student to ask 
 ' How are we to distinguish those attributes which form 
 part of the connotation of a term, from the attributes 
 which are inferred from them ? ' This is a question
 
 DEFINITIONS. 57 
 
 which in many individual cases it would be extremely 
 difficult to answer, and there might be great differences 
 of opinion as to what attributes were to be regarded as 
 differentiae, and what as properties. It is in fact the 
 same question as ' What are primary, and what are 
 derived qualities ? ' The only general answer that can 
 be given is that, wherever one attribute or quality can 
 be inferred from another, it is to be regarded as a 
 derived quality or a logical property, and that all those 
 attributes that cannot be so derived are to be regarded 
 provisionally as an assemblage of primary qualities or, 
 in logical language, the connotation of the term. As 
 our knowledge advances, it is of course possible that 
 many of these primary qualities may be resolved into 
 secondary, i. e. many of the supposed differentiae may be 
 resolved into properties. 
 
 Note 2. The scholastic logicians distinguished between 
 real and nominal definitions, meaning by a real definition 
 the explication* of the nature of a thing, by a nominal 
 definition the explication of the meaning of a term. The 
 first would give an answer to such a question as ' What 
 is man ? ' the second to such a question as ' What do we 
 mean by the term man ? ' As the meaning we attach to a 
 term ought exactly to correspond with our knowledge of 
 the primary or underived attributes of the thing, this dis- 
 tinction is now usually regarded as nugatory. Mr. Mill 
 has however revived the expressions ' real ' and ' nominal ' 
 definition to mark a distinction between those definitions 
 which assume or imply the existence of the object defined
 
 58 DEFINITIONS. 
 
 and those which carry with them no such assumption or 
 implication. ' All definitions,' he says, ' are of names and 
 of names only ; but, in some definitions, it is clearly 
 apparent that nothing is intended except to explain the 
 meaning of the word ; while in others, besides explaining 
 the meaning of the word, it is intended to be implied that 
 there exists a thing corresponding to the word.' Thus 
 the definition of a ' horse ' or a ' triangle ' would be called 
 a real definition, that of a ' centaur ' a nominal definition. 
 See Mill's Logic, Bk. I. ch. viii. s. 5. 
 
 Note 3. Sometimes we may explain a term by a 
 synonym, an etymology, or a translation, which may 
 accidentally be better known to the hearer or reader 
 than the term so explained. These explanations cannot 
 be accepted as definitions in our sense of the word, inas- 
 much as they do not analyse the connotation of the 
 term ; but they would have been regarded as instances 
 of nominal definitions by the older logicians.
 
 CHAPTER VIII. 
 
 On Divisions and Classifications. 
 
 A DIVISION is an exposition of the denotation of 
 a term. It may always be represented in the form of 
 a proposition, of which the term divided forms the subject 
 and the exposition the predicate. 
 
 In divisions the denotation of a term is expounded 
 by enumerating, not the individuals (which would in most 
 cases be impossible), but the smaller groups which the 
 term denotes. The terms denoting these smaller groups 
 are called the dividing members (membra dividentia) in 
 contradistinction to the divided term (called by the older 
 logicians the ' divided whole,' Mum divisum), 
 
 It is plain that common terms, or abstract terms which 
 are employed as common terms, are alone capable of 
 being divided. Abstract terms and attributives have, in 
 themselves, no denotation, while singular and collective 
 terms are incapable of being divided into smaller groups. 
 A collective term may however easily be transformed into 
 a common term, and so rendered capable of being divided ; 
 thus ' the fourteenth regiment ' may become ' soldiers of 
 the fourteenth regiment,' and in this form may be divided 
 into officers and privates, or other groups. The same 
 remark holds good of abstract terms and attributives.
 
 60 DIVISIONS AND CLASSIFICATIONS, 
 
 It may be laid down as a test of a logical division that 
 the term divided must be predicable of each dividing 
 member. Thus ' figure ' is predicable alike of triangle, 
 square, &c., ' man/ of white man and black man. In this 
 manner it is distinguished from partition of a physical 
 whole into its parts, as of ' man ' into head, arms, legs, &c., 
 or of the ' world ' into Europe, Asia, Africa, and America. 
 But this test, though sufficient to distinguish a division 
 from a partition, is not sufficient to distinguish it from 
 two other forms of propositions, which nevertheless we 
 must beware of confounding with it. These are an 
 enumeration of individuals, and a distinction of an equi- 
 vocal term according to its various meanings, as e. g. of 
 ' humanity,' according as it means human nature, the 
 human race collectively, the virtue of being humane, or 
 the study of polite letters. In a distinction the same 
 definition is not predicable of each of the terms dis- 
 tinguished, but in a division the same definition is pre- 
 dicable of each dividing member. 
 
 In dividing a term into terms expressive of smaller 
 groups (or, as they are frequently called, subject classes), 
 I invariably try to think of some attribute which is pre- 
 dicable of certain members of the group, but not of 
 others. This attribute suggests what is called the fun- 
 damentum divisionis or principle of division (i. e. some 
 character of the group, which is a source of differ- 
 ences amongst its members). Thus, if asked to divide 
 ' triangles,' it may first occur to me that some triangles 
 have equal sides and others not; in this case the
 
 DIVISIONS AND CLASSIFICATIONS. 6 1 
 
 property of a triangle that the lengths of its sides may 
 be variously related, or, in other words, the relation 
 of the sides, becomes the fundamentum divisionis, and 
 I divide triangles into equilateral, isosceles, and scalene. 
 Or it may first occur to me that some triangles are right- 
 angled, and others not ; in this case the measure of the 
 angles becomes the fundamentum divisionis, and I divide 
 triangles into right-angled, obtuse-angled, and acute- 
 angled. Or, to take one more instance, if asked to divide 
 ' governments,' I may reflect that in some governments the 
 sovereignty is divided, in others it is placed entirely in the 
 hands of one person or order, and I may divide ' govern- 
 ments ' accordingly into pure and mixed, proceeding to 
 divide pure governments, according to the number of 
 persons in whose hands the sovereignty is placed, into 
 monarchies, oligarchies, and democracies. Any division 
 in which two or more fundamenta divisionis are con- 
 founded 1 , or cut across one another, is called a cross- 
 division and is logically inadmissible. Thus a division 
 of triangles into isosceles, scalene, and right-angled, or of 
 governments into monarchies, free governments, and 
 mixed governments, or of men into Frenchmen, Asiatics, 
 the unproductive classes, and barbarians, would be a 
 cross-division. In the last example there is a confusion 
 of no less than four fundamenta divisionis. 
 
 It is maintained by many logicians, and with justice, 
 
 1 Bnt,as in Natural Classifications (see p. 63 below), we may em ploy 
 any number of fundamenta divisionis, provided that their results 
 coincide.
 
 6*2 DIVISIONS AND CLASSIFICATIONS. 
 
 that in every legitimate division (or, at least, in every 
 division which we have sufficient reason for knowing 
 to be legitimate), the process by which the division is 
 arrived at, if strictly analysed, may be described as follows. 
 Taking, for instance, ' triangles,' we reflect, say, that some 
 are equilateral ; we then divide triangles into equilateral 
 and those which are not equilateral, and again, still think- 
 ing of equality of sides, those which are not equilateral 
 into those which have two sides equal (isosceles), and 
 those which have none (scalene). Similarly, taking ' men,' 
 and thinking of race as our fundamentum divisionis, 
 we divide mankind into Aryans and those who are not 
 Aryans, the latter into Semites and those who are not, 
 the latter into Turanians and those who are not, and 
 so on, till our division is complete. This process, when 
 formally drawn out, is called Division by Dichotomy, and 
 the rule by which it proceeds is in each division to take 
 two terms which admit no medium between them. Thus 
 such pairs of terms as productive and unproductive, 
 fallible and infallible, white and not white, would answer 
 the purpose. 
 
 The divided term stands of course to the dividing 
 members as a genus to species. We can also gather 
 the differentia from the fundamentum divisionis. Thus, 
 in dividing a term, we virtually define the subject terms., 
 A pure government, for instance, may be defined as a 
 government in which the sovereignty is undivided, and 
 a mixed government as a government in which the 
 sovereignty is divided. In defining also we virtually
 
 DIVISIONS AND CLASSIFICATIONS. . 63 
 
 divide. Thus the definition of man as a rational animal 
 implies a division of animals into men and brutes, and 
 the definition of a plane triangle as a three-sided recti- 
 lineal figure implies a division of rectilineal figures into 
 three-sided and not three-sided (i. e. quadrilaterals and 
 polygons). 
 
 The rules for a legitimate division may, in accordance 
 with what has already been said, be stated as follows : 
 
 1. Each dividing member must be a common term, or 
 an abstract term which is used as a common term. 
 
 2. The divided term must be predicable of each 
 dividing member. 
 
 3. The division must be exhaustive, i. e. the dividing 
 members, when taken together, must be equal in extent 
 to the term divided. 
 
 4. The dividing members must be mutually exclusive, 
 i. e. no subordinate species must be included under more 
 than one of them ; otherwise we have a cross-division. 
 
 The surest mode of satisfying the last condition is to 
 employ only one fundamentum divisionis, and in artificial 
 classifications this method is adopted, but it is the dis- 
 tinctive characteristic of natural classifications, which 
 alone are adequate to many of the purposes of science, 
 to employ simultaneously a number of principles of divi- 
 sion. (See Inductive Logic, ch. ii. 2 (i), 6th ed. pp. 
 52, &c. In the latter case, therefore, the observation of 
 this rule becomes a most important check on unskilful 
 classification 2 . 
 
 * In order to adapt the rules of Division, as here given, to the
 
 64 DIVISIONS AND CLASSIFICATIONS. 
 
 The student may easily frame for himself examples of 
 illegitimate divisions. If we were absurdly to divide 
 Europeans into Celts, Teutons, Sclaves, Frenchmen, 
 Spaniards, the Emperor of Russia, and the President 
 of the United States of America, we should have an 
 example of all the faults incident to a division. 
 
 In speaking of division by dichotomy I have already 
 introduced the notion of sub-division. For scientific 
 accuracy, and often even for practical purposes, it may 
 be necessary to sub-divide the dividing members, again 
 to sub-divide the results of this division, and so on. 
 The relation of these various divisions and sub-divisions, 
 one to another, has given rise to several logical terms, 
 and is of sufficient importance in itself to require a brief 
 treatment. It is best to commence with an example, 
 and I select a mathematical one, as being of the simplest 
 kind : 
 
 Figure. 
 
 r 
 Curvilinear. 
 
 
 Rectilinear. 
 
 - i 
 
 
 r 
 Triangle. 
 
 Quadrilateral. 
 
 Polygon. 
 
 Equilateral. 
 
 Isosceles. 
 
 Scalene. 
 
 In a series of divisions and sub-divisions like the fore- 
 going, the term at the head of the series (in this case 
 Figure) is called the Summum Genus. The terms at the 
 bottom of the series (equilateral triangles, circles, &c.) 
 
 Natural Classifications of Science as well as to the Artificial Classifi- 
 cations of ordinary life, an important change has been made in the 
 statement of Rule 4 in the later editions of this work.
 
 DIVISIONS AND CLASSIFICATIONS. 65 
 
 are called Infimce Species. The intermediate terms are 
 called Subaltern Genera, or Subaltern Species, viz. sub- 
 altern genera with reference to the terms immediately 
 below them, and subaltern species with reference to the 
 terms immediately above them. Thus triangle would be 
 a subaltern genus with reference to equilateral triangle, 
 a subaltern species with reference to rectilinear figure. 
 Species which fall immediately under the same genus, as 
 e. g. triangle, quadrilateral, and polygon, are sometimes 
 called Cognate Species, but might, perhaps, with greater 
 propriety be called Co-ordinate Species. A Cognate Genus 
 is any one of the ascending genera under which the 
 species falls. Thus plane triangle, rectilinear figure, figure, 
 are all genera cognate to equilateral triangle. A differentia 
 which constitutes, as is said, the species of which we 
 happen to be speaking, that is, which distinguishes it 
 from its co-ordinate species, is called a Specific Difference, 
 one which constitutes any of its cognate genera is called 
 a Generic Difference. Thus 'equilateral' is a specific 
 difference, 'three-sided' a generic difference of an equi- 
 lateral triangle. Or, ' three-sided ' would be regarded as 
 a specific difference, and ' rectilinear ' a generic difference 
 of a triangle. Lastly, a property derived from an attri- 
 bute or attributes connoted by the species of which we 
 happen to be speaking is called a Specific Property ; a 
 property which is derived from any of its cognate genera 
 is called a Generic Property. It is, for instance, a pro- 
 perty of all rectilineal figures that the sum of their angles 
 is equal to twice as many right angles as the figure has 
 * F
 
 66 DIVISIONS AND CLASSIFICATIONS. 
 
 sides, minus four right angles. Thus the angles of a 
 plane triangle are together equal to two right angles, 
 those of a quadrilateral to four, those of a pentagon to six, 
 and so on. It is also a property of a plane triangle that 
 it may be generated by the section of a cone, but this 
 is not a property common to other rectilinear figures. 
 Hence the latter would be called a specific, the former 
 a generic property. 
 
 The instance I have given is one of the simplest that 
 could be selected. If I had taken instead of it, say, 
 the division of animals into vertebrate and invertebrate, 
 of vertebrate animals into fishes, amphibia, reptiles, birds, 
 and mammals, of mammals into the various species of 
 men, horses, oxen, &c., it would have required a long 
 scientific discussion to distinguish the various species and 
 genera, to state the specific and generic differences, and 
 to give instances of specific and generic properties. And 
 yet it is exactly in such a case as this that divisions and 
 sub-divisions (or, in one word, Classifications) are most 
 important. In fact, the sciences of Botany and Zoology 
 (in the vulgar acceptation of these words) consist en- 
 tirely of classifications. To give rules for so important 
 and complicated a process as scientific classification, 
 or even to attempt any precise definition of the word, 
 would be to go beyond the scope of an elementary 
 work like this 3 . It may be sufficient to suggest that 
 where, as in the case of plants and animals, species are 
 
 8 The reader will find a special section on Classification in the 
 Author's ' Elements of Inductive Logic.'
 
 DIVISIONS AND CLASSIFICATIONS. 67 
 
 separated from one another by an indefinite number of 
 attributes, and may be separated by many attributes of 
 which we are still ignorant, our classifications, like our 
 definitions, should always be regarded as provisional. 
 To this I may add two plain rules, which meet with 
 universal acceptance : first, that our classifications should 
 proceed as gradually as possible ; and second, that we 
 should select as our main principles of division attributes 
 the most fruitful in their consequences, i. e. attributes from 
 which the largest number of important properties can be 
 derived 4 . Thus the natural system of Botany, founded, 
 in its main division, on differences in the seed-vessels 
 of plants, is far more instructive than the Linnaean system, 
 founded on differences in the numbers of the pistils and 
 stamens. 
 
 Note. I have employed the expressions 'summum 
 genus ' and ' infima species,' as if they were entirely rela- 
 tive to any particular classification. But in the Isagoge 
 of Porphyry, and by the Scholastic logicians who, for 
 the most part, adopted his account, both summa genera 
 and infimae species, as well as all the subaltern genera and 
 species, were regarded as unalterably fixed by nature. 
 Thus the ten Categories of Aristotle (Substance, Quan- 
 tity, Quality, Relation, &c.) were regarded as the summa 
 genera, and terms like man, horse, &c. were regarded as 
 
 * Such attributes are called by the French physiologists caracterts 
 dominateurs. See Milne Edwards, Cours letnentairc de Zoologie, 
 edition septieme, 367. 
 
 F 2
 
 68 DIVISIONS AND CLASSIFICATIONS. 
 
 expressing infimse species. Classes like 'black men,' 
 ' Arabian horses,' &c. would not have been admitted to 
 be species at all. We, on the contrary, conceive that 
 there is no limit to our power of making classes ; how- 
 ever specialised a group may be, we can almost always 
 think of some attribute, the addition of which will make 
 it more special still.
 
 PART III. OF INFERENCES. 
 
 CHAPTER I. 
 
 On the Varioits Kinds of Inferences. 
 
 THE third and most important part of Logic treats 
 of Inferences *. Wherever we assert a proposition in con- 
 sequence of one or more other propositions, or, in other 
 words, wherever we regard one or more propositions as 
 justifying us in asserting a proposition distinct from any 
 that has preceded, the combination of propositions may 
 be regarded as an inference. Thus defined, infererjces- 
 may be divided into inductive and deductivejjand de r , 
 ductive inferences may be sub-divided into mediate_and 
 immediate. I shall attempt to make these distinctions 
 clear by examples. 
 
 1 The word ' inference ' is employed in no less than three different 
 senses. It is sometimes used to express the conclusion in conjunction 
 with the premiss or premisses from which it is derived, as when we 
 speak of a syllogism or an induction as an inference ; sometimes it is 
 used to express the conclusion alone ; sometimes the process by which 
 the conclusion is derived from the premisses, as when we speak of 
 Induction or Deduction as inferences or inferential processes. Except 
 where the meaning is obvious from the context, I shall endeavour to 
 confine the word to the first named signification. The terms Induc- 
 tion and Deduction will be appropriated to express processes which 
 result, the former in inductions or inductive inferences, the latter in 
 deductions or deductive inferences, these last being subdivided into 
 syllogisms and immediate inferences*
 
 70 VARIOUS KINDS OF INFERENCES. 
 
 I mix tartaric acid and carbonate of soda in certain 
 proportions in water, and I observe that the mixture is 
 followed by an effervescence ; from this I infer that, 
 whenever tartaric acid and carbonate of soda are mixed 
 in water in these proportions, effervescence will follow. 
 I put a poker into the fire, and I observe that after a time 
 it becomes red-hot ; from this I infer that incandescence 
 can always be produced in iron by a certain degree of 
 heat. I observe five points in the orbit of a planet, and, 
 assuming that the orbit is a curve of the second degree, 
 my knowledge of mathematics enables me to say that they 
 are situated in an ellipse : from this I infer that the entire 
 orbit of the planet is elliptical, and that, in all future 
 revolutions of the planet, a similar orbit will be described. 
 Now what in these cases do I mean -by the word ' infer'? 
 That the mixture \& followed \yy effervescence is a matter 
 of observation ; but it is only an inferential process which 
 justifies me in asserting that, inasmuch as it could have 
 been produced by nothing else, the effervescence was 
 produced by the mixture, and that, whenever in future I 
 see a similar mixture, I may expect to see it followed by 
 similar results. Two assumptions, it will be seen, under- 
 lie this inference : ist, that every event has a cause, which 
 leads me to assume that the effervescence must have been 
 produced by some cause or other ; 2nd, the belief in the 
 uniformity of nature, which leads me to expect that, 
 whenever similar circumstances are repeated, they will 
 be followed by similar results. The reasoning therefore 
 in these cases may be represented as follows :
 
 VARIOUS KINDS OF INFERENCES. J I 
 
 The mixture of the tartaric acid with the carbonate 
 of soda is followed by effervescence. (Original 
 Proposition.) 
 
 .'. (Owing to the special circumstances of the case and 
 in accordance with the principle that every event 
 must have a cause), the effervescence was produced 
 by the mixture. 
 
 .'. (In accordance with the principle of the uniformity 
 of nature), a similar mixture will always be fol- 
 lowed by an effervescence. 
 
 We may represent the reasoning in the third example 
 in the same manner : 
 
 We may assert (by virtue of our knowledge of 
 mathematics) that five points which we have ob- 
 served in the orbit of the planet Mars are, on the 
 assumption above stated, situated in the arc of 
 an ellipse. (Original Proposition.) 
 
 .*. As there are, comparatively speaking, no causes de- 
 termining the position of the planet at any given 
 moment, except the attraction of the sun and the 
 continued effects of the initial velocity, we may 
 infer that the fact of the five points observed in 
 the planet's course being all situated in the arc 
 of an ellipse is due to the combination of these 
 two causes. 
 
 .'. (In accordance with the principle of the uniformity
 
 72 VARIOUS KINDS OF INFERENCES. 
 
 of nature), it may be inferred that all other points 
 in the orbit of the planet are situated in an 
 ellipse, and that, in all future revolutions, a similar 
 orbit will be described ; i. e. the orbit of the planet 
 Mars may be regarded as elliptical. 
 Now inferences of this kind are called Inductive. The 
 instances I have selected are remarkably simple, but 
 they are sufficient to shew that an induction may be 
 defined as an inference in which we argue from parti- 
 culars to adjacent particulars, or (if we speak of the 
 adjacent particulars collectively) from particulars to uni- 
 versals, in accordance with the laws of universal causation 
 and of the uniformity of nature. As to the circumstances 
 which justify us in asserting that one phenomenon or set 
 of phenomena is the cause or the effect of, or is invariably 
 conjoined with, another (for this is the problem of Induc- 
 tion), the student is referred to works specially treating of 
 Inductive Inference. It is sufficient here to distinguish 
 inductive from the deductive inferences which it is our 
 more special business to explain 2 . 
 
 2 An Analogy is a form of imperfect induction, and, though justify- 
 ing a conclusion more or less probable, never leads to certainty. If 
 two objects resemble each other in several important respects, and 
 we argue that any particular attribute which we know to be predicable 
 of the one, and do not know to be either predicable or not predicable 
 of the other, is, on account of the general resemblance of the two 
 objects, also predicable of the other, the argument is called an argu- 
 ment from analogy ; and, in the same way, if two objects are dis- 
 similar, we may argue that an attribute which is predicable of the 
 one, is, on account of their dissimilarity, not predicable of the other. 
 Thus, from the similarity between the earth and the moon, we might
 
 VARIOUS KINDS OF INFERENCES. J<$ 
 
 Beginning where induction ended, we may state such 
 a proposition as this : ' All iron when heated to a 
 
 argue that the latter is inhabited, or, from their dissimilarity, that it 
 is not inhabited. The value of the inference always depends on the 
 ratio of the ascertained resemblances to the ascertained differences 
 (it being understood that the resemblances which we take into account 
 are none of them derived, as properties, from each other, and so with 
 the differences), providing that our knowledge of the objects is suf- 
 ficiently large to justify us in drawing any inference at all. For a more 
 detailed analysis of this mode of reasoning, and an estimate of the 
 value to be attached to its conclusions, the student is referred to the 
 author's Elements of Inductive Logic, ch. iv., and to Mr. Mill's Logic, 
 Bk. III. ch. xx., one of the most instructive and important chapters 
 in his work. 
 
 It should be noticed that an analogy, as here described, is not 
 identical with the Analogy of Aristotle, the Aristotelian Analogy 
 being an equality of relations (laorijs A^ew). Thus the expression, 
 
 The intellect : the soul = the sight : the body, 
 
 is an ava\oyia. From this analogy it is argued that anything which 
 may be predicated of the one pair of terms maybe predicated also of 
 the other. Or, to take a non-Aristotelian instance, which will be 
 more intelligible to beginners : 
 
 A colony : the mother-country = & child : a parent. 
 From this analogy it is argued that the reciprocal rights and duties 
 of a colony and the mother-state are the same as those of a child and 
 a parent. In this form of argument, if the relations between the two 
 sets of terms were precisely the same in all respects, the conclusion 
 would be invariably valid ; as it is usually found in practice, how- 
 ever, the relations are the same in some respects, but not in others, 
 and, consequently, the conclusion is valid, when based on those 
 points in which the relations are the same, and invalid, when based 
 on those points in which the relations are not the same. Thus, it 
 might be maintained that, in many respects, the relation of the child 
 to the parent is not the same as that of a colony to the mother- 
 country, and,, hence, that many of the rights and duties which exist
 
 74 VARIOUS KINDS OF INFERENCES. 
 
 certain degree becomes red-hot.' This, if combined with 
 another proposition ' This is a piece of iron,' leads to the 
 conclusion ' This piece of iron, if heated to a certain 
 degree, will become red-hot.' Now it is plain that the con- 
 clusion we have just drawn was arrived at in a different 
 manner from those noticed above. Instead of being the 
 conclusion of a process by which we argue from parti- 
 culars to adjacent particulars or from particulars to 
 universals (i. e. from cases which are within the range of 
 our observation to others which are without), it is simply 
 a combination of two propositions into one, being an 
 obvious inference from what has been previously stated 
 in the premisses. Induction has been not inaptly com- 
 pared to the establishing of a formula, Deduction (for 
 that is the appropriate name of the process which I am 
 now discussing) to the reading it off. Induction leads 
 to truths entirely new, Deduction combines, metho- 
 dizes, and developes those which we have already 
 gained. 
 
 A Syllogism may be called a Mediate Inference, 
 because the two terms of the conclusion are compared 
 in the premisses by means of a third. It is thus 
 opposed to an Immediate Inference, which consists of 
 two propositions only, and in which the inferred propo- 
 sition is derived from a single proposition without the 
 aid of any other term or proposition, expressed or 
 
 in the one case do not exist in the other. A Metaphor is an analogy 
 of this kind compressed into a single word or phrase. 
 The fallacy of False Analogy will be noticed below.
 
 VARIOUS KINDS OF INFERENCES. 75 
 
 implied. Both mediate and immediate inferences may 
 be styled deductive as opposed to inductive. 
 
 This division may easily be shewn to be exhaustive. In 
 any inference, we argue either to something already 
 implied in the premisses 3 or not; if the latter, the 
 inference is inductive, if the former, deductive. If the 
 deductive inference contain only a single premiss, it is 
 immediate ; if it contain two premisses and the conclusion 
 be drawn from these jointly, it is mediate and is called 
 
 * If we state explicitly all the assumptions made in the inductive 
 process, the conclusion is contained in the premisses, and the form of 
 the reasoning becomes deductive ; but it is seldom that we do state 
 our assumptions thus explicitly. The most essential distinction, 
 however, between inductive and deductive reasoning consists not in 
 the form of the inferences, but in the nature of the assumptions on 
 which they rest. Deductive reasoning rests on certain assumptions 
 with regard to language and co-existence (namely, the Law of Con- 
 tradiction, the Lawof Excluded Middle.ar.d theCanons of Syllogism), 
 while inductive reasoning assumes over and besides these laws the 
 truth of the Laws of Universal Causation, of the Uniformity of Nature 
 and, as implied in the latter, of the Conservation of Energy ; or, if 
 it be of the unscientific description which is known as Inductio per 
 Enumerationem Simplicem, it merely assumes, instead of them, the 
 vague and wide principle that the unknown resembles, or will 
 resemble, the known. It hardly needs to be added that all reasoning 
 alike assumes the trustworthiness of present consciousness and of 
 memory. 
 
 Amongst the assumptions or pre-suppositions of reasoning, I 
 have not included the so-called Law of Identity ; as to say that All 
 A is A, or a thing is the same as itself, appears to me to be an 
 utterly unmeaning proposition. Mr. Mill (Examination of Hamilton, 
 ch. 21), in attempting to give a meaning to this maxim, really trans- 
 forms it into a perfectly distinct proposition, namely, that Language 
 may express the same idea in different forms of words.
 
 76 VARIOUS KINDS OF INFERENCES. 
 
 a syllogism. All deductive inferences which apparently 
 contain more premisses than two admit of being analysed 
 into a series of syllogisms. 
 
 Note i. I am here departing from the ordinary scheme 
 of division adopted by logicians. Inferences are generally 
 divided into mediate and immediate, and mediate infer- 
 ences are subdivided into inductive and deductive. As 
 however I regard inductions as more strongly contrasted 
 with both syllogisms and immediate inferences than either 
 of these classes is with the other, it seems preferable to 
 make inductions one of the main members, rather than 
 one of the subordinate members of the division. Nor is 
 there any reason why an immediate inference should not 
 be regarded as deductive. 
 
 It should also be noticed that Sir W. Hamilton would 
 deny the title of inferences to inductions (as they have 
 been here explained), whereas Mr. Mill would deny that 
 either a syllogism or an immediate inference can properly 
 be called an inference. Mr. Mill maintains that all In- 
 ference is 'from the known to the unknown'; Sir W. 
 Hamilton defines Inference as the 'carrying out into 
 the last proposition what was virtually contained in the 
 antecedent judgments.' 
 
 Note 2. The Aristotelian induction, in which the 
 conclusion affirms or denies of a group what was in the 
 premisses affirmed or denied of each member of the 
 group severally, is, according to the above method of 
 treatment, obviously regarded as a deductive inference.
 
 VARIOUS KINDS OF INFERENCES. JJ 
 
 If I predicate some quality of each member of a group, 
 and thence infer that all members of the group possess 
 this quality, the conclusion is plainly contained in the 
 premisses, and the inference is a syllogism. It may be 
 represented in the form 4 
 
 x, y, z are B, 
 
 The individuals (or subordinate species) constituting 
 
 the group A are x, y, z ; 
 .'. The individuals (or subordinate species) constituting 
 
 the group A are B. 
 
 Such an inference is altogether different from what we 
 now understand by an induction. On this subject the 
 student may with advantage read Mr. Mill's chapter on 
 ' Inductions improperly so called.' See Mill's Logic, 
 Bk. III. ch. ii. An account of the Aristotelian induction 
 will be found in Appendix G to Dr. Mansel's edition of 
 Aldrich ; in Sir W. Hamilton's Essay on Logic, and in his 
 Lectures on Logic, Lect. xvii. and Appendix vii. These 
 authors, as already noticed in the case of Sir W. Hamil- 
 ton, regard inductions, in the modern sense of the word, 
 as extra-logical. The advanced student may also consult 
 with advantage Mr. De Morgan's chapter on ' Induction,' 
 Formal Logic, ch. xi. 
 
 * By Aristotle himself the inductive inference is analysed thus : 
 x, y, z are B, 
 
 x, y, z are (i. e. constitute) A ; 
 .-.AisB. 
 
 The minor premiss, when stated in so peculiar a form, of course 
 admits of simple conversion, and thus assumes the form given in the 
 text
 
 :HAPTER n. 
 
 On Immediate Inferences. 
 
 i. AN Immediate Inference may be formally defined 
 as a combination of two propositions of which one is 
 inferred from the other, the proposition inferred being 
 virtually included in the proposition from which it is 
 inferred. Of Immediate Inferences the most important 
 forms are Oppositions, Conversions, Permutations \ 
 
 2. On Oppositions. 
 
 Two propositions are said to be opposed when they 
 have the same subject and predicate, but differ in quan- 
 tity or quality or both. An Opposition may be defined 
 as an immediate inference in which from the truth 
 or falsity of one proposition we infer either the truth 
 or falsity of another, this proposition having the same 
 subject and predicate as the former, but differing in 
 quantity or quality or both. Thus from the propo- 
 sition 'That all X is Y is true' we may infer the pro- 
 position 'That no X is Y is false,' or 'That some X 
 is Y is true,' or ' That some X is not Y is false.' 
 
 1 It is the more common practice to speak of Opposition, Con- 
 version, and Permutation, but I have adopted the plural number in 
 order to draw altention to the fact that Logic is concerned with the 
 results rather than with the processes by which they are arrived at.
 
 OPPOSITIONS. 
 
 79 
 
 The opposition between 
 
 A and E is called a Contrary Opposition. 
 
 I and O, a Subcontrary Opposition. 
 
 A and I, or E and O, a Subaltern Opposition. 
 
 A and O, or E and I, a Contradictory Opposition. 
 
 These forms of Opposition are exhibited in the annexed 
 scheme : 
 
 A 
 
 . . Contrary . . 
 
 
 
 r/i 
 
 * 
 
 
 
 n 
 
 
 
 o- 
 
 $> \*y 
 
 ^* 
 
 3 
 
 A 
 </ %. 
 
 n 
 3 
 
 I 
 
 . Subcontrary . . 
 
 
 
 If A be true ; E is false, I true, O false. 
 
 If A be false ; E is unknown, I unknown, O true. 
 
 If E be true ; A is false, I false, O true. 
 
 If E be false ; A is unknown, I true, O unknown. 
 
 If I be true ; A is unknown, E false, O unknown. 
 
 If I be false ; A is false, E true, O true. 
 
 If O be true ; A is false, E unknown, I unknown. 
 
 If O be false ; A is true, E false, I true. 
 
 "It will be observed that it is only in a Contradictory 
 Opposition (where the opposed terms differ both in 
 quantity and quality) that from the truth or falsity of 
 one proposition we can invariably infer the truth or 
 falsity of another, the conclusion which we draw in this 
 case being from the truth or falsity of the one propo-
 
 8o OPPOSITIONS. 
 
 sition to the falsity or truth respectively of the other. 
 Hence logicians have called contradictory the most per- 
 fect form of opposition. It is a rule of practical Logic 
 that a contradictory should always in disputations be 
 used in preference to a contrary opposition ; for it serves 
 equally well the purpose of contradicting an opponent, 
 and the particular proposition which it asserts affords 
 less ground for attack than an universal. Thus, if my 
 opponent asserts A (as e.g. All philosophers are un- 
 imaginative), I may meet his assertion by the contra- 
 dictory O (Some philosophers, as e. g. Plato, Goethe, &c., 
 are not unimaginative), and from this position I cannot 
 well be dislodged. But suppose I assert in opposition 
 to him an E proposition (No philosophers are unima- 
 ginative), he will probably be able to adduce instances of 
 some philosophers who, according to the ordinary mean- 
 ing of the word ' imaginative,' would be called unimagi- 
 native, and so, by meeting my E with an I proposition, 
 gain an apparent victory. As a fact, we should each have 
 made assertions too wide, but he would have succeeded in 
 dislodging me from my position, whereas (owing to my 
 neglect of the laws of contradiction) I should not have 
 succeeded in dislodging him from his. 
 
 Note. It is plain that, according to the ordinary 
 meaning of the word ' opposition,' it is somewhat of 
 an abuse of language to speak of A and I, or E and 
 O propositions as being opposed. It would be better
 
 CONVERSIONS. 8 1 
 
 if this form of inference were called Subalternation or 
 Subordination. 
 
 Nor, strictly speaking, can the relation between I and 
 O be called one of opposition, for they may both be true 
 together. Accordingly, Aristotle says that in reality (nor' 
 aXrjdfiav) there are three forms of opposition (those be- 
 tween A and E, A and O, E and I), though in language 
 (Kara TTJV \egiv) there are four (adding that between I and 
 O). What is called Subaltern Opposition he does not 
 recognise. 
 
 3. On Conversions. 
 
 A proposition is said to be converted when its terms are 
 transposed, so that the subject becomes the predicate, and 
 the predicate the subject. A Conversion may be denned 
 as an immediate inference in which from one proposition 
 we infer another having the same terms as the original 
 proposition, but their order reversed. This inference in 
 some cases necessitates a change of quantity in passing 
 from one proposition to the other, and then it is called 
 a Conversion per accidens ; when it necessitates no such 
 change, it is called a Simple Conversion*. 
 
 I and E may both be converted simply. Thus, from 
 ' Some X is Y,' or ' Some poets are philosophers,' I may 
 infer ' Some Y is X,' or ' Some philosophers are poets.' 
 From ' No X is Y,' or ' No savages are trustworthy, 
 may infer ' No Y is X,' or ' No trustworthy persons are 
 savages.' 
 
 1 It is proposed by Sir W. Hamilton to call the original proposi- 
 tion the ' Convertend,' the inferred proposition the ' Converse.' 
 
 * G 
 
 ets.' 
 r.'I
 
 8 2 CONVERSIONS. 
 
 A can only be converted per accident. For though it 
 may sometimes happen that the subject and predicate of 
 an A proposition are co-extensive, and therefore convert- 
 ible, this circumstance is not implied in the form of the 
 proposition, and it is with what is implied in the form of 
 the proposition that we are alone concerned. Thus, if I 
 assert the proposition ' All plane triangles are three-sided 
 rectilineal figures,' it happens in this particular case that I 
 am justified, without any change of quantity, in stating 
 the converse, ' All three-sided rectilineal figures are plane 
 triangles.' But if I state that 'All plane triangles are 
 rectilineal figures,' I am only justified in inferring that 
 ' Some rectilineal figures are plane triangles.' As, there- 
 fore, the general form of an A proposition does not 
 imply the simple convertibility of the subject and predi- 
 cate, I am only justified in inferring from ' All X is Y,' 
 that ' Some Y is X.' 
 
 In those cases, however, in which the form of the pro- 
 position implies that the subject and predicate are co- 
 extensive, the proposition, though an A proposition, may 
 be converted simply. Thus, from the propositions ' The 
 second legion is the only legion quartered in Britain,' 
 ' Virtue is the condition of Happiness,' ' All plane tri- 
 angles may be defined as three-sided rectilineal figures,' 
 it may be inferred by simple conversion that ' The only 
 legion quartered in Britain is the second legion,' ' The 
 condition of Happiness is Virtue,' ' All three-sided recti- 
 lineal figures may be called plane triangles.' 
 
 An O proposition cannot be converted at all. From
 
 PERMUTA TIONS. 8 3 
 
 ; Some X is not Y,' it does not follow that ' Some Y is 
 not X.' for Y may stand to X in the relation of a species 
 to a genus. Thus from the proposition ' Some Euro- 
 peans are not Frenchmen,' I cannot infer that 'Some 
 Frenchmen are not Europeans.' 
 
 4. On Permutations 3 . 
 
 A Permutation may be defined as an immediate Infer- 
 ence in which from one proposition we infer another 
 differing jn quality, and having, therefore, instead of the 
 original predicate its contradictory. Thus : 
 
 From All X is Y, we may infer that No X is not-Y. 
 
 From No X is Y, All X is not-Y. 
 
 From Some X is Y, Some X is not not-Y. 
 
 From Some X is not Y, . . . Some X is not-Y. 
 
 The legitimacy of these inferences is apparent from the 
 fact that contradictory terms (A and not- A) admit of no 
 medium, so that, if I predicate the one affirmatively, I may 
 always predicate the other negatively, and vice versa. 
 
 The O proposition, when permuted from ' Some X is 
 not Y,' into ' Some X is not-Y,' may of course be con- 
 verted into 'Some not-Y is X.' This combination of 
 permutation and conversion is improperly described by 
 Whately and many previous logicians as a single inference, 
 and styled ' Conversion by Centra-Position or Negation.' 
 
 3 The term Permutation is borrowed from Mr. Karslakc's Aids to 
 Logic. The same inference is sometimes called Infinitation, from the 
 Nomen Infmitum, or, more properly, Nomen Indennitum (not-Y, as 
 the contradictory of Y), which is employed as the predicate. 
 
 G 2
 
 84 PERMUTATIONS. 
 
 It may assist the student if I add some further in- 
 stances of permutations : 
 
 All men are fallible, .*. No men are infallible. 
 No men are infallible, .'. All men are fallible. 
 Some poets are reflective, .'. Some poets are not 
 
 unreflective. 
 Some poets are not unreflective, .'. Some poets are 
 
 reflective. 
 All poets are men of genius, .'. (by permutation) No 
 
 poets are not-men-of-genius ; /. (by conversion) 
 
 No not-men-of-genius (=None but men of-genius) 
 
 are poets. 
 
 Note. I have here employed an expression 'Con- 
 tradictory Terms,' which in most works on Logic is 
 explained in the first part, as included under the doctrine 
 of Opposition of Terms. It seemed, however, desirable 
 to introduce there only those distinctions of terms which 
 were likely to be frequently required in the sequel of 
 the work. I may here state that ' Contradictory Terms,' 
 such as white and not-white, lawful and un-lawful, are 
 terms which admit of no medium, i. e. terms which are 
 not both predicable of the same thing, while one or other 
 of them must be predicable of it. ' Contrary Terms,' like 
 good and bad, black and white, are terms which are the 
 most opposed under the same genus ; they cannot both 
 be predicated of the same thing, but it is not necessary 
 that one or other of th6m should be predicable of it.
 
 CHAPTER III. 
 On Mediate Inference or Syllogism. 
 
 i. The Structure of the Syllogism. 
 
 A SYLLOGISM may be defined as a combination of 
 
 two propositions, necessitating a third in virtue of their 
 mutual connexion ; or as an inference in which one 
 proposition is inferred from two others conjointly, the 
 inferred proposition being virtually contained in the pro- 
 positions from which it is inferred. This is obviously a 
 definition of a legitimate syllogism. There may (as will 
 appear below) be apparent syllogisms, which do not 
 fulfil the conditions of this definition. We may take as 
 instances of syllogisms : 
 
 (1) All B is A, 
 All C is B ; 
 
 .-. All C is A. 
 
 (2) All sovereign powers are invested with supreme 
 
 authority over their subjects, 
 All republics are sovereign powers ; 
 /. All republics are invested with supreme authority 
 over their subjects. 
 
 (3) No rectilinear figure is bounded by one line, 
 A circle is bounded by one line ; 
 
 .'. A circle is not a rectilinear figure.
 
 86 MEDIATE INFERENCE OR SYLLOGISM. 
 
 The proposition inferred is called the Conclusion, the pro- 
 positions from which it is inferred the Premisses, either 
 of them singly being called a Premiss, 
 
 As the conclusion is virtually contained in the pre- 
 misses conjointly, it is plain that the two terms of the 
 conclusion must occur in the premisses, one in either. 
 If both terms occurred in the same premiss, the other 
 premiss would be entirely alien to the conclusion. The 
 remaining term of each premiss must be the same ; else 
 there would be nothing in common between the two 
 premisses, and the conclusion could not be said to be 
 inferred from the two conjointly. This third term, with 
 which the two terms of the conclusion may be regarded 
 as compared, is called the middle term. The predicate 
 of the conclusion is called the major term, and the subject 
 the minor term; the premiss, in which the major and 
 middle terms are compared, is called the major premiss, 
 and should always be stated first ; that in which the minor 
 and middle terms are compared is called the minor premiss. 
 Thus in a syllogism, formally stated, there are always 
 three propositions including three terms, the premisses 
 occurring first and the conclusion last. But practically, 
 in reasoning, we frequently state the conclusion first, 
 introducing one or both premisses with such a word as 
 ' for ' or ' because,' as stating our reason for the assertion. 
 Thus I may say ' I will not go out to-day, for it is raining,' 
 or, ' I will not go out to-day, for it is raining, and the 
 rain may give me a cold.' When stated in this form, the 
 conclusion is called by the older logicians the Problema
 
 STRUCTURE OF THE SYLLOGISM. 87 
 
 or Qucestio, being regarded as a question to which the 
 reason or reasons assigned furnish the answer. It will also 
 have occurred to the student that, as a fact, we usually 
 state only one premiss, leaving the other (which may 
 be either the major or minor) to be understood. Thus, 
 instead of stating Syllogism (2) formally, as above, I 
 should in an actual discussion say, ' A republic is invested 
 with supreme authority over its subjects, for every so- 
 vereign power is invested with such authority,' or, ' A 
 republic is, &c., for it is a sovereign power,' or briefly, 
 ' A republic (being a sovereign power) is invested,' &c. ; 
 or, the premiss coming first, ' Inasmuch as every so- 
 vereign power is invested, &c., I maintain a republic to be 
 invested with that authority,' or, ' Inasmuch as a republic 
 is a sovereign power, it is invested with,' &C. 1 Instead 
 of suppressing one of the premisses, I may, for brevity's 
 sake, suppress the conclusion. Thus I may say ' Every 
 sovereign power is invested with supreme authority over 
 its subjects, and a republic is a sovereign power,' leaving 
 it to the hearer or reader to draw the conclusion for him- 
 self. The syllogism does not pretend to be the form, or 
 even a form, in which our reasonings are usually stated, 
 but simply one of the ultimate analyses of them. 
 
 As every term in the syllogism occurs twice, it should 
 be noticed that, on both occasions, it should be used in 
 the same sense, or, to adopt technical language, every 
 
 1 A syllogism with a suppressed premiss is by Aldrich wrongly 
 identified with the Enthymeme of Aristotle. Such a syllogism was 
 called by the Stoics a av
 
 88 MEDIATE INFERENCE OR SYLLOGISM. 
 
 term in the syllogism should be used univocally. If we 
 use a term equivocally, i. e. in two entirely different senses, 
 or even analogously, i. e. in two different senses having 
 some relation to each other, it is plain that, logically 
 speaking, we are using two different terms, and con- 
 sequently the syllogism will include four terms instead 
 of three. This caution includes the rule usually given by 
 logicians against an ambiguous middle. The neglect of it, 
 palpable as it might be supposed to be, is often, espe- 
 cially in a long course of reasoning, very difficult of 
 detection, and is a fertile source of fallacy. I may adduce 
 as very simple instances : 
 
 Humanity is a moral virtue, 
 The study of polite letters is humanity ; 
 .'. The study of polite letters is a moral virtue. 
 
 The church is the aggregate of all Christian people, 
 This particular congregation (or particular building) 
 is the church (meaning at some particular place) ; 
 .'. This particular congregation (or particular building) 
 
 is the aggregate of all Christian people. 
 In the former case, the term ' humanity ' has come to be 
 used in such widely different senses, that it may be re- 
 garded as used equivocally ; in the latter case, the senses 
 of the word ' church ' are perhaps sufficiently nearly allied 
 to be regarded as analogous. All cases of what are 
 termed ' Verbal Fallacies ' may be referred to this head. 
 
 Note. The words ' major,' ' minor,' and ' middle,' as 
 applied to the terms in a syllogism, have been inherited
 
 STRUCTURE OF THE SYLLOGISM. 89 
 
 by all subsequent logicians from the nomenclature of 
 Aristotle. He regarded what we shall presently call the 
 First Figure (B is or is not A, C is B, .*. C is or is 
 not A) as the perfect type of syllogism, and, amongst 
 other modes, stated it in the form C is in B (TO r eWtV eV 
 oXw TW B), B is or is not in A, /. C is or is not in A. 
 Thus stated, C appears to be the smallest, B the inter- 
 mediate, and A the largest term in extent. See Prior 
 Analytics, Bk. I. ch. iv. In negative propositions, however, 
 we have no means of determining the relative extent of 
 the subject and predicate, and consequently Aristotle's 
 nomenclature does not properly apply to negative syl- 
 logisms. To affirmative syllogisms in the first figure, 
 whether universal or particular, it applies only in a 
 modified shape, for the propositions All X is Y, Some 
 X is Y, though they imply that Y cannot be less in 
 logical extent than All X in the one case or than Some X 
 in the other, do not exclude the possibility of the subject 
 and predicate being co-extensive. Hence, however con- 
 venient it may be, Aristotle's nomenclature applies only, 
 and that not with strict accuracy, to two forms of syllo- 
 gism (Barbara and Darii) in the first figure. 
 
 2. On Moods and Figures. 
 
 I now proceed to consider the possible, not the 
 legitimate, forms of syllogism. Here there are two cir- 
 cumstances to be taken into consideration : ist, that 
 syllogisms may vary according to the quantity and quality
 
 90 MEDIATE INFERENCE OR SYLLOGISM. 
 
 of the propositions (A, E, I, O) of which they are com- 
 posed ; 2nd, that they may vary according to the position 
 of the terms in the premisses. The first consideration 
 gives us the number of possible moods, the second the 
 number of possible figures. It is by combining these 
 two sources of variation that we shall obtain the number 
 of possible syllogisms. 
 
 There are, if we take into consideration the conclu- 
 sion, sixty-four possible arrangements of the propositions 
 A, E, I, O, i.e. in technical language, sixty-four possible 
 moods, viz. AAA, AAE, AAI, AAO, &c. But if we con- 
 sider the premisses only, the number of possible moods 
 is limited to sixteen, viz. AA, AE, AI, AO, EA, EE, 
 El, EO, IA, IE, II, IO, OA, OE, OI, OO. In deter- 
 mining what possible moods are legitimate, we may either 
 ask ' Is this conclusion justified by these premisses ? ' 
 or ' To what conclusion do these premisses lead ? ' If we 
 ask the former question, we must examine the sixty-four 
 possible moods in which the conclusion appears as well 
 as the premisses ; if the latter, an examination of the six- 
 teen possible arrangements of premisses is sufficient. 
 
 With respect to the possible arrangements of the terms 
 in the premisses (i. e. the figures, as they are technically 
 called) there are also two methods of proceeding. Taking 
 no account of the conclusion (and therefore not knowing 
 which is the major term and which the minor), and 
 asking simply ' In how many ways can the middle term 
 be combined with the other terms in the premisses ? ' 
 there are three possible figures ; viz. ist, that in which the
 
 MOODS AND FIGURES. 91 
 
 middle term is subject in one premiss and predicate in 
 the other ; 2nd, that in which it is predicate in both pre- 
 misses ; 3rd, that in which it is subject in both. But if we 
 take account of the conclusion, we are able to distinguish 
 the major and minor terms, and consequently the major 
 and minor premisses. In this case, there are four possible 
 figures, viz. ist, that in which the middle term is subject 
 in the major premiss and predicate in the minor ; 2nd, 
 that in which it is predicate in both premisses ; 3rd, that 
 in which it is subject in both ; 4th, that in which it is 
 predicate in the major premiss and subject in the minor. 
 These four figures may be exhibited thus : 
 
 Fig. i. Fig. 2. Fig. 3. Fig. 4. 
 
 BA AB BA AB 
 
 CB CB BC BC 
 
 .-.CA .-.CA .-.CA .-.CA. 
 
 If we take no account of the conclusion, either extreme 
 in the premisses may become the major term, and the 
 three figures may be represented thus : 
 
 Fig. i. Fig. 2. Fig. 3. 
 
 BA AB BA 
 
 CB CB BC 
 
 ..CAorAC .-. CAorAC .'. CA or AC. 
 
 3. Determination of the Legitimate Moods of Syllogism. 
 
 Note. Few difficulties in elementary Logic are more 
 likely to embarrass the beginner than the variety of 
 methods of constituting the Legitimate Moods of Syllo- 
 gism. Sir W. Hamilton, as a consequence of quantifying
 
 92 MEDIATE INFERENCE OR SYLLOGISM. 
 
 the predicate, is able to represent all syllogisms as equa- 
 tions, and thus to exhibit every affirmative syllogism as 
 a direct application of what is called the Law of Identity 
 (Every A is A), and every Negative Syllogism as a direct 
 application of the Law of Contradiction (No A is not-A) 2 . 
 Besides Sir W. Hamilton, other ' logicians who do not, 
 like him, quantify the predicate, have also attempted 
 to enunciate general principles equally applicable to 
 all syllogisms. See e. g. Port Royal Logic, Part III. 
 ch. x. Others (as Abp. Thomson, Laws of Thought, 
 96, and Lambert, as quoted by Dr. Mansel in his 
 Notes on Aldrich, ch. iii. 6) enunciate a distinct 
 principle for each figure. Others (and pre-eminently 
 Aristotle) enunciate a canon for the first figure 5 , and test 
 
 a These two Laws (or Principles) together with the Law or Principle 
 of Excluded Middle (A either is or is not B) and the Law or Principle 
 of Sufficient Reason (Infer nothing without a ground or reason), are 
 often called the Fundamental Laws of Thought. See Thomson's 
 Laws of Thought, 114, and Hamilton's Lectures on Logic, Lects. vi. 
 and vii. See also p. 75, note 3, above. 
 
 3 Afyo/**!/ Si TO Hard, iravTOs KaryyopeTaOai, orav fjirjStv TJ \a0ttv 
 TOJV TOV viroK(ifj.tvov, KaO' ov OaTtpov ov \fxOri<r(Tai' KO.I TO Kara 
 fiijSfvos waavToos, An. Pr. I. I ; oaa KarcL TOV Ka.Trjyopovfi.evov \tytTcu 
 iravTa Kal KdTci TOV viroKfifj.tvov faOfiatTcu, Cat. 3. This principle or 
 canon in its Latin form was called by the Schoolmen the Dictum de 
 Omni et Nullo, It is thus stated by Sanderson : ' Dictum de Omni 
 est hujusmodi : Quidquid affirmatur Universaliter de aliquo Subjecto, 
 affirmari necesse est de iis quse sub eo continentur. Dictum de Nullo 
 hujusmodi : Quidquid negatur Universaliter de aliquo Subjecto, 
 negari necesse est de iis quse sub eo continentur.' By Aldrich it is 
 stated in a more compressed form, as follows : ' Quod prsedicatur 
 Universaliter de alio (i. e. de .termino distribute), sive affirmative, 
 sive negative, prsedicatur similiter de omnibus sub eo contentis.'
 
 LEGITIMATE MOODS OF SYLLOGISM. 93 
 
 the validity of syllogisms in all other figures by reducing 
 them to the first. Lastly, a favourite method amongst 
 logicians is to enumerate the faults which are incident 
 to a syllogism, and then reject those moods in which 
 they are found. This method is often combined with 
 one or more of the others. Aldrich, for instance, enun- 
 ciates general canons of syllogism, then uses the method 
 I have last explained, and finally reduces syllogisms in 
 the other figures to their corresponding forms in the first. 
 
 In Accordance with the ordinary practice of elementary 
 treatises, and as being perhaps at first more intelligible 
 to the learner, I shall take into consideration the con- 
 clusion, and consequently regard the number of figures as 
 four, and that of possible moods as sixty-four, reserving for 
 a note the shorter and more scientific procedure. The pro- 
 blem therefore now before us is to determine which of the 
 sixty-four moods are admissible in each of the four figures. 
 
 In the first figure our task is easy. There we are able 
 to establish a canon which will determine directly the 
 legitimate moods. 
 
 With a little attention the student will be able to per- 
 ceive the truth of the following propositions : 
 
 (a) If one term be affirmed of another (provided the 
 
 ^ j - ' ' ^ ^^^B 
 
 latter be taken in its entire extent), and this term 
 of a third, the first may be affirmed of the 
 third. 
 
 (|3) If one term be denied of another (provided the 
 
 -\
 
 94 MEDIATE INFERENCE OR SYLLOGISM. 
 
 latter be taken in its entire extent), and this term 
 affirmed of a third, the first may be denied of 
 the third. 
 
 (y) If one term be affirmed of another (even though 
 the latter be taken in its entire extent), and this 
 . term denied of a third, we are not justified in 
 drawing any conclusion as to the relation of the 
 first to the third. For, if one term be denied of 
 another, it does not follow that whatever may 
 be predicated of this first term may also be 
 denied of the other : thus I may deny ' red ' of 
 ' blue,' but it does not follow that ' colour,' which 
 I predicate of ' red,' may also be denied of ' blue.' 
 
 (8) If one term be denied of another (even though 
 the latter be taken in its entire extent), and this 
 term denied of a third, no conclusion can be 
 drawn as to the relation of the first to the third. 
 For, because I deny one term of another, it does 
 not follow that whatever I can deny of the 
 first can also be denied of the other, nor does 
 it follow that it can be affirmed of it : thus, be- 
 cause I can deny ' white ' of crows, and ' black ' 
 of ' white ' (or rather of the corresponding com- 
 mon term ' white things '), it does not follow 
 that I can deny ' black ' of crows ; nor, because 
 I can deny ' white ' of crows as well as ' yellow ' 
 of ' white ' (or ' white things '), does it follow that 
 I can affirm ' yellow ' of crows. 
 
 Putting together these results, we obtain the following
 
 LEGITIMATE MOODS OF SYLLOGISM. 95 
 
 canon of reasoning in the first figure : If one term can be 
 affirmed or denied of another (provided that the latter be 
 taken in its entire extent), and this term affirmed of a third, 
 the first can be affirmed or denied (respectively) of the 
 third ; and, if these conditions are not fulfilled, no con- 
 clusion can be drawn 4 . The only moods which fulfil the 
 conditions of the canon are AAA, EAE, All, and EIO. 
 The conclusions of two other moods, namely, AAI and 
 EAO, might be inferred, by Subaltern Opposition, from 
 those of AAA and EAE, and hence these are called 
 Subaltern Moods. 
 
 We have obtained, it will be observed, forms of syl- 
 logism capable of proving any one of the four propo- 
 sitions, A, E, I, or O, and into one or other of the types 
 accepted as legitimate moods of the first figure all our 
 mediate reasonings may be thrown. Here, then, our 
 enquiry might terminate, if it were simply our object to 
 obtain a sufficient number of legitimate types of reason- 
 ing, but the problem before us is to state exhaustively all 
 possible forms which can be accepted as legitimate. 
 
 There being no canon which distinguishes with equal 
 precision the legitimate and illegitimate moods of the 
 other figures, we must, in discussing them, have recourse 
 to some other method. I shall first enumerate and ex- 
 plain certain syllogistic rules (derived from the definition 
 
 * It will be plain from the statement of the Canon that the major 
 premiss of a syllogism in the first figure must be universal. At the 
 suggestion of Mr. St. G. Stock of Pembroke College, this fact has 
 been made plainer in the statement of the Canon itself than was the 
 case in the earlier editions.
 
 96 MEDIATE INFERENCE OR SYLLOGISM. 
 
 of a syllogism) which will exclude illegitimate moods, 
 and then, before accepting the remainder, I shall test 
 them by reducing them to the first figure. 
 
 Syllogistic Riiles. 
 
 y 
 
 I. The middle term must be distributed at least once. For, 
 if in both premisses it were used in only a partial signifi- 
 cation, it might denote entirely different objects in the 
 one premiss from those which it denoted in the other, 
 and so there might be no connexion between the two 
 premisses. Thus, in the premisses ' All men are animals,' 
 ' All horses are animals,' the part of the group ' animals ' 
 which is coincident with 'men' may be, and here is, 
 entirely distinct from that portion of the group which 
 is coincident with ' horses,' and consequently we can 
 draw no conclusion as to the relation between men and 
 lorses. This fallacy is called Undistributed Middle. 
 
 II. If a term be distributed in the conclusion, it must have 
 ^been previously distributed in the premisses. The reason is 
 
 obvious. If we use a term in a partial signification in 
 the premisses, we cannot legitimately use it in its entire 
 signification in the conclusion. To do so would be to 
 argue from part to whole, or, in other words, to employ 
 a term in a wider signification in the conclusion than 
 that in which it is employed in the premisses. 
 
 This fallacy is called illicit process of the major or minor, 
 according as the term illegitimately distributed in the con- 
 clusion is the major or minor term. In the syllogism,
 
 SYLLOGISTIC RULES. 97 
 
 Some A is not B, 
 All B is C, 
 . . Some C is not A, 
 
 we have illicit process of the major ; in the syllogism, 
 All B is A, 
 Some C is B, 
 . . All C is A, 
 illicit process of the minor. 
 
 III. Two negative premisses prove nothing. For they 
 simply assert that there is no connexion between the 
 middle term and the extremes; consequently we can 
 draw no conclusion with respect to the relation of the 
 extremes. 
 
 IV. If either of the premisses be negative, the conclusion 
 must be negative. For the other premiss is affirmative, 
 and, if in one premiss we affirm a connexion between 
 the middle term and one of the extremes, and in the 
 other premiss deny any connexion between the middle 
 term and the other extreme, there can be no connexion 
 between the two extremes. 
 
 V. If the conclusion be negative, one of the premisses must 
 be negative. For we cannot deny that there is any con- 
 nexion between the extremes, except we have previously 
 denied that there is any connexion between one of the 
 extremes and the middle term. 
 
 VI. ' Two particular premisses prove nothing. For they 
 cannot be both negative (O, O). Nor can they be both 
 affirmative (I, I), for then the middle term would be undis-
 
 98 MEDIATE INFERENCE OR SYLLOGISM. 
 
 tributed. The only remaining case is that of one affirma- 
 tive and one negative premiss (I, O). But this combina- 
 tion of premisses would leave no term to be distributed in 
 the conclusion. Hence the conclusion would be an I pro- 
 position, an affirmative conclusion inferred from a negative 
 premiss, which (according to Rule IV) is illegitimate. 
 
 VII. If one premiss be particular, the conclusion must be 
 particular. 
 
 The premisses must be either both affirmative, or one 
 affirmative and one negative (see Rule III). 
 
 Now, if they are both affirmative, they will (by Rule VI) 
 be A and I. This combination of premisses, as it contains 
 only one distributed term, and the middle term must be 
 distributed at least once (Rule I), leaves no term to be 
 distributed in the conclusion : consequently the conclusion 
 must be I. 
 
 If the premisses are one affirmative and one negative, 
 they must (by Rule VI) be either O and A or I and E. In 
 either case the premisses distribute only two terms, and, 
 as one of them must be the middle term (by Rule I), there 
 remains only one term to be distributed in the conclusion. 
 But the conclusion must be negative (by Rule IV). There- 
 fore, it must be O 5 . 
 
 The converse of this Rule, viz. that a particular con- 
 clusion necessitates a particular premiss, is not true. 
 The only cases however in which we find a particular 
 
 s This proof is substituted for the somewhat more elaborate proof 
 given in the earlier editions.
 
 SYLLOGISTIC RULES. 99 
 
 conclusion without a particular premiss are those in 
 which the premisses assume more than is required in 
 order to prove the conclusion. This fact will be apparent 
 to the student from an examination of the individual 
 cases, and it might be laid down as a rule that, wherever 
 there is a particular conclusion without a particular pre- 
 miss, something superfluous is invariably assumed in the 
 premisses 6 . 
 
 Of the above Rules, it is plain that Rules III, IV, V, 
 VI, VII are applicable to the moods before they are re- 
 ferred to the several figures, Rules I and II are applicable 
 only when the moods are referred to some particular 
 figure. 
 
 By the application of the first set of Rules, the sixty- 
 four possible moods are reduced to twelve, viz. 
 AAA, AAI, AEE, AEO, All, AGO, 
 EAE, EAO, EIO, IAI, IEO 7 , OAO. 
 Thus EEE is rejected because it has two negative pre- 
 misses, EAA because it has a negative premiss without 
 a negative conclusion, AAE because it has a negative 
 
 * The syllogistic rules are comprised in the mnemonic lines : 
 Distribuas medium; nee quartus terminus adsit. 
 Utraque nee prsemissa negans, nee particularis. 
 Sectetur partem conclusio deteriorem. 
 Et non distribuat, nisi cum prsemissa, negetve. 
 7 It has been suggested to me by Professor Park that IEO might 
 be rejected by the application of Rule II, even before it is referred to 
 any particular figure. For the conclusion, O, distributes its predicate, 
 that is the major term of the syllogism. But the major premiss, 
 being I, evidently does not distribute this term. Consequently, there 
 is invariably Illicit Process of the Major. 
 H 2
 
 100 MEDIATE INFERENCE OR SYLLOGISM. 
 
 conclusion without a negative premiss, III because it has 
 two particular premisses, IAA because it has a particular 
 premiss without a particular conclusion. 
 
 By the application of Rules I and II to these twelve 
 moods, when referred to the several figures, there 
 remain : 
 
 in fig. 2, EAE, AEE, EIO, AGO, EAO, AEO; 
 in fig. 3, AAI, EAO, IAI, OAO, All, EIO; 
 in fig. 4, AAI, AEE, IAI, EAO, EIO, AEO. 
 I append a few examples of the method of testing the 
 moods, when referred to the figures. 
 
 Take AEE in figure 2. 
 
 A All A is B, 
 
 E No C is B ; 
 
 E . . No C is A. No fault. 
 
 Take IEO in figure 3. 
 
 I Some B is A, 
 
 E No B is C ; 
 
 . * . Some C is not A. 
 
 Illicit process of major. 
 
 Take All in figure 4. 
 
 A All A is B, 
 
 1 Some B is C ; 
 
 I . ' . Some C is A. Undistributed middle. 
 
 It will be seen that of the sixty-four moods, when re- 
 ferred to the four figures, there are only six in each which 
 have not been rejected. It now remains further to test
 
 REDUCTION. 1 01 
 
 these moods in the second, third, and fourth figures by 
 reducing them to moods in the first. . //^*"*7 
 
 M Reduction. 
 
 As we have adopted no canon for the second, third, and 
 fourth figures, we have as yet no positive proof that the six 
 moods remaining in each of those figures are valid ; we 
 merely know that they do not offend against any of the 
 syllogistic rules. But, if we can reduce them, i. e. bring 
 them back to the first figure, by shewing that they are 
 only different statements of its moods, or, in other words, 
 that precisely the same conclusions can be obtained from 
 equivalent premisses in the first figure, their validity will 
 be proved beyond question. There are two methods of 
 performing this operation : ist, that called Ostensive Re- 
 duction, which consists in employing one or more of 
 the processes of conversion, permutation, and trans- 
 'position of premisses ; 2nd, that called Reductio per im- 
 possibile, which consists in shewing, by means of the* first 
 figure and the laws of opposition, that the contradictory 
 of the conclusion is false, and therefore the conclusion 
 itself true. Either of these methods is applicable to all 
 the eighteen moods, and the result is that all are proved 
 to be valid. I shall give instances of the application of 
 each method. 
 
 By ostensive reduction I shall test EAO in the 
 fourth, IAI in the third, AEE and AGO in the second 
 figures.
 
 102 MEDIATE INFERENCE OR SYLLOGISM. 
 
 Fig. 4. Fig. i. 
 
 E' No A is B. . . No B is A. (Simple Conversion.) 
 
 A All B is C. . ' . Some C is B. (Conversion per ace.) 
 O . ' . Some C is not A. Some C is not A. 
 
 Fig. 3. Fig. i. 
 
 I Some B is A. ~^^- All B is C. 
 
 A All B is C. '-^ >< ^- . . Some A is B. (Simple Conversion.) 
 I . . Some C is A. Some A is C. 
 
 . . Some C is A. (Simple Conversion.) 
 
 Fig. 2. Fig. i. 
 
 A All A is B. -^ . . No B is C. (Simple Conversion.) 
 E No C is B. ^-" All A is B. 
 
 E . . No C is A. No A is C. 
 
 . . No C is A. (Simple Conversion.) 
 
 Fig. 2. Fig. i. 
 
 A All A is B. . . No A is not-B. (Permutation.) 
 
 . . No not-B is A. (Simple Con version.) 
 
 O Some C is not B. . . Some C is not-B. (Permutation.) 
 
 O . .Some C is not A. Some C is not A. 
 
 The mark x shews that the premisses are transposed ; 
 the sign . . on the right-hand side of the page is here 
 appropriated to express the employment of conversion or 
 permutation. The last example is interesting, because 
 AOO in fig. 2, and OAO in fig. 3, inasmuch as they 
 contain O premisses, cannot be reduced by the ordinary 
 methods of transposition ' of premisses and conversion. 
 Hence the older logicians (who, with few exceptions, did 
 not recognise permutation) applied to them the tedious 
 method of reductio per impossibile (or, if we write it in full, 
 veductio per deductionem ad impossibile). This method is 
 equally applicable to all the imperfect moods, as the moods 
 of the three last figures are often called. I now proceed
 
 is C. > Syll. II. 
 
 REDUCTION. 103 
 
 to give an example of it, and shall select AAI in the 
 third figure. 
 
 A All B is A, 
 
 A All B is C ; 
 
 I . . Some C is A. 
 
 This conclusion must be true : for, if not, suppose 
 it to be false ; 
 
 Then its contradictory must be true, i. e. 
 No C is A. 
 
 But (from the premisses) All B 
 . ' . (By figure i) No B is A. 
 
 But (from the premisses) All B is A. 
 
 Now these two (being contrary propositions) cannot 
 
 both be true. 
 
 But the proposition All B is A is assumed to be true. 
 . ' . The proposition No B is A must be false. 
 
 Hence, either the reasoning of Syll. II. is faulty, or 
 
 one of the premisses is untrue. 
 But the reasoning (being in the first figure) must be 
 
 valid. 
 
 . . One of the premisses is false. 
 
 Now the premiss ' All B is C,' being one of the pre- 
 misses of the original syllogism, is assumed to be 
 true. 
 
 . ' . The other premiss (No C is A) must be false. 
 . ' . Its contradictory (Some C is A) is true. 
 
 Q. E. D.
 
 104 MEDIATE INFERENCE OR SYLLOGISM. 
 
 As the positive test of reduction confirms in every case 
 the negative test of the syllogistic rules, it follows that six 
 moods (though not the same six moods) are valid in each 
 figure. These moods may be remembered by means of 
 the mnemonic lines : 
 
 Barbara, Celarent, Darti, Ferioque, prioris : 
 Cesare, Camestres, Festino, Baroko, secundas : 
 Tertia, Darapti, Disamis, Datisi, Felapton, 
 Bokardo, Ferison, habet : Quarta insuper addit 
 Bramantip, Camenes, Dimaris, Fesapo, Fresison : 
 Quinque Subalterni totidem Generalibus orti, 
 Nomen habent nullum, nee, si bene colligis, usum. 
 
 In the above lines, the initial consonants, B, C, D, F, 
 shew that the mood in the second, third, or fourth figure 
 to which they are prefixed is to be reduced to the mood 
 correspondingly marked in the first. Thus Disamis, when 
 reduced, will become Darii. The vowels shew the 
 moods ; thus Disamis represents IAI in the third figure. 
 The letter s, when it occurs after a vowel, shews that the 
 proposition for which that vowel stands is to be converted 
 simply, the letter/ that it is to be converted per accident 8 . 
 
 * It should be noticed that when these letters follow the conclusion, 
 as is the case in Camestres, Disamis, Bramantip, Camenes, Dimaris. 
 they apply not to the conclusion of the mood given for reduction 
 but to the conclusion of the equivalent mood in the first figure, to 
 which such mood is to be reduced. Thus, in reducing Bramantip, 
 the student will find that the / affects not the I conclusion of 
 Bramantip, but the A conclusion of the corresponding syllogism in 
 Barbara. See, for other instances, p. 102.
 
 REDUCTION. 105 
 
 The letter m shews that the premisses are to be trans- 
 posed, k that the mood is to be reduced per impossibile. 
 It will be noticed that k occurs only in two moods, 
 Baroko and Bokardo, but I have shewn that the per 
 impossibile method is equally applicable to all imperfect 
 moods, and that these two moods can be reduced osten- 
 sively by means of permutation, so that any imperfect 
 mood may be reduced either ostensively or per impos- 
 sibile 9 . The initial B in Baroko and Bokardo shews that 
 the per impossibile method, in their case, assumes the 
 validity of Barbara, but in other cases the operation 
 may assume the validity of some one of the other moods 
 in the first figure ; thus, in the particular instance I 
 have taken above, it is performed by means of Celarent. 
 It is perhaps needless to add that all letters, not already 
 explained in the mnemonic lines, are non-significant. 
 
 The nature of the subaltern moods has already been 
 explained. They are, AAI, EAO in fig. i, EAO, AEO in 
 fig. 2, and AEO in fig. 4, included respectively in AAA, 
 EAE, EAE, AEE, AEE. They cannot properly be re- 
 garded as illegitimate, inasmuch as the conclusions are 
 valid, but they are superfluous, inasmuch as they infer 
 less than is justified by the premisses. 
 
 3 If we take * to signify the employment of permutation, Baroko 
 and Bokardo maybe replaced respectively by Fa/fso/ro and Dosamos/r. 
 These terms are adapted from Whately's Logic, Bk. II. ch. iii. 5.
 
 J06 MEDIATE INFERENCE OR SYLLOGISM. 
 
 The Special Rules. 
 
 Besides the general syllogistic rules, already enunciated 
 and proved, certain Special Rules have been enunciated 
 for each figure. I give them below as generally stated. 
 Those for the first figure have been proved in establishing 
 its canon ; those for the other figures the student may 
 verify for himself by applying the rules, already laid 
 down, on the distribution of terms. 
 
 Fig. i. (a) The minor premiss must be affirmative. 
 
 (/3) The major premiss must be universal. 
 Fig. 2. () One or other premiss must be negative. 
 (/3) The conclusion must be negative. 
 (y) The major premiss must be universal. 
 Fig. 3. (a) The minor premiss must be affirmative. 
 
 (ft) The conclusion must be particular. 
 Fig. 4. (a) When the major premiss is affirmative, the 
 
 minor must be universal. 
 (3) When the minor premiss is affirmative, the 
 
 conclusion must be particular. 
 (y) In negative moods the major premiss must 
 
 be universal. 
 
 (8) The conclusion cannot be an universal affir- 
 mative, nor either of the premisses a par- 
 ticular negative.
 
 INDIRECT MOODS. 107 
 
 Note. If, leaving out of consideration the conclusion, 
 we regard the number of possible figures as three and 
 that of possible moods as sixteen, we may proceed as 
 follows. 
 
 Having enunciated the canon of the first figure, we 
 may constitute the moods Barbara, Celarent, Darii, and 
 Ferio. The subaltern moods, AAI and EAO, are not 
 admissible, as the question here before us is not ' What 
 conclusions are justified by such and such premisses,' 
 but ' To what conclusions do such and such premisses 
 lead?' Now, from this point of view, the conclusions 
 of the subaltern moods are not directly inferred from 
 the premisses, but are inferred by subalternation from 
 the universal conclusions to which the premisses directly 
 lead. The same observation will of course apply to the 
 subaltern moods in the other figures. 
 
 If we take no account of the conclusion, we have 
 no means of determining which is the major and which 
 is the minor term. Consequently, the premisses may 
 lead to two kinds of conclusions : ist, those in which 
 the predicate of the first premiss is predicated of the 
 subject of the second ; and, those in which the subject 
 of the second premiss is predicated of the predicate of 
 the first. Now the canon of the first figure applies only 
 to the first case ; consequently we are bound to ask if 
 any conclusions, falling under the second head, may be 
 inferred from the premisses. These cannot be deter- 
 mined directly by the canon, but must be determined in 
 the same manner as conclusions in the second and third
 
 108 MEDIATE INFERENCE OR SYLLOGISM. 
 
 figures. Here we proceed by a method similar to that 
 employed in the text. The syllogistic rules exclude seven 
 of the sixteen possible moods, viz. EE, EO, OE, OO, II, 
 IO, OI. When the moods are referred to their several 
 figures, we find that, where the extreme employed in the 
 first premiss becomes the predicate, and the extreme 
 employed in the second premiss the subject of the con- 
 clusion, the results are, in the second figure, Cesare, Ca- 
 mesfres, Festino, Baroko ; in the third, Darapti, Disamis, 
 Datisi, Felapton, Hokardo, Ferison, the subaltern moods 
 of the second figure EAO, AEO, being inadmissible. 
 Where the extreme employed in the first premiss 
 becomes the subject, and the extreme employed in 
 the second premiss the predicate of the conclusion, 
 the results are, in the first figure, AAI, AEO, AH, 
 EAE, IEO, which, when we transpose the premisses, 
 become respectively^/-^ mantip, Fesapo, Dimaris, Camenes, 
 and Fresison in the fourth figure. Hence, according 
 to this mode of treatment, the moods of the fourth 
 figure are regarded as indirect moods of the first. 
 Similarly, in the second figure we may constitute the 
 indirect moods AEE, EAE, IEO, OAO. These, if we 
 transpose the premisses, are merely a repetition of the 
 ordinary moods of the second figure. This is also the 
 case with the indirect moods of the third figure, viz. AAI, 
 AEO, AH, AGO, IAI, IEO. It will therefore be seen 
 that, with the exception of rejecting the subaltern moods, 
 which even there we regarded as superfluous, we arrive 
 practically at the same results as in the text. The moods
 
 INDIRECT MOODS. 109 
 
 of the fourth figure are recognised, but, instead of being 
 regarded as moods of a distinct figure, they are treated as 
 indirect moods of the first. By the expression ' indirect 
 moods,' it will be seen, we mean moods in which the 
 extreme employed in the first premiss becomes the sub- 
 ject, and the extreme employed in the second premiss the 
 predicate of the conclusion.
 
 CHAPTER IV. 
 
 On Trains of Reasoning. (The Sorites?) 
 
 SYLLOGISMS may be combined in what is called 
 a Train of Reasoning. Thus the major and minor pre- 
 misses, or either, of our ultimate syllogisms may them- 
 selves be proved by syllogisms ; the major and minor 
 premisses of these, or either, by other syllogisms, and 
 so on, till at last we come to premisses not admitting 
 of syllogistic proof. Such premisses are either assumed 
 without any proof at all, or they are the result either of 
 direct observation or of the testimony of others or of 
 Induction. 
 
 In a train of reasoning, any syllogism proving a pre- 
 miss of a subsequent syllogism is called with reference 
 to the subsequent syllogism a Pro- Syllogism, and the 
 subsequent syllogism with reference to it an Epi-Syllo- 
 gism. It is obvious that the very same syllogism in 
 different relations may be called a Pro-Syllogism or an 
 Epi-Syllogism. 
 
 The Sorites (or, as it is sometimes called, the chain- 
 argument] is a common instance of a train of reasoning 
 in a compressed form. It consists, in its proper and 
 most usual form, of a series of propositions, in which 
 the predicate of the preceding is always the subject of 
 the succeeding premiss. The conclusion predicates the 
 last predicate of the first subject.
 
 THE SORITES. Ill 
 
 Thus, All A is B, 
 
 All B is C, 
 
 All C is D, 
 
 All D is E ; 
 
 .-.All A is E. 
 
 When expanded, the Sorites contains as many syllo- 
 gisms as there are propositions intermediate between the 
 first proposition and the conclusion. These syllogisms 
 are in the first figure, and the conclusion of each becomes 
 the minor premiss of the next. Thus, the above Sorites 
 contains three syllogisms, viz. 
 
 (1) All B is C, 
 All A is B ; 
 
 . . All A is C. 
 
 (2) All C is D, 
 All A is C ; 
 
 .-.All A is D. 
 
 (3) All D is E, 
 All A is D ; 
 
 . . All A is E. 
 
 In a Sorites, only one premiss canjbe particular, viz. 
 the first ; and only one negative, viz. the last l . 
 
 1 The first premiss, if particular, may be stated in the form ' Some 
 B is A,' instead of in the usual form ' Some A is B ' ; the first syllogism 
 of the expanded Sorites will then be in the third figure instead of the 
 first. Similarly, the last premiss, if negative, may be stated in the 
 form ' No E is D,' instead of in the form ' No D is E,' which will
 
 1 I 2 TRAINS OF REASONING. 
 
 For, if there were a particular premiss in any place 
 except the first, there would be a particular major, which, 
 in the first figure, is inadmissible. 
 
 Again, if any premiss except the last were negative, 
 there would be a negative conclusion in one of the pre- 
 vious syllogisms ; this conclusion would necessitate, in the 
 following syllogisms, a negative minor, which, in the first 
 figure, is inadmissible. 
 
 Note. Besides the above form of Sorites, there is 
 another called the Regressive or Godenian Sorites (so 
 called from Goclenius, who first noticed it). Its pro- 
 perties are exactly the reverse of those of the ordinary 
 Sorites. The subject of each premiss becomes the pre- 
 dicate of the next, the conclusion predicates the first 
 predicate of the last subject, the conclusion of each of 
 the expanded syllogisms becomes the major premiss of 
 the next, and the rules by which it is governed are that 
 the first premiss only can be negative and the last par- 
 ticular. It may be stated thus : 
 
 All E is F, 
 
 All D is E,' 
 
 All C is D, 
 
 All B is C, 
 
 All A is B ; 
 . . All A is F. 
 
 make the last syllogism of the expanded Sorites a syllogism of the 
 second figure. No advantage, however, is gained by this mode of 
 statement, and it is not nearly so simple as the usual form.
 
 CHAPTER V. 
 
 On Complex (Hypothetical} Propositions and 
 Syllogisms. 
 
 HITHERTO I have treated only of simple (or, as 
 they have been inaccurately termed, Categorical *) pro- 
 positions and syllogisms. A Complex (or, as it is com- 
 monly called, a Hypothetical] Syllogism is one in which 
 one or more complex (or hypothetical) propositions 
 occur. A complex proposition is a combination of two 
 or more simple propositions in one sentence, the pro- 
 positions being so related that the truth or falsity of one 
 proposition or set of propositions is made to depend on 
 the truth or falsity of the other proposition or set of 
 propositions. If the two propositions or sets of propo- 
 sitions be associated together, so that the truth of one 
 depends on the truth of the other, the complex propo- 
 sition may be called Conjunctive 2 . If they be dissociated, 
 
 1 The word categorical (icaTTjyopiKoi) properly means affirmative, 
 and is always used in that sense by Aristotle. 
 
 3 I have, in accordance with more ancient usage, employed the 
 word ' conjunctive ' in place of the word ' conditional,' which is 
 employed by Aldrich and other logicians of his time. Instead of 
 simple and complex propositions, they speak of categorical and 
 hypothetical, -subdividing hypothetical into conditional and disjunc- 
 tive. Besides the improper use of the word categorical (noticed 
 *
 
 114 COMPLEX PROPOSITIONS AND SYLLOGISMS. 
 
 so that the truth of one depends on the falsity of the 
 other, and the falsity of one on the truth of the other, 
 the complex proposition may be called Disjunctive. Thus 
 we may take as instances of Conjunctive Propositions : 
 
 If (or When, Where, Provided that, &c.) A is B, C is D ; 
 If A is not B, C is D ; If A is not B, C is not D ; If A is 
 B and C is D, E is F ; If A is B, either C is D or E is F 
 or G is H ; If either A is B or C is D, E is F. 
 
 It will be noticed in the second and third examples 
 that negatives are introduced, but they are, notwith- 
 standing, examples of conjunctive propositions, for C 
 being D in the first case, and C not being D in the 
 second, are made to depend on the truth of A not 
 being B. As instances of Disjunctive Propositions we 
 may take the following : 
 
 Either A is B, or C is D ; Either A is B, or C is D, or 
 E is F ; A is either B or C or D ; Either A or B or C is 
 U ; Either A is not B, or C is not D ; Either A is B, or 
 C is not D. 
 
 This form of proposition implies that the truth of one 
 member involves the falsity of the other, and, vice versa, 
 the falsity of one member the truth of the other. 
 
 It should be noticed that both conjunctive and dis- 
 junctive propositions admit of being reduced to the 
 simple form. Thus : 
 
 above), it is extremely awkward to make hypothetical and conditional 
 (which are synonyms) stand respectively for the genus and species. 
 The words conjunctive and disjunctive serve also to point out that the 
 division of complex propositions is exhaustive.
 
 CONJUNCTIVE SYLLOGISMS. 1 15 
 
 4 If A is B, C is D ' becomes ' The case of A being B 
 is a case of C being D ' or ' A being B involves as a con- 
 sequence C being D.' 
 
 The disjunctive proposition, when analysed, contains 
 four conjunctive propositions, each of which may be 
 reduced to a simple proposition. Thus, ' Either A is B, 
 or C is D' is equivalent to the four conjunctive pro- 
 positions : If A is B, C is not D ; If A is not B, C is D ; 
 If C is D, A is not B ; If C is not D, A is B. Of these 
 four propositions, however, the third is implied in the first, 
 and the fourth in the second. 
 
 I now proceed to consider Complex Syllogisms, i. e. 
 syllogisms which contain Complex Propositions. 
 
 $ 2. I. Conjunctive Syllogisms. 
 
 A Conjunctive Syllogism is a syllogism, one_or both 
 of whose premisses are conjunctive propositions ; if only 
 one premiss be conjunctive, the other must be simple. 
 If both premisses be conjunctive, inasmuch as all con- 
 junctive propositions rank as universal affirmatives, the 
 syllogism, to be valid, must be conformed to Barbara in 
 the first figure. Thus, 
 
 If A is B, C is D, 
 
 If C is D, E is F ; 
 
 . . If A is B, E is F, ^ 
 
 is a valid syllogism ; but the following would not be valid : 
 If A is B, C is D, 
 If A is B, E is F ; 
 .'. If Cis D, E is F. 
 
 I 2
 
 II 6 COMPLEX PROPOSITIONS AND SYLLOGISMS. 
 
 Far the most common form however of a conjunctive 
 syllogism is that in which the major is a conjunctive, 
 and the minor a simple proposition. Of this form there 
 are four possible varieties, of which two are valid and 
 two invalid. These may be represented thus : 
 
 If A is B, C is D. (Major premiss.) 
 
 (i) A is B ; 
 .-. C is D. 
 (a) A is not B ; 
 
 No conclusion. 
 
 (3) C is D ; 
 
 No conclusion. 
 (2) C is not D 
 .'.A is not B. 
 
 Hence we obtain the rule that, if we affirm the antece- 
 dent, we must affirm the consequent, or, if we deny the 
 consequent, we must deny the antecedent ; but, tfwedeny 
 the antecedent or affirm the consequent, no conclusion 
 can be drawn. The reason of this rule will be obvious 
 on a little reflexion. We assert that 'A being B involves 
 as a consequence C being D ' ; hence, if we grant that A 
 is B, it must follow that C is D ; if we deny that C is D, 
 it must follow that what involves it as a consequence 
 must also be untrue ; but C might still be D, though A 
 were not B, nor would it follow from C being D that A 
 was also B. 
 
 Syllogism (i) is called a Constructive conjunctive 
 syllogism. 
 
 Syllogism (2) is called a Destructive conjunctive 
 syllogism. 
 
 It may be useful to add a few examples of valid 
 conjunctive syllogisms.
 
 DISJUNCTIVE SILL CIS MS. 
 
 117 
 
 (i) 
 
 (2) 
 
 If A is B, C is not D. 
 Cis D; 
 . * . A is not B. 
 
 If A is not B, C is D. 
 A is not B ; C is not D ; 
 
 .-.CisD. .-.AisB. 
 
 (3) If A is not B, C is not D. 
 
 A is not B ; C is D ; 
 
 .-.CisnotD. .-.AisB. 
 
 (4) If A is B, either C is D or F is G. 
 
 A is B; 
 .-.Either C is D orF is G. 
 
 Neither C is D nor F is G ; 
 .'.A is not B. 
 
 (5) If either C is D or F is G, either X is Y or V is W. 
 
 Either C is D or F is G ; 
 .-. Either X is Y or Vis W. 
 
 Neither X is YnorVisW; 
 . . Neither CisD nor F is G. 
 
 $ 3. II. Disjunctive Syllogisms. 
 
 A Disjunctive Syllogism is a syllogism of which the 
 major premiss is a disjunctive, and the minor a simple 
 proposition, the latter affirming or denying one of the 
 alternatives stated in the former. 
 
 We may indeed combine two disjunctive propositions, 
 and draw conclusions from them, but we can only do so 
 after reducing the disjunctive propositions to the con- 
 junctive form. Thus from the two propositions Either
 
 tl8 COMPLEX PROPOSITIONS AND SYLLOGISMS. 
 
 A is B or C is D, Either A is B or E is F, we may draw 
 four conclusions, viz. If C is D, E is F ; If C is not D, E is 
 not F ; If E is F, C is D ; If E is not F, C is not D. But, 
 as these conclusions are really drawn from conjunctive 
 propositions which are involved in the two disjunctive 
 propositions, we are not justified in calling the syllogisms 
 disjunctive. Hence, as will be noticed, my definition of 
 disjunctive is not so wide as that of conjunctive syllo- 
 gisms. 
 
 The disjunctive syllogism admits of four conclusions, 
 which may be exhibited thus : 
 
 Either A is B, or C is D. 
 
 w 
 
 A is B; 
 
 (3) 
 
 C is D; 
 
 
 .-. C is not D. 
 
 
 .'. A is not B. 
 
 (*) 
 
 A is not B ; 
 
 (4) 
 
 C is not D ; 
 
 
 .-.C is D. 
 
 
 .-.A is B. 
 
 I add a few examples : 
 
 Either A is B, or C is not D. 
 
 (1) AisB; (3) CisnotD; 
 . \CisD. .-.AisnotB. 
 
 (2) A is not B ; (4) C is D ; 
 .. C is not D. .-.A is B. 
 
 Either A is B, or C is D, or E is F. 
 
 (1) A is B ; . '. Neither C is D nor E is F. 
 
 (2) A is not B ; .'. Either C is D or E is F. 
 
 (3) Neither C is D nor E is F ; . . A is B.
 
 DISJUNCTIVE SYLLOGISMS. 
 
 119 
 
 (4) Either C is D or E is F ; . . A is not B. 
 
 (5) Either A is B or C is D ; . . E is not F. 
 
 &c. &c. 
 
 He is either a fool or a knave. 
 
 (1) He is a fool ; 
 
 . . He is not a knave. 
 
 (2) He is a knave ; 
 
 . . He is not a fool. 
 
 (3) He is not a fool ; 
 .-. He is a knave. 
 
 (4) He is not a knave ; 
 . . He is a fool. 
 
 Note. Mr. Mill (in his Examination of Sir W. Hamil- 
 ton's Philosophy, ch. xxiii.) maintains that a disjunctive 
 proposition merely implies that the two alternatives cannot 
 both be false, but that it does not exclude the possibility 
 of both of them being true. Thus, in the last example, 
 he would maintain that there is nothing in the form of 
 the assertion to exclude the supposition of the man being 
 both a fool and a knave. In this opinion he is preceded 
 by many other logicians, but it seems to me that in the 
 
 expression ' either or ' we distinctly exclude the 
 
 possibility of both alternatives being true, as well as of 
 both being false. In fact, when we do not wish to ex- 
 clude the possibility of both being true, we add the words 
 ' or both,' thus : ' He is either a fool or a knave, or both ' ; 
 ' I shall come either to-day or to-morrow, or perhaps both 
 days.'
 
 120 COMPLEX PROPOSITIONS AND SYLLOGISMS. 
 
 \ 4. The Dilemma. 
 
 There remains the case in which one premiss of the 
 complex syllogism is a conjunctive and the other a dis- 
 junctive proposition, it being, of course, understood that 
 the disjunctive proposition deals only with expressions 
 which have already occurred in the conjunctive pro- 
 position. This form is called a Dilemma. The order of 
 the premisses is indifferent, but it seems more natural that 
 the conjunctive proposition should be the major. If we 
 consider the case in which the major consists of one 
 antecedent and several consequents, there is only one 
 valid form of argument, and that is destructive. 
 
 (1) If A is B, C is D and E is F ; 
 
 But either C is not D or E is not F ; 
 .*. A is not B. 
 
 If we asserted in the minor ' C is D and E is F ' there 
 would be no conclusion, and if we asserted ' Neither C is 
 D nor E is F;' the minor would not be disjunctive. The 
 assertion ' Either C is D or E is F ' is, according to my 
 view of the significance of a disjunctive proposition, 
 equivalent to the assertion ' Either C is not D or E is not 
 F,' and leads to the same conclusion. 
 
 If the major consist of several antecedents, and one 
 consequent, there is only one valid form of argument, 
 and that is constructive. 
 
 (2) If A is B or if E is F, C is D ; 
 But either A is B or E is F ; 
 
 .-.CisD.
 
 THE DILEMMA. 121 
 
 If we asserted in the minor ' C is not D,' it would not 
 satisfy the requirements of the definition by being a dis- 
 junctive proposition. 
 
 In the remaining case, where there are several ante- 
 cedents and several consequents, there are two valid 
 forms, one constructive and the other destructive. 
 
 (3) If A is B, C is D ; and if E is F, G is H ; 
 But either A is B, or E is F ; 
 
 .-.Either C is D, or G is H. 
 
 (4) If A is B, C is D ; and if E is F, G is H ; 
 But either C is not D, or G is not H ; 
 
 . . Either A is not B, or E is not F. 
 
 It is evident that we may form a Trilemma, Tetra- 
 lemma, &c., by increasing the number of antecedents 
 or consequents or both, thus : 
 
 If A is B, or if E is F, or if G is H, C is D ; 
 But either A is B, or E is F, or G is H ; 
 .'.C is D. 
 
 If A is B, C is D ; and if E is F, G is H ; and if 
 
 I is J, K is L ; 
 
 But either A is B, or E is F, or I is J ; 
 . '. Either C is D, or G is H, or K is L. 
 
 It is not uncommon to mistake for dilemma what 
 is really only a conjunctive syllogism. Thus the two 
 following syllogisms, when examined, will be found 
 to be, the first a constructive, the second a destructive 
 conjunctive.
 
 122 COMPLEX PROPOSITIONS AND SYLLOGISMS. 
 
 (i) Whether geometry be regarded as a mental dis- 
 cipline or as a practical science, it deserves 
 to be studied ; 
 But geometry may be regarded as both a mental 
 
 discipline and a practical science ; 
 .'.It deserves to be studied. 
 
 ' (2) If we go to war, we must either contract a debt, 
 or increase the taxation, or indemnify ourselves 
 at the enemy's expense ; 
 We shall not be able to do any of these ; 
 . . We are not able to go to war. 
 
 In disputation, the adversary who is refuted by a 
 dilemma is said to be ' fixed on the horns of a dilemma ' ; 
 he is said to rebut the dilemma, if he meet it by another 
 with an opposite conclusion. Thus (to tell an old story) 
 Protagoras the Sophist is said to have engaged with his 
 pupil, Euathlus, that half the fee for instruction should be 
 paid down at once, and the other half remain due till 
 Euathlus should win his first cause. Euathlus deferred 
 his appearance as an advocate, till Protagoras became 
 impatient and brought him into court. The Sophist then 
 addressed his pupil as follows : ' Most foolish young 
 man, whatever be the decision, you must pay your 
 money ; if the judges decide in my favour, I gain my fee 
 by the decision of the court, if in yours by our bargain.' 
 This dilemma Euathlus rebutted 'by the following : ' Most 
 sapient master, whatever be the decision, you must lose 
 your fee ; if the judges decide in my favour, you lose it
 
 THE DILEMMA. 123 
 
 by the decision of the court ; if in yours, by our bargain, 
 for I shall not have gained my cause.' 
 
 In practical logic, the Dilemma will be found to be a 
 most unsatisfactory form of argument. The disjunctive 
 minor frequently omits to state all the possible alter- 
 natives, and, in the major premiss, owing to the complex 
 character of the proposition, it may easily escape notice 
 that one or more of the consequents does not really 
 follow from its antecedent, or that more consequents 
 than those actually specified do follow from the ante- 
 cedents. Moreover, it is a form of argument in which 
 ambiguity of language is peculiarly apt to lurk. Hence 
 the ease with which it is so frequently ' rebutted, the 
 process of rebutting usually consisting either in drawing 
 other consequents than those already stated from the 
 antecedents adduced in the major premiss, or in negating 
 the antecedents and then drawing from thenrthe opposite 
 conclusions. 
 
 Note i. Of the four cases of dilemma which I have 
 given, the first would not be admitted by Abp. Whately 
 and Dr. Mansel, who define dilemma as ' A syllogism 
 having a conditional (i. e. conjunctive) major premiss with 
 more than one antecedent, and a disjunctive minor.' 
 Having however a disjunctive minor, it cannot properly 
 be regarded as a conjunctive syllogism, and it seems less 
 arbitrary and more systematic to define dilemma as ' a 
 syllogism of which one premiss is a conjunctive and the 
 other a disjunctive proposition ' than to limit it as above.
 
 124 COMPLEX PROPOSITIONS AND SYLLOGISMS. 
 
 Note 2. Few parts of Logic have occasioned more 
 differences of opinion or nomenclature than the theory 
 of complex (or hypothetical) propositions and syllogisms. 
 Sir W. Hamilton (see his Lectures on Logic, Lecture xiii. 
 and Appendix viii.) finally arrives at the opinion that 
 ' hypothetical and disjunctive judgments ' are not more 
 complex than ordinary propositions, and that 'hypo- 
 thetical and disjunctive reasonings ' are really forms of 
 immediate inference. Thus he would represent the con- 
 junctive syllogism in the form : 
 
 If A is B, C is D ; 
 
 .'.A being B, C is D. 
 
 The disjunctive syllogism he would represent in the 
 
 form : 
 
 Either A is B or C is D ; 
 
 .'.A not being B, C is D. 
 
 The other inferences from the premisses would, of 
 course, be drawn similarly. 
 
 The dilemma would assume the form : 
 
 If A is B, C is D ; and if E is F, G is H ; 
 .'. Either A being B, or E being F, it follows that 
 
 C is D, or G is H ; 
 
 or .'. Either C not being D, or G not being H, it follows 
 that either A is not B, or E is not F. 
 
 Without attempting to discuss the arguments that have 
 been adduced on either side, I may express my own 
 opinion that complex (or hypothetical) propositions and
 
 THE DILEMMA. 125 
 
 syllogisms are rightly so called, and that the latter are to 
 be regarded as mediate, and not as immediate, forms 
 of inference. Though no new term is introduced in 
 the minor premiss, the major and minor premisses are 
 entirely distinct propositions, and the conclusion is the 
 result not of one proposition but of two propositions 
 taken conjointly.
 
 CHAPTER VI. 
 
 On the words 'Most', ' Many ',' &c., as express- 
 ing the Quantity of Propositions. 
 
 TO all particular propositions I have hitherto prefixed 
 the word ' some.' Both in conversation and reasoning, 
 however, it frequently happens that we use some other 
 sign of particularity, such as ' many,' ' most,' &c. Nor does 
 there seem any valid reason why these forms should not 
 be recognised by Logic. From what has already been said 
 of particular premisses, it will be seen that wherever one 
 premiss is universal and the other modified by some sign 
 of particularity, as ' some,' ' many,' ' most,' &c., the con- 
 clusion must be particular, the degree of particularity in 
 no case transcending (though, in some cases, it may fall 
 below) that denoted by the particular premiss. Thus, if 
 we state as our premisses ' All crimes are to be punished,' 
 ' Many offences against individual persons are crimes,' we 
 must draw the conclusion that ' Many offences against 
 individual persons are to be punished.' But if we state 
 as our premisses ' All crimes are to be punished,' ' Most 
 crimes are offences against individuals,' we are only justi- 
 fied in drawing the conclusion that ' Some offences against
 
 1 MOST,' ' MANY, 'ETC. 12J 
 
 individuals are to be punished.' The student will, from 
 the principles already laid down, be easily able to dis- 
 tinguish between the two classes of cases. 
 
 ' Two particular premisses prove nothing.' This is a 
 general rule, and is strictly true where the premisses are 
 
 quantified as ' some ' ' some.' But there is one case 
 
 in which two particular premisses necessitate a conclu- 
 sion. I will begin with a simple instance of it. If 
 two different predicates can both be predicated affirma- 
 tively of the greater number of individuals denoted by 
 the same common term, there must be some individuals 
 of which they can both be predicated, i.e. in certain 
 cases the predicates must be predicable of each other. 
 Thus, from the premisses 
 
 Most A are B, 
 Most A are C, 
 
 we must necessarily infer that Some A is both B and C, 
 and consequently that Some B are C and Some C are B. 
 
 But we may draw the same conclusion, even in those 
 cases in which both premisses are not quantified by the 
 word ' most,' provided that the sum of the quantities by 
 which the subjects are affected exceeds unity. Thus 
 from the premisses 
 
 Three-fourths of A are B, 
 One-third of A is C, 
 
 it follows that at least one-twelfth of A is both B and C ; 
 but if B and C be both predicable of the same objects, 
 either must be, partially, predicable of the other. If, for 
 instance, three men out of four exceed a certain height
 
 128 'MOST' l MANY; ETC. AS EXPRESSING 
 
 and one out of three a certain weight, at least one out of 
 twelve must exceed both the given height and the given 
 weight, and we may affirm both that Some men who 
 exceed a certain height also exceed a certain weight, and 
 that Some men who exceed a certain weight also exceed 
 a certain height. 
 
 Of course, when we use such an indefinite word as 
 ( most ' in either premiss, the other premiss must be 
 quantified by an expression signifying at least one-half; 
 else we cannot be sure that the quantities of the two 
 premisses, when added together, exceed unity. 
 
 A conclusion of this kind can only be drawn where 
 the subject in both premisses is the same term, i.e. in 
 the third figure ; for, in the mere form of a logical pro- 
 position, we have no data to guide us with regard to the 
 quantity of the predicate. Thus, from the premisses 
 
 Nineteen-twentieths of A are B, 
 
 Nine-tenths of B are C, 
 
 we can draw no conclusion as to the relation of A and C ; 
 for the tenth of B which is not C might be precisely that 
 portion which was coincident with, or which contained, 
 the nineteen-twentieths of A. Though, however, these 
 syllogisms are confined to the third figure, they may be 
 either affirmative or negative. Thus, from the premisses 
 
 Three-fourths of A are not B, 
 
 Two-thirds of A are C, 
 
 we may infer that five-twelfths at least of A are C and 
 not B, and consequently that some C is not B, and some 
 things which are not B are C.
 
 THE QUANTITY OF PROPOSITIONS. 
 
 129 
 
 Note. The propositions employed in the above chapter 
 have usually been regarded as Particulars, though they 
 have sometimes been classed with Universals. See Sir 
 W. Hamilton's Lectures on Logic, vol. ii., first ed. p. 354 ; 
 second ed. p. 361.
 
 CHAPTER VII. 
 On Probable Reasoning. 
 
 IN discussing the copula, it was maintained that any 
 modification of our assertions, such as the qualifications 
 introduced by the words ' probably,' ' possibly,' &c., was, 
 in the ultimate analysis of the proposition, to be referred 
 to the predicate and not to the copula. Thus such a 
 proposition as 'A is probably B,' when stated in its 
 strictly logical form, would become ' That A is B is a 
 probability.' It would however be tedious and prac- 
 tically useless to reduce all our propositions to such a 
 form. I may therefore proceed to lay down rules for 
 reasoning from propositions whose copula is modified, 
 remembering however that they are not stated in strictly 
 logical language. 
 
 The correctness of the following rule will be apparent. 
 If a premiss whose copula is modified be combined with 
 another premiss whose copula is unmodified, the copula 
 of the conclusion must be modified also ; the modality, of 
 course, never transcending that of the premiss. Thus 
 from the premisses 'All true poets are men of genius,' 
 ' Sophocles is probably (certainly, possibly, &c.) a true 
 poet,' I infer that Sophocles is probably (certainly, pos- 
 sibly, &c.) a man of genius. From a certain and a
 
 PROBABLE REASONING. 13! 
 
 probable premiss, therefore, arranged according to the 
 ordinary laws of syllogism, we can never infer more than 
 a probable conclusion. To this head may most con- 
 veniently be referred those syllogisms in which the major 
 is a particular proposition introduced by the word ' most,' 
 and the minor a singular proposition. Thus from the pre- 
 misses, ' Most philosophers are men of vivid imagination, 
 ' A B is a philosopher,' I infer, as the conclusion, A B 
 is probably a man of vivid imagination. If most phi- 
 losophers possess certain characteristics, any particular 
 philosopher will probably possess them, so that the major 
 premiss is, in fact, equivalent to the proposition, 'A 
 philosopher is probably a man of vivid imagination.' 
 
 Using the word 'probable' in the sense of 'more 
 likely than not,' two probable premisses do not lead to a 
 probable conclusion. This fact will be obvious from an 
 easy example. Suppose there are in a bag four red, five 
 blue, and six white balls : I may say with truth ' Any ball 
 drawn at random from the bag is probably a red or 
 blue ball ' ; I may also say with truth ' Any ball drawn 
 at random from the red and blue balls is probably a blue 
 ball ' ; but I cannot infer that ' Any ball drawn at random 
 from the bag is probably a blue ball.' I shall only be 
 justified in drawing the conclusion 'Any ball drawn at 
 random from the bag is possibly a blue ball.' But, 
 where our information is so special as in the above 
 instance, a conclusion of this kind is far too vague. Is 
 there no method which will enable me to state in the 
 conclusion the exact value of the expectation that any 
 K 2
 
 13 a PROBABLE REASONING. 
 
 particular ball drawn at random may be blue, red, or white ? 
 For such a method I must have recourse to mathematics. 
 Though the word ' probable ' is used in the sense of 
 ' more likely than not,' the word probability is used as 
 the equivalent of ' chance ' or ' expectation.' If it be three 
 to two that a certain event will happen, 3 : 2 is called 
 the odds for, 2 : 3 the odds against the event. Now the 
 ' probability ' or ' chance ' of the event happening would 
 be expressed by $, that of its not happening by f , the 
 denominator in both cases being expressed by the sum of 
 the terms of the odds, the numerator in the former case 
 by the term of the odds for, in the latter case by the term 
 of the odds against. If two events are independent of 
 each other, the joint or compound probability that they 
 will both happen must be much smaller than the pro- 
 bability that either of them will happen alone, and it is 
 discovered by multiplying together the fractions which 
 express the probabilities of their happening separately '. 
 Thus, in the above instance, the chance of my drawing 
 a red or .blue ball = T n T ; the chance of my drawing out 
 of the red and blue balls a blue ball=| ; .'. the chance 
 of my drawing a blue ball out of a bag which contains 
 all= T 9 T xf=g, a result at which, in this particular in- 
 stance, I could of course have arrived more directly. 
 Hence, when both premisses are affected by words like 
 'probably,' 'possibly,'&c.,the probability of the conclusion 
 
 1 The truth of this proposition, with regard to two, three, or any 
 number of events, is proved at length in Peacock's Arithmetical 
 Algebra, 469.
 
 PROBABLE REASONING. 133 
 
 may always be discovered by multiplying together the pro- 
 babilities of the premisses, the conclusion being therefore 
 less probable than either premiss. I append a few in- 
 stances of conclusions drawn from probable premisses : 
 
 (1) This plant will probably sprout up during the 
 
 winter months. (Let the probability =f.) 
 Whatever plant sprouts up during the winter will 
 probably be bitten by the frost. (Let the pro- 
 bability =4.) 
 
 . . This plant may sprout up and be frost-bitten. 
 (Here the probability=f xf = H-) 
 
 . * . The odds against the event are 23 to 12, and those 
 in favour of it 12 to 23. 
 
 (2) Two thirds of these men will be enlisted. 
 Half the men enlisted are killed in battle. 
 
 . . The probability of any particular man being en- 
 listed and killed in battle =f x ^=. 
 
 . . It is two to one against any particular man here 
 being enlisted and killed in battle. 
 
 (3) A warm day may possibly be a rainy day. (Let 
 
 the probability = ^.) 
 A rainy day is probably a calm day. (Let the 
 
 probability = |.) 
 
 . . A warm day may possibly be both rainy and calm 2 . 
 (The probability = T 4 T .) 
 
 2 I am indebted to Professor Shaw, of Deny, for pointing out an 
 inaccuracy in the conclusion of this example, as stated in the earlier 
 editions, and to Professor Park for the suggestion that it is a pecu- 
 liarity of all arguments of this kind that, strictly speaking, both 
 premisses should be expressed in the conclusion.
 
 134 PROBABLE REASONING. 
 
 N. B. It is most important for the student to bear 
 in mind the ambiguous use of the words ' probably,' 
 ' probable,' ' probability.' The adverb ' probably ' we 
 seem always to use in the sense of ' more likely than not.' 
 The adjective ' probable,' when employed as a predicate, 
 seems also to be invariably used in the same sense ; thus 
 we say ' It is probable that he will do so and so,' ' This 
 event is probable.' But when used to qualify a substantive, 
 as in such expressions ' probable premisses,' ' probable 
 reasonings,' &c., it may be employed either in the above 
 sense or simply as contrasted with certainty, and in the 
 latter case the 'probability,' as we say, may vary from 
 certainty to zero. Lastly, the word ' probability ' may 
 simply be equivalent to ' chance,' as explained above, or 
 in some expressions it may have the meaning of ' being 
 more likely than not,' as when we say ' The probability 
 is that he will do so and so.' By ' probable reasoning ' 
 at the head of this section I of course mean reasoning 
 which falls short of certainty, and the value of which may 
 vary to any extent so long as it does not rise to certainty 
 or fall to zero.
 
 CORROBORATIVE EVIDENCE. 135 
 
 On the Combination of Probable Arguments. 
 
 [Cumulative or Corroborative Evidence, including 
 Circumstantial Evidence.] 
 
 Probable arguments may be combined together in a 
 chain 3 (or, as it has been more appropriately called, a coil) 
 of reasoning, each argument leading to the same conclu- 
 sion. Instead of weakening each other, as is the case 
 with probable premisses, such arguments, being all in- 
 dependent testimonies to the truth of the same conclusion, 
 mutually strengthen each other. If the value of any 
 single argument amounts to certainty, the conclusion 
 must be true. In this case therefore we have to calculate 
 the chances of failure in each separate argument ; these, 
 when multiplied together, give the probability of all the 
 arguments together failing to prove the conclusion ; and 
 this fraction, when subtracted from unity (which repre- 
 sents certainty), gives the probability, resulting from all 
 the arguments jointly, in favour of the conclusion. Thus 
 suppose the probabilities in favour of certain probable 
 arguments to be represented respectively by ^, f, ; 
 
 3 Chain-reasoning would be the proper designation for a series of 
 arguments (or links of evidence) which are all inter-dependent, so 
 that, if one argument fails (or one link snaps), the reasoning breaks 
 down altogether. Much legal evidence is of this kind, as when 
 A testifies that he received a certain parcel from B, B that he 
 received it from C, and so on. In this case, any one untrustworthy 
 witness would invalidate the whole evidence. On the other hand, 
 in corroborative evidence the various parts strengthen one another.
 
 136 PROBABLE REASONING. 
 
 the chances of their failing to prove the conclusion will 
 be represented respectively by f , \, \ (or the differences 
 between the favourable chances and unity) ; the chance 
 therefore of their all failing to prove the conclusion 
 = l x \ x i = sV > consequently the probability in favour 
 of the conclusion, as based upon all the arguments jointly, 
 is ^, i. e. the odds in favour of it are 29 to i. 
 
 I may illustrate this case by an example, which will 
 also serve to shew the characteristic uncertainty attaching 
 to this method of reasoning. Suppose a man to be 
 found lying dead on a road from the effects of a wound. 
 On the same evening on which he died, another man was 
 seen running away from the neighbourhood of the place. 
 On this man's house being searched, his clothes are found 
 to be stained with blood ; his footsteps correspond with 
 those leading to and from the place where the dead 
 man was lying ; and moreover he is known to have 
 possessed a weapon, now not to be found, which was 
 capable of inflicting the wounds. The presumption in 
 favour of his guilt is very great ; each argument, taken 
 alone, possesses some cogency, and when all the argu- 
 ments are taken together they appear to be irresistible. 
 But suppose the suspected man, when arrested, to give 
 this account of the affair : he was walking along the 
 road, armed with a dagger ; he was suddenly attacked 
 by another man ; a scuffle ensued, and in the scuffle 
 he killed his assailant ; finding that he had killed him, 
 he was seized with a sudden panic, threw away his 
 weapon, and ran home. Such an account, in the case
 
 CORROBORATIVE EVIDENCE. 137 
 
 of a timid and secretive man, might possibly be true, 
 and, in estimating the counter-probabilities, we should 
 have to consider the characters of the accused and the 
 dead man, and the nature of the motive, if any, which 
 could have led to the supposed crime. Suppose the 
 dead man's pockets were rifled, and the accused (who 
 had been previously convicted of a felony) were in 
 possession of his money, there could be little doubt 
 that he had committed a murder ; but suppose that the 
 character of the accused was good, and no likely motive 
 could be assigned for the commission of the crime, his 
 own version of the affair might be accepted as probably 
 true, or at least as throwing considerable doubt on the 
 supposition of his guilt *. 
 
 1 As illustrating the danger of exaggerating the value to be attached 
 to this kind of evidence, I could hardly adduce a more forcible 
 example than the following passage from Lord Coke (quoted by 
 Bentham in his Rationale of Judicial Evidence, Bk. V. ch. xv. 2) : 
 
 ' Violenta presumptio is many times plena probatio ; as if one be 
 run thorow the bodie with a sword in a house, whereof he instantly 
 dieth, and a man is seen to come out of that house with a bloody 
 sword, and no other man was at that time in the house.' 
 
 To this Bentham replies by two counter-suppositions : 
 
 ' i. The deceased plunged the sword into his own body, as in the 
 case of suicide ; the accused, not being in time to prevent him, drew 
 out the sword, and so ran out, through confusion of mind, for 
 chirurgical assistance. 
 
 ' 2. The deceased and the accused both wore swords. The 
 deceased, in a fit of passion, attacked the accused. The accused, 
 being close to the wall, had no retreat, and had just time enough to 
 draw his sword, in the hope of keeping off the deceased ; the deceased, 
 not seeing the sword in time, ran upon it, and so was killed. 
 
 Other suppositions might be started besides these ; nor do these
 
 138 PROBABLE REASONING. 
 
 The commonest example of evidence of this kind (which 
 may be called Cumulative or Corroborative Evidence) is 
 Circumstantial Evidence^ so called from the fact that 
 
 exculpative ones either of them seem in any considerable degree less 
 probable than that criminative one : if so, the probability of de- 
 linquency, instead of being conclusive, is but as I to 2.' 
 
 Sometimes the individual arguments in evidence of this kind are 
 of so little value that, even when several of them are accumulated, 
 they have no practical force. ' Presumptio probabilis,' Lord Coke 
 says rightly, ' moveth but little, but presumptio levis seu temeraria 
 moveth not at all.' 
 
 On the other hand, the force of this evidence may amount to that 
 of moral certainty. ' If,' says Mr. Wills, ' it be proved that a party 
 charged with crime has been placed in circumstances which com- 
 monly operate as inducements to commit the act in question, 
 that he has so far yielded to the operation of those inducements as 
 to have manifested the disposition to commit the particular crime, 
 that he has possessed the requisite means and opportunities of 
 effecting the object of his wishes, that recently after the com- 
 mission of the act he has become possessed of the fruits or other con- 
 sequential advantages of the crime, if he be identified with the corpus 
 delicti by any conclusive mechanical circumstances, as by the im- 
 pressions of his footsteps, or the discovery of any article of his apparel 
 or property at or near the scene of the crime, if there be relevant 
 appearances of suspicion, connected with his conduct, person, or 
 dress, and such as he might reasonably be presumed to be able, if 
 innocent, to account for, but which, nevertheless, he cannot or will 
 not explain, if, being put upon his defence recently after the crime, 
 under strong circumstances of adverse presumption, he cannot shew 
 where he was at the time of its commission, if he attempt to 
 evade the force of those circumstances of presumption by false or 
 incredible pretences, or by endeavours to evade or pervert the course 
 of justice, the concurrence of all or many of these cogent cir- 
 cumstances, inconsistent with the supposition of his innocence and 
 unopposed by facts leading to a counter-presumption, naturally, 
 reasonably, and satisfactorily establishes the moral certainty of his
 
 CIRCUMSTANTIAL EVIDENCE. 139 
 
 several circumstances are adduced as all supporting the 
 same conclusion. It will be readily seen that the utmost 
 caution is required in estimating its value. We are bound 
 to consider not only the circumstances which point to 
 the conclusion, but also those which make against it, or 
 in favour of any counter-supposition. It is only when 
 we feel certain that we have exhausted all possible sup- 
 positions, consistent with the circumstances of the case, 
 and considered carefully the value of the arguments, or 
 series of arguments, pointing to each of them, that we 
 are entitled to pronounce with confidence in favour of 
 any particular conclusion. 
 
 Any single syllogism in a coil of circumstantial evi- 
 dence may be represented as an argument with one 
 probable and one certain premiss, thus : 
 
 A man who was seen running away, in order to 
 escape observation, from the place where the 
 dead man was lying, immediately after his death, 
 was probably the murderer, 
 This man was seen running away, &c. ; 
 
 . ' . He was probably the murderer. 
 
 The major premiss of each of these syllogisms is the 
 result of an analogical argument ; and its value must be 
 estimated according to the rules of analogy, already 
 explained. 
 
 guilt, if not with the same kind of assurance as if he had been seen 
 to commit the deed, at least with all the assurance which the nature 
 of the case and the vast majority of human actions admit.' Wills on 
 Circumstantial Evidence, 4 th ed., pp. 276, 7.
 
 140 PROBABLE REASONING. 
 
 Note i. It is more usual to regard the separate syllo- 
 gisms in - a coil of circumstantial evidence as syllogisms 
 in the second figure, involving an undistributed middle, 
 and justifying a probable conclusion. Thus the above 
 syllogism would be represented in the form : 
 
 The murderer would, to escape observation, run 
 
 away, &c., 
 This man, to escape observation, ran away, &c. ; 
 
 . . This man is probably (or possibly) the murderer. 
 It seems however extremely awkward to represent such 
 reasonings as fallacies, and then, by way of compensation, 
 to regard them as probable arguments. This mode of 
 treatment, no doubt, originated in the desire to conform 
 the arguments in circumstantial evidence to those Enthy- 
 mematic syllogisms of Aristotle which employ the (r^flov 
 in the second figure. For an account of the Enthymeme 
 and its subdivisions, the student is referred to Trendelen- 
 burg's Elements, 37, and Dr. Mansel's Appendix to 
 Aldrich, Note F. 
 
 Note 2. -There are some cases, as, for instance, those 
 in which the witnesses may be suspected of lying, or in 
 which they are actuated by violent passions, where circum- 
 stantial evidence may be of far greater value than direct 
 evidence. See some remarks on this subject in an article 
 contributed to the Fortnightly Review for January, 1873, 
 by Sir H. Maine, and since reprinted at the end of 
 Village Communities. On circumstantial evidence, gene- 
 rally, the student would do well to consult Sir Fitzjames 
 Stephen's Introduction to the Indian Evidence Act, Wills
 
 CIRCUMSTANTIAL EVIDENCE. 141 
 
 on Circumstantial Evidence 5 , and Taylor's Treatise on the 
 Law of Evidence, Pt. I. ch. 4. In Direct Evidence, the 
 witness testifies to the precise fact alleged ; in Indirect or 
 Circumstantial Evidence to some fact or facts indicative 
 of the fact alleged. The rules for estimating the logical 
 value of circumstantial evidence apply also to direct evi- 
 dence in all those cases in which we have any reason for 
 questioning either the veracity or the competence of the 
 principal witness, and in which, therefore, his evidence 
 requires corroboration from independent testimony. 
 
 5 The work of Mr. Wills is exceedingly interesting and instructive; 
 but the reader must be on his guard against an erroneous statement 
 on the mathematical value of a coil of circumstantial evidence.
 
 CHAPTER VIII. 
 
 On Fallacies. 
 
 i. A FALLACY is, strictly speaking, a defective 
 inference, but the word is, by common usage, extended 
 to any error either in the premisses or in the conclusions 
 of our arguments. In deductive Logic (for we are not 
 here concerned with the fallacies incident to induction * 
 
 1 The fallacy of False Analogy (which consists either in over- 
 estimating, in some particular case, the value of the argument from 
 analogy, or in supposing an analogy where none exists) falls 
 properly within the domain of Inductive Logic, and is discussed in 
 the author's ' Elements of Inductive Logic,' ch. vi. It is not to be 
 confounded with the fallacy arising from the employment in a 
 syllogism of a word used analogously, as if it were used univocally r 
 which, as already noticed, is one case of the fallacy of ambiguous 
 terms. Thus to argue, because there are certain points of re- 
 semblance between the development of the individual and the 
 development of the race, that, therefore, since the individual dies, 
 the race will probably die also, or, because there are certain points of 
 resemblance between the earth and the other planets, that, therefore, 
 the other planets are certainly, or very probably, inhabited, would 
 both be instances of false analogy, the former being the assumption 
 of an analogy which appears to have no existence, the latter being 
 an exaggeration of the value, in that particular case, of the probable 
 argument. But to argue, because art (i. e. artistic skill) requires the 
 highest intellectual gifts, and dissimulation is art (i. e. deceit), that, 
 therefore, dissimulation requires the highest intellectual gifts, is 
 obviously a mere play upon words, and owes its semblance of reason- 
 ing simply to the ambiguity of language.
 
 FALLACIES. 143 
 
 or to the operation subsidiary to it, observation) these 
 errors are traceable to one of four sources : the assumpr 
 tipn_oafalse premiss,"neglect of the laws of deductiye 
 
 ^ ' " M ^ "T^E^""^"^^* 1 ^* *^^"^^**" """""^""""^^^ ^^ 
 
 inference, irrelevancy, and 'ambiguity of language. Any 
 conclusions, therefore, or series of conclusions, which 
 transgress no law of inference, which are derived from 
 true premisses, which are relevant to the matter under 
 discussion, and which, with their premisses, are expressed 
 in unambiguous language, may be regarded as faultless. 
 
 2. I. A false premiss, borrowed from some science 
 which is not under investigation, can only be detected by 
 a special knowledge of the science from which it is taken. 
 Many fallacies, described in the old books on Logic, are 
 really instances of the assumption of a false premiss, and 
 therefore specially concern other sciences rather than 
 logic. Thus the celebrated fallacy of Achilles and the 
 tortoise (see p. 177) rests upon a false assumption, viz. 
 that when the distances between the two become infini- 
 tesimal they will be traversed by Achilles in finite and equal 
 (and not, as will actually be the case, in infinitesimal and 
 rapidly diminishing) times. 
 
 The phrase ' False Analogy ' is also applied to a perversion of the 
 Analogy of Aristotle (see p. 73) ; namely, to those cases in which 
 the conclusion is based upon relations wherein the two sets of terms 
 compared do not agree. Thus, though, in many respects, the relation 
 of a king to his subjects is the same as that of a father to his 
 children, it is plain that invalid conclusions might be based on this 
 general relation, by extending it to points in which it does not 
 obtain. Such invalid conclusions would be called ' False Ana- 
 logies.'
 
 144 FALLACIES. 
 
 3. II. The fallacies due to thp npgWt nf \\\c* 
 ofdeductive^inference (which, strictly speaking, are the 
 only fallacies to be detected by a mere knowledge of 
 Deductive Logic) have already, to some extent, been 
 discussed. The principal sources of fallacy in a single 
 inference are illicit process and undistributed middle. 
 
 Undistributed middle often occurs in the following 
 form : 
 
 All Conservatives (or Liberals, Roman Catholics, 
 Protestants, Englishmen, Frenchmen, &c.) hold 
 such and such opinions, do such and such things, 
 or possess such and such characteristics ; 
 A B holds such and such opinions, does such and 
 such things, or possesses such and such charac- 
 teristics ; 
 
 . . A B is a Conservative (Liberal, Roman Catholic,&c.). 
 We might, of course, argue quite as legitimately that, 
 because both men and cats are animals, all men are cats. 
 If, however, the argument assumed this shape, 
 
 None but Liberals (Roman Catholics, &c.) hold such 
 
 and such opinions, or do such and such things ; 
 This man holds such and such opinions, or does 
 
 such and such things ; 
 . * . He is a Liberal (Roman Catholic, &c.), 
 it would be perfectly legitimate. 
 
 The major premiss in this case (see p. 84) is equivalent 
 to the proposition ' All men who hold such and such 
 opinions, or do such and such things, are Liberals (Roman 
 Catholics, &c.).' As was shewn in the Chapter on Proba-
 
 FALLACIES. 145 
 
 bilities, we might also advance a perfectly legitimate argu- 
 ment of the following kind : ' A man who holds such 
 and such opinions, or does such and such things, is 
 probably a Liberal (Roman Catholic, &c.) ; this man holds 
 such and such opinions, or does such and such things ; 
 therefore he is probably a Liberal (Roman Catholic, &c.).' 
 Of Illicit Process the following syllogisms may serve as 
 examples : 
 
 No form of democracy excludes the great mass of 
 
 the people from political power, 
 Any form of government which excludes the great 
 mass of the people from political power is subject 
 to violent revolutions ; 
 
 . . No form of democracy is subject to violent revo- 
 lutions. 
 
 The early history of some nations is full of incredible 
 
 events, 
 A history which is full of incredible events is not 
 
 worthy of serious study ; 
 . ' . The early history of any nation is not worthy of 
 
 serious study. 
 
 The former syllogism (AEE in the first figure) involves 
 illicit process of the major, the latter (EIE in the first 
 figure) illicit process of the minor. It will be observed 
 that the various propositions are not stated in strictly 
 logical form, though they easily admit of being so stated, 
 and the premisses of both syllogisms require to be 
 transposed. 
 
 Where there is a long train of reasoning in which one
 
 146 FALLACIES. 
 
 syllogism is employed to prove the premiss of another, 
 and so on, a fallacy frequently occurs, which often 
 escapes detection. This is called the Argument in a 
 Circle. A book is written, or a speech is made, with the 
 object of proving some controverted opinion. The author 
 or speaker, being full of one idea, after a little preliminary 
 matter, assumes the proposition to be proved, slightly dis- 
 guised, probably, under some equivalent form ; from this 
 proposition he deduces various conclusions, and these 
 conclusions, when put together, of course triumphantly 
 establish, from various sides, his view of the controversy. 
 This is not an unfair analysis of many elaborate argu- 
 ments, the fallacy being, in the great majority of in- 
 stances, undesigned, and imposing on the author or 
 speaker himself quite as much as on his readers or 
 hearers. The fallacy, when expressed in its naked form, 
 may be described as the assumption, in a train of reason- 
 ing, of the conclusion of a subsequent syllogism as a 
 premiss of a precedent syllogism. It may be represented 
 thus : 
 
 Syll. (i) B is A, Syll. (2) C is A, 
 
 C is B ; B is C ; 
 
 . . C is A. . . B is A. 
 
 Thus, when asked why B is A, we reply, because C is 
 A ; and when asked why C is A, we reply, because B is A. 
 
 Of course, in actual argument, hundreds of interme- 
 diate syllogisms might occur between syll. (i) and syll. (2). 
 The larger the number of intermediate steps, the more 
 likely is the fallacy to escape detection, and, conversely,
 
 FALLACIES. 147 
 
 the true mode of exposing the fallacy, as Whately 
 observes, is to narrow the circle by cutting out the 
 intermediate steps, and exhibiting the assumption of 
 the conclusion in its naked form. The fallacy is to be 
 regarded as a breach of the laws of inference, because, 
 when reduced to its simplest terms, it is a proving of 
 the conclusion by means of itself, instead of by means 
 of premisses which jointly necessitate it. But, unlike the 
 fallacies of illicit process, &c., already treated, it cannot 
 be detected from the inspection of a single syllogism, but 
 requires the comparison of two syllogisms or more. 
 
 The argument in a circle is the most important case of 
 the fallacy called Petitio Principii (or, as it is more 
 properly called, Petitio Qu&siti, begging the question}. 
 The other cases of petitio principii generally enumerated, 
 though the enumeration is by no means exhaustive, are 
 (2) when the conclusion simply re-asserts a premiss of the 
 same syllogism 2 , (3) when it is exactly synonymous with 3 
 
 * If a syllogism, in which one of the simpler forms of petitio 
 principii occurs, were stated at length, one of the premisses would 
 be otiose (i.e. would not contribute towards the conclusion), but, 
 as already noticed, in our reasonings, as actually expressed, we 
 generally suppress one of the premisses. 
 
 3 ' The English language,' says Archbishop Whately {Elements of 
 Logic, Bk. III. 13), 'is perhaps the more suitable for the fallacy 
 of petitio prineipii, from its being formed from two distinct lan- 
 guages, and thus abounding in synonymous expressions which have 
 no resemblance in sound and no connexion in etymology ; so that a 
 sophist may bring forward a proposition expressed in words of Saxon 
 origin, and give as a reason for it the very same proposition stated 
 in words of Norman origin ; e.g. " to allow every man an unbounded 
 
 L 2
 
 148 FALLACIES. 
 
 one of the premisses, (4) when one of the premisses is 
 equally unknown with the conclusion, (5) when it is more 
 unknown. Cases (4) and (5) are really instances of the 
 assumption of a false premiss, or at least of a premiss 
 which is not known to be true. Cases (2) and (3) arise 
 from a neglect of the laws of syllogism, for, instead of 
 proving the conclusion from the two premisses jointly, we 
 simply re-assert one of the premisses 4 . 
 
 Connected with this fallacy is the rhetorical device of 
 question-begging epithets. Thus, though the matter we are 
 discussing is open to dispute, we may speak of a ne- 
 farious project, a laudable ambition, an astute act, a far- 
 sighted policy, and so on, attempting, by means of a 
 carefully-selected epithet, to assume the point at issue, or 
 at least to create an unfair prejudice in the mind of the 
 hearer or reader whom we address. 
 
 freedom of speech must always be, on the whole, advantageous to 
 the State ; for it is highly conducive to the interests of the com- 
 munity that each individual should enjoy a liberty, perfectly un- 
 limited, of expressing his sentiments." ' 
 
 4 It has sometimes been maintained that every syllogism is a 
 petitio principii. Of course the controversy entirely turns upon the 
 meaning of the terms, but, according to the account I have given of 
 the two, a syllogism is so far from being a petitio principii, that 
 every petitio principii is a distinct breach of the laws of syllogism. 
 The conclusion of a syllogism is indeed implied by the two premisses 
 taken in combination, and is, in fact, the compression into a single 
 proposition of what, as premisses, were two distinct propositions, 
 but, in a petitio principii, the conclusion is merely a re-assertion of 
 one of the premisses : in the simpler cases, of a premiss in the same 
 syllogism ; in the argument in a circle, of a premiss in one of the 
 preceding syllogisms of the series.
 
 FALLACIES. 149 
 
 4. III. The fallacy of Irrelevancy (or, as it is some- 
 times called, shifting ground) is technically termed Igno- 
 ratio Elenchi, i. e. ignorance of the syllogism required for- 
 the refutation of an adversary. Thus, in the strictest 
 sense of the words, ignoratio elenchi is committed by a 
 person who in a disputation does not confine himself to 
 proving the contradictory or contrary of his adversary's 
 assertion, or who proves a proposition other than the 
 contradictory or contrary. But, like many other terms 
 borrowed from the dialectical disputations of the ancients, 
 this has now received a wider meaning. Whenever an 
 argument is irrelevant to the object which a speaker or 
 writer professes to have in view, it is called an ignoratio 
 elenchi. Thus, if I am endeavouring to convince a person 
 that some particular measure is for his personal interest, 
 and I adduce arguments to prove that it contributes to 
 the general utility, or that it is the necessary consequence 
 of other acts of legislation, I am guilty of an ignoratio 
 elenchi, as I should also be if, when it was my object 
 to establish either of the other two conclusions, I were 
 to appeal to his personal interest. When the question 
 at issue is the truth of an opinion, it is an ignoratio 
 elenchi to attack it for its novelty, or for its coming from 
 a foreign source, or for any supposed consequences 
 which may result from it, or to try to throw discredit on 
 its author by saying that it has often been started before, 
 and so is no discovery of his. 
 
 This fallacy is more common in spoken addresses than 
 in books, as the feelings both of speaker and hearers
 
 150 FALLACIES. 
 
 being more excited, and their judgment less critical, they 
 are less likely to insist on relevancy of argument. On 
 such occasions it most commonly takes the form of an 
 argumentum ad hominem, whereby the speaker, in support 
 of the truth of his assertions, or to throw discredit on 
 an adversary, appeals, not to the unbiassed judgment of 
 his auditors, but to their passions, interests, prejudices, 
 sentiments and associations. The argumentum ad homi- 
 nem, however, is not confined to set speeches ; it some- 
 times occurs in writings, and frequently in debates. In 
 the latter, it often assumes the shape of an appeal to the 
 previous acts, or the previously expressed convictions of 
 the opponent ; ' That measure, or that argument, or that 
 proposal does not come well from you, who once pro- 
 posed such a measure, or expressed such an opinion, or 
 advanced such an argument, or did such and such acts.' 
 There are occasions when the argumentum ad hominem 
 may legitimately be used as a retort, but it must be 
 advanced as such, and not as an argument. It is so 
 called in opposition to the argumentum ad rent or ad 
 judirium. Similar phrases are used to express other 
 forms of the ignoratio elenchi, as e. g. the argumentum 
 ad verecundiam, argumentum ad baculum, &c. The argu- 
 mentum ad populum I have treated as identical with the 
 argumentum ad hominem ; if called on to distinguish them, 
 which seems unnecessary, I should refer the first to 
 addresses made in the presence of a large auditory, the 
 second to disputations with one or a few individuals 5 . 
 5 The student will find some amusing examples of ignoratio
 
 FALLACIES. 151 
 
 5. IV. The fallacy originating in ambiguity of 
 language I noticed when warning the student against 
 the employment of equivocal terms. This fallacy (whe- 
 ther we call it that of equivocal terms, of ambiguous 
 terms, or of ambiguity of language) of course includes 
 fallacies arising from any ambiguity which may attach 
 to the quantity of the subject, as e. g. the fallacy arising 
 from the ambiguous use of the word ' all,' which will be 
 noticed below. 
 
 I now proceed to notice one or two common cases 
 of this fallacy. The same term may often be used in 
 one place distributively and in another collectively, and 
 we may argue as if the term in both places had the same 
 meaning. This is galled the fallacy of Composition or 
 Division ; of composition, if we argue from a term taken 
 distributively as if it were taken collectively ; of division, 
 if we argue from a term taken collectively as if it were 
 taken distributively. Thus (to give common instances) 
 7 and 2 are (distributively) odd and even, nine is 7 
 and 2 (collectively) ; . . nine is odd and even. Here 
 we argue from 7 and 2 taken distributively, as if they 
 had been taken collectively, and the fallacy is one of 
 composition. Five is one number, 3 and 2 (collectively) 
 are five ; . ' . 3 and 2 (distributively) are one number. 
 Here the fallacy is one of division. Again, The people 
 of England have a prejudice against the French, he is 
 one of the people of England ; . . he has a prejudice 
 
 elenchi, or irrelevant argument, in Sydney Smith's well-known jeu 
 d'esprit, the Noodle's Oration.
 
 152 FALLACIES. 
 
 against the French. The major premiss might be quite 
 true, and still the particular man spoken of might have 
 a strong sympathy with the French, and be a warm 
 admirer of their institutions. Here we argue from the 
 term ' people,' taken collectively, as if it had a distribu- 
 tive signification and whatever were predicable of the 
 English people might be predicated of every single in- 
 dividual amongst them ; hence the fallacy is one of 
 division. The last instance is an example of a very 
 common source of deception. A certain people, corpo- 
 ration, or society, in its collective capacity, has certain 
 characteristics, has performed certain acts, passed cer- 
 tain resolutions, or is known to have expressed certain 
 sentiments ; hence it is unreflectingly supposed that any 
 particular individual belonging to the class has the same 
 characteristics, participates in the same sentiments, and 
 has joined in the same acts. In many cases, of course, 
 he may be a strong dissentient, and may have actively 
 opposed the measures adopted. 
 
 The ambiguous use of the word ' all ' furnishes a good 
 instance of the fallacies of composition and division. We 
 may argue from 'all,' meaning all taken together, as if 
 it meant all severally, and thus commit the fallacy of 
 division ; or from ' all,' meaning all severally, as if it 
 meant all taken together, and thus commit the fallacy of 
 composition. Thus, when I say, ' All these boxes weigh 
 so much,' or ' All these men can eat so much,' I leave it 
 doubtful whether I mean all taken together or all taken 
 severally. The ambiguity may be removed by substituting
 
 FALLACIES. 1 53 
 
 for the word 'all,' when used in a distributive sense, 'every,' 
 and, when used in a collective sense, ' the whole of.' 
 
 Another pair of fallacies which falls under the head of 
 ' ambiguous terms ' is the pair known as the Fallada 
 Accidentis (or the Fallada a dicto simp Hater ad dictum 
 secundum quid) and the Fallada a dicto secundum quid ad 
 dictum simplidter. In the first we argue from what is 
 true as a general rule (i. e. unless there be some modi- 
 fying circumstances) as if it were true under all circum- 
 stances ; in the second from what is true under certain 
 special circumstances as if it were true as a general 
 rule. Thus a particular walk may be an agreeable 
 one, but it does not follow that it would be so in 
 wet or windy weather ; plain-speaking, frugality, gene- 
 rosity, may all be virtues, but it does not follow that 
 it would be virtuous to practise them on all possible 
 occasions. Or, to take instances of the second fallacy, 
 a political revolution may, under particular circum- 
 stances, be necessary to the welfare or existence of a 
 country, but it does not follow that a state of society, 
 in which political revolutions are frequent, is either 
 necessary or desirable ; it may be necessary if I am 
 suffering from a particular disease that I should take 
 opium or abstain from labour, but it does not follow 
 that these practices would be good for me when I am 
 restored to health. The fallacies are due to our not 
 sufficiently qualifying the terms which we use, and, by 
 insisting on precision of language, they may always be 
 avoided.
 
 154 FALLACIES. 
 
 Though the definitions I have given of this pair of 
 fallacies are conformable to the usage of most modern 
 logicians 6 , and are stated in a form which is most likely 
 to be of practical service to the student, they do not 
 exactly correspond with the original meaning of the 
 expressions. The ' Fallacia Accidentis ' and the ' Fallacia 
 a dicto secundum quid ad dictum simpliciter/ according 
 to their original usage, applied to those cases in which a 
 term, when not implying accidents, was confounded with 
 the same term, when implying accidents. Thus, to take 
 the common instance (which is sufficiently absurd): 'What 
 you buy in the market you eat ; raw meat is what you 
 buy in the market ; . . raw meat is what you eat.' Here 
 it may be replied that what we buy in the market we do 
 indeed eat, but not necessarily in the same state in which 
 we buy it at market 7 . This particular instance is an 
 
 6 As, for instance, Mill (Logic, Bk. V. ch. vi. 4), Port Royal 
 Logic (Part III. ch. xix. 5, 7). The latter virtually treats both 
 fallacies as if they were a dicto secundum quid ad dictum simpliciter. 
 
 7 Mr. de Morgan adduces one of Boccaccio's stories as affording 
 an amusing instance of the fallacia accidentis. It is the old example 
 of the ' raw meat ' in another form : 
 
 ' A servant who was roasting a stork for his master was prevailed 
 upon by his sweetheart to cut off a leg for her to eat. When the 
 bird came upon table, the master desired to know what was become 
 of the other leg. The man answered that storks had never more 
 than one leg. The master, very angry, but determined to strike his 
 servant dumb before he punished him, took him next day into the 
 fields where they saw storks, standing each on one leg, as storks do. 
 The servant turned triumphantly to his master, on which the latter 
 shouted, and the birds put down their other legs and flew away. " Ah, 
 sir," said the servant, "you did not shout to the stork at dinner
 
 FALLACIES. 1 55 
 
 example of the Fallacia Accidentis.. From their technical 
 meaning, these fallacies would easily pass into their pre- 
 sent signification, which is both more intelligible and of 
 greater practical service. 
 
 I may notice one more example of the errors due 
 to ambiguous language, viz. the fallacy of what may be 
 called Paronymous Terms. The same word may often 
 assume different forms, as substantive, adjective, adverb, 
 or verb, but it does not follow, when it has assumed 
 these different forms, that they all retain corresponding 
 meanings. It has been already noticed that the words 
 probably, probable, probability, though the two last are 
 themselves ambiguous, vary in meaning according as we 
 use the adverb, the adjective, or the substantive. Thus, 
 if I hear some one ask the question ' What is the pro- 
 bability of my throwing an ace with a die at a single 
 throw ? ' I cannot infer that in any single throw I shall 
 probably throw an ace. Again, because a man has done 
 something unjust (i. e. has committed an act which in 
 tts results is unjust), I cannot infer that he has acted un- 
 justly (i. e. with intentional injustice), nor, even if he has 
 acted unjustly (i. e. in one or more instances), can I infer 
 that he is an unjust man (i. e. a man of unjust habits or 
 character). To take an old instance, because projectors 
 are unfit to be trusted, and this man has formed a pro- 
 ject, it does not follow that he is unfit to be trusted. 
 Nor from the meaning attached to the expressions, kingly, 
 
 yesterday: if you had done so, he would have shewn his other leg 
 too." '
 
 156 FALLACIES. 
 
 nobly, gentlemanly, can we argue to the usual qualities 
 of a king, a nobleman, or a gentleman ; nor, on the 
 meanings of the words ' to trow,' ' to represent,' can we 
 base any sound argument as to the nature of truth, or 
 the duties of a representative. All instances of this fal- 
 lacy, when stated syllogistically, involve four terms, and 
 so offend against the rules for the construction of a 
 syllogism, but, as we do not ordinarily state our argu- 
 ments in a syllogistic shape, and these fallacies undoubt- 
 edly impose on us through the ambiguity of language, 
 it is better to consider them here rather than under the 
 second head. 
 
 Many other forms of fallacy may be regarded as due 
 to ambiguities of language, but it has perhaps been the 
 tendency of modern logicians, and especially of Whately, 
 to overload this division of fallacies, and to treat as merely 
 differences of language what are in reality radical differ- 
 ences of opinion. At the same time it cannot be denied 
 that terms expressive of fundamental conceptions in their 
 several sciences, such as faith, church, election, law, loyalty, 
 federation, justice, value, capital, force, nature, natural, &c., 
 are frequently used, in the same discussion, in the most 
 widely divergent senses, and are consequently the source 
 of endless confusion in our reasonings. Thus the term 
 ' faith ' may mean either a belief "in certain propositions, or 
 confidence, trust, and repose in a certain person ; the word 
 ' church ' may mean the whole body of Christians (and, 
 of course, in this sense its signification will vary accord- 
 ing to the meaning attached to the term Christian), a,
 
 FALLACIES. 157 
 
 particular section of Christians, a congregation meeting 
 in a certain place, the place of meeting, and, lastly, 
 by a strange perversion of the term, the clergy as dis- 
 tinguished from the laity ; the term ' loyalty ' may mean 
 either attachment to the laws of a country in general, 
 special attachment to some particular portion of the laws, 
 or, in its most restricted sense, personal attachment to the 
 supreme ruler ; ' capital ' may mean either the amount of 
 money possessed by a trader, or his whole stock of 
 commodities available for future production ; ' natural ' 
 may express either the original condition of a thing, or 
 the state into which it is ultimately developed, besides 
 having countless other meanings. On account of the 
 various significations which may be attached to the same 
 term, it is necessary, in entering on any investigation, 
 carefully to define the terms to be employed, and never, 
 without express notice, to deviate from the sense thus 
 imposed upon them 8 . 
 
 8 The so-called ' Fallacia plurinm interrogationnm ' has not been 
 noticed in the text, because it is a rhetorical artifice, rather than 
 a logical fallacy. It consists in covertly putting as a single question 
 what is in reality two, as, for instance, ' Are gall and honey sweet ? ' 
 'Have you cast your horns?' (known as 'cornutus'). 'What did 
 yon take, when you broke into my house last night ? ' ' Have you 
 given up beating your father?' The object is to entrap the re- 
 spondent into an admission which he would otherwise not be likely 
 to make.
 
 CHAPTER IX. 
 
 On Method as applied to the arrangement of 
 Syllogisms in a Train of Reasoning. 
 
 I DO not propose to treat of Method in general (for 
 this would involve a discussion of induction and the various 
 relations in which it stands to deductive inference), but it 
 may be useful to the student if I offer a few remarks on 
 Method under the limitation stated in the heading of this 
 chapter. When syllogisms are combined in a train of 
 reasoning, we may either commence with the conclusion, 
 and ask what reasons we have for believing it, and then go 
 on to ask the reason for believing the premisses, and so 
 on, till at last we arrive at some propositions of which there 
 is no doubt, or in which we at least can acquiesce ; or 
 else we may follow the reverse process, and commencing 
 with propositions which are the result of some previous, 
 investigation, or which we at all events accept as true, 
 may go on combining them with each other, till at last 
 we arrive at some conclusion which we regard as suffi- 
 ciently important to terminate our enquiries. The former 
 method will be familiar to my readers as that by which 
 we solve what are called 'geometrical deductions,' and 
 in fact as the method which we generally though not
 
 ANALYTICAL AND SYNTHETICAL METHODS. 159 
 
 universally employ when we are attempting to resolve 
 difficulties for ourselves ; the latter as the method by 
 which the propositions in Euclid are proved, and ir. 
 fact as the method which we generally though not uni- 
 versally employ, when it is our object to teach others 
 either orally or by book. Now the former method is 
 called Analytical (from the Greek word ai/oAuem), because 
 it may be regarded as the breaking up of a whole into its 
 parts, the resolution of the final conclusion of a series 
 of syllogisms into the various premisses on which it de- 
 pends, and of which it is, as it were, the total expression. 
 The latter method is called Synthetical (from the Greek 
 word (Tvvdfais), because it may be regarded as the putting 
 together of the parts into a whole, the combination of the 
 various premisses into a conclusion which is, as it were, 
 their total result. The Synthetical Method is also 
 sometimes called Progressive, and the Analytical Method 
 degressive, for reasons which will be apparent from what 
 has already been said. 
 
 The words a priori and a posteriori may also be used 
 to express the same distinction. In inductive inference 
 (to which these terms are more properly applied) we are 
 said to proceed a posteriori, when, a certain event having 
 taken place, we attempt to trace the steps by which it 
 came about, or, a certain phenomenon being presented 
 to us for examination, we attempt to infer the mode of 
 its production ; and, vice versa, we are said to proceed 
 a priori, when, from our knowledge of certain circum- 
 stances, we attempt to predict an event, or, by putting in
 
 160 METHOD AS APPLIED 70 THE ARRANGEMENT 
 
 operation certain causes, we attempt to discover their effect. 
 Similarly, in deductive inference, if, a conclusion being 
 assumed as provisionally true, we attempt to discover 
 reasons for it, we may be said to proceed a posteriori ; if, 
 starting with the premisses, we go on combining them to 
 see whither they will lead us, we may be said to proceed a 
 priori. In the former method of reasoning, we are pecu- 
 liarly liable to impose on ourselves or others by availing 
 ourselves of premisses which are fanciful, obscure, in- 
 capable of proof, questionable, or untrue, especially if the 
 conclusion express some cherished conviction or some 
 position which it is the interest of ourselves, our class, 
 or our party to accept and to disseminate. Whenever, 
 therefore, we argue from our conclusions backwards, 
 especial caution is required, if it be our sincere desire to 
 test our convictions impartially. 
 
 There is also a more general employment of these 
 latter expressions, according to which the term a posteriori 
 is appropriated to designate inductive reasoning, which 
 ought always to be based on individual facts of observa- 
 tion ; a priori to designate deductive reasoning, which 
 proceeds from general principles. The expression a priori 
 is often applied by way of censure to deductive reasoning, 
 when the general principles from which it proceeds are 
 supposed to rest on no ultimate inductions from fact, but 
 to be mere assumptions arbitrarily taken for granted by 
 the author who employs them.
 
 OF SYLLOGISMS IN A TRAIN OF REASONING. l6l 
 
 Note. For an account of the various senses in which 
 the words ' analysis ' and ' synthesis ' are or have been 
 employed, the student is referred to Sir W. Hamilton's 
 Lectures on Logic, Lect. xxiv, and Dr. Mansel's edition 
 of Aldrich, Appendix G.
 
 APPENDIX. 
 
 On the Five Words 'Genus', ' Species ',' 
 1 Differential 'Property! 'Accident' 
 
 WHEN two classes are so related to each other that one 
 is contained under the other, the larger or containing class is 
 called the Genus, and the smaller or contained class is called 
 the Species. Thus, if we compare animal and man, man is 
 a species, and animal the genus ; if a man and Englishman, 
 man is the genus, and Englishman a species : if we compare 
 moss-rose and rose, moss-rose is a species, and rose the 
 genus ; if rose and flower, flower is the genus, and rose a 
 species. 
 
 Genera and Species are denoted by Common Terms, which 
 themselves also, as well as the groups which they denote, 
 are called Genera and Species. 
 
 In the A proposition, a genus can be predicated of a 
 species, but not a species of a genus. Thus we can say 
 'All men are animals,' or 'Man is an animal,' but not 'All 
 animals are men,' or 'An animal is a man.' In the I pro- 
 position, on the other hand, the genus may be the subject, 
 and in the O proposition, if the terms compared are genus 
 and species, must be. 
 
 The distinction between Differentia, Property, and Acci- 
 dent is more difficult, but may be explained by reference 
 to what has been said (Pt. I. ch. ii.) on the Connotation 
 of Terms. 
 
 As the former distinction was applicable to classes and the 
 common terms which denote them, so this is applicable to
 
 APPENDIX. 163 
 
 attributes and the attributives by which attributes are ex- 
 pressed. It may be noticed also that a Differentia, Property, 
 or Accident, being expressed by an Attributive, must be 
 a predicate and cannot be a subject. Now, taking any 
 common term, or any abstract term used as a common 
 term, like triangle, an attributive predicated of it may ex- 
 press either part of its connotation or not. Thus, if we 
 assert that ' A triangle is a three-sided rectilineal figure,' the 
 term ' three-sided,' like the genus ' figure,' is connoted by the 
 very term ' triangle.' Moreover, the term ' three-sided ' 
 serves to differentiate or distinguish ' triangle ' from all other 
 rectilineal figures, such as quadrilateral, pentagon, &c. Hence 
 we may define differentia as on p. 46. Here however a 
 difficulty occurs. Two or more species falling under the 
 same genus may be distinguished by more than one dif- 
 ferencing attribute. In this case we should speak of the 
 differentia, or we might speak of the differentia as the sum 
 of the differentia. 
 
 But, in case the attributive does not express any part of the 
 connotation of the term, it may, nevertheless, express some 
 attribute which follows from the connotation. Thus, if we 
 say ' A triangle is a rectilineal figure having the sum of its 
 angles equal to two right angles,' we are predicating by the 
 expression ' having ' &c., not part of the connotation of 
 the word triangle, but an attribute which may be directly 
 inferred from part of the connotation. Or, again, if we were 
 dealing with some moral or physical phenomenon, the attri- 
 bute might follow, not as a conclusion from a premiss, but as 
 an effect from a cause. Thus we might predicate of man that 
 he is ' capable of progress,' this capability being regarded as 
 an effect of his rationality ; or of animal and vegetable tissues 
 that they are liable to decay, this liability being regarded 
 as an effect of the material of which they are composed 
 and the influences to which they are subject. Hence the 
 definition of Property on p. 46. 
 
 M 2
 
 1 64 APPENDIX. 
 
 Lastly, the attributive may neither express any part of 
 the connotation of the term, nor any attribute which follows 
 from part of the connotation. In this case it is called an 
 Accident. But accidents are of two kinds. If an accident may 
 be predicated of all the individuals denoted by a common 
 term, as, to take the conventional instance, blackness of crows, 
 it is called an Inseparable Accident. In the most common 
 case, where it is predicable of some of the individuals and 
 not of others, as, for instance, blackness of men, it is called 
 a Separable Accident. 
 
 The student is recommended to compare, throughout, this 
 explanation with the definitions given on p. 46.
 
 EXAMPLES.
 
 EXAMPLES. 
 
 EXAMINE the following Definitions or Descriptions 
 (pointing out their faults, if any, and, where they 
 are sufficient, stating under what head of Defini- 
 tion or Description they fall). 
 
 (1) A square is a four-sided rectilinear figure, having all its 
 
 sides equal. 
 
 (2) Monarchy is a form of political government in which 
 
 one man is sovereign. 
 
 (3) An University is a corporation which grants learned 
 
 degrees. 
 
 (4) Logic is the Art of Reasoning. 
 
 (5) A plane triangle is a figure generated by the section of 
 
 a cone passing through the vertex and perpendicular 
 to the base. 
 
 (6) Wealth is the sum of things useful, necessary, and 
 
 agreeable. 
 
 (7) Man is a mammal having hands, and cooking his own 
 
 food. 
 
 (8) An animal is a sentient organised being. 
 
 (9) A liquid is that which can be poured out. 
 
 (10) A Federation is a political union the members of which 
 are bound together for purposes of offence and de- 
 fence. 
 
 (n) Man is a mammal possessing the power of articulate 
 speech. 
 
 (12) Political Philosophy is the science of the laws which 
 govern the equilibrium and development of human 
 society.
 
 1 68 EXAMPLES. 
 
 Examine the following Divisions, substituting, where they 
 are incorrect, one or more correct ones. 
 
 (1) Men into Aryans, Mongolians, Africans, and Americans. 
 
 (2) Quadrilateral Figures into Squares, Rectangles, Paral- 
 
 lelograms, and Rhomboids. 
 
 (3) The Fine Arts into Painting, Drawing, Sculpture, 
 
 Architecture, Poetry, and Photography. 
 
 (4) Governments into Monarchies, Tyrannies, Oligarchies, 
 
 and Democracies. 
 
 (5) Books into entertaining and unentertaining. 
 
 (6) Men into those who lend and those who borrow. 
 
 (7) The Sciences into Physical, Social, Ethical, Logical, and 
 
 Metaphysical. 
 
 (8) Plants into Flowering Plants, Mosses, Ferns, and Pines. 
 
 (9) The origin of Colonies is to be traced either tc the 
 
 necessity for frontier garrisons (as amongst the 
 Romans) or to the poverty or discontent of the in- 
 habitants of the mother-country (as amongst the Gieeks 
 and ourselves). 
 
 (10) 'The general stock of any country or society is the 
 same with that of all its inhabitants or members, 
 and therefore naturally divides itself into the same 
 three portions, each of which has a distinct function 
 or office : 
 
 1st, that portion which is reserved for immediate con- 
 sumption, and of which the characteristic is that 
 it affords no revenue or profit ; 
 
 2nd, the fixed capital, of which the characteristic is that 
 it affords a revenue or profit without circulating or 
 changing masters ; 
 
 3rd, the circulating capital, of which the characteristic 
 is that it affords a revenue only by circulating or 
 changing masters.' Adam Smith's Wealth of Nations, 
 Vol. ii. ch. i.
 
 EXAMPLES. 169 
 
 Convert the following propositions (previously permuting 
 them, where necessary). 
 
 (1) All plane triangles are rectilinear figures. 
 
 (2) All plane triangles are'three-sided rectilinear figures. 
 
 (3) All plane triangles may be defined as three-sided rec- 
 
 tilinear figures. 
 
 (4) Some branches of Mathematics admit of a direct prac- 
 
 tical application. 
 (5^ Men of fair promises arejoften not to be trusted. 
 
 (6) Some members of the Government are not prepared to 
 
 accept the measure. 
 
 (7) Virtue is a condition of Happiness. 
 
 (8) Virtue is /the condition of Happiness. 
 
 (9) A syllogism is a form of inference. 
 (10) With man many things are impossible. 
 
 (n) Some men of great powers of imagination are not poets. 
 
 (12) None but persons of great powers of imagination are 
 
 poets. 
 
 (13) What I have written, I have written. 
 
 (14) Propositions are either simple or complex. 
 
 (15) The proper study of mankind is man. v 
 
 (16) Only the ignorant affect to despise knowledge. 
 
 (17) He can't be wrong whose life is in the right. 
 
 State in logical form (where necessary) and examine the 
 following arguments. 
 
 (1) Every book is liable to error, 
 Every book is a human production ; 
 
 .'. All human productions are liable to error. 
 
 (2) All tulips are beautiful flowers, 
 No roses are tulips ; 4. 
 
 /. No roses are beautiful flowers.
 
 EXAMPLES. 
 
 V r | , 
 
 (3) Some men are wise, ' 
 
 
 Some men are good ; 
 /. Some wise men are good. 4/ 
 
 (4) All wise men are good, (X/ 
 Socrates was a wise man ; V 
 
 /. He was good. Q,y 
 
 (5) Some mathematicians are logicians, 
 
 No logicians are unacquainted with the works of 
 
 Aristotle ; 
 
 ^ .*. Some mathematicians are not unacquainted with the 
 works of Aristotle. 
 
 (6) No persons destitute of imagination are true poets, 
 Some persons destitute of imagination are good 
 
 logicians ; 
 .'. Some good logicians are not true poets. 
 
 (7) No persons destitute of imagination are true poets, 
 Some persons destitute of imagination are good 
 
 logicians ; 
 /. Some true poets are not good logicians. 
 
 (8) If Caesar was a tyrant, he deserved to die, 
 Caesar was not a tyrant ; 
 
 .'. He did not deserve to die. 
 
 M) If virtue is involuntary, vice is also involuntary, 
 _^ Vice is voluntary ; 
 
 /. Virtue is also voluntary. 
 
 (10) All valid syllogisms have three terms, 
 This syllogism has three terms ; 
 
 /. It is a valid syllogism. 
 
 (11) Some learned men have become mad, 
 He is not a learned man ; 
 
 .'. He will not become mad. 
 
 (12) The Reformers were bitter enemies of the Papal 
 
 Supremacy,
 
 A B was a Reformer (for he was prominent in sup- 
 porting the Reform Bill of 1832) ; 
 .'. He was a bitter enemy of the Papal Supremacy. 
 
 (13) Logic is either a science or an art, Fi* v^T^.. 
 It is a science ; ^ &L 
 
 /. It is not an art. .Jlji 
 
 (14) Six and seven are even and uneven, 
 Thirteen is six and seven ; 
 
 /. Thirteen is even and uneven. 
 
 (15) He must be a Mahommedan, for only Mahommedans 
 
 hold these opinions. 
 
 (16) He must be a Mahommedan, for all Mahommedans 
 
 hold these opinions. \}j t K .-t. .-'^ 
 
 (17) To reject this proposal would be unreasonable, and 
 
 consequently to accept it is reasonable. 
 
 (18) This event happened either at Rome, Naples, or 
 
 Florence ; it did not happen at Rome or Naples, 
 and consequently it must have happened at 
 Florence. 
 
 (19) Logic is indeed worthy of being, cultivated, if Aristotle 
 
 is to be regarded as infallible ; but he is not : Logic, 
 therefore is not worthy of being cultivated. 
 
 (20) An indissoluble association of ideas commands belief, 
 
 and consequently every belief is the consequence jpf r\ 
 an indissoluble association of ideas. *r$J&. 0) *M* 
 
 (21) This measure would be destructive of the national - 
 
 prosperity, and I cannot adduce a more cogent - 
 argument than that, five years ago, you were your- 
 self of the same opinion. X. wvxn/MA^ 1 
 
 (22) If a man cannot make progress towards perfection, he 
 
 must either be a brute or a divinity ; but no man is '. t 
 either: therefore every man is capable of such progress. 
 
 (23) Lias lies above New Red Sandstone, New Red Sand- 
 
 /, Y&^ ** * /Wvt */? 
 
 v\ *-wve u*-*JL ^k^ 
 
 - ' * : .
 
 172 EXAMPLES. 
 
 A 
 
 stone lies above coal ; therefore Lias lies above 
 Coal. 
 
 24) My hand touches the pen ; the pen touches the pa. , v 
 _ therefore my hand touches the paper. 
 
 25) A, B, C, D, and E, are the only German students I 
 
 know : they are all men of considerable intellectual 
 attainments, and consequently I may infer that all 
 German students are men of considerable intellec- 
 tual attainments. 
 
 All equilateral triangles are equiangular, and therefoprfV^ 
 all equiangular triangles must be equilateral. 
 
 (27) These two figures are equal to the same figure, and 
 
 therefore to one another. 
 
 (28) For those who are bent on cultivating their "minds by 
 
 diligent study, the incitement of academical honours 
 is unnecessary ; and it is ineffectual for the idle and 
 such as are indifferent to mental improvement : 
 therefore the incitement of academical honours is * 
 either unnecessary or ineffectual. 
 
 (29) He has no appreciation of beauty, for he has no taste 
 
 T .. < . *i_ f i 
 
 for Pictures. 
 
 ^{26 
 
 (30) Warm countries alone produce wines, Spain is a warm 
 
 country ; therefore Spain produces wines. < 
 
 (31) The Germans are a literary nation ; therefore A B, 
 
 who is a German, is a literary man. 
 
 (32) We must increase the income-tax, for war has become 
 
 a necessity, and we cannot go to war without money, 
 and money can only be raised by taxation, and the 
 only tax which the resources of the country can bear 
 is the income-tax, which will fall on the richer part 
 of the population." ^V 
 
 (33) Governors of dependencies should be vested with ab- 
 
 solute power, for otherwise it is impossible to crush 
 rebellion.
 
 EXAMPLES. 173 
 
 (34) A is larger than B, and B is larger than C ; therefore, 
 
 a fortiori, A is larger than C. 
 
 (35) Alexander is the son of Philip, and therefore Philip is 
 
 the father of Alexander, c^ >***>* *^**- 
 
 (36) If ' to improve is to change, and to be perfect is 
 
 have changed often,' what hope can we entertain o 
 those who oppose change ? IJ&A/^^^^^' 
 
 \ (37) Luxury is at once beneficial and injurious to society ; 
 for luxury is the using the gifts of Providence, either 
 to the injury of the user, or to the injury of others 
 towards whom the user stands in any relation which 
 obliges him to aid and assistance ; but luxury causes 
 expenditure of money, and therefore is beneficial to 
 society. j*&s^ 
 
 (38) Old age is wiser than youth ; therefore it is only 
 
 reasonable that we should be guided by the de-^- 
 cisions of our ancestors. 
 
 (39) A man cannot always be right in his opinions, and 
 
 therefore we ought continually to distrust our 
 judgments. 
 
 (40) Had an armistice been beneficial to France and Ger- 
 
 many, it would have been agreed upon by those 
 powers ; but such has not been the case : it is 
 plain, therefore, that an armistice would not have 
 been advantageous to either of the belligerents. 
 
 (41) If education is popular, compulsion is unnecessary ; 
 
 if unpopular, compulsion will not be tolerated. 
 * (42) I will not do this act, because it is unjust ; I know 
 that it is unjust, because my conscience tells me so, 
 and my conscience tells me so, because the act is 
 wrong. 
 
 (43) This proposition is too good to be practicable. 
 
 (44) Such and such a system of education has produced 
 
 several distinguished men ; therefore it does not 
 admit of any improvement.
 
 1 74 EXAMPLES. 
 
 (45) Slavery is a natural institution ; but what is natural is 
 
 just, and what is just it is unjust to abrogate ; and 
 consequently it would be unjust to abrogate slavery. 
 
 (46) ' Mercy but murders, pardoning those that kill.' 
 
 Romeo and Juliet. Act iii. Sc. I. 
 
 (47) A, B, and C have distinguished themselves both in 
 
 athletic sports and intellectual pursuits ; therefore 
 those who are most famous for their excellence in 
 athletic sports are generally most famous for their 
 intellectual attainments as well. 
 
 (48) What is called a 'constitutional monarchy' is impos- 
 
 sible, for the sovereign authority of a state cannot 
 be limited by law ; now the king is sovereign, and, 
 as such, cannot be subject to any superior authority. 
 
 (49) Parallel lines are equi-distant ; for, if from two points 
 
 in one of them perpendiculars be drawn to the 
 other, these perpendiculars are parallel (Euc. I. 28), 
 and the two lines intercepted between them are 
 parallel ; therefore a parallelogram is formed, of 
 which the perpendiculars are opposite sides and 
 therefore equal. 
 
 (50) If Bacon's opinion is right, it is improper to stock a 
 
 new colony with the refuse of jails ; but this course we 
 must allow not to be improper, if our method of 
 colonising New South Wales be a wise one : if this 
 be wise, therefore, Bacon's opinion is not right. 
 
 (51) 'Profit' is interpreted in the dictionary 'advantage'; 
 
 to take profit, then, is to take advantage : it is 
 wrong to take advantage of one's neighbour : there- 
 fore it is wrong to take profit. 
 
 (52) Romulus must be a historical person, because it is not 
 
 at all likely that the Romans, whose memory was 
 only burdened with seven kings, should have for- 
 gotten the most famous of them, namely, the first. 
 
 (53) You maintain that an action can only be called virtuous,
 
 (EXAMPLES^ 175 
 
 if it contribute to the welfare of mankind or of some 
 section of mankind : hence you are bound to regard 
 every convenient object, for instance a horse, a tree, 
 or a chair, as virtuous. 
 
 (54) The knowledge of things is more useful than the know- 
 
 ledge of words ; and, therefore, the study of nature 
 is more improving to the mind than the study of 
 language. 
 
 (55) In a lottery it is improbable that any particular ticket- 
 
 holder will draw the prize. But some one must draw 
 the prize. Therefore something improbable must 
 happen. 
 
 (56) My informant A heard his story from B, who would 
 
 certainly tell it as originally told to him ; B heard it 
 from C, who would probably tell it accurately ; 
 C from D, who would also probably tell it accurately ; 
 D from E, who, I have no reason to suppose, would 
 tell it inaccurately : I may consequently receive A's 
 story as probably accurate. 
 
 (57) Large colonies are as detrimental to the power of a 
 
 state as overgrown limbs to the vigour of the human 
 body. 
 
 (58) All law is an abridgment of liberty, and consequently 
 
 of happiness. 
 
 (59) I am under an obligation to do it, but he who is obliged 
 
 has no power of resistance ; consequently I have no 
 choice about the matter. 
 
 (60) You never give an opinion without believing yourself 
 
 to be right, and therefore you must suppose yourself 
 to be infallible. 
 
 (61) If man be not a necessary agent, determined by plea- 
 
 sure and pain, there is no foundation for rewards and 
 punishments. These would be useless, unless men 
 were necessary agents, and were determined by 
 pleasure and pain : because, if men were free and
 
 176 EXAMPLES. 
 
 indifferent to pleasure and pain, pain could be no 
 motive to cause men to observe the law. 
 
 (62) Night invariably precedes day, and therefore night must 
 
 be the cause of day. 
 
 (63) The planet Mars resembles the Earth in the possession of 
 
 an atmosphere, clouds, and water, and has a tempera- 
 ture in which terrestrial life might exist, and, therefore, 
 it is probably inhabited as the earth is. 
 
 (64) ' If it be fated that you recover from your present dis- 
 
 ease, you will recover, whether you call in a doctor 
 or not; again, if it be fated that you do not re- 
 cover from your present disease, you will not recover, 
 whether you call in a doctor or not : but one or other 
 of these contradictories is fated, and therefore it can 
 be of no service to call in a doctor.' (Ignava Ratio?) 
 
 (65) The story of the formation of the human race by Prome- 
 
 theus must be true, for the clay from which he formed 
 it was shown in Greece within historical times. 
 
 (66) The Latin word ' virtus ' originally meant ' manliness ' ; 
 
 hence the virtue of manliness or courage is the highest 
 virtue and the type of all other virtues. 
 
 (67) This person may reasonably be supposed to have com- 
 
 mitted the theft, for he can give no satisfactory ac- 
 count of himself on the night of the alleged offence ; 
 moreover he is a person of bad character, and, being 
 poor, is naturally liable to a temptation to steal. 
 
 (68) Opium produces sleep, for it possesses a soporific virtue. 
 
 (69) The student of History is compelled to admit the truth 
 
 of the Law of Progress, for he finds that Society has 
 never stood still. 
 
 (70) You are inconsistent with yourself, for you told me 
 
 yesterday that there was a presumption of this man's 
 guilt, and now, when I say that I may presume his 
 guilt, you contradict me. 
 
 (71) 'Suppose one man should by fraud or violence take from
 
 EXAMPLES. 177 
 
 another the fruit of his labour with intent to give it to 
 a third, who, he thought, would have as much pleasure 
 from it as would balance the pleasures which the first 
 possessor would have had in the enjoyment and his 
 vexation in the loss of it ; suppose also that no bad con- 
 sequences would follow ; yet such an action would 
 surely be vicious.' Butler, On the Nature of Virtue. 
 
 (72) There exist many differences of opinion and much 
 
 uncertainty with regard to many questions connected 
 with Geology ; consequently Geology is not a science, 
 and any arguments which assume the truth of geo- 
 logical theories must invariably be regarded with 
 considerable suspicion. 
 
 (73) ' Suppose Achilles to move ten times as fast as the 
 
 Tortoise, but the Tortoise to have the start of 
 Achilles, say, by one-tenth of the distance to be 
 traversed : when Achilles has arrived at the point 
 from which the Tortoise started, the Tortoise will 
 still be one-hundredth part of the whole distance in 
 advance of him ; when Achilles has reached this point, 
 the Tortoise will still be one-thousandth part of the 
 whole distance in advance of him ; and so on. Thus 
 Achilles will never be able to pass the Tortoise.' 
 
 {Fallacy of Achilles and the Tortoise?) 
 
 (74) ' Epimenides the Cretan says that " all the Cretans are 
 
 liars," but Epimenides is himself a Cretan ; therefore 
 he is himself a liar. But if he be a liar, what he 
 says is untrue, and consequently the Cretans are 
 veracious ; but Epimenides is a Cretan, and there- 
 fore what he says is true ; hence the Cretans are 
 liars, Epimenides is himself a liar, and what he says 
 is untrue. Thus we may go on alternately proving 
 that Epimenides and the Cretans are truthful and 
 untruthful.' (Fallacy of Mentiens.) 
 
 (75) The idea of the obligation to virtue is innate, for it is 
 
 N
 
 178 EXAMPLES. 
 
 found in all men, and it could not be universal if it 
 were acquired by experience. 
 
 (76) Berkeley's Theory of the Non-existence of Matter is 
 
 palpably absurd, for it is impossible even to place 
 one's foot on the ground without experiencing the 
 resistance of matter. 
 
 (77) I have no hesitation in saying that the proposition, 
 
 however good in theory, is in practice utterly absurd. 
 
 (78) If any objection that can be urged would justify a change 
 
 of established laws, no laws could reasonably be main- 
 tained ; but some laws can reasonably be maintained : 
 therefore no objection that can be urged will justify 
 a change of established laws. 
 
 (79) I cannot accept your opinion as true, for it seems to me 
 
 that its general recognition would be attended with 
 the most injurious consequences to society. 
 
 (80) Why should any but professional moralists trouble 
 
 themselves with the solution of moral difficulties ? 
 For, as we resort to a physician in case of any 
 physical disease, so, in the case of any moral doubt 
 or any moral disorganisation, it seems natural that 
 we should rely on the judgment of some man spe- 
 cially skilled in the treatment of such subjects. 
 
 (81) 'Wood, stones, fire, water, flesh, iron, and the like things, 
 
 which I name and discourse of, are things that I know. 
 And I should not have known them but that I per- 
 ceived them bymy senses; and things perceived by the 
 senses are immediately perceived ; and things imme- 
 diately perceived are ideas ; and ideas cannot exist 
 without the mind ; their existence therefore consists 
 in being perceived ; when, therefore, they are actually 
 perceived there can be no doubt of their existence.' 
 Berkeley, Third Dialogue between HylasandPhilonous. 
 
 (82) 'And because the greatest part of men are such as 
 
 prefer their own private good before all things, even
 
 EXAMPLES. 179 
 
 that good which is sensual before whatsoever is most 
 divine ; and for that the labour of doing good, toge- 
 ther with the pleasure arising from the contrary, 
 doth make men for the most part slower to the one 
 and proner to the other, than that duty prescribed 
 them bylaw can prevail sufficiently with them : there- 
 fore unto laws that men do make for the benefit of men 
 it hath seemed always needful to add rewards, which 
 may more allure unto good than any hardness deter- 
 reth from it, and punishments, which may more deter 
 from evil than any sweetness thereto allureth.' 
 
 Hooker, Eccl. Pol. Bk. I. x. (6.) 
 
 (83) ' The scarcity of a dear year, by diminishing the de- 
 
 mand for labour, tends to lower its price, as the high 
 price of provisions tends to raise it. The plenty of 
 a cheap year, on the contrary, by increasing the 
 demand, tends to raise the price of labour, as the 
 cheapness of provisions tends to lower it. In the 
 ordinary variations of the price of provisions, those 
 two opposite causes seem to counterbalance one 
 another ; which is probably in part the reason why 
 the wages of labour are everywhere so much more 
 steady and permanent than the price of provisions.' 
 Adam Smith, Wealth of Nations, Bk. I. ch. viii. 
 
 (84) ' I am a Jew. Hath not a Jew eyes ? hath not a Jew 
 
 hands, organs, dimensions, senses, affections, passions ? 
 fed with the same food, hurt with the same weapons, 
 subject to the same diseases, healed by the same 
 means, warmed and cooled by the same winter and 
 summer, as a Christian is ? If you prick us, do we 
 not bleed ? If you tickle us, do we not laugh ? If you 
 poison us, do we not die ? and if you wrong us, shall 
 we not revenge ? If we are like you in the rest, we 
 will resemble you in that.' 
 
 Merchant of Venice, Act iii. Sc. i. 
 N 2
 
 180 EXAMPLES. 
 
 (85) ' The most striking and important of the effects of heat 
 consist, however, in the liquefaction of solid 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 cir- 
 cumstances, owe their liquidity to heat, and would 
 freeze or become solid if their heat could be suffi- 
 ciently reduced. In many we see this to be the case 
 in ordinary winters ; for some, severe frosts are requi- 
 site ; others freeze only with the most intense arti- 
 ficial colds ; and some have hitherto resisted all our 
 endeavours ; yet the number of these last is few, and 
 they will probably cease to be exceptions 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 liquid 
 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, no- 
 thing 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.' 
 
 Herschel, On the Study of Natural Philosophy. 
 (86) ' We are not inclined to ascribe much practical value to
 
 EXAMPLES. 1I 
 
 that analysis of the inductive method which Bacon has 
 given in the second book of the Novum Organum. It 
 is indeed an elaborate and correct analysis. But it is 
 an analysis of that which we are all doing from morn- 
 ing to night, and which we continue to do even in our 
 dreams.' Macaulay, Essay on Bacon. 
 
 (87) 'Promises are not binding where the performance is 
 
 unlawful. There are two cases of this : one, where 
 the unlawfulness is known to the parties, at the time 
 of making the promise ; as where an assassin promises 
 his employer to despatch his rival or his enemy; or a 
 servant to betray his master. The parties in these 
 cases are not obliged to perform what the promise 
 requires, because they were under a prior obligation to 
 the contrary. From which prior obligation what is 
 there to discharge them ? Their promise, their own 
 act and deed. But an obligation, from which a man 
 can discharge himself by his own act, is no obligation 
 at all. The guilt therefore of such promises lies in 
 the making, not in the breaking of them ; and if, in 
 the interval betwixt the promise and the performance, 
 a man so far recover his reflection, as to repent of his 
 engagements, he ought certainly to break through 
 them.' 
 
 Paley, Moral and Political Philosophy, 
 
 Bk. III. Part I. ch. v. 
 
 (88) ' This, I think, any one may observe in himself, and 
 
 others, that the greater -visible Good does not always 
 raise men's desires in proportion to the greatness it 
 appears, and is acknowledged to have : Though every 
 little Trouble moves us, and sets us on work to get 
 rid of it. The Reason whereof is evident from the 
 Nature of our Happiness and Misery itself. All pre- 
 sent Pain, whatever it be, makes a part of our present 
 Misery : But all absent Good does not at any time
 
 1 82 EXAMPLES. 
 
 make a necessary part of our present Happiness, nor 
 the absence of it make a part of our Misery. If it did, 
 we should be constantly and infinitely miserable ; there 
 being infinite degrees of Happiness, which are not in 
 our possession. All Uneasiness therefore being re- 
 moved, a moderate portion of Good serves at present to 
 content men ; and some few degrees of pleasure in a 
 succession of ordinary Enjoyments make up a Happi- 
 ness, wherein they can be satisfied. If this were not 
 so, there could be no room for those indifferent, and 
 visibly trifling Actions, to which our Wills are so 
 often determined ; and wherein we voluntarily waste 
 so much of our Lives ; which remissness could by no 
 means consist with a constant determination of Will 
 or Desire to the greatest apparent Good.' 
 
 Locke, Essay concerning Human Understanding, 
 
 Bk. II. ch. xxi. 44. 
 
 (89) ' There is onlyone part of the Protectionist scheme which 
 requires any further notice: its policytowardscolonies, 
 and foreign dependencies ; that of compelling them 
 to trade exclusively with the dominant country. A 
 country which thus secures to itself an extra foreign 
 demand for its commodities, undoubtedly gives itself 
 some advantage in the distribution of the general gains 
 of the commercial world. Since, however, it causes 
 the industry and capital of the colony to be diverted 
 from channels, which are proved to be the most pro- 
 ductive, inasmuch as they are those into which industry 
 and capital spontaneously tend to flow; there is a loss, 
 on the whole, to the productive powers of the world, 
 and the mother country does not gain so much 
 as she makes the colony lose. If, therefore, the 
 mother country refuses to acknowledge any reciprocity 
 of obligation, she imposes a tribute on the colony in 
 an indirect mode, greatly more oppressive and in-
 
 EXAMPLES. 183 
 
 jurious than the direct. But if, with a more equitable 
 spirit, she submits herself to corresponding restrictions 
 for the benefit of the colony, the result of the whole 
 transaction is the ridiculous one, that each party loses 
 much, in order that the other may gain a little.' 
 
 Mill's Political Economy, Bk. V. ch. x. i. 
 (90) ' The money to replace what has been burned will not 
 be sent abroad to enrich foreign manufactures ; but, 
 thanks to the wise policy of protection which has 
 built up American industries, it will stimulate our 
 own manufactures, set our mills running faster, and 
 give employment to thousands of idle workmen. 
 Thus in a short time our abundant natural resources 
 will restore what has been lost, and in converting 
 the raw material our manufacturing interests will 
 take on a new activity.' 
 
 New York Tribune of Oct. 24, 1871, quoted by 
 Professor Cairnes in ' Some Leading Prin- 
 ciples of Political Economy.' 
 
 %* A syllogism, when not stated in logical form, 
 usually appears to contain four, or perhaps more, terms. 
 We must not, however, reject it on that account, till we 
 have previously attempted to translate the propositions of 
 which it is composed into equivalent propositions, con- 
 taining among them three terms only. The cases in 
 which this cannot be done are either those in which the 
 terms of the conclusion, or at least one of them, are 
 distinct, not in form only, but in meaning, from any of 
 the terms employed in the premisses, or those in which 
 there is no term common, or capable of being repre- 
 sented as common, to the two premisses. Thus the 
 syllogism ' Lias lies above New Red Sandstone, New Red
 
 184 EXAMPLES. 
 
 Sandstone lies above Coal ; therefore Lias lies above 
 Coal,' obviously admits of being stated in the form, 
 ' Whatever lies above New Red Sandstone lies above 
 Coal, Lias lies above New Red Sandstone; therefore 
 Lias lies above Coal,' and consequently ought not to 
 be rejected as having four terms. But the premisses 
 'Lias lies above New Red Sandstone, the Cretaceous 
 System lies above the Oolitic,' contain no term common, 
 nor any term capable (from a mere inspection of the 
 language) of being represented as common, to the pre- 
 misses, and hence they might fairly be rejected as con- 
 taining four terms, and consequently leading to no con- 
 clusion. Even here, however, by any one who possessed 
 sufficient special knowledge of Geology to be aware that 
 the Oolitic System lies above Lias, the premisses might 
 be represented as containing three terms only, and as 
 necessitating the conclusion ' The Cretaceous System lies 
 above New Red Sandstone.' But from such premisses 
 as ' Lias lies above New Red Sandstone,' ' A painting 
 should represent beauty of colour as well as beauty of 
 form,' no conclusion whatever could be drawn by means 
 of either logical or special knowledge. The premisses 
 are, in fact, utterly alien to each other, or, in other words, 
 they are not in pari materia. In examining an argument, 
 the student may always avail himself of any special know- 
 ledge which he may possess, provided that, in his answer, 
 he carefully distinguish between what is due to such 
 special knowledge and what to a knowledge of the 
 ordinary usages of language and of the rules of Logic.
 
 EXAMPLES. 1 85 
 
 In the first example given above, a mere knowledge of 
 the rules of Logic, without any reference whatever to the 
 usages of language, would not justify us in drawing any 
 conclusion from the premisses ; the slightest acquaintance 
 with the usages of language would however enable us to 
 represent the terms, which are apparently four, as three, 
 and to infer the conclusion 'Lias lies above Coal.' 
 But in the second example no acquaintance either 
 with the rules of Logic or with the ordinary usages of 
 language would enable us to draw the conclusion, ' The 
 Cretaceous System lies above New Red Sandstone ; ' 
 such a conclusion, though valid, is only justified by a 
 special knowledge of Geology : no person, unacquainted 
 with the facts of Geology, would be justified in admitting 
 the conclusion as an inference from the premisses. 
 
 Where it is obvious that an argument is intended to be 
 syllogistic, and only one premiss is stated, it is of course 
 expected that the student will supply the other premiss. 
 
 In some of the examples, it may be an useful exercise 
 to discuss the truth of the premisses as well as the 
 legitimacy of the conclusion.
 
 INDEX. 
 
 Abstract terms, p. 13. 
 
 different senses in which the 
 expression has been employ- 
 ed, 15. 
 
 sometimes used as common 
 
 terms, 14, 15, 21. 
 Accident, 45. 
 
 defined, 46. 
 
 inseparable, 42, 43. 
 
 separable, 43, 44. 
 Accidental propositions, 49. 
 Accidentis fallacia, 153-155. 
 Act, ambiguity of the word, 4. 
 
 or operation employed in 
 
 preference to power or 
 faculty, 4. 
 ' All,' ambiguous use of the word, 
 
 ^-ISS- 
 Ambiguous middle, 88. 
 
 terms, fallacy of, 88, 143, 
 
 I5I-I57- 
 
 Am pi iative judgments, 49. 
 Analogously, terms used, 88. 
 Analogy, 72, 73. 
 
 fallacy of false, 142-143. 
 
 of Aristotle, 73, 143. 
 Analytical judgments, 49. 
 
 method, 1 59. 
 
 A Posteriori method, 159-160. 
 A Priori method, 159-160. 
 Argument in a circle, 145-147. 
 
 Argumentum ad hominem, 150. 
 
 ad populum, ad verecundiam, 
 
 &c., 150. 
 Attributives, 13, 14-16. 
 
 sometimes used as common 
 
 terms, 14, 15, 21. 
 
 when employed as predicates, 
 
 regarded by Mr. Mill as 
 common terms, 18. 
 
 Begging the question, fallacy of, 
 147. 
 
 Canon of reasoning in the first 
 figure, 93-95. 
 
 Categorematic words, 12. 
 
 Categorical propositions and syl- 
 logisms, these expressions 
 not hereemployed, 113-114. 
 
 Categories of Aristotle, ix. 67. 
 
 Chain-argument, no. 
 
 Chain-reasoning, 135. 
 
 Circle, argument in a, 145-147. 
 
 Circumstantial evidence, 135- 
 141. 
 
 Classifications, 66-68. 
 
 rules for, 66-67. 
 
 difference between Natural 
 
 and Artificial, 63. 
 Collective terms, 12, 13. 
 
 results of thought, 17.
 
 1 88 
 
 INDEX. 
 
 Common terms, 12, 13, 17-18. 
 Comparison (reflexion or 
 
 thought), definition of, i. 
 Composition, fallacy of, 151-152. 
 Concepts employed by Sir W. 
 
 Hamilton in preference to 
 
 terms, 8. 
 Conclusion, 10, 85. 
 
 negative, 97. 
 
 particular, 98, 99. 
 
 Concrete terms, 15. 
 
 Conditional propositions and syl- 
 logisms, these expressions 
 not here employed, 113-114. 
 
 Connotation of terms, 19-23. 
 Contradiction, law of, 75, 92. 
 Contradictory terms, 84. 
 Contrary terms, 84. 
 Conversion by contraposition or 
 
 negation, 83. 
 Conversions, 81-83. 
 Copula, 9, 24-28, 130. 
 Corroborative Evidence, 135- 
 
 141. 
 
 Cross-division, 61. 
 Cumulative Evidence, 135-141. 
 
 Definitions, 38, 45, 50-58. 
 
 final, 52, 53. 
 
 incomplete, 53, 54. 
 
 provisional, 53, 54. 
 
 real and nominal, 57, 58. 
 
 what terms are incapable of, 
 
 50. 
 
 why discussed under the se- 
 
 cond part of logic, 47. 
 
 rules for legitimate, 56. 
 Denotation of terms, 19-23. 
 
 Description of a singular or col- 
 lective term, 50. 
 
 of a common term, 54, 55. 
 Designations, 40, 45. 
 Dichotomy, division by, 62. 
 Differentia, 39. 
 
 defined, 46. 
 
 generic, 65. 
 
 specific, 65. 
 Differentiae, 51, 52. 
 
 difficulty of distinguishing 
 
 from properties, 56, 57. 
 Dilemma, 120-125. 
 Distinction distinguished from 
 
 division, 60. 
 
 Distribution of terms, 34-36. 
 Divided term, 59. 
 Dividing members, 59. 
 Division, principle of, 60-6 1. 
 
 by dichotomy, 62. 
 
 fallacy of, 151-152. 
 
 rules for a legitimate, 63. 
 
 what terms are capable of 
 
 being divided, 59. 
 Divisions, 59-68. 
 
 why discussed under the se- 
 
 cond part of logic, 47. 
 Duns Scotus, his employment of 
 Connotation, 19. 
 
 Enthymeme of Aristotle, 87, 
 
 140. 
 Enumeration distinguished from 
 
 division, 60. 
 Epi-syllogism, no. 
 Equivocal terms, fallacy of, 151- 
 
 157. 
 Equivocally, terms used, 88.
 
 INDEX. 
 
 189 
 
 Essential propositions, 49. 
 
 Evidence, cumulative or corro- 
 borative (including circum- 
 stantial), 135-141. 
 
 Excluded middle, law of, 75, 92. 
 
 Explicative judgments, 49. 
 
 Extensive capacity of a term, 22. 
 
 Fallacia accidentis, 153-155. 
 
 a dicto simpliciter ad dictum 
 
 secundum quid, 153-155. 
 
 plurium interrogationum, 157. 
 Fallacies, 142-157. 
 
 Fallacy of Achilles and the Tor- 
 toise, 143, 177. 
 
 of ambiguous or equivocal 
 
 terms, or of ambiguity of 
 language, 143, 151-157. 
 
 of composition, 151-152. 
 
 of division, 151-152. 
 
 of false analogy, 142-143. 
 
 of illicit process, 96, 145. 
 
 of irrelevancy or ignoratio 
 
 elenchi, 149-151. 
 
 of paronym ous terms, 155- 
 
 156- 
 
 of petitio principii, 146-148. 
 
 of undistributed middle, 96, 
 
 I44-I45- 
 Figures, 90-91. 
 
 are there three or four? 90- 
 
 91. 
 
 moods of the fourth may be re- 
 
 presented as indirect moods 
 of the first, 107-109. 
 
 special rules of the, 106. 
 Four terms, 86, 88, 183-185. 
 Fundamentum divisionis, 60-61. 
 
 Genus, 38, 39. 
 
 cognate, 65. 
 
 defined, 46. 
 
 subaltern, 65. 
 
 summum, 64, 67. 
 
 Heads of predicables, 37-48, 
 162-164. 
 
 why discussed under the se- 
 
 cond part of logic, 46, 47. 
 
 Identity, law of, 75, 92. 
 iSiov of Aristotle, 38-42, 45. 
 Ignoratio elenchi, 149-151. 
 Illicit process of major or minor 
 
 term, 96, 145. 
 Imagination, definition of, I. 
 
 simple or reproductive as 
 
 distinguished from complex 
 or productive, 3. 
 
 Import of propositions, 47, 48. 
 
 Indefinite or indesignate propo- 
 sitions, 30, 31. 
 
 Induction, sense in which the 
 word is employed, 69. 
 
 Inductions, Aristotelian, 76-77. 
 
 distinguished from deductions, 
 
 70-75- 
 
 instances of, 70-71. 
 
 sense in which the word is 
 
 employed, 69. 
 
 Inference, different senses of the 
 word, 69. 
 
 limitations of the word by Sir 
 
 W. Hamilton and Mr. Mill, 
 75-76. 
 
 Inferences, deductive, 69, 73-76, 
 1 60.
 
 190 
 
 INDEX. 
 
 Inferences, defined, 69. 
 
 immediate, 69, 74-76, 78-84. 
 
 inductive, 69-72, 75-77, 159- 
 
 160. 
 
 instances of, 10. 
 
 mediate, 69, 74-77. 
 
 various kinds of, 69-77, Z 59~ 
 
 1 60. 
 
 Infinitation, 83. 
 Inseparable accident, 42, 43. 
 Intensive capacity of a term, 22. 
 Irrelevancy, fallacy of, 149-151. 
 
 Judgments, employed by Sir W. 
 Hamilton in preference to 
 propositions, 8. 
 
 Language, its relation to thought, 
 
 7- 
 Laws of inductive and deductive 
 
 reasoning, 75, 92. 
 Logic, definition of, 5, 6. 
 
 its relation, to psychology, 3. 
 
 Mr. Mill's definition of, 6. 
 
 Major and minor premisses, 86. 
 Major and minor terms, 86. 
 
 illicit process of, 96-97, 145. 
 
 sense in which they were em- 
 
 ployed by Aristotle, 89. 
 
 Mental philosophy (or psycho- 
 logy), definition of, I. 
 
 Metaphor, 73. 
 
 Method as applied to the arrange- 
 ment of syllogisms in a train 
 of reasoning, 158-161. 
 
 Middle term, 86. 
 
 ambiguous, 88. 
 
 Middle term, sense in which it 
 was employed by Aristotle, 
 89. 
 
 undistributed, 96, 144-145. 
 Mnemonic lines for the syllogistic 
 
 rules, 99. 
 
 for the valid moods, 104. 
 Modality, question of, 27-28, 
 
 13. 
 Moods, 90. 
 
 determination of the legiti- 
 
 mate, 91-93. 
 
 indirect, 108-109. 
 
 subaltern, 95, 105, 107-108. 
 
 ' Most,' ' many,' &c., as express- 
 ing the quantities of propo- 
 sitions, 126-129, 131. 
 
 Nomen infinitum or indefinitum, 
 83. 
 
 Occam, referred to, 19. 
 
 Odds, meaning of the expression, 
 
 132. 
 Oppositions, 78-81. 
 
 Aristotelian, 81. 
 
 Paronymous terms, fallacy of, 
 
 155-156. 
 Partition, 60. 
 
 Perception, definition of, i. 
 Permutations, 83, 84. 
 Prantl, referred to, 19. 
 Predicables, heads of, 37-48, 
 
 162-164. 
 Predicate of a proposition, 9, 24. 
 
 its relation to the subject of a 
 
 proposition, 40-48. 
 Predicated, meaning of, 24, 25.
 
 INDEX. 
 
 Predication, theory of, 47, 48. 
 Premisses, 10, 86. 
 
 major and minor, 86. 
 
 negative, 97. 
 
 particular, 97-99. 
 Principle of division, 60, 61. 
 Probable, signification of the 
 
 word, 131, 134. 
 
 reasoning, 130-141. 
 Probability, signification of the 
 
 word, 132, 134. 
 Probably, signification of the 
 
 word, 134. 
 Problema, 86. 
 Progressive method, 159. 
 Property, 41, 42. 
 
 defined, 46. 
 
 difficulty of distinguishing 
 
 from differentia, 56, 61. 
 
 generic, 65-66. 
 
 specific, 65-66. 
 Propositions, complex (hypothe- 
 tical), 113-115, 124-125. 
 
 conjunctive and disjunctive, 
 
 113-115. 
 
 definition of, 24. 
 
 disjunctive, dispute as to their 
 
 meaning, 119. 
 
 division of, according to their 
 
 quantity and quality, 29- 
 
 33- 
 
 employed in preference to 
 
 judgments, 7. 
 
 import of, 47-48. 
 
 instances of, 9. 
 
 quantity of, as expressed by 
 
 ' most,' ' many,' &c., 1 26- 
 129, 131. 
 
 Propositions, secundi adjacentis 
 and tertii adjacentis, u. 
 
 verbal and real, 49. 
 
 whose copula is modified, 
 
 27-28, 130-131. 
 Pro-syllogism, no. 
 Psychology, definition of, I. 
 
 its relation to logic, 3. 
 
 Qusestio, 87. 
 
 Quality of propositions, 29. 
 
 Quantification of the subject, 29- 
 
 3i. 
 
 predicate, 31-33. 
 Quantity of propositions, 29-31. 
 
 as expressed by 'most,' 'many,' 
 
 &c., 126-129. 
 Question-begging epithets, 148. 
 
 Real propositions, 49. 
 Reasoning, probable, 130-141. 
 Reduction, 101-105. 
 
 ostensive, 101-102. 
 
 per impossibile, 101-105. 
 Reflexion (comparison or 
 
 thought), definition of, i. 
 Regressive or Goclenian sorites, 
 112. 
 
 method, 159. 
 
 Zrjuttov of Aristotle, 140. 
 Separable accident, 43, 44. 
 Simple ideas, 16. 
 Singular terms, 1 2 . 
 
 propositions rank as univer- 
 
 sals, 29, 30. 
 Sorites, 110-112. 
 
 Goclenian or regressive, 112.
 
 192 
 
 INDEX. 
 
 Special rules for the syllogistic 
 
 figures, 1 06. 
 Species, 39-40. 
 
 cognate or co-ordinate, 65. 
 
 co-ordinate but exclusive, 45. 
 
 defined, 46. 
 
 infima, 64-65, 67-68. 
 
 overlapping, 44, 45. 
 
 subaltern, 65. 
 Subaltern opposition, 79, 81. 
 
 moods, 95, 105, 107-108. 
 Subalternation, 81. 
 Sub-division, 64-65. 
 
 Subject of a proposition, 9, 24. 
 Subordination, 81. 
 Sufficient reason, law of, 92. 
 Syllogism, ambiguity of the word, 
 8. 
 
 is the a petitio principii, 148. 
 legitimate forms of, 91-109. 
 
 possible forms of, 89-91. 
 
 structure of the, 85-89. 
 ^v\\oytaft&s fiovo^fifnaros, 87. 
 Syllogisms, complex (hypothe- 
 tical), 113-125. 
 
 conjunctive, 115-117, 123- 
 
 125. 
 
 disjunctive, 117-119, 124-125. 
 Syllogistic rules, 96-101. 
 Syncategorematic words, n. 
 Synonyms, 38, 45. 
 Synthetical judgments, 49. 
 
 method, 159. 
 
 Tautologous propositions, 49. 
 Terms, connotation and denota- 
 tion of, 19-23. 
 
 contrary and contradictory, 
 
 84. ' 
 
 definition of, n. 
 
 employed in preference to 
 
 concepts, 7. 
 
 distribution of, 34-36. 
 
 instances of, 9. 
 
 used univocally, equivocally, 
 
 and analogously, 87-88. 
 
 various kinds of, 11-18. 
 Thought, definition of, i. 
 
 or thinking, as an act or ope- 
 
 ration, distinguished from 
 thought or thoughts, as a 
 result, 2. 
 
 its relation to language, 7. 
 
 its products, 2. 
 Trains of reasoning, 1 10. 
 
 on method as applied to the 
 
 arrangement of syllogisms 
 in, 158-161. 
 Trilemma, tetralemma, &c., 121. 
 
 Undistributed middle, 96, 144- 
 
 145- 
 Univocally, terms used, 87-88. 
 
 Verbal propositions, 49. 
 
 fallacies, 88, 143, 151-157- 
 
 THE END.
 
 Aeries 
 
 INDUCTIVE LOGIC 
 
 FOWLER
 
 Bonbon 
 
 HENRY FROWDE 
 
 OXFORD UNIVERSITY PRESS WAREHOUSE 
 
 AMEN CORNER, E.G. 
 
 Qtcw ?)orft 
 
 112 FOURTH Avtxut
 
 Aeries 
 
 THE ELEMENTS 
 
 OF 
 
 INDUCTIVE LOGIC 
 
 DESIGNED MAINLY 
 FOR THE USE OF STUDENTS IN THE UNIVERSITIES 
 
 THOMAS FOWLER, D.D. 
 
 President of Corpus Christi College 
 
 And formerly Professor of Logic in the University of Oxford 
 Honorary Doctor of Laws in the University of Edinburgh 
 
 SIXTH EDITION, CORRECTED AND REVISED 
 
 AT THE CLARENDON PRESS 
 
 M DCCC XCII
 
 Ojrforfc 
 
 PRINTED AT THE CLARENDON PRESS 
 BY HORACE HART, PRINTER TO THE UNIVERSITY
 
 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 
 by far more numerous and intricate examples. But, 
 on the other hand, it is more interesting both to the
 
 VI PREFACE TO THE FIRST EDITION. 
 
 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 
 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
 
 PREFACE TO THE FIRST EDITION. Vll 
 
 introduction, not to science, but to scientific method. Its 
 object is not to give a resume of the sciences, physical 
 or social, a task for 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 Effects, have, if alluded to 
 at all, been only briefly noticed. Any detailed examina- 
 tion of these more intricate questions seemed to lie 
 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
 
 Vlil PREFACE TO THE FIRST EDITION. 
 
 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 THIRD EDITION 
 
 [The student is requested to read this Preface in 
 connexion with Chapter III.] 
 
 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 book 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. Jevons 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 1 .' And again: 'We can 
 never recur too often to the truth that our knowledge of 
 
 1 Vol. i. p. 260.
 
 X PREFACE TO THE THIRD EDITION. 
 
 the laws and future events of the external world is only 
 probable 2 .' 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 3 .' 
 
 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 
 
 i 
 the air will certainly fall upon a flat side, so that either 
 
 the head or tail will be uppermost 4 ,' 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 5 .' 
 
 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 
 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 
 
 a Vol. i. p. 271. s Id. p. 257. 
 
 * Id. p. 228. Mr. Jevons, however, curiously enough is not cer- 
 tain about the truth of the Law of Gravitation. See below. 
 5 Id. p. 270.
 
 CERTAINTY OF INDUCTIVE REASONING, xi 
 
 Method of Difference, and, as actual 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 
 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 actual constitution of nature which we may accept 
 with certainty, while, with respect even to the distant
 
 xii PREFACE TO THE THIRD EDITION. 
 
 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 6 . 
 
 There is, then, I contend, no special uncertainty 
 attaching to the truths arrived at by induction. They 
 are, indeed, like 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 alike 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 induc- 
 
 * 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.
 
 JEVONS' THEORY OF INDUCTION. xiii 
 
 live 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 con- 
 ditions 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 on 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 established generalisations of mechanics, optics, 
 or chemistry, 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 7 .' 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 
 7 p. 3-
 
 XIV PREFACE TO THE THIRD EDITION. 
 
 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 uncertain, 
 where, according to Mr. Jevons, are we to find certainty ? 
 ' Certainty belongs only to the deductive process and to 
 the teachings of direct intuition 8 .' Does it then belong 
 to the conclusions of deduction ? Apparently not, for, 
 at the very beginning of the work 9 , 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 can be more 
 certain than the premisses. The conclusions of geo- 
 metry, therefore, partake of the same ' uncertainty ' as the 
 results of the physical sciences, and the region of 
 ' certainty ' is confined to our direct intuitions and to the 
 rules of syllogism (supposing, that is, a difference to be 
 intended between the ' deductive process ' and deductive 
 results). I 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 charac- 
 teristic of that method, but one which it shares with all 
 our so-called knowledge. 
 
 8 p. 39- ' P- H-
 
 ALL REASONING HYPOTHETICAL. XV 
 
 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, which, ac- 
 cording to different theories, are either obtained 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 Uni- 
 formity 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 10 . Induction 
 
 10 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
 
 XVI PREFACE TO THE THIRD EDITION. 
 
 would only be hypothetical in a special sense, if we 
 had any reasonable ground for doubting the truth of 
 the hypotheses 11 on which it rests. 
 
 But as, ' in its ultimate origin or foundation, all 
 knowledge' (including, of course, that of the laws 
 which govern the syllogistic process itself) 'is induc- 
 tive,' Professor 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 inconsistencies 
 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 
 
 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. 
 
 11 I need hardly say that I am not here using the word ' hypothesis ' 
 in the sense of an unverified assumption. Reasoning, both in- 
 ductive and 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 I 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.
 
 JEVONS' THEORY OF INDUCTION. xvii 
 
 hypotheses 12 , 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 
 parallel drawn between Nature and a ballot-box. 
 ' Events,' says Mr. Jevons, ' come out like balls from 
 the vast ballot-box of Nature 13 .' 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 
 entities having no connexion 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 Induction 
 would undoubtedly be the true one, and I should 
 agree with him that 'no finite number of particular 
 verifications of a supposed law will render that law 
 certain.' But, just because we believe that the opera- 
 tions 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 that 
 
 12 See chap. i. pp. 11-13, of this work. " Vol. i. p. 275. 
 
 b
 
 xviii PREFACE TO THE THIRD EDITION. 
 
 Induction is simply the inverse method of Deduction. 
 If Induction simply consists in framing hypotheses, 
 deducing consequences from the hypotheses, and then 
 comparing these consequences with individual facts for 
 the purpose of verifying them by specific experience 14 , 
 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 maintain the 
 following theses, which are explained and defended in 
 the course of my work : i. That our inductions are 
 not always preceded by hypotheses (and it might be 
 added that, even where they are, the hypothesis 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 some- 
 thing of which we have had experience) ; 2. That the 
 mere verification of our hypotheses by specific experi- 
 ence is not sufficient to constitute a valid induction, 
 unless the instances conform with the requirements of 
 one of the inductive methods, or (as in the case of the 
 fundamental laws of 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 
 14 Vol. i. pp. 307, 308.
 
 ASSUMPTIONS OF REASONING. xix 
 
 to the general, from the known to the unknown, and 
 the nature of this inference it is impossible to re- 
 present adequately by reference to the forms of 
 deduction 15 . 
 
 15 For the word ' adequately,' I ought to substitute the expression, 
 ' without a considerable amount of circumlocution,' as the essential 
 difference between inductive and deductive reasoning consists, not so 
 much in the form of the argument, as in the nature of the assump- 
 tions made: scientific induction postulating, in addition to the 
 assumptions made in deductive reasoning, the laws of Universal 
 Causation and of Uniformity of Nature, in its strictest sense (see 
 p. 9, note 7) ; and Inductio per Enumerationem Simplicem, the 
 latter law in its vaguer sense. I think it may be useful to the 
 student here to transcribe a note which first appeared in the 9th, 
 and is now repeated, with some modifications, in the loth edition 
 of my Deductive Logic (p. 75, note 3). 
 
 ' If we state explicitly all the assumptions made in the inductive 
 process, the conclusion is contained in the premisses, and the form of 
 the reasoning becomes deductive ; but it is seldom that we do state 
 our assumptions thus explicitly. The most essential distinction, 
 however, between inductive and deductive reasoning consists not in 
 the form of the inferences, but in the nature of the assumptions on 
 which they rest. Deductive reasoning rests on certain assumptions 
 with regard to language and co-existence (namely, the Law of Con- 
 tradiction, the Law of Excluded Middle, and the Canons of Syl- 
 logism), while inductive reasoning assumes over and besides these 
 laws the truth of the Laws of Universal Causation, of the Uniformity 
 of Nature and, as implied in the latter, of the Conservation of 
 Energy ; or, if it be of the unscientific description which is known as 
 Inductio per Enumerationem Simplicem, it merely assumes, instead 
 of them, the vague and wide principle that the unknown resembles, 
 or will resemble, the known. It hardly needs to be added that 
 all reasoning alike assumes the trustworthiness of present con- 
 sciousness and of memory. 
 
 Amongst the assumptions or pre-suppositions of reasoning, I have 
 not included the so-called Law of Identity ; as to say that all A is A, 
 
 ba
 
 XX PREFACE TO THE THIRD EDITION. 
 
 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 16 : 'In its ultimate origin or 
 foundation all knowledge is inductive,' and 'only when 
 we possess such knowledge, in the form of general 
 propositions and natural laws, can we usefully apply 
 the reverse process of deduction to ascertain the exact 
 information required at any moment.' When we com- 
 pare 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, 
 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 
 
 or a thing is the same as itself, appears to me to be an utterly un- 
 meaning proposition. Mr. Mill (Examination of Hamilton, ch. 21), 
 in attempting to give a meaning to this maxim, really transforms 
 it into a perfectly distinct proposition, namely, that Language may 
 express the same idea in different forms of words.' 
 16 Vol. i. p. 14.
 
 PREFACE TO THE FIFTH EDITION. xxi 
 
 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. 
 
 %* In the third Edition some new matter was in- 
 troduced, bearing mainly on the following subjects : 
 Uniformities of Coexistence, the Historical Method, 
 the distinction between Inductio per Enumerationem 
 Simplicem and the Method of Agreement, the constant 
 alternation in practice of the inductive and deductive 
 processes, and the Argument from Universal Consent. 
 In the fourth Edition the principal alterations were the 
 introduction of new foot-notes on the definition of 
 Induction and on the Plurality of Causes, and some 
 additional remarks on the nature of the Method of 
 Residues and on Empirical Laws. 
 
 In the fifth Edition, the alterations were more nu- 
 merous than in either of the two preceding editions. 
 Through the kindness of my friend, Mr. George Griffith
 
 xxii PREFACE TO THE SIXTH EDITION. 
 
 of Harrow, I was enabled to state some of the scientific 
 examples in a more precise form than in the preceding 
 editions, notably those on Double-Weighing (p. 47), on 
 the 'Red Flames' seen during a total eclipse of the 
 Sun (pp. 50-1), and on Spectrum Analysis as applied to 
 the constitution of the Sun and other heavenly bodies 
 (pp. 165-7). The principal alterations or additions in 
 the logical matter were on pp. 204-5 ( tne Historical 
 Method), p. 206 (the Comparative Method), pp. 277-8 
 (the Fallacy of 'Exaggerated Comparison'), and the 
 addition of an important foot-note (note 15, p. xix) to 
 the 'Preface to the Third Edition,' on the peculiar 
 nature of Inductive Reasoning and on the assumptions 
 made in it. The following foot-notes were either new 
 or contained additional matter : n. 4, p. 6 ; n. n, p. 13 ; 
 n. 22, p. 23; n. 41, pp. 107-8; n. 5, p. 129; n. 27, 
 p. 166 ; n. 44, p. 191 ; n. 54, p. 205 ; n. 55, pp. 205-7 ; 
 n. 63, p. 214; n. 24, pp. 281-2 ; n. 26, p. 282 ; n. 29, 
 p. 283 ; n. 80, p. 343. 
 
 Besides a few corrections in some of the scientific 
 examples, occasioned by recent discoveries, the principal 
 difference between this (the sixth) and former editions is 
 the addition and alteration of certain passages in the 
 notes on the Argument from Final Causes, pp. 342-4. 
 
 C. C. C. 
 
 Aug. 18, 1892.
 
 CONTENTS 
 
 I. The Nature of Inductive Inference 
 
 II. Processes subsidiary to Induction ...... 
 
 i . Observation and Experiment .... 
 
 2. Classification, Nomenclature, and Terminology 
 
 (1) Classification 
 
 (2) Nomenclature ...... 
 
 (3) Terminology 
 
 3. Hypothesis 
 
 III. The Inductive Methods 
 
 Method of Agreement ...... 
 
 Method of Difference 
 
 Double Method of Agreement 
 
 Method of Residues 
 
 Method of Concomitant Variations (including the 
 
 Historical Method) 183 
 
 IV. Imperfect Inductions 219 
 
 Inductio per Enumerationem Simplicem . . .219 
 
 Argument from Analogy 226 
 
 Imperfect applications of the Inductive Methods (or 
 
 Incomplete Inductions) 237
 
 CONTENTS. 
 
 CHAP. PAGE 
 
 V. The Relation of Induction to Deduction, and Verification 241 
 
 VI. The Fallacies incident to Induction . . . -254 
 
 A. Fallacies incident to the subsidiary processes . -254 
 
 i. Fallacy of Non-observation, consisting in neglect either 
 
 (1) of some of the instances (including Fallacy 
 
 arising from the confusion between Ab- 
 solute and Relative Frequency) . . -254 
 or (2) of some of the circumstances attendant on a 
 
 given instance ...... 268 
 
 II. Fallacy of Mai-observation (including Fallacy of 
 
 Exaggerated Comparison) ..... 272 
 
 in. Errors incidental to the operations of Classification, 
 
 Nomenclature, Terminology, and Hypothesis . 278 
 
 B. Fallacies incident to the Inductive process itself, or Falla- 
 
 cies of Generalisation ...... 279 
 
 iv. Error originating in the employment of the Inductio 
 per Enumerationem Simplicem (including the ille- 
 gitimate use of the Argument from Authority and 
 V of that from Universal Consent) . . . .280 
 
 v. Errors common to the employment of the various In- 
 
 ductive Methods ....... 298 
 
 ( 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) . 300 
 
 (2) Mistaking a for the sole cause, when a and c 
 
 are the joint causes, either as 
 
 (a) both contributing to the total effect . . 306 
 or (0) being both essential to the production of 
 
 any effect whatever ..... 309 
 
 (3) Mistaking joint effects for cause and effect . 314
 
 CONTENTS. XXV 
 
 CHAP. PAGE 
 
 (4) Mistaking the remote cause for the proximate 
 
 cause, or the reverse 318 
 
 (5) Neglecting to take into account the mutual 
 
 action (mutuality) of cause and effect . .322 
 
 (6) Inversion of cause and effect . . . < .325 
 
 vi. False analogy (including the illegitimate use of the 
 Argument from Antiquity, and of the Argu- 
 ment from Final Causes) . . . .329 
 
 INDEX . .357
 
 'EK Trpoyiv(i)(TKop.eva>v 8f nava 8i8acrKa\ia, &(nrep KOI fv TOIS 
 dva\VTiKois \eyofjLev' r] p.ev yap Si' fTraytoyrjs, r) 5e <7uXXo-yi(T/Li<Jp. 
 'H p.ev 8f) fTTayatyrj dpx*) f'^ 1 " 4 * a ' TOV KaddXov, 6 8e <rvX\o'ytoyios' 
 f< r5)V Ka6o\ov. Eto'ii' apa ap^ai f &v 6 (rv\\oyi(Tfj.6f, &v OVK 
 e&Ti tTvXKoyiafios' eVayco-yj) 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 praecipue nota sint (ab univer- 
 salibus enim ad particularia ratiocinando oritur scientia), ipsa tamen 
 universalium in intellectu comprehensio a singularinm in sensibns 
 nostris perceptione exsurgit. 
 
 Preface to Harvey's Treatise De Generatione Animalium.
 
 ELEMENTS 
 
 OF
 
 *** 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. 
 
 nPWO bodies of unequal weight (say a guinea and a 
 feather) are placed at the same height under the 
 exhausted 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 with 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 we 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 In- 
 ference or an Induction l . 
 
 1 The student must throughout bear in mind the ambiguous use of 
 the words Induction, Inference, &c., as signifying both the result 
 and the process by which the result is arrived at. See Dedtictive 
 Logic, Preface, and Part III. ch. i. note I. 
 
 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 2 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 
 ~lake~piace 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 
 reflecting portion of mankind, though the grounds on 
 which it is admitted have been variously stated; some 
 
 * 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.
 
 . 
 
 /^ !.T^ 
 
 INDUCTIVE INFERENCE. 5 
 
 Justifying it by an appeal to the continuous and uncon- 
 
 tradicted experience not only of the individual himself 
 
 ' f^^ 
 
 but of the human race, others by^an appeal to the 
 
 necessities 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 3 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, wheneverjlxe 
 same antecedents.^and none others, are introduced, the 
 j>ajn consequents will invariably follow. This assump- 
 tion (or law) TsTTiklT tTieforme^7^rn1ver^aTly~admitted by 
 mankind, or the reflecting portion of mankind, though the 
 grounds on which it is admitted have been variously stated, 
 
 3 The expression ' will ' is used for the sake of brevity. The 
 argument, however, is not simply from the present to the future, but 
 from cases within the range of our experience to all cases, past, 
 present, or future, without that range. See p. 32, note 31.
 
 6 NATURE OF 
 
 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 
 Jaw_rnaybe called the Law of the Uniformity of Nature\_ 
 
 The argument, then, in the case which we have taken 
 as our instance, may be represented as follows \- 
 
 I observe that these two bodies (though of unequal 
 weight) reach the bottom of the receiver at the 
 same moment. 
 This fact must be due to some cause or combination 
 
 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). 
 
 4 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, 
 or, more strictly speaking (see pp. 127, 8), the same portion of an 
 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. 
 
 The Law of the Uniformity of Nature implies, I conceive, the truth 
 of the law of the Persistence or Conservation of Energy (namely, that 
 no cause, or part of a cause, will ever be ineffective, or, in other words, 
 that no energy is ever lost% and hence I have not thought it necessary 
 tq introduce any express mention of this latter law in the text.
 
 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 inductions 
 with which science is mainly concerned, and of which I 
 shall have, for the most part, to treat in the present work. 
 But there are other inductions of a simpler character, the 
 validity of which is assured not by any artificial process 
 of elimination, but merely by a series of uncontradicted 
 experiences. This kind of induction is usually distin- 
 guished by logicians as Inductio per Enumerationem 
 Siniplicen^, 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 
 I conceive, the Laws of Uniformity of Nature and Uni- 
 versal Causation themselves, as well as the axioms of 
 mathematics and certain facts of co-existence 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 I may specify the co-existence throughout 
 matter of the properties of inertia and gravity, and the
 
 8 NATURE OF 
 
 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 co-existing facts of this nature 
 may possibly be due to some causal connexion, 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 co-existence, and established 
 only by an inductio per enumerationem simplicem, or 
 uncontradicted experience. 
 
 Mr. Bain 5 enumerates three kinds of uniformities, which 
 may be established by induction, those of Co-existence, 
 Causation, and Equality, Uniformities of Co-existence 
 and Equality can be established only by Inductio per 
 Enumerationem '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 the above classification I ought 
 to add the Laws of Uniformity of Nature and Universal 
 Causation, both of which, as already remarked, I conceive 
 to be established by uncontradicted experience, or, in 
 other words, by an Inductio per enumerationem sim- 
 plicem coextensive with all human knowledge 6 . These 
 fundamental laws, thus verified by a constant experience, 
 
 5 Logic, Bk. III. ch. ii. 
 
 6 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 
 
 are assumed in all scientific inductions concerning Caus- 
 ation, whereas, in mere inductions per Enumerationem 
 Simplicem, all that is assumed is the much vaguer and 
 less precise belief that, under similar circumstances, the 
 unknown resembles, or will resemble, the known, a 
 belief which experience shows to be subject to many 
 modifications 7 . 
 
 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, I 
 shall in the following work limit myself almost entirely 
 to their consideration. The inductions of Co-existence, 
 with which I shall, to some extent, be concerned in the 
 section on Classification, I shall regard as subservient to 
 these 8 . 
 
 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 that Induction may be 
 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 
 examined. Thus, from the proposition that a guinea 
 
 7 This belief is what is frequently understood by the Law of the 
 Uniformity of Nature, but I have thought it desirable to confine that 
 expression to the more precise statement with regard to the uniform 
 action of causes. 
 
 8 I shall briefly recur to the subject of Inductions of Co-existence 
 in the fourth chapter, under the head of Inductio per Enumerationem 
 Simplicem.
 
 10 NATURE OP 
 
 and a feather, if placed under the exhausted receiver of 
 an air-pump, will fall through equal vertical spaces in 
 equal times, may be inferred inductively the proposi- 
 tion 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 whatsoever, when exposed 
 to the same circumstances, and as we might make the 
 same assertion of any two or more bodies, and conse- 
 quently of all bodies, it will be seen that Induction is 
 not only an inference of the unknown from the known ; 
 ut,in virtue of that fact, of the general from the particular. 
 In every inductive argument, in fact, it is implied that 
 wherever or whenever the same circumstances are re- 
 peated, the same effects will follow. Induction may, 
 therefore, also be defined as the legitimate inference of the 
 general from the particular, or (in order to include those 
 cases where general propositions are themselves 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 9 . 
 
 9 This is a better and more accurate definition than that given at 
 the beginning of the paragraph, because, if we adopt the theory that 
 all our fundamental beliefs are derived from experience, there is no 
 kind of inference which does not involve the assumption that we 
 may argue from the known to the unknown, and from the pnst to 
 the present and the future. In the case of some of these beliefs, 
 however, as the so-called ' laws of thought,' and the belief in the 
 trustworthiness of our present consciousness and of memory, the 
 assumption has been made so often and so constantly that we have 
 almost ceased to be conscious of making it.
 
 INDUCTIVE INFERENCE. II 
 
 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 hypotheses, as they are usu- 
 ally called), one being that bodies fall quicker in propor- 
 tion to their weights, the other that the weight of the body, 
 when the resistance of the atmosphere is removed, 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 inductions are often, 
 as in this case, the result of an attempt to decide between 
 rival hypotheses, or a reply to the question whether some 
 particular hypothesis be true or not, the hypothesis or 
 hypotheses suggesting the particular experiment to be 
 tried. Sometimes, however, we have no assistance of 
 this kind, and we try experiments 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. Supposing 
 the experiments to have been properly conducted, the 
 inductions at which he arrives will be perfectly valid, 
 though he may have formed no previous theories as to the 
 results of his researches. Occasionally, too, an induction 
 will not be the result of any definite course of investi-
 
 12 NATURE OF 
 
 gation, but 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.' 
 ' The laws of crystallography were obscure, and its causes 
 still more so, till Haiiy fortunately 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 with those of the crystal in 
 its entire state, but to belong to another form ; and follow- 
 ing out the hint thus casually obtruded on his 
 
 notice, he discovered the beautiful laws of the cleavage, 
 and the primitive forms of minerals 10 .' 
 
 Thus, we perceive that our inductions are sometimes 
 preceded by hypotheses, at other times not. In most 
 cases, probably, we have formed some supposition (or 
 hypothesis) as to the character of a phenomenon before 
 we enter upon, or, at least, before we complete, its in- 
 vestigation. Such suppositions (or hypotheses) are often 
 of the utmost service in directing the course which our 
 experiments and observations shall take. Frequently, 
 also, it is impossible to perform any experiment, or to 
 institute any series of observations, which shall be de- 
 cisive of the question before us. In this case, unless 
 we altogether suspend our judgment, we must rest con- 
 tent with an unproved theory, and it becomes of prime 
 importance to determine to what conditions such a 
 10 HerscheFs Discourse on the Study of Natural Philosophy , 191.
 
 INDUCTIVE INFERENCE. 13 
 
 theory", supposition, or hypothesis must conform in 
 order to entitle it to rank as a probable or possible 
 solution of our difficulties. A subsequent section will 
 be specially devoted to these questions, but meanwhile 
 it seemed desirable at once to direct the attention of the 
 student to the distinction between hypothesis and in- 
 duction. He must bear in mind that, though the forma- 
 tion of hypotheses is frequently an important step in the 
 inductive process, a hypothesis must be carefully dis- 
 tinguished from a valid induction. Without at present 
 attempting any formal definition of a 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 
 introduction of any of which, might frustrate the event. 
 Thus, to take the homely instance of lighting a fire. 
 
 11 The word ' theory ' is, unfortunately, employed in two mean- 
 ings : (i) as = hypothesis, as when we speak of the undulatory 
 theory, the Darwinian theory, or two or more ' rival theories'; (2) 
 as an ascertained truth, or body of truths, as when we speak of the 
 ' lunar theory,' or the ' theory of equations.*
 
 14 NATURE OF 
 
 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 in- 
 stance, 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 prevent the fuel from igniting. In assigning 
 the cause of a phenomenon, it is seldom that the nega- 
 tive conditions are mentioned. It is generally under- 
 stood 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, completes the assemblage of conditions, 
 and stands in closest proximity to the effect. Thus, 
 in our example, the combustion 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. Mill, 
 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 
 conditions, 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 purpose of our immediate dis-
 
 INDUCTIVE INFERENCE. 15 
 
 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 scientific accuracy, we ought to enumerate 
 all the conditions, or, at least, all the positive conditions, 
 on which a phenomenon depends, unless we have a right 
 to presume that there is no likelihood of their being 
 overlooked by those whom we address :2 . 
 
 In tif% science of Medicine, the cause which com- 
 pletes the assemblage of conditions is often distinguished 
 as the exciting cause, the other causes being called pre- 
 disposing. Thus, the peculiarities of constitution, age, 
 sex, occupation, &c., which render a person more than 
 ordinarily liable to any particular disorder, would be 
 called the predisposing causes ; the contagion (by which 
 the body is brought into contact with some specific 
 poison), a sudden chill, bodily fatigue, mental depres- 
 sion, or any circumstance, on the supervention of which 
 the disease is immediately consequent, would be called 
 
 12 The subject of this paragraph is treated with great ability in 
 Mr. Mill's Logic, Bk. III. ch. v. 3.
 
 1 6 NATURE OF 
 
 the exciting cause ls . 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 situa- 
 tions ; the summer and autumn seasons : the exciting 
 causes as contagion ; a peculiar poison diffused through 
 the atmosphere.' 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. 
 
 Note I M . Mr. Mill (Logic, Book II. ch. iii.) maintains 
 that, in an act of induction we usually, though not in- 
 variably, argue directly from one particular case to an- 
 other. 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. WhewelPs language (which is that 
 ordinarily employed), I cannot recognise the importance 
 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 as- 
 
 18 See Dr. Watson's Lectures on Physic, Lecture VL 
 
 M 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. if 
 
 signable respects, is virtually to say that it is true of any 
 and every case which presents these points of resem- 
 blance. What is true of each or any case, taken in- 
 differently, 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 pro- 
 position ' That object will cause me pain now, if I ap- 
 proach 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 reflexion, only be justified by granting 
 the truth of the general one, 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 15 .' 
 
 Though agreeing with Dr. Whewell in his main 
 position, I must express my entire dissent from the dis- 
 tinction which, throughout this discussion, he attempts 
 to draw between our reasonings in the ordinary affairs 
 
 14 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 tiizlogical 
 justification of such inferences is to be found in the general statement. 
 
 C
 
 1 8 NATURE OF 
 
 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 compassing 
 pleasure or avoiding pain, but I believe the mental 
 process to be essentially the same in both cases. 
 
 Note 2. Since the time of Hume, the nature of our 
 conception of Cause has formed one of the chief topics 
 of philosophical controversy. Previously to his time, it 
 appears to have been taken for granted by the great 
 majority of modern philosophers of all schools I6 (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 17 ), that the idea of causation necessarily 
 implies the idea of power or necessary connexion ; 
 
 16 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. 
 
 17 Still, even according to these philosophers, every act of causa- 
 tion 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.
 
 INDUCTIVE INFERENCE. 19 
 
 necessary connexion, that is to say, between the cause and 
 effect, at 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 18 , 
 ' 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 
 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 ; and so comes by 
 the 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 de- 
 stroyed, 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 
 18 Locke's Essay, vol. ii. ch. xxi. I. 
 C 2
 
 20 NATURE OF 
 
 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 connexion between two events? Do we ob- 
 serve any such connexion 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 
 of power or necessary connexion, in all the sources from 
 which we could suppose it to be derived. It appears 
 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 any force or power, by which the cause 
 operates, or any connexion 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
 
 INDUCTIVE INFERENCE. 21 
 
 whole, there appears not, throughout all nature, any one 
 instance of connexion, which is conceivable by us. All 
 events seem entirely loose and separate. One event 
 follows another ; but we never can observe any tie be- 
 tween 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 conclusion seems to be, that we have no idea 
 of connexion or power at all, and that these words are 
 absolutely without any meaning, when employed either 
 in philosophical reasonings, or common life 19 .' Does 
 Hume then deny ihefact of causation, namely, that, when 
 we have been accustomed to observe one event invari- 
 ably followed by another, we may confidently expect, 
 other circumstances remaining the same, that the one 
 will continue to be followed by the other in the future, 
 and that, if we perceive a change in any phenomenon, 
 we may be confident that some other event has pre- 
 ceded that change ? Certainly not. There is, in Hume's 
 writings, absolutely no foundation for the virulence with 
 which he is attacked by Reid 20 . What he called in 
 
 M Hume's Essays. Essay on the Idea of Necessary Causation. 
 
 80 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 an 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 hist been started ; and
 
 22 NATURE OF 
 
 question was not the invariableness of the fact of causa- 
 tion, 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 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 n that we might speak of day as the cause of night, 
 and of night as the cause of day. That there are ex- 
 pressions in the Essay, in which the cause seems to be 
 absolutely identified with the invariable antecedent or 
 the sum of the invariable antecedents, cannot be denied. 
 Such is the following : ' Suitably to this experience, 
 
 what is there so ridiculous as not to be maintained by some phi- 
 losopher ? ' 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 generally 
 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, other than that of mathe- 
 matics. Sir William Hamilton's note requires only to be compared 
 with the following passage from the Essay : ' But when one par- 
 ticular 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.* 
 21 Active Powers, Essay IV. ch. iii.
 
 INDUCTIVE INFERENCE. 23 
 
 therefore, we may define a cause to be an object, fol- 
 lowed 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 not been, the second never had 
 existed? Now this alternative definition is not open to 
 Reid's objection 22 , 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 23 . 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, perhaps, it might be more simply stated 
 thus : ' An Effect is so related to its Cause or its alter- 
 native Causes, that if the latter or one of the latter had 
 not been, the former had never existed 24 .' 
 
 M The alternative definition, however, introduces a new idea, not 
 contained in the first definition, that of dependence of the effect upon 
 the cause, which it is not easy to distinguish from the idea of neces- 
 sary connexion. Hence, Hume appears unconsciously to recur to 
 the very position which he is attacking. It seems to me that the 
 relation of cause and effect, or the dependence of effect on cause, is 
 an idea sui generis, and cannot be resolved into the mere idea of 
 time, or antecedence and consequence. The introduction of the 
 word ' power,' however, or even of the word ' necessary/ into the 
 statement of the relation, occasions needless obscurity and difficulty. 
 
 43 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. 
 
 ** This definition is, it must be confessed, somewhat deficient in
 
 24 NATURE OF 
 
 Both Dr. Thomas Brown and Mr. Mill attempt to meet 
 Reid's objection. 
 
 Brown holds that the cause is that invariable ante- 
 cedent which immediately precedes the effect ; thus the 
 position of the sun at a given moment, that which we 
 call sun-rise, is the cause of day. 
 
 Mill attempts to meet the same objection by having 
 recourse to the idea of ' unconditionalncss? The cause 
 of a phenomenon is ' the antecedent or concurrence of 
 antecedents on which it is invariably and unconditionally 
 consequent,' i.e. which not only invariably precedes it, 
 but which is followed by the effect without the occur- 
 rence of any other condition. Now night cannot be 
 called the 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. 
 
 simplicity. But I venture to suggest that it will bear closer ex- 
 amination than that of Mr. Mill, who defines ' cause ' as the ' uncon- 
 ditional invariable antecedent.' Whether by the term 'unconditional' 
 he means ' not depending on any previous condition,' or ' not com- 
 bined with any concurrent condition,' it may be objected that there 
 is no such phenomenon in nature. If, as seems clear from the con- 
 text, the term be used in the latter sense, we shall not only be ex- 
 cluded 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 production 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 negative, which are essential 
 to its operation.
 
 INDUCTIVE INFERENCE. 2.5 
 
 The objection to Brown's account is that we frequently 
 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 2S . 
 
 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 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' 
 
 ** It is curious that Mill, in attempting to answer Reid, takes no 
 notice of Brown's answer. - ...
 
 26 NATURE OF 
 
 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 2 V 
 Hume's position is also accepted by James Mill in his 
 Analysis of the Phenomena 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 connexion ' to show how we 
 can have become acquainted with it. Does it come from 
 our experience of the external world, or from our 
 experience of the control of our will over our own acts or 
 our own 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 
 
 M Brown's Lectures on the Philosophy of the Human Mind, 
 Lecture IX. Cp. Lecture II.
 
 INDUCTIVE INFERENCE. 27 
 
 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 external 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 operations. ' 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 of 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 constitu- 
 tion of the earth, and the architecture of the heavens : 
 we seek the boundary line of their junction, 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 
 modifications ; a course open to those who admit an 
 immediate consciousness of self, and to them only. My
 
 28 NATURE OF 
 
 first and only presentation of power or causality is thus 
 to be found in my consciousness of 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 28 .' 
 : 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, and however great our inability to 
 conceive how one event is followed by another, there is, 
 \ " Prolegomena Logica, pp. 138, 139. * Ibid. p. 140;
 
 INDUCTIVE INFERENCE. 2Q 
 
 at least, sufficient definiteness in the conception to 
 entitle it to be accepted as the basis of scientific reason- 
 ing. Whether we acknowledge 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 invariableness which makes the connexion or con* 
 junction, whichever we may call it, a fitting object of 
 scientific research. But remove the element of invari- 
 ableness, and suppose, if it be supposable, that the same 
 antecedent or set of antecedents is sometimes followed 
 by one consequent, and sometimes by another, and some^ 
 times 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 Connexion ; Dugald Stewart's Dissertation, Part 
 II. sect. 8 ; Mill's Logic, Book III. ch. v ; Sir W. Hamil- 
 ton's Lectures on Metaphysics, Lectures XXXIX, XL; 
 Mansel's Prolegomena 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- 
 wards repudiated by the author as containing an imma?
 
 30 NATURE OF 
 
 ture expression of his opinions 29 . In the Advertisement 
 to his Essays, he desires that ' the following Pieces may 
 alone be regarded as containing the author's philoso- 
 phical sentiments and principles.' 
 
 Note 3. That a cause is ,.....; that every 
 event has a cause ; that the same cause is always attended 
 with the same effect ; are obviously three distinct pro- 
 positions, 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 (if com- 
 pleted) would be the Definition of Cause, the predicate, 
 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 Causation, 
 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 of causation. Few believe in universal causation ; 
 
 89 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.
 
 INDUCTIVE INFERENCE. 3! 
 
 and those few not till after considerable reflexion 3 V He 
 then proceeds to adduce the case of a student of chem- 
 istry, who could not be convinced of the truth of the 
 Law, but ' looked upon the argument as an unwarrant- 
 able assumption.' Now I venture to suggest 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 circum- 
 stances 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 ac- 
 quiesced in. Like all other propositions, however, of 
 wide import, they may be both understood and ac- 
 quiesced 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 precision the circumstances which he 
 is investigating. The scientific man, on the other hand, 
 insists on invariably referring the phenomena in which 
 80 Lewes' History of Philosophy, -Article oh Kant.
 
 #2 . NATURE OF 
 
 he is interested to their several causes, and is satisfied 
 with nothing but the most rigorous enquiry into the 
 relation between these causes and their effects. 
 
 But, it may be asked, if the Laws of Universal Causa- 
 tion and of the Uniformity of Nature are, on reflexion, 
 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 S1 (what we now call the Law of Uniformity 
 of Nature), says, ' The wise Author of our nature hath 
 
 Jl 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 concern 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.
 
 INDUCTIVE INFERENCE. 33 
 
 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 connexions 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 3 V 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 3 V 
 
 M Reid's Inquiry into the Human Mind on the Principles of 
 Common Sense, ch. vi. 24. 
 
 - M Whewell's History of Scientific Ideas, Bk. III. ch. ii. i. 
 
 D
 
 34 NATURE OF 
 
 The opposite school of psychologists (of which Mr. 
 Mill and Professor 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 reflexion, we all 
 acquiesce, and cannot but acquiesce, in the statements 
 which generalise these facts. This, it is held, is a suffi- 
 cient explanation of that universality and necessity, which, 
 by the advocates of the intuitional theory, described in 
 the last paragraph, are supposed to distinguish the ' fun- 
 damental 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 conjunc- 
 tion, therefore, is incessant ; and, of course, the union 
 of the ideas perfectly inseparable. We can no more 
 have the idea of an event without having the ideas of 
 its antecedents and its consequents, than we can have
 
 INDUCTIl'E INFERENCE. 35 
 
 the idea and not have it at the same time S V But here 
 occurs a difficulty. If the Laws of Universal Causation 
 and of the Uniformity of Nature are inferred from par- 
 ticular facts of causation, are generalisations from ex- 
 perience, or, in other words, inductions, how is it that 
 they are made the grounds of all other inductions ? Is 
 not this to argue in a circle? The answer to this diffi- 
 culty is that the Laws in question are the result of an 
 uniform and constant experience, co-extensive not with 
 the life of he single individual who employs them, but 
 with the entire history of the human race ; that, con- 
 sequently, when we adduce them as the grounds on 
 which our other inductions rest, we are performing 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 which we happen to be making) 
 must be allowed to be true, unless we are prepared to 
 deny one or other of the much wider generalisations 
 which constitute the Laws of Universal Causation and 
 of the Uniformity of Nature. To recur to the instance 
 adduced in the text, the proposition that bodies, subject 
 to the action of gravity only, fall through equal vertical 
 spaces in equal times, can be called in question only on 
 
 34 James Mill's 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. 
 
 D 2
 
 36 NATURE OF 
 
 peril of doubting one or other of the fundamental laws ; 
 thus, the doubt which might attach to it is shifted to 
 two other propositions which no one would think of 
 questioning. Or, to state the same position 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 approved; as, there- 
 fore, it differs in no essential respect from them, it claims 
 to be admitted also. There is, indeed, 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 knowledge is alto- 
 gether impossible 35 . 
 
 There is a third theory of the origin of universal be- 
 liefs 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 iriind.' The word 
 
 35 It should be noted 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 guaranteed by our actual experience.' Mansel's 
 Metaphysics, Chapter on Necessary Truths. Cp. Prolegomena 
 Logica, ch. v. Dr. Mansel's treatment of these questions is, in many 
 respects, peculiar to himself.
 
 INDUCTIVE INFERENCE. 37 
 
 'experience,' as ordinarily employed by psychologists, 
 includes not only the experience of the individual, but 
 the recorded experience of mankind. On the theory, 
 however, of which I am now speaking, it has a still 
 more extended meaning ; it includes experience, or, to 
 speak more strictly, a peculiar aptitude 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, con- 
 natural, as it were, to the human mind. We assume 
 them, often unconsciously, in our special perceptions, 
 and when the propositions, which embody them, are 
 propounded to us, we find it impossible, on reflexion, 
 to doubt their truth. It is by personal experience of 
 external objects and their relations that each man re- 
 cognises 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 experience whatever on the part of the individual. 
 This theory, to which much of modern speculation ap- 
 pears to be converging, is advocated with great ability in 
 the works of Mr. Herbert Spencer M . 
 
 The student who wishes for further information on the 
 questions discussed in this Note is referred to Dugald 
 34 See especially his work on the Principles of Psychology.
 
 38 NATURE OF INDUCTIVE INFERENCE. 
 
 Stewart's Philosophy of the Human Mind, Part II. ch. v. 
 2 s7 (' Of that Permanence or Stability in the order of 
 Nature which is presupposed in our Reasonings con- 
 cerning Contingent Truths ') ; Reid's Intellectual Powers, 
 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 Meta- 
 physics, Lectures XXXIX, XL; James Mill's Analysis 
 of the Phenomena of the Human Mind, ch. xi ; Mill's 
 Logic, Book III. chs. iii-v, xxi ; Mansel's Prolegomena 
 Logica, ch. v ; Mansel's Metaphysics, Section on Neces- 
 sary Truths ; Mill on Hamilton, ch. xvi ; Lewes' History 
 of Philosophy, Article on Kant ; Bain's Moral and Mental 
 Science, Book II. ch. vi, with Appendix B ; Herbert 
 Spencer's Principles of Psychology. The student, in em- 
 ploying 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 suffi- 
 cient care. 
 
 37 In Sir W. Hamilton's edition of Stewart's Works, the corre- 
 sponding reference is Part II. Subdivision I. ch. ii. section 4, sub- 
 section t.
 
 ,, 
 
 CHAPTER 
 
 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 experiment} 
 is, not only to observe, but also to place the phenomena 
 under peculiarly favourable circumstances, as a pre- 
 liminary to observation. Thus, every experiment implies 
 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 ground, and I attend 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
 
 40 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 has not inaptly compared experiment with the torture of 
 witnesses l . A^h^ill distinguishes between the two pro- 
 cesses, by saying mat in observation -we find our instance 
 in nature, in experiment we make it, by an artificial ar- 
 rangement of circumstances. '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*. ,' 
 
 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 3 , 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 
 
 1 ' Quemadmodum enim in civilihus ingenium cujusque, et occultus 
 animi affectuumque sensus, melius elicitur, cum quis in pertnrbatione 
 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. 
 
 a Thomson and Tail's Natural Philosophy, vol. i. 369. 
 
 8 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.
 
 OBSERVATION AND EXPERIMENT. 41 
 
 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 we 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 was 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 advance 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,
 
 42 PROCESSES SUBSIDIARY TO INDUCTION". 
 
 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 
 Observation, 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 try the effects of different medicaments, 
 different modes of diet, and the like, but he will also 
 watch 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
 
 OBSERVATION- AND EXPERIMENT. 43 
 
 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 re- 
 versed, 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
 
 44 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 experi- 
 ments 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 by the extreme simplicity of the pheno- 
 mena, 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 imprac- 
 ticable 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
 
 OBSERVATION AND EXPERIMENT. 45 
 
 enquiries (as, for instance, in respect to crime, educa- 
 tion, trade, taxation, &c.) is often very large, and, by 
 carefully comparing and systematising them, we may 
 frequently detect some relation between two circum- 
 stances which enables us, with great probability, to 
 infer that one has something to do with the production 
 of the other. I am here, however, trenching on the 
 province of those chapters which treat more peculiarly 
 of inductive inference. 
 
 The following Rules may be laid down for the right 
 conduct of Observations and Experiments : 
 
 Rule I. They 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 
 devices may be given, amongst instruments, the tele- 
 scope, 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, frac- 
 tions both vulgar and decimal, the divisions of time, 
 the various contrivances for the measurement of space, 
 the method of double-weighing, the method of least
 
 46 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 squares, the personal equation in astronomical obser- 
 vations. To these 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 Ther- 
 mometer and the Method of Double-Weighing furnish 
 such striking exemplifications of the assistance thus 
 afforded, that, though they are probably familiar to 
 most of my 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 cir- 
 cumstances, so that what at one time affects us with 
 the sensation of hot will 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, while the pressure remains unaltered, 
 an augmentation of temperature, with certain rare ex- 
 ceptions (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
 
 OBSERVATION AND EXPERIMENT. 47 
 
 of measurements along the side, we are enabled, by 
 noting the degree of expansion of the substance in the 
 tube, to estimate, at least approximately, the degree 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 inequality in the effective arms of the beam 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, as- 
 sured of the precise equivalence in weight of the body 
 to be weighed and the standard weight or weights, pro- 
 vided, of course, that we can depend on the instrument 
 giving the same results in successive weighings. 
 
 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
 
 48 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 compensated by an error in the other, and that an aver- 
 age, 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 
 character of the climate at any particular place, the ob- 
 servations I consult must extend over a considerable 
 number of years ; if I wish to estimate truly the skill 
 of the marksman, 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 4 . 
 
 Rule II. But, though it is necessary to be precise in 
 our observations and experiments, it is also important, 
 in order to avoid distraction and waste of time, to attend 
 only to the material circumstances of the case we are in- 
 vestigating. 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 
 gathering herbs for his decoctions, think it of any con- 
 sequence to notice the phase of the moon. A caution 
 should, however, be added. Before neglecting any cir- 
 cumstance in our observations, it is of the utmost im- 
 
 * The student who may wish for further information in connexion 
 with Rule I. is referred to Dr. Whewell's Novum Organon Reno- 
 vatum, Bk. III. ch. ii., and Herschel's Discourse on the Study of 
 Natural Philosophy, 387-9. On the importance of taking an 
 average of observations, see Herschel's Discourse, 226-30.. .
 
 OBSERVATION AND EXPERIMENT. 49 
 
 portance to have ascertained beyond doubt that it is not 
 material to the subject of our enquiries 5 . To neglect 
 this caution would be a violation of the first Rule. 
 
 Rule III, The circumstances under which an observa- 
 tion or experiment is made should, except in the very 
 simplest cases, be varied as much as possible. A phy- 
 sician, in studying the character of a disease, will note 
 its effects on persons of different ages, constitutions, 
 habits of life, 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 various 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 cir- 
 cumstances will not be carried beyond the point at 
 which there is some probability of its adding to our 
 knowledge. 
 
 5 The neophyte in science requires to be reminded that observa- 
 tions which might at first be supposed to be immaterial are often 
 afterwards 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.' 
 
 E
 
 50 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 Rule IV.JThe phenomenon under investigation_should 
 if possible be isolated from all 7>ther pfienomena^or, at 
 least, from all those which are likely to interferjgith our 
 v^study__Qf_itIn 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 
 isolating 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 6 . 
 
 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 certain rose-coloured protuberances, pro- 
 jecting, as it were, from the dark edge of the moon, but, 
 in fact, proceeding from 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 incandescent hydrogen in 
 which the sun is enveloped, and which often shoots out 
 
 * 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.
 
 OBSERVATION AND EXPERIMENT. 51 
 
 in these flames to distances estimated, on one or two 
 occasions, at no less than 300,000 miles 7 . They can 
 now be seen, whenever the sun is shining, by means of 
 the spectroscope ; but had it not been for the isolation 
 of the phenomenon thus produced by the intervention 
 of the moon, astronomers would have till quite recently 
 been ignorant of its existence. Here, to use a bold 
 metaphor, we might say that Nature herself performs an 
 experiment for us. 
 
 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 extra- 
 neous circumstances on a patient subject to medical 
 regime, but, by due care, we may minimise the excite- 
 ment, fatigue, ennui, or other unfavourable conditions 
 which might interfere with our treatment. 
 
 The circumstances under which we perform our 
 experiments 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. 
 
 7 See Yonng on the Sun, p. 202. 
 E 2
 
 52 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 2. On Classification, Nomenclature, and Terminology. 
 
 (i) OF CLASSIFICATION. 
 
 A classification, in the widest sense of the term, is a 
 division, or a series of divisions and subdivisions 8 . The 
 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 admitting 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 I am about 
 to treat, though the same in kind with that which we 
 employ in the affairs of 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 
 8 See Deductive Logic, Part II. ch. viii.
 
 CLASSIFICATION. 53 
 
 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 
 classification being suggested by some distinct purpose), 
 a scientific classification must take account of all the 
 points of difference which are in any way likely to facili- 
 tate 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 investigates. Thus, if Botany be defined as the 
 science which investigates the organisation (including 
 under that term the form, structure, and functions) of 
 plants, a botanical classification, in order to be strictly 
 scientific, must not omit to take into account any part 
 of that organisation. But it is evident that such a 
 requirement would produce endless confusion, unless we 
 could discover some mode of subordinating the char- 
 acters, 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 char- 
 acters 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 proceeding to the attempt to ascertain induc- 
 tively facts of co-existence or causation amongst a vast
 
 54 PROCESSES SUBSIDIARY TO INDUCTION'. 
 
 mass of phenomena, it is often highly important, if not 
 essential, to arrange these phenomena in groups, as well 
 as to determine the order in which these groups them- 
 selves shall be arranged. Hence the importance of laying 
 down correct rules for Classification in a System of In- 
 ductive Logic. It is exclusively as subsidiary to Induction 
 that I shall here consider the subject of Classification 9 . 
 
 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 oj 
 
 9 It will probably occur to the student that the materials for 
 Classification can themselves only be obtained by Induction. And 
 this is true. All Classification implies the prior employment of an 
 Inductio per Enumerationem Simplicem, 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 I 
 regard Classification as mainly subordinate. I say ' mainly subor- 
 dinate,' 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 attri- 
 butes, 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 con- 
 nexion between, say, a and b, or a, b, and c.
 
 CLASSIFTCATION. 55 
 
 the entire subject under investigation. ' The general pro- 
 blem of classification,' says Mr. Mill 10 , ' in reference to 
 these [namely, scientific] purposes may be stated as 
 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 different kinds of 
 animals and plants which are found on the surface of the 
 globe : this fact 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 of discovering 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 arranging 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 
 10 Mill's Logic, Bk. IV. ch. vii. r.
 
 56 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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. An examination of the natural system will 
 enable us to lay down certain rules for scientific classi- 
 fication, and I shall conclude with such remarks as may 
 seem necessary 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 series, subordinated to the more important. 
 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 which 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 
 presently, is purely artificial. Though of little use, except 
 as a preliminary effort, for the purposes of science,
 
 CLASSIFICATION. 57 
 
 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 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. 
 I now proceed to offer illustrations. 
 
 In Botany, the most celebrated artificial system is that 
 known as the Linnsean, though Linnaeus also did much 
 towards the establishment of a natural system. In this 
 system, which was a great advance on preceding artifi- 
 cial 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 n ) 
 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 con- 
 stituted according to the Linngean system. It should be 
 premised that the stamens are the male organs, and the 
 pistils the female organs of a plant. 
 " 716, 717-
 
 58 PROCESSES SUBSIDIARY TO INDUCTION'. 
 
 TABULAR VIEW OF THE CLASSES OF THE LTNN^EAN SYSTEM. 
 
 A. Flowers present, or evident Stamens and Pistils (Phanerogamia). 
 
 I. Stamens and Pistil in every flower. 
 
 1. 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 XI. Dodecandria. 
 
 20 ) inserted on Calyx XII. Icosandria. 
 or more i on Receptacle... XIII. Polyandria. 
 
 b. Stamens of different 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 different flowers ; 
 
 on the same Plant XXI. Monoecia. 
 
 on different Plants XXII. Dicecia. 
 
 III. Stamens and Pistil in the same or j 
 
 in different flowers on the > XXIII. Polygamia. 
 same or on different Plants ) 
 
 B. Flowers absent, or Stamens and Pistils ) . 
 
 not evident . I XXIV. Cryptogarma.
 
 CLASSIFICA TION. 
 
 59 
 
 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 LINN^AN SYSTEM. 
 
 Class I.v Monogynia 12 I Free Style. 
 
 II. Digynia 2 Free Styles. 
 
 III. Trigynia ; 3 
 
 IV. Tetragynia 4 
 
 V. Pentagynia 5 
 
 VI. Hexagynia 6 
 
 VII. vHeptagynia 7 
 
 VIII. Octogynia 8 
 
 IX. Enneagynia 9 
 
 X. Decagynia 10 
 
 XI. Dodecagynia 12-19 ' 
 
 XII. Polygynia 20 and upwards. 
 
 XIII. 
 
 ( Gymnospermia Fruit formed by four Achsenia. 
 
 XIV. < Angiospermia Fruit, a two-celled Capsule with 
 
 ( many seeds. 
 
 I Siliculosa Fruit, a Silicula. 
 
 x - v< { Siliquosa Fruit, a Siliqua. 
 
 XVI ' 
 XVII ' Triandria, Decandria, &c. (number of Stamens), as in 
 
 XVIII.' ( Classes ' 
 
 Polygamia -tfujualis Florets all hermaphrodite. 
 
 Superflua Florets of the disk hermaphro- 
 
 dite, those of the ray pistilli- 
 ferous and fertile. 
 
 Frustranea ... Florets of the disk hermapb.ro- 
 
 XIX. { dite, those of the ray neuter. 
 
 Necessaria ... Florets of the disk staminiferous, 
 
 those of the ray pistilliferous. 
 
 Segregata Each floret having a separate 
 
 involucre. 
 \Monogamia Anthers united, flowers compound. 
 
 1S 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.
 
 60 PROCESSES SUBSIDIARY TO INDUCTION". 
 
 Monandria, Diandria, &c. (number of Stamens), as in the 
 
 xxiU Classes - 
 
 ^Moncecia ..................... Hermaphrodite, staminiferous 
 
 and pistilliferous flowers on the 
 
 XXIII. J 
 
 same plant. 
 
 Dioecia on two plants. 
 
 Tricecia on three plants. 
 
 IFilices Ferns. 
 Musci Mosses. 
 Hepaticse Liverworts. 
 Lichenes Lichens. 
 Algre Sea-weeds. 
 Fungi Mushrooms. 
 
 ' Even as an artificial method,' says Professor Balfour 13 , 
 ' 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 Linnasus 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 Linnsean system coincide with those 
 of the natural system. The same is mostly the case with 
 13 Balfour's Manual of Botany, 718.
 
 CLASS I PICA TION. 6 1 
 
 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, 
 attempt 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 coin- 
 cidence 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 acotyledonous and cotyledonous, and the 
 sub-division of vascular or cotyledonous plants into 
 monocotyledonous and dicotyledonous, furnish remark- 
 able instances of such a coincidence, and may conse- 
 quently be regarded as corresponding 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
 
 6 2 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 acotyledonous ; the former being divisible into monocotyle- 
 donous, having one cotyledon, and dicotyledonous, having 
 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 ar- 
 rived at : 
 
 i. Cellular... Acotyledonous. Heterorhizal. Acrogenous. j 
 
 _- . JMonocotyledonous. Endorhizal. Endogenous. | Phanero- 
 - Vascular - Dicotledonous. Exorhizal. Exoenous. amous 14 .' 
 
 - (Dicotyledonous. 
 
 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 
 usually 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 Exogenae ' is sub-divided into four 
 
 14 Balfour's Manual of Botany, 723, 5-24.
 
 CLASSIFICATION. 63 
 
 sub-classes, one of which is the ' Thalamiflorae,' char- 
 acterised as having ' calyx and corolla present, petals 
 distinct and inserted into the thalamus or receptacle, 
 stamens hypogynous.' This sub-class is divided into a 
 number of orders (sixty in Professor Balfour's Manual], 
 one of which is Hypericaceae, 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 dots, aestivation contorted. Stamens hypogynous, in- 
 definite in number; generally polyadelphous, very rarely 10, and 
 monadelphous or distinct ; filaments filiform : anthers bilocular, 
 with longitudinal dehiscence ; carpels 2-5, united round a central or 
 basal placenta ; styles the same number as the carpels, usually 
 separate ; stigmas capitate or simple. Fruit either fleshy or cap- 
 sular, multilocnlar, and multivalvular, rarely unilocular. Seeds 
 usually indefinite in number, minute, anatropal, usually exalbu- 
 minous ; embyro usually straight. Herbaceous plants, shrubs, or 
 trees, with exstipnlate 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 : 
 
 ' Hypericnm, 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, com- 
 bined at the base into three or five sets, with small roundish 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.'
 
 64 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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.' 
 
 The sub-genus or section is again divided into sub- 
 sections, one of which is characterised as having ' stems 
 round, sepals with ciliary glands.' This sub-section con- 
 tains amongst its species the well-known Hypericum 
 Pulchrum, ' Elegant St. John's- wort,' thus described : 
 
 ' Stems erect, bent at the base, round, glabrous, simple or branch- 
 ing. 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 15 .' 
 
 The first peculiarity which strikes us in these 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 instance, the description of the sub-class simply 
 informs us of the presence of a calyx, while each suc- 
 cessive division (except the sub-genus) gives us more 
 and more definite information as to the number, posi- 
 tion, form, &c. of the sepals which constitute the calyx. 
 
 15 See Irvine's Handbook of British Plants, under Order CIII.
 
 CLASSIFICATION. 65 
 
 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), which are employed in the higher divisions, 
 disappear from the lower, as no longer affording grounds 
 of difference. 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 
 difference 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. Whewell 1S , ' which, in 
 w History of the Inductive Sciences, Bk. XVI. ch. vii. 
 F
 
 66 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 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 classifi- 
 cation 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 subdivisions 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 com- 
 binations they may lead.' 
 
 'By the natural method? says M. Milne Edwards 17 
 (whose remarks on Zoological Classifications and the ; 
 Primary Divisions and Classes of the Animal Kingdom 
 
 17 See Milne Edwards' Zoologie (in the Cours llementaire cThistoire 
 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.
 
 CLASSrFrCATION. 67 
 
 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 
 furnished by each animal, arranged according to their 
 degree of respective importance ; thus, in knowing the 
 place which the animal occupies, we also know the more 
 remarkable traits of its organisation, and the manner in 
 which its principal functions are exercised. 
 
 'The rules to be observed in arriving at a natural 
 classification of the animal kingdom are of extreme sim- 
 plicity, but often there is much difficulty in the appli- 
 cation. They may be reduced to two, for the object of 
 the zoologist in establishing such a classification is, 
 
 ' ist. 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 amongst them.' 
 
 The Primary Divisions of the animal kingdom, accord- 
 ing to the natural system, are four, there being four types 
 of structure and of nervous organisation, to which animal 
 life conforms. 
 
 ' These four principal fqrms may be understood by a 
 
 F 2
 
 68 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 modifications introduced into the structure of animals, 
 it was necessary to distribute these beings into four 
 principal groups or divisions ; and this is, in fact, what 
 Cuvier did. 
 
 'The animal kingdom is divided into vertebrate animals, 
 articulated or annulated 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 important 
 influence, as modifying the localisation of the functions 
 and the division of the physiological result lg .' 
 
 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 
 
 18 Milne Edwards, 372, 373.
 
 CLASSIFICATION. 69 
 
 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 characteristics we may add that the principal 
 muscles are attached to an internal skeleton, composed of separate 
 pieces, connected together, and 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 19 .' 
 
 The Primary Division (embranchement) ' Vertebrate 
 Animals ' is subdivided 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 cerebellum 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 df demarcation is by no means so distinct. 
 
 19 Milne Edwards, 374.
 
 76 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 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 
 numerous, 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 
 nourishment from the mother by means of a pla- 
 centa. 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 abdo- 
 men have no osseous supports 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, ordinary mam- 
 mals and pisdform mammals. 
 
 1 The ordinary mammals are organised principally to 
 live on solid ground; the skin is provided with hairs.
 
 CLASSIFICATION. 7! 
 
 These animals are further subdivided into ten orders: 
 the bimana, quadrumana, cheiroptera, insectivora, 
 rodentia, edentata, carnivora, amphibia, pachydermata, 
 and ruminantia. The first eight of these orders have 
 flexible fingers and toes, with nails covering only the 
 dorsal aspect 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 en- 
 closed 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 
 progression 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 2 V 
 
 Here the Order is co-extensive 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,' &c. 
 Again, the Genus ' dog ' comprises the dog properly 
 so called, the wolf, and the fox. The Genus ' cat ' com- 
 prises 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 
 20 Milne Edwards, 409-412.
 
 72 PROCESSES .SUBSIDIARY TO INDUCTION. 
 
 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 unguiculnted 
 mammals ; the form of their dentition is complete, but they have 
 no opposing 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 temporal-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, some- 
 times adapted merely for cutting, in others surmounted 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 carnivorous 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 exclu- 
 sively composed of flesh or mixed with other matters, may be 
 judged of by the varying proportions of these cutting or tuber- 
 culated 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 extra- 
 ordinary 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
 
 CLASSIFICA TION. *] 3 
 
 the best developed of all their senses. They see well by day and. 
 night, but they are not far-sighted ; in some the pnpil 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 homy and very rough 
 pqints. 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. 
 
 ' 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 21 .' 
 
 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 
 
 21 Milne Edwards, 414.
 
 74 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 the rules which may be laid down for the right conduct 
 of a Natural Classification. 
 
 I. Not only the lower, but the hjgher groups of th6 
 ries 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. 
 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. 
 
 II. 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 important 
 attributes,' says Mr. Mill 22 / '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 account 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 
 
 a Mill's Logic, Bk. IV. ch. viii 2.
 
 CLASSIFICATION. 75 
 
 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 char- 
 acters, a character is regarded as of more or less impor- 
 tance, according as it accompanies a greater or smaller 
 number of other differences. Thus, in the classification 
 of animals, the characters from which the classes ungui- 
 culata 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 
 endogenous 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
 
 76 .PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 divisions 
 various other divisions are interpolated, according to the 
 seeming requirements of each particular system, and often 
 according to the views of each individual author. More- 
 over, 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 2S : 
 
 I. PRIMARY DIVISION . . . Cotyledones. 
 
 II. CLASS Dicotyledones. 
 
 Subclass Calyciflorae. 
 
 III. ORDER Leguminosae. 
 
 Suborder Papilionacese. 
 
 Tribe Loteoe. 
 
 Subtribe Genisteae. 
 
 IV. GENUS Anthyllis. 
 
 Subgenus or Section . . . Vulneraria. 
 
 V. SPECIES Vulneraria 2 *. 
 
 Variety Dillenii. 
 
 Race Floribus coccineis. 
 
 Variation Foliis hirsutissimis. 
 
 23 Balfour's Manual of Botany, 725. 
 
 81 It is not uncommon in the classificatory sciences, as in this
 
 CLASSIFICA TION; 7 7 
 
 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 divi- 
 sions often disappear ; if a genus consist of only a small 
 number of species, and there be no very striking points 
 of difference 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 
 coextensive 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 their dissimilarity. 
 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 subsequent 
 induction, it is plain that it is of the utmost importance 
 not widely to dissever groups which present many phe- 
 nomena 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 Subordination 
 
 instance, to assign the same name to a higher and lower division, 
 the lower division exhibiting in a marked manner the characters 
 possessed in common by the various members of the higher division.
 
 7 8 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 considerable distances 
 from each other. But it is not sufficient to observe the 
 rule of the Subordination of Characters. The arrange- 
 ment 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'" 
 b' b" C-, B into the genera m' m" n o p' 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 m' m", and/'/" in juxtaposition 
 with x f 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 
 presented in the greatest intensity the principal pheno- 
 mena of the class of objects under investigation would
 
 CLASSIFICATION. 79 
 
 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 pre- 
 sented in the greatest intensity the principal phenomena 
 of animal life, and in Botany those which presented in 
 the greatest intensity the principal phenomena of veget- 
 able life. It is, of course, seldom, in the arrangement of 
 natural objects, that we are able to draw up an exact 
 table of precedence 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 collection 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 is 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 
 properties 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 
 precedence ; but there remains a large number of cases 
 tp which the rule is inapplicable, or to which, at least, it: 
 has not yet been successfully applied. This is especially
 
 8o PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 many cases among the 
 subdivisions, especially of Monocotyledons and Dicoty- 
 ledons, where no order of precedence can as yet be 
 satisfactorily established. But, even if the rule were of 
 universal application, and if we were perfectly acquainted 
 with all 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 Classifica- 
 tion 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 25 , 
 ' to arrange allfl/aces (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 
 complete, when it has descended as low as species, 
 a species being regarded as a group consisting of indi- 
 viduals, all of which have descended from a common 
 stock. Or, if the process be reversed, and the classifica- 
 tion be an ascending 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 
 M Bk. IV. ch. viii. i. Note.
 
 CLASSIFICATION. 8 1 
 
 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 question a very large section of natur- 
 alists 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 regarded as distinct, it may be asked 
 on what grounds this supposition rests. Different vari- 
 eties 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 difficulty in sup- 
 posing 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 20 , ' that I look at the term species, as one arbi- 
 trarily given for the sake of convenience to a set of 
 individuals closely resembling 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 comparison with mere individual 
 differences, is also applied arbitrarily, and for mere 
 36 Darwin's Origin of Species, ch. ii. 
 G
 
 82 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 convenience' sake.' It does not fall within my 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 2. As our knowledge of the external world 
 becomes enlarged, the number of natural groups, recog- 
 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. Whe- 
 well 2T , ' were 10,000 at the time of Linnaeus, and are now 
 [A.D. 1858] probably 60,000.' The increase in the num- 
 ber of recognised varieties, sub-varieties, &c., is even still 
 more rapid. One common effect of these constant dis- 
 coveries 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, some- 
 times, is this continuity, that it becomes very difficult 
 to distinguish the groups by any fixed characters. Two 
 
 91 History of Scientific Ideas, Bk. VIII. ch. ii. 6. Of course, since 
 Dr. Whewell's time, the number has, again, been constantly on the 
 increase.
 
 CLASSIFICATION. 83 
 
 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. Car- 
 penter, as quoted by Sir W. Grove 28 , ' that a very wide 
 range of variation exists among Orbitolites, not merely 
 as regards external form, but also as to plan of develop- 
 ment ; and not merely as to the shape and aspect of the 
 entire organism, but also with respect to the size and 
 configuration of its component 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 lines 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 persistency of type, which is 
 the result of the laws of hereditary transmission ; if there 
 were no such persistency, the attempt to group natural 
 
 88 Essay on Continuity, printed at the end of the Fifth Edition of 
 The Correlation of Physical Forces, pp. 326, 327, 
 
 G 2
 
 84 PROCESSES SUBSIDIARY TO INDUCTION: 
 
 objects would be fruitless and absurd. But, at the same 
 time, when we have succeeded in establishing 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. Whe- 
 well, 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 
 characters by which classes or groups are distinguished, 
 one from another, is to be found, not invariably, but only 
 usually or occasionally in the members of the group. 
 Thus, in the description of the Order Rosacese, we find 
 that ' the seeds are erect or inverted, usually exalbumin- 
 ous. . . . Flowers sometimes unisexual.' Such indefinite 
 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 invariably, 
 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
 
 CLASSIFICATION. 85 
 
 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 of 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. ' The Characteristick,' says Dr. Whe- 
 well 29 , 'is an Artificial 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. Dr. 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 
 29 History of Scientific Ideas, Bk. VIII. ch. ii. 7.
 
 86 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 enumeration of the characters which are common to the 
 dog, wolf, and fox (the species comprised in the genus), 
 but by approximation to the type-species dog : similarly, 
 the Order Rosaceae 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 to the type-genus Rosa. Dr. WhewelPs 
 view will be understood 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, which is considered as eminently 
 possessing 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 
 degrees. 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
 
 CLASSIFICATION: 87 
 
 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 erery family, is, then, one which possesses all the 
 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 
 promirent 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 30 .' 
 
 30 fastory of Scientific Ideas, Bk. VIII. ch. ii. 3. art. 10. Mr. 
 Mill (~ogic, Bk. IV. ch. vii. 3, 4) examines Dr. Whewell's views 
 at considerable length. He appears to me, in this examination, to 
 insist 'oo emphatically on what he calls ' distinctions of kind,' and 
 to asssrt, without sufficient warrant, that ' the species of Plants are 
 not oily real kinds, but are probably, all of them, real lowest kinds,
 
 88 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 constitute the groups into a distinct class. But it is 
 not 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-con- 
 stituted class, and which, at the same time, distinguish 
 them from the members of other classes, with the addi- 
 tion, 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 determined (or ' given' to use 
 Dr. Whewell's expression) by an enumeration of char- 
 acters. But, when the class is once familiar to is, 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 chaiacters 
 by which the class was determined ; and it is by reference 
 to this central specimen, as it were, that we fix the posi- 
 tion of the other groups and adjudicate on the clains of 
 
 Infimae Species, which if we were to subdivide into sub-classs, the 
 subdivision would necessarily be founded on definite distinction, not 
 pointing (apart from what may be known of their causes or eFects) 
 to any difference beyond themselves.'
 
 NOMENCLATURE. 89 
 
 any newly-discovered 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 con- 
 venient 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 recol- 
 lected by ourselves nor communicated to others, unless 
 they were fixed by the imposition of names. A Nomen- 
 clature 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 
 impossible 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, 
 now probably far exceeds 60,000, and, if we took into ac- 
 count 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 
 distinguish a large number of groups. Botany and 
 Chemistry furnish admirable examples of the employ- 
 ment of such an artifice, and some knowledge of the 
 principles which guide the imposition of names in those
 
 90 PROCESSES SUBSIDIARY TO INDUCTION". 
 
 two sciences (a knowledge which may be easily acquired) 
 would probably be of more service to the student than 
 anything which he might learn from a body of rules for 
 Nomenclature in general. 
 
 In Botany, the higher groups (including genera) have 
 distinct names. Thus, we have Dicotyledones, Rosacese, 
 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 re- 
 presented in the British Isles by thirteen species, called 
 respectively Geranium phaeum, G. nodosum, G. sylva- 
 ticum, G. pratense, G. sanguineum, G. pyrenaicum, G. 
 pusillum, G. dissectum, G. columbinum, G. rotundi- 
 folium, G. molle, G. lucidum, G. robertianum. The 
 specific names are selected 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 
 we are told by Dr. Whewell 31 ) ' gave the name of Bau- 
 hinia 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 remembered, serves 
 81 History of Scientific Ideas, Bk. VIII. ch. ii. 6.
 
 NOMENCLATURE. 91 
 
 the main purpose of a nomenclature, which is to distin- 
 guish 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 
 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, ous, ate, ite, &c., and the prefixes mono, 
 di, tri, sesqui, &c., each having a special significance, 
 though, unfortunately, not always an unambiguous one. 
 
 It would transcend the limits of this work to give an 
 account, sufficiently clear and precise, of the Nomen- 
 clature 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 constructed, can refer to Watts' Dictionary of 
 Chemistry, vol. iv. art. Nomenclature.
 
 92 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 (3) OF TERMINOLOGY. 
 
 / A Nomenclature of a Science is, as \ve_liaye-seeii, 
 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 
 genus 'Rosa ' have 'their corolla imbricated before flower- 
 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 32 , ' 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 Linnaean Reform. " Tourne- 
 fort," says Decandolle, "appears to have been the first 
 who really perceived the utility of fixing the sense of terms 
 
 38 History of Scientific Ideas, Bk. VIII. ch. ii. 2.
 
 TERMINOLOGY. 93 
 
 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 
 was successively distinguished into the cafyx, 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, pinnalilobate, 
 palmatifid, 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 bilobate 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.
 
 94 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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, I have said, comprises the terms 
 appropriated to express, not only the parts of objects, 
 but also their properties. Thus, in the foregoing ex- 
 ample, 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 technical 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 convention, 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
 
 TERMINOLOGY. 95 
 
 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 in- 
 tended. 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 sen- 
 sation, and not to the parts of this term ; for these enter 
 into the compound merely as a help to the memory, 
 whether the suggestion be a natural connexion 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 connected 
 with it through the vague usages of common language. 
 The memory must retain the sensation ; and the tech- 
 nical word must be understood as directly as the most 
 familiar word, and more distinctly. When we find such 
 terms as tin-white or pinchbeck-brown, the metallic colour 
 so denoted ought to start up in our memory without 
 delay or search 3 V 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 
 83 History of Scientific Ideas, Bk. VIII. ch. ii. 2.
 
 96 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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,' ' light,' ' 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 34 , is in- 
 dispensably requisite in giving fixity to a Nomenclature. 
 Thus, in Botany, ' the recognition of the kinds of plants 
 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. WhewelPs style and mode of treat- 
 ment, 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. chs. iii-vi) on ' Naming ' 
 and the ' Requisites of a Philosophical Language,' and, 
 in addition to the passage already referred to, Dr. Whe- 
 well treats these subjects in his History of Scientific Ideas, 
 Bk. I. ch. ii ; Bk. VIII. ch. ii. 2 and 6 ; Bk. VIII. 
 s * Novum Organon Renovatum, Bk. IV. Aphorism ii.
 
 HYPOTHESIS. 97 
 
 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. 
 
 3. On Hypothesis. ^ , 
 
 When 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-existence or 
 succession. 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 
 cases, as we have seen in the first chapter 35 , 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 than 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. These theories, assumptions, or suppositions, 
 when employed provisionally in scientific enquiry and 
 
 M See pp. n, 12. 
 H
 
 98 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 falling short of ascertained truths, are called hypotheses, 
 and have already been alluded to in the first chapter. 
 The word 'hypothesis,' as commonly employed, is ex- 
 clusive of propositions which rest upon absolute proof, 
 whether inductive or deductive, and is generally used 
 in contradistinction to them. 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 
 which, at least in the eyes of its framer, did not possess 
 some amount of plausibility. A hypothesis 36 may be de- 
 scribed as a supposition made without evidence or without 
 sufficient evidence, in order that we may deduce from it 
 conclusions agreeing with actual facts. 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 
 ch occur uniformly but are not connected by any 
 uiown law of causation into a series which is so con- 
 iccted, or the reduction of complex laws of causation 
 
 86 The following sentences, to the end of the paragraph, are 
 slightly altered from Mr. Mill's Logic, Bk. III. ch. xiv. 4.
 
 HYPOTHESIS, 99 
 
 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 ways. In 
 the first place, it may afford a solution, more or less 
 probable, of a problem which is incapable of any definite 
 solution, or which, at least, has not yet been 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 
 started as a hypothesis may ultimately be established by 
 positive proof, as has been the case with the elliptical 
 theory of planetary motion, and, as many suppose, with 
 the undulatory theory of light. Thirdly, even though 
 a hypothesis may ultimately be 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 
 H 2
 
 IOO PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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. 
 
 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 1 
 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 untrue, that is to say, it must not be inconsistent with 
 facts already ascertained or the inferences to which they
 
 HYPOTHESIS. 10 1 
 
 lead". It would 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 
 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 
 to admit of verification or disproof, or at least of being 
 rendered more or less probable, by subsequent investiga- 
 tions 38 . 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. 
 
 37 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 con- 
 flict with any laws of nature, or of mind, which we hold as true." 
 Principles of Science, vol. ii. p. 139. 
 
 34 It may occur to the student that I 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 some- 
 thing provisional, something which, on further enquiry, may be either 
 confirmed or weakened, rendered more or less probable than it 
 now is.
 
 102 PROCESSES SUBSIDIARY TO INDUCTION". 
 
 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 of ap- 
 proximation 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 
 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
 
 HYPOTHESIS. 103 
 
 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 3D . 
 
 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 Lyell's Principles 
 of Geology 40 : 
 
 ' 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 
 
 39 The superstitions connected with dreams afford a similar in- 
 stance : ' The ancients were convinced that dreams were usually 
 supenatural. If the dream was verified, this was 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 creams should sometimes be interpreted by contraries. If the 
 dreair bore no relation to subsequent events unless it were trans- 
 formel into a fantastic allegory, it was still supernatural, for allegory 
 was oie of the most ordinary forms of revelation. If no ingenuity 
 of interpretation could find a prophetic meaning in a dream, its 
 supenatural character was even then not necessarily destroyed, for 
 Homer said there was a special portal through which deceptive 
 visiois passed into the mind, and the Fathers declared that it was 
 one if the occupations of the daemons to perplex and bewilder us 
 with unmeaning dreams.' Lecky's History of European Morals, 
 vol.i. p. 385. 
 
 40 Lyell's Principles of Geology, ch. iii.
 
 104 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 gene- 
 rated 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 
 1 574, faithful figures of the fossil shells preserved by Pope 
 Sixtus V. in the Museum of the Vatican, expressed an ophion 
 that they were mere stones, which had assumed their peculiar 
 configuration 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 then 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 spontaieous 
 generation, then taught in all the schools. For men who had 
 been taught, in early youth, that a large proportion of Iving 
 animals and plants was formed from the fortuitous conourse 
 of atoms, or had sprung from the corruption of organic mitter, 
 might easily persuade themselves, that organic shapes, aften 
 imperfectly preserved in the interior of solid rocks, owed iheir 
 existence to causes equally obscure and mysterious.' 
 
 'As to the nature of petrified shells, Quirini conceived ihat, 
 as earthy particles united in the sea to form the shelb of 
 mollusca, the same crystallizing process might be efifectec on 
 the land ; and that, in the latter case, the germs of the
 
 HYPO THESIS. 1 05 
 
 animals might have been disseminated through the sub- 
 stance 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 ; for 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, 
 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 
 afforded 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.
 
 106 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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. 
 
 It .vill be observed that I regard hypotheses as ad- 
 missible, even though they are not likely ever to be 
 positively proved or disproved, provided that the ac- 
 cumulation 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, I conceive, have a legi- 
 timate 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 probabilities. Instances of hypo- 
 theses such as I have in view are the Darwinian 
 hypothesis and the Meteoric theory of the repair of 
 Solar Heat, to be. noticed presently. 
 
 III. The hypothesis must be applicable to the descrip-
 
 HYPOTHESIS. 107 
 
 tion or explanation of all the observed phenomena, and, 
 if it assign a cause, must assign a cause fully adequate 
 to have produced them. 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 
 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 gener- 
 ation 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 41 : 
 
 11 Heat a Mode of Motion, 3rd ed. 689-693. Sir William 
 Thomson, however, from various considerations, arrived at the con-
 
 108 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 ( 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 
 of the earth's surface, without the appearance of at least one 
 meteor. Twice a year (on the 1 2th of August and 1 4th 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 
 
 elusion that ' the sun's expenditure [of heat], though originated, is 
 not maintained by mechanical impact ; the low rate of cooling and 
 the consequent constancy of the emission being considered by him 
 as due, in great part, to the high specific heat of the matter of the 
 sun.' See Tyndall's Heat, &c., 701. Other physicists (see Young 
 on the Sun, pp. 270-7) conjecture that the heat of the sun is partly 
 due to its gradual contraction and the increase of temperature thus 
 generated.
 
 HYPOTHESIS. 109 
 
 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 
 approached thousands of miles nearer to the sun. 
 
 ' Following up these reflexions, 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 
 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 equa4 
 asteroid of solid coal ; while the shock, in the latter case, 
 would generate eat 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.
 
 110 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 1 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 42 : 
 
 'Sir 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 43 centigrade (each 1390 foot pounds) 
 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, 1 500 Ibs. 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 
 
 12 Heat a Mode of Motion, 700. 
 
 43 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 from a height of 1390 feet against the earth. The term/00/- 
 pound expresses the energy requisite to lift one pound to the height 
 of a foot.
 
 HYPOTHESIS. Ill 
 
 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 might for a time be as large as the 
 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
 
 1 12 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 legitimate hypothesis, though it must conform to still more 
 rigorous requirements before it can be accepted as a 
 complete Induction, or even be regarded as possessing 
 any great amount of probability. 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 
 of a large number of meteors on a body of considerable 
 density, 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 legi- 
 timate as a hypothesis, before we could accept the 
 Meteoric theory as a Valid or Complete Induction,
 
 HYPOTHESIS. 113 
 
 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, */ they 
 were falling or had fallen 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 deflexion of the planets from their rectilinear 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 direction 
 whatever, the planet would not describe equal areas in 
 equal times. It being thus shown that no other hypo- 
 
 i
 
 114 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 thesis would accord with the facts, the assumption was 
 proved ; the hypothesis became an inductive truth. Not 
 only did Newton ascertain by this hypothetical process 
 the direction of the deflecting force ; he proceeded in 
 exactly the same manner to ascertain the law of variation 
 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 4 V 
 
 It will be noticed that the course of demonstration 
 pursued 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 therefore, of course, for the particular facts of ob- 
 servation on which those Laws were founded ; (5) ;t is 
 shown (and this, together with the next step, is what 
 properly constitutes the demonstration) that this assump- 
 tion 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 
 * Mill's Logic, Bk. III. ch. xiv. 4.
 
 HYPOTHESIS. 115 
 
 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 
 Induction 45 by the application of one or other of the 
 Inductive Methods (to be described in the next Chapter), 
 or, if we insist on strict accuracy of proof, of such of 
 them as furAish absolutely certain conclusions. 
 
 Note i. -+- According to the view here taken, which 
 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 
 
 45 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 evidence. 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 induc- 
 tive methods. 
 
 I 2
 
 Il6 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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, ABC, 
 a b c, and B C, b 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), 
 (together with other effects be) ; the planets without a 
 central force give b c (a set of motions) without 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 b c, and B C only b 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 4 V 
 
 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 
 
 ** Mill's Logic, Bk. III. ch. xiv. 4. I have slightly altered this 
 passage, as it stands in Mill, and as it stood in my earlier editions, 
 so as to make it plainer to the student.
 
 HYPOTHESIS. 117 
 
 % 
 
 them of such modifications as that comparison may 
 render necessary 47 . 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 foretell 
 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 
 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 useful 48 .' 
 
 a 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 theory, together with other points 
 of difference between Professor Jevons and myself, I have noticed in 
 the Preface to the third edition, reprinted in the present one. 
 
 ** Novum Organon Renovatum, Bk. II. ch. v. art. 10.
 
 Il8 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 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 have 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
 
 HYPOTHESIS. 119 
 
 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 of 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 
 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
 
 120 PROCESSES SUBSIDIARY TO INDUCTION'. 
 
 should thus leap to the same point, can only arise from 
 that 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 [mean] 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 connexion 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 striking and surprising coincidence, which 
 gave to the theory a stamp of truth beyond the power 
 of ingenuity to counterfeit 49 .' 
 
 It is undeniable that a theory which thus appears to 
 afford an explanation of different classes of facts strikes 
 49 Novum Organon Renavatum, Bk. II. ch. v. art. 1 1 .
 
 HYPOTHESIS. 121 
 
 the imagination with considerable force, and that its very 
 simplicity furnishes prima 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 consilience 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 ad&quata 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 
 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. Whewell's Philosophy of 
 Discovery, ch. xviii. 5, &c. The expression cannot
 
 122 PROCESSES SUBSIDIARY TO INDUCTION. 
 
 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 
 little 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 ''gra- 
 tuitous hypothesis.' By this phrase is meant the assump- 
 tion 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 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
 
 HYPOTHESIS. 123 
 
 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 ; in the ' electrical fluid ' of 
 the early electricians ; and in the dnoppoiat of Democritus 
 or the 'intentional species' of the Peripatetics, which, 
 being invented for the purpose of explaining the per- 
 ception of material objects by the mind, were themselves 
 equally in need of explanation. 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 be a legitimate 
 inference from the known to the unknown. But the 
 unknown must not be entirely unknown. It must be 
 known to agree in certain circumstances with the known, 
 and it is in virtue of this agreement that the inference 
 is 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, b> c, but it will not follow because X exhibits 
 the quality tn, 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 con- 
 taining thousands of blue hyacinths, but this fact would 
 not justify us in expecting that the next time we saw
 
 INDUCTIVE METHODS. 125 
 
 a hyacinth, it would be a blue one. This form of induc- 
 tion (Inductio per Enumerationem Simplicem} may have no 
 value whatever. In most cases, the condemnation passed 
 on it by Bacon 1 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 uncontra- 
 dicted experience, that there are no cases to the contrary, 
 no stronger argument (to us individually) can be adduced. 
 It is not often, however, that an Inductio per Enumera- 
 tionem Simplicem can afford us this certainty 2 . Our 
 trustworthy inductions are, in the 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, d of X, a is the cause 
 of c, 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 <: as well; or, if we 
 
 1 Novum Organum, Lib. I. aph. cv. 
 
 * 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.
 
 126 INDUCTIVE METHODS. 
 
 observe the phenomenon c in Y, we infer that it is not 
 unlikely 3 that a may be present as well. The problem 
 of Induction, therefore, resolves itself (except in the 
 cases in which we may legitimately employ Inductio per 
 Enumerationem Simplicem, or the cases 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 I shall describe as the Inductive 
 Methods. 
 
 These Methods, it will be noticed as we proceed, are all 
 methods of elimination, or devices \)y 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. 
 
 (1) 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. 13-16), 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.' 
 
 * I 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. 127 
 
 (3) The same effect may be due to several distinct 
 causes, or combinations of causes, being due sometimes 
 to 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] for which a recent 
 writer (Mr. Carveth Read) has proposed to substitute 
 the expression ' Vicariousness of Causes,' in order to 
 distinguish clearly the case of alternative from that of 
 co-operating or concurrent causes, noticed in the last 
 paragraph 4 . 
 
 4 It is sometimes doubted whether the same effect is ever really 
 due to different causes, and it may be conceded, I think, that dif- 
 ferent causes never do produce precisely the same aggregate of effects. 
 Together with certain common effects, they produce certain divergent 
 effects, and it is the presence of these, indeed, that enables us to 
 determine the particular cause which has been at work in the par- 
 ticular instance. There is, however, nothing in this circumstance 
 inconsistent with the occurrence of some one or more effects common 
 to all the causes. Thus, the whole group of effects produced severally 
 by heat, electricity, impact, differs widely, but, at the same time, 
 the motion of a needle may be a common part of the effect in all 
 three instances, and, when we see the needle in motion, we may be 
 unable to say to which of the three causes motion is due. Similar 
 considerations may be applied to the cases of ignition, and death, 
 which are favourite illustrations of the operation of a plurality of 
 causes. Taking A, B, C, D as causes or combinations of causes, and 
 a, b, c, &c. as individual portions of the aggregate effects produced 
 by the causes, we may conceive A as producing a b c d e, B as pro-
 
 128 INDUCTIVE METHODS. 
 
 (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 affinity, is excited, the rest are developed simul- 
 
 ducing d e f g h, C as producing c d e i k /, D as producing e m n o. 
 In this case, e may be regarded as an effect due to any one of the 
 causes A, B, C, D, though the ' attendant circumstances,' as they are 
 often called, are widely different in each instance. If, therefore, we 
 were to state the doctrine of Plurality or ' Vicariousness ' of Causes 
 exactly, we should say, not that the same effect may be due to dif- 
 ferent causes, but that, of the total effects due to different causes, a 
 certain portion is often found to be common to all. For purposes 
 of practice, however, the ordinary mode of statement is sufficiently 
 precise. 
 
 It seems hardly necessary to remark that it is no valid objection 
 to the doctrine of Plurality of Causes that we are sometimes able to 
 detect between the alternative causes and the identical effect some 
 set of conditions which is the same in all cases. This discovery only 
 removes the plurality of causation one step further back, and the 
 doctrine can only be consistently denied by those who maintain that 
 at no single point in the series of receding causes can we find the 
 same effect produced, or capable of being produced, by distinct
 
 INDUCTIVE METHODS. 129 
 
 taneously 5 . 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 
 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. 
 
 \ now proceed to the statement of the Inductive 
 Methods. 
 
 * See Grove's Correlation of Physical Forces, Concluding Remarks. 
 What Sir W. Grove calls ' Force ' would now be denominated 
 ' Energy,' and the doctrine of the ' Correlation of Physical Forces ' 
 would be subsumed under that of the ' Conservation of Energy.'
 
 330 - INDUCTIVE METHODS. 
 
 METHOD OF AGREEMENT. 
 
 CANON 6 . 
 
 If two or more instances of the phenomenon under investi- 
 gation have only one other circumstance in common, that 
 circumstance may be regarded, with more or less of proba- 
 bility, as the cause (or effect] of the given phenomenon, or, at 
 least, as connected with it through some fact of causation. 
 
 Wherever the phenomenon a is found, we observe that 
 b is found, either invariably or frequently 7 , in conjunction 
 with it. This fact leads us to suspect that there is some 
 causal connexion between them. On what grounds, 
 and under what circumstances, are we justified in drawing 
 such an inference ? 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 I 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, /3, y, &c. When circumstances are not 
 distinguished as antecedents and consequents, I shall 
 employ the small Roman letters, a, b, c, &c. 
 
 6 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. 
 
 7 I add ' or frequently,' as it is not necessary that the conjunction 
 should be invariable. The student need not, however, at present 
 trouble himself with this distinction, which will be fully explained 
 below. See pp. 137-8, 145-7.
 
 METHOD OF AGREEMENT. 131 
 
 Now, suppose that we have A B followed by a , and 
 A C by a y ; it might, at first sight, appear that A must 
 be the cause of o, or, if we were attempting to ascertain 
 the effect of a given cause (which, however, is a much 
 rarer application of this method), that a must be the 
 effect of A. And there is much plausibility in this sup- 
 position, for, provided that all the other circumstances 
 remain the same, whatever can, in any given instance, be 
 excluded, or, to use the technical term, eliminated without 
 prejudice to a phenomenon, cannot have any influence on 
 it in the way of causation, nor, making the same proviso, 
 can an effect which disappears be due to a cause which 
 continues to 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 
 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 /3 cannot be its effect, for it is 
 absent in one of the cases where A is present, and simi- 
 larly 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 exemplified in the familiar cases of motion, 
 death, disease, &c.), this reasoning would be perfectly 
 just. Now it will be observed that, when B was re- 
 moved, it was replaced by C. It is, therefore, conceivable 
 that a may have been due to B in the first instance, and 
 
 K 2
 
 132 INDUCTIVE METHODS. 
 
 to C in the second, it being, of course, in each case, only 
 a portion of the effect, the remaining portions being re- 
 spectively ft, y, and A having been throughout inoperative. 
 This consideration, it is plain, vitiates the reasoning, 
 whether we are attempting to discover 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 sub- 
 stance, which is the same in each case ; if the principles 
 of the above reasoning were correct, 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 Method of Agreement is open to so serious 
 an objection, it may be asked on what grounds is it 
 recognised as an Inductive Method ? The answer is 
 that, by the multiplication and variation of instances, 
 the possible error due to the Plurality of Causes may 
 be rendered less and less probable, till, at last, for all 
 practical purposes, it may be regarded as having disap- 
 peared. Thus, if to the instances A B, a ; A C, ay ; we 
 can add A D, 08 ; A E, at, &c. &c. ; it is plain that we 
 may, at each step, be very considerably diminishing the 
 possibility of an error in our reasoning, and, after a-
 
 METHOD OF AGREEMENT. 133 
 
 certain number of instances, may be justified in feeling 
 morally certain that we have avoided it. It 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 cases, be due to different causes. The chance of an 
 inert substance being successively mixed with two potent 
 drugs, and of the effects which are really due to them 
 being erroneously ascribed to it, is, in the present state 
 of medical science, but a very slight one ; but the prob- 
 ability 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, I have assumed groups of 
 two antecedents and two consequents (A B, a/3 ; A C, 
 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 lan- 
 guage, a vast mass of antecedents all, or most of them, 
 contributing to a complex effect), 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- 
 culty, therefore, of rigidly satisfying the requirements of 
 the Method must be added to what Mr. Mill calls its
 
 134 INDUCTIVE METHODS. 
 
 characteristic imperfection, namely, the uncertainty at- 
 taching to its conclusions from the consideration of 
 the Plurality of Causes. 
 
 But there is still a third difficulty incident to the 
 Method of Agreement, which however is, in a majority 
 of cases, of a theoretical rather than a practical nature. 
 If we insisted literally on the fulfilment of the condition 
 that the instances presenting the given phenomenon 
 should have only one other circumstance in common, it 
 would be simply impossible to find such instances. All 
 instances will be found to agree in a number of circum- 
 stances which are immaterial to the point under inves- 
 tigation. 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 circum- 
 stance in common,' we must be understood to mean 
 'only one material circumstance,' and to exclude all 
 circumstances which a wide experience or previous in- 
 ductions 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 circumstances, the greatest caution is often required. 
 
 But, suppose we have ascertained (when enquiring 
 into the cause of a given effect) that the instances agree
 
 METHOD OF AGREEMENT. 135 
 
 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, 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 difficulties arising 
 from Plurality of Causes, and the complexity of the 
 phenomena. Supposing, however, these to be overcome, 
 and two circumstances only, a and b, to have been ascer- 
 tained to be common to all the instances, what conclusion 
 shall we be justified in drawing with reference to the 
 connexion between a and b? It is only reasonable 
 to suppose that they must be causally connected in 
 some way, else their connexion would be a mere casual 
 coincidence : a supposition which we assume to have 
 been excluded by the number and variety of the in-
 
 136 INDUCTIVE METHODS. 
 
 stances examined. But they need not necessarily stand 
 to each other in the relation of cause and effect, for they 
 may be common effects (in the same, or in different de- 
 grees of descent) of some cause which has itself ceased 
 to operate. In social and physiological phenomena this 
 is frequently the case. 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^ach other in the relation of cause and effect, are thus 
 causally connected. The social condition of any old 
 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 should be noticed that the Method of Agreement is 
 mainly, though not exclusively, a Method of Observation 
 rather than of Experiment, and that it is applied far more 
 frequently 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-
 
 METHOD OF AGREEMENT. 137 
 
 cumstances, as being causally connected. If the common 
 circumstances be a, b, c, d, this is all that we can infer. 
 But, if they be A, B, C, , 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, o, , y. Thus, for instance, a, 0, y 
 might all be joint effects of A, or a might be its im- 
 mediate effect, and , y effects of o, 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 the case, 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 con- 
 sequent, such an instance may only point to a counter- 
 acting cause which, in this exceptional case, frustrates
 
 138 INDUCTIVE METHODS. 
 
 the supposed effect. The only condition essential to 
 an application of the Method of Agreement is that 
 the cases on which the inference is founded shall pre- 
 sent only two circumstances 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 conjunction no other common cir- 
 cumstance can be detected. I shall recur to this subject 
 below 8 . 
 
 In the statement of the Canon, I have thought it 
 desirable to introduce the expression ' with more or less 
 of probability,' in order to show that, under no circum- 
 stances, does an inference drawn in accordance with the 
 Method of Agreement attain to absolute and formal cer- 
 tainty, though, as we have seen, it may attain to moral 
 certainty. 
 
 As familiar examples of the employment of the Method 
 of Agreement, the following may be adduced : 
 
 After taking 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, I am invari- 
 ably ill; I am justified in regarding the food 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 
 8 See pp. 145-7.
 
 METHOD OF AGREEMENT. 139 
 
 one in question, but it is very unlikely, if the number 
 of occasions on which the inference is based be con- 
 siderable, that it has been a different viand on each of 
 them. 
 
 I find that a certain plant always grows luxuriantly 
 on a particular kind of soil ; if my experience of the 
 other conditions be sufficiently various, I am justified in 
 concluding that the soil probably possesses certain chemi- 
 cal constituents which are peculiarly favourable to the 
 production of the plant. 
 
 Trade is observed to be in a languishing condition 
 wherever there exist certain restrictions, such as high 
 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. 
 
 I 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
 
 140 INDUCTIVE METHODS. 
 
 is some causal connexion 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 system 
 of almsgiving has prevailed, the population has, sooner 
 or later, become indolent and pauperised. This fact 
 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 
 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 being understood, of course, 
 that pressure and other circumstances, as, for instance, 
 the chemical condition of the body, remain the same).
 
 METHOD OF AGREEMENT. 141 
 
 It has been supposed by some writers on physics that we 
 may go further than this conclusion, and state that 
 augmentation of temperature is invariably followed by 
 augmentation of volume, and diminution of temperature 
 by diminution of volume, the exceptions of water 9 as 
 well as of bismuth and of the casting-metals 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 10 . 
 
 ' 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 some- 
 what boldly explained by Sir W. Grove as due to the setting in o 
 the process of crystallization , 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.) 
 
 10 I adduce this instance as an example of the Method of Agree- 
 ment 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 found 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 
 combined in the same proof. In the present instance, as will be 
 seen below, the argument as applied to each particular kind of body
 
 142 INDUCTIVE METHODS. 
 
 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* 1 : 
 
 ' A great number of transparent substances, when exposed, 
 in a certain particular manner, to a beam of light which has 
 been prepared by undergoing certain reflexions or refractions 
 (and has thereby acquired peculiar properties, and is said 
 to be "polarized"), 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 
 
 (mercury, for instance) is an argument based on the Method of 
 Concomitant Variations ; but when we proceed to extend the experi- 
 ment 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 Varia- 
 tions 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. 
 11 9.
 
 METHOD OF AGREEMENT. 143 
 
 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 pro- 
 pounded it, but in all cases which have since occurred on 
 further enquiry, without a single exception ; so that the 
 proposition is general, and entitled to be regarded as a law 
 of nature.' 
 
 The experiments by which Dr. Wells 12 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, 
 
 12 Dr. Wells' Memoir on the Theory of Dew, which had become 
 very scarce, was reprinted by Longmans and Co. in 1 866. 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.
 
 144 INDUCTIVE METHODS. 
 
 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 analo- 
 gous phenomena 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.' 
 
 It is by the Method of Agreement that we discover the 
 symptoms of a disease, the signs of a political revolution, 
 national characteristics, the order of superposition among 
 geological strata, grammatical rules, and the like. 
 
 The first division of Bacon's instantia solitaries coin- 
 cides with the cases contemplated in the Method of 
 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 I may adduce it as an additional instance of the 
 Method of Agreement : 
 
 ' Exempli gratia : si fiat inquisitio de natura coloris, 
 instantice solitaries sunt prismata, gemmae crystallinse, quae
 
 METHOD OF AGREEMENT. 145 
 
 reddunt colores, non solum in se, sed exterius supra 
 parietem. Item rores, &c. Istse enim nil habent com- 
 mune cum coloribus fixis in floribus, gemmis coloratis, 
 metallis, lignis, &c. prseter ipsum colorem. Unde facile 
 colligitur, quod color nil aliud sit quam modificatio ima- 
 ginis lucis immissse et receptse : in priore genere, per 
 gradus diversos incidentiae ; in posteriore, per texturas et 
 schematismos varios corporis. Istse autem instantice sunt 
 solitaries quatenus ad similitudinem ls .' 
 
 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 . I say 'a cause/ for 
 the fact that a may be present without A is a proof that 
 A is not the only cause. My 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 cir- 
 cumstance in common. From these facts it may be 
 reasonably inferred that the passage from a fluid to 
 
 13 Novum Organum, Lib. II. aph. xxii. 
 L
 
 146 INDUCTIVE METHODS. 
 
 a solid state is a cause, though not the only cause, of 
 crystallization u . 
 
 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 <>, 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 
 disease, we seem to be justified in regarding this occupation 
 or mode of living as a cause of the disease, and in explain- 
 ing 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 15 , and, in the cases where 
 
 14 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. 
 
 15 The invariable conjunction of two phenomena, when the pre- 
 sence 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 invari- 
 ably preceded or invariably 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
 
 METHOD OF AGREEMENT. 147 
 
 they are found together, there occurs, so far as we can 
 ascertain, no other common circumstance, we are justified 
 in suspecting that there exists some causal connexion 
 between them. 
 
 The student, who is acquainted with the science of 
 Medicine, will find a good illustration of th,e extreme 
 difficulty attending the application of the Method of 
 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 
 
 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, however, as already pointed 
 out, not in the in variableness of the conjunction, 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 Agree- 
 ment consists. But of this fact invariableness of antecedence (or of 
 consequence) furnishes one of the strongest proofs, i^tismuch as such 
 invariableness implies a very wide variation of circumstances ; hence 
 the stress laid upon it in some of the examples adduced above. 
 L 2
 
 148 INDUCTIVE METHODS. 
 
 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 16 . 
 
 METHOD OF DIFFERENCE. 
 
 CANON. 
 
 If an instance in which the phenomenon under investi- 
 gation occurs, and an instance in which it does not occur, 
 have every circumstance in common save one, that one oc- 
 curring only in the former ; the circumstance in which 
 alone the two instances differ, is the effect, or cause, or a 
 necessary part of the cause, of the phenomenon. 
 
 The circumstances a, b, c are found in conjunction 
 with d, e, f, and the omission 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- 
 
 " See a paper by Dr. William Ogle in the St. Georges 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 
 Rolleston, for ^heir kindness in supplying me with information on 
 this interesting subject, and regret that my space prevents me from 
 pursuing it at greater length.
 
 METHOD OF DIFFERENCE. 149 
 
 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, 
 and d the effect. 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 
 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
 
 J50 INDUCTIVE METHODS. 
 
 which effect. ' The Method of Agreement,' says Mr. 
 Mill, ' stands on the ground that whatever can be eli- 
 minated, is not connected with the phenomenon by any 
 law. The Method of Difference has for its foundation 
 that whatever can not be eliminated, is connected with 
 the phenomenon 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 
 we 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 
 various instances to see in what they agree ; the other 
 is called the Method of Difference, because we compare 
 an instance in which the phenomenon occurs with 
 another in which it does not occur, in order to see 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 
 must be due to that 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
 
 METHOD OF DIFFERENCE. 151 
 
 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 all these 
 instances, there is the introduction of a new antecedent, 
 x, to which the new consequent, y, must be due. But, 
 if the omission of one circumstance be attended by the 
 omission 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 
 book to the withdrawal of my support. A man is 
 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 antecedents, 
 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 crucial instances (instantiae 17 crucis, as they are 
 
 ;T ' Inter prserogativas instantiarum ponemus loco decimo quarto 
 instantias crucis; translate vocabulo a crucibus, quse, erectae in 
 biviis, indicant et signant viarum separationes. Has etiam instantias
 
 152 INDUCTIVE METHODS. 
 
 called by Bacon) are applications of the Method of Dif- 
 ference. A crucial instance is some observation or ex- 
 periment which enables us at once to decide between 
 two or more rival hypotheses. It will be familiar to 
 every one in the form of the chemical test, as where we 
 apply an 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 lft . 
 
 ' 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 
 
 decisorias, etjudiciales, et in casihus nonnullis instantias oraculi, et 
 mandati, appellare consuevimus. E: rum ratio talis est. Cum in 
 inquisitione naturae alicujus, intellectus ponitnr tanquam in aequili- 
 brio, ut incertus sit, utri naturarum e duabus, vel quandoque pluribus, 
 causa naturae inquisitae attribui aut assignari debeat, propter com- 
 plurinm naturarum concursum frequentem et ordinarium ; instantia 
 cruets ostendnnt consortium unius ex naturis (quoad naturam in- 
 quisitam) 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 maximae 
 lucis, et quasi magnse auctoritatis ; ita ut curriculum interpretationis 
 quandoque in illas desinat, et per illas perficiatur. Interdum autem 
 instantite crucis ilia; occurrunt et inveniuntur inter jampridem 
 notatas ; at ut plurimum novae sunt, et de industria atque ex com- 
 posite quaesitae et applicatae, et diligentia sedula et acri tandem 
 erutae.' Nowum Organum, Lib. II. aph. xxxvi. 
 M Discourse on the Study of Natural Philosophy, 218.
 
 METHOD OF DIFFERENCE. 153 
 
 Newton and Huyghens, have divided philosophers ;' 
 that is, between what is called 'the emission theory,' 
 according to which light consists of actual particles 
 emitted from luminous 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 between 
 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 reflexion 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 
 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 19 .' 
 
 19 Mr. Mill (Logic, Bk. III. ch. xiv. 6) maintains that it does not 
 follow from this experiment that ' the phenomena of light are results
 
 154 INDUCTIVE METHODS. 
 
 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 refract- 
 ing 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 ex- 
 periment ; and it was established by himself and M. 
 -Fizeau that the velocity of light is less in water (the 
 more highly refracting medium) than in air, in the in- 
 verse proportion of the refractive indices. The result 
 is, therefore, decisive in 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 experiment 
 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 brilliant red precipitate at 
 
 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 un- 
 doubtedly decisive as against the Emission Theory. It may be 
 necessary to add that the term ' fluids ' would now be repudiated by 
 those wl o hold the Undilatory Theory. 
 
 80 See Lloyd's Wave Theory of Light, 3rd ed. Arts. 41, 42 ; 
 Ganot's Physics, English translation, I2th edition, Art. 506.
 
 METHOD OF DIFFERENCE. 155 
 
 the bottom. There can be no hesitation in ascribing 
 this result to the mixture of the two liquids ; 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 - l : 
 
 ' Here is a brass tube, four inches long, and of three- 
 quarters of an inch interior diameter. It is stopped at the 
 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.' 
 
 21 Third Edition, ch. i. 14-16.
 
 156 INDUCTIVE METHODS. 
 
 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 
 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 working 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 " L ' i . 
 
 13 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.
 
 METHOD OF DIFFERENCE. 157 
 
 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 deflexion 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 deflexion 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 Agree- 
 ment 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 confirma- 
 tion is adduced by Mr. Mill in the case of Crystallization. 
 The Method of Agreement has already led us to the 
 conclusion that the solidification of a substance from 
 a fluid state is a very frequent antecedent of its crystal- 
 lization, and so, probably, 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-
 
 158 INDUCTIVE METHODS. 
 
 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 of Difference is 
 specially adapted to the discovery of the effects of given 
 causes, whereas, where it is our object to discover the 
 cause of a given effect, we are usually compelled to have 
 recourse to the Method of Agreement. The Method of 
 Agreement is, in fact, mainly a Method of Observation, 
 whereas the Method of Difference is mainly a Method 
 of Experiment. We may indeed arrange the conditions 
 of an experiment so as to satisfy the requirements 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 experiments under 
 the latter Method. It is hardly necessary to add that, 
 wherever we have our choice between the two methods, 
 we should invariably select the Method of Difference. 
 
 23 Mill's Logic, Bk. III. ch. viii. i. I have been obliged, in 
 accordance with what has been said on p. 146, to state, with con- 
 siderable 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. 159 
 
 In the employment of the Method of Difference, the 
 greatest care should be taken to introduce only one new 
 antecedent, or at least only one new antecedent which 
 can influence the result. As the whole force of the 
 argument based on this Method depends on the assump- 
 tion that any change which takes place in the phenome- 
 non is due to the antecedent then and there introduced, 
 it is plain that we can place no reliance on our conclusion 
 unless we feel perfectly assured that no other antecedent 
 has intervened. If, for instance, it is our object to as- 
 certain 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 
 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.
 
 l6o INDUCTIVE METHODS. 
 
 DOUBLE METHOD OF AGREEMENT. 
 
 CANON. 
 
 If two or more instances in which the phenomenon occurs 
 have only one other circumstance in common, while two or 
 more instances, falling within the same department of in- 
 vestigation 24 , from which the phenomenon is absent have 
 nothing in common save the absence of that circumstance ; 
 that circumstance is the effect, or the cause, or a necessary 
 part of the cause, of the phenomenon. Moreover (supposing 
 the requirements of the Method to be rigorously fulfilled], 
 the circumstance proved by the Method to be the cause is the 
 only cause 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 extent, remedied by the 
 employment of what is called by Mr. Mill the Joint Method 
 
 of Agreement and Difference, or the Indirect Method of 
 
 
 
 M In recent editions 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 materid. Thus, if the subject of enquiry 
 is language, the negative as well as the positive instances must be 
 sought in the department of language ; or, if the subject of enquiry 
 lies 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 departments. Practically, however, 
 there is no occasion for definite rules on this head, as the common- 
 sense of the investigator is quite sufficient to keep him within the 
 limits of the enquiry.
 
 DOUBLE METHOD OF AGREEMENT. l6l 
 
 Difference. This Method consists in a double employ- 
 ment of the Method of Agreement and a comparison of 
 the results thus obtained, the comparison assimilating it 
 to the Method of Difference. We, first of all, compare 
 cases in which the phenomenon occurs, and, so far as we 
 can ascertain, find them to agree in the possession of 
 only 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 cases 
 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 
 instances, and we may argue thus : The positive in- 
 stances agree in nothing but the presence of the given 
 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. I 
 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 
 
 M
 
 1 62 INDUCTIVE METHODS. 
 
 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 versa, 
 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. The Single Method of Agreement, as we have 
 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 
 cause of the other). ' In the joint method,' says Mr. 
 Mill M , ' it is supposed not only that the instances in 
 Mill's Logic, Bk. III. ch. x. a. .
 
 DOUBLE METHOD OF AGREEMENT, 163 
 
 which a is agree only in containing A, but also that the 
 instances in which a is not agree only in not containing 
 A. 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.' 
 
 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 (bearing in 
 mind, of course, what has already been said on pp. 48-9, 
 1 34, of the exclusion of immaterial circumstances), invari- 
 able conjunction may be regarded as a sign that the con- 
 
 M 2
 
 1 64 INDUCTIVE METHODS. 
 
 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 Indirect Method of Difference, or, as I should prefer 
 to call it, the Double Method of Agreement) is being 
 continually 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. I have observed that a certain plant is invariably 
 plentiful on a particular soil ; if, with a wide experience, 
 I fail to find it growing on any other soil, I feel con- 
 firmed in my belief that there is in this particular soil 
 some chemical constituent, or some peculiar combination 
 of chemical constituents, which is highly favourable, if 
 not 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. Mill a6 ) '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, 
 
 * Mill's Logic, Bk. III. ch. ix. 3.
 
 DOUBLE METHOD OF AGREEMENT. 165 
 
 m this only, that they either radiate heat rapidJy 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 within. 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. I 
 shall select one which is peculiarly interesting on account 
 of its employment in the attempt to determine the consti- 
 tution of the sun and some of the other heavenly bodies. 
 
 A very thin sheet of light proceeding from incandescent 
 hydrogen is passed through a prism, and it is invariably 
 found (with the exception of the third case mentioned in 
 note 27) that in the spectrum thus obtained there are, in 
 proportion to the intensity of the light, one, two, or 
 more bright lines occupying precisely the same rela- 
 tive position. Moreover, very thin sheets of white 
 light proceeding from various incandescent substances 
 are passed through incandescent hydrogen, and the 
 emergent light is then separated into its constituent 
 elements by a prism. In the spectra thus obtained it is
 
 1 66 INDUCTIVE METHODS. 
 
 found that there are invariably (with the above-named 
 exception) dark (or, under certain circumstances, bright 27 ) 
 lines occupying exactly the same positions in the spectrum 
 as the lines above mentioned. Hence it is inferred, by 
 the Method of Agreement, that a sheet of light, whether 
 it proceed directly from incandescent hydrogen itself, or 
 be transmitted through it from some other incandescent 
 substance, will (allowing for the above exception) invari- 
 ably produce these 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 lines in question. 
 
 Here, then, we have the negative instances of the 
 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 lines is invariably due either to a sheet 
 of light proceeding directly from incandescent hydrogen, 
 or to a sheet 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 
 
 17 The darkness of the lines is due to the property possessed by 
 incandescent media of absorbing sheets of light of the same refran- 
 gibility as those emitted by them. When the absorption exerted 
 upon the transmitted 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 sheet of light proceeds directly 
 from incandescent hydrogen itself. There is still a third case. When 
 the hydrogen emits as much light as it absorbs, there will be no line, 
 dark or bright.
 
 DOUBLE METHOD OF AGREEMENT. 167 
 
 in the spectrum of these 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 
 sheets must have been transmitted. Wherever, there- 
 fore, dark lines occupying these positions occur in 
 the spectrum we may infer (deductively) the passage 
 of the sheet 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 28 . 
 
 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 
 
 28 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 was the exact coincidence of 
 the bright lines in the hydrogen spectrum with the dark lines 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.
 
 1 68 INDUCTIVE METHODS. 
 
 French Tongue, lays down the position 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 suppression 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 belonging to popular and real French respect the Latin 
 accent ; all such words as porttque from pdrticus, or viatique from 
 viaticum, 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 transfor- 
 mation from Latin to French. We may lay it down as an infallible 
 law, that The Latin accent continues in French in all words of 
 popular origin ; all words which violate this law are of learned 
 origin : thus 
 
 LATIN. POPULAR WORDS. 
 
 LEARNED WORDS. 
 
 Alumiiie 
 
 aliin 
 
 alumine 
 
 Angelas 
 
 dnge 
 
 angeliis 
 
 Blasphemum 
 
 blame 
 
 blaspheme 
 
 Cancer 
 
 chdncre 
 
 cancer 
 
 Computum 
 
 c6mpte 
 
 compiit 
 
 D6bitura 
 
 dette 
 
 debit 
 
 D6cima 
 
 dime 
 
 ddcime, &c. 
 
 " Dr. Kitchin's Translation, p. 32, 7th ed. pp. 44-48.
 
 DOUBLE METHOD OF AGREEMENT. 169 
 
 ' 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 always remains ; but of the atonies the 
 short vowel, -which immediately precedes the tonic vowel, always dis- 
 appears in French : as in 
 
 Bon(i)t&tem bonte 
 
 San(i)tatem sante 
 
 Pos(i)t1ira posture 
 
 Clar(i)tatem clarte 
 
 Sep(ti)m&na semaine (O. Fr. sepmaine) 
 
 Com(i)tatus comte 
 
 Pop(u)latus peuple, &c. 
 
 ' Words such as clrculer, circulars, 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 follow- 
 ing examples : 
 
 LATIN. POPULAR WORDS. LEARNED WORDS. 
 
 Ang u latus angtt angule 
 
 Blasph(e)mare bl&mer (O. Fr. blasmer) blasphemer 
 Cap(i)tale cheptel capital 
 
 Car(i)tatein chert charite 
 
 Circ(u)lfire cercler circttler, &c. 
 
 ' The third characteristic, serving to distinguish popular from 
 learned words, is the loss of the medial consonant, i. e. of the con-, 
 sonant which stands between two vowels, like the t in maturus. 
 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 innu- 
 merable examples of this : as 
 
 LATIN. POPULAR WORDS. LEARNED WORDS. 
 
 Au(g)ustus aout auguste 
 
 Advo(c)atus avoue avocat
 
 1 70 INDUCTIVE METHODS. 
 
 LATIN. 
 Anti'ph ona 
 Cre(d)ntia 
 C om m un i (c) fire 
 
 POPULAR WORDS. 
 antienne 
 creance 
 communier 
 
 LEARNED WORDS. 
 anti phone 
 credence 
 communiquer, &c.' 
 
 The requisitions of the Double Method of Agreement 
 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 connexion 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 only 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 connexion. The precise 
 character of this causal connexion 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. 
 
 Sir John Herschel conceives that he has detected a 
 connexion 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
 
 DOUBLE METHOD OF AGREEMENT. Ijl 
 
 the eye a tendency of which we have assured ourselves 
 by long-continued and registered observation/ The pre- 
 cise nature of the causal connexion 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 30 .' 
 
 In this example, there is not, of course, an invariable 
 connexion 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 con- 
 nexion between the two phenomena, that we should find 
 a calm night proportionably oftener, and oftener in a 
 considerable proportion, when there is a full moon than 
 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 (I am, of 
 course, taking an imaginary case), and the proportion on 
 ordinary nights to be as 3 to 2, there can be little doubt 
 
 * Herschel's Familiar Lectures on Scientific Sttbjects, pp. 146, 
 147.
 
 172 INDUCTIVE METHODS. 
 
 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 connexion 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 
 there is anything exceptional in the soil, the climate, the 
 habits or occupations of the people, and the like, 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
 
 METHOD OF RESIDUES. 173 
 
 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. 
 
 Subtract from any phenomenon such part as is known 
 to be 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, /3, 
 y, 8, *, of which y, 8, e 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 
 antecedents A, B. Given 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 residue 
 of the result must necessarily be due to the remaining 
 antecedents. This rule appears so obvious as to be 
 hardly worth stating; it has, however, as will be seen
 
 174 INDUCTIVE METHODS. 
 
 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 31 , '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.' 
 
 There is one difficulty connected with this Method. 
 Subtraction being a deductive process, why is the Method 
 of Residues included among the inductive methods ? The 
 Method, it must be confessed, is rather of a deductive 
 than an inductive character, but as, in assigning the re- 
 sidual consequent to the residual antecedent, we assume 
 the Law of Universal Causation, and as, moreover, the 
 method is generally applied to the result of previous in- 
 ductions and generally suggests subsequent inductions, it 
 may vindicate its claim to discussion in this place. It is 
 by induction that we usually ascertain that y, 8, e are due 
 to C, D ; by the Method of Residues we determine that 
 the remaining consequents a, /3 must be due to the re- 
 maining antecedents A, B ; we then generally proceed to 
 decide by one of the other inductive methods which of 
 the remaining consequents is due to which of the re- 
 maining antecedents. 
 
 The following are instances of the employment of the 
 31 Discourse on the Study of Natural Philosophy, 158.
 
 METHOD OF RESIDUES. 175 
 
 Method of Residues, and it will be noticed that the 
 science of astronomy is peculiarly rich in such ex- 
 amples 32 : 
 
 '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 those 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 inclined 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 
 registered. 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 import- 
 ance : 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 difficulty in making such prediction 
 (starting from the time of some one observed eclipse of each 
 as an epoch) ; provided always each eclipse were seen at the 
 identical moment when it actually happened. Moreover, on 
 that supposition, the times recorded of all the subsequent 
 
 82 In the first and second 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 
 later editions.
 
 1 76 INDUCTIVE METHODS. 
 
 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 discordance, the 
 difference either way increasing to a maximum, then 
 diminishing, vanishing, and passing over to a maximum the 
 other way, and the total amount of fluctuation to and fro 
 being about l6 m 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 instantaneous. 
 This suggestion was converted into a certainty by Roemer, a 
 Danish astronomer, who ascertained that they always hap- 
 pened 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 fluctua- 
 tion the l6 m 27 s 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 revolutions. 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 dis- 
 crepancy in question between the observed and predicted 
 times has ceased to exist 3 V 
 
 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 
 of the planet Uranus was subject to an amount of per- 
 
 83 Herschel's Familiar Lectures on Scientific Subjects, p. 226, &c.
 
 METHOD OF RESIDUES. 177 
 
 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 
 disturbance, 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 
 observed 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, "given the disturbances to find 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 
 in the annals of astronomy Dr. Galle, one of the astronomers 
 
 N
 
 178 INDUCTIVE METHODS. 
 
 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 
 magnitude 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 New- 
 tonian law of gravity, the observed anomalies in the motion 
 of Uranus were owing S V 
 
 Besides furnishing an instance of the method of Resi- 
 dues, the above example is also a happy illustration of 
 the combination of deduction with observation which has 
 been so eminently fertile in astronomical research. 
 
 'Almost all the greatest discoveries in astronomy have 
 resulted 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. 
 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 
 phenomena from that portion of the changes of the apparent 
 
 34 Herschel's Outlines of Astronomy, Fourth Edition, 767, 768.
 
 METHOD OF RESIDUES. 
 
 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 weight 
 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 thought of Glauber to examine what everybody else 
 threw away 36 .' 
 
 '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 
 
 a Herschel's Outlines of Astronomy, 856. 
 
 ** Herschel's Discourse on the Study of Natural Philosophy, 161. 
 
 N 2
 
 180 INDUCTIVE METHODS. 
 
 phenomenon, we seek an explanation until it is furnished by 
 the incidental operation of some collateral cause. For ex- 
 ample, 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 
 supposing that the consumption of beef has increased faster 
 than that of mutton. There is, therefore, a residuary pheno- 
 menonviz, 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 con- 
 venience 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 3T , 
 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 consumption of spirits and beer, have not 
 increased the consumption 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 83 .' 
 
 87 This passage 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 in- 
 creased (First Edition, 1870). On the other hand, owing to the 
 spread of Temperance Societies, and of more temperate habits in all 
 classes, the consumption of all alcoholic drinks has now, for some 
 years, been steadily diminishing, in proportion to the population. 
 
 38 Sir George Cornewall Lewis on the Methods of Observation and 
 Reasoning in Politics, vol. i. p. 356.
 
 METHOD OF RESIDUES. l8l 
 
 I shall conclude my instances with what Sir John 
 Herschel truly calls 'a very elegant example,' the dif- 
 ference between the observed and calculated velocities 
 of sound. I quote from Professor TyndalFs 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 calcu- 
 lation, 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 
 instantaneously through the particles themselves. He then 
 supposed 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 com- 
 pletely solve the 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
 
 182 INDUCTIVE METHODS. 
 
 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 
 rarefied, cold is developed. This brass box contains a 
 quantity of condensed air. I open the cock, and permit the 
 air to discharge 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 39 .' 
 
 It is not necessary, for our purposes, to pursue the 
 quotation, but the student, who wishes to see an ex- 
 ample 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. 
 
 s * Lectures on Sound, ch. L
 
 METHOD OF CONCOMITANT VARIATIONS. 183 
 METHOD OF CONCOMITANT VARIATIONS. 
 
 CANON. 
 
 Whatever phenomenon varies in any manner whenever 
 another phenomenon varies in some particular manner, is 
 either a cause or an effect of that phenomenon, or is con- 
 nected with it through some fact of causation 40 . 
 
 This Method is really a peculiar application, or series 
 of applications, of the Method of Difference. It is em- 
 ployed in those cases where a phenomenon cannot be 
 made to disappear altogether, but where we have the 
 power of augmenting or diminishing its quantity, or at 
 least where Nature presents it in greater or smaller 
 amounts. Thus, suppose we drop a quantity of quick- 
 silver into a glass tube, we shall find that every sensible 
 augmentation of the temperature of the surrounding 
 atmosphere is accompanied by a sensible augmentation 
 of the volume of the quicksilver in the tube, and, vice 
 versa, that every sensible diminution of the tempera- 
 ture is accompanied by a sensible diminution of the 
 volume of the quicksilver. Now each particular ex- 
 periment 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 
 
 40 On p. 1 86 will be found a rider to this Canon.
 
 184 INDUCTIVE METHODS. 
 
 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 intermediate 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 con- 
 tract at two definite points must, if it continue to act, 
 and if it be counteracted by no other cause, operate at 
 all intermediate points ; 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 fact is implied in the very notion of 
 Causation. We arrive, then, at the conclusion that the 
 volume of the quicksilver is invariably dependent on 
 the temperature of the surrounding medium ; in other 
 words, that augmentation of temperature is the cause of 
 its expansion 4l . 
 
 It may be asked, Why not employ the Method of 
 
 41 The student acquainted with the phraseology of Mathematics 
 will understand my meaning, when I say that the Method of Con- 
 comitant Variations is really an integration of a (supposed) infinite 
 number of applications of the Method of Difference.
 
 METHOD OF CONCOMITANT VARIATIONS. 185 
 
 Difference once and for all ? Because, ex hypothesi, 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 
 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
 
 l86 INDUCTIVE METHODS. 
 
 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 experi- 
 ments 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 un- 
 certainty as to whether the requisitions 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. I 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 may affirm 
 that the one phenomenon is either the cause or the effect of 
 the other. 
 
 The Method of Concomitant Variations may be used 
 for two purposes, either to establish a causal connexion, 
 or to determine the law according to which two pheno- 
 mena vary. Thus, 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
 
 METHOD OF CONCOMITANT VARIATIONS. 187 
 
 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 Variations. 
 In the latter class of enquiries, the attempt to deter- 
 mine the numerical relations according to which two 
 phenomena 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 
 intervention 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 
 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 observations 
 is confined within comparatively narrow limits. ' Any 
 one,' says Mr. Mill 42 , 'who has the slightest acquaint- 
 42 Mill's Logic, Bk. III. ch. viii. 7.
 
 188 INDUCTIVE METHODS. 
 
 ance with mathematics, is aware that very different laws 
 of variation may produce numerical results which differ 
 but slightly from one another within narrow limits ; 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 mistakes. 
 "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 the theoretical 
 structures which have been erected on them.'" This, 
 however, it must be noticed, is an uncertainty which does 
 not vitiate the method, but simply renders necessary the 
 exercise of the utmost caution in its application. 
 
 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
 
 METHOD OF CONCOMITANT VARIAl^IONS. 189 
 
 in a straight line with uniform velocity until acted upon 
 by some new force. 
 
 'This assertion,' I am quoting from Mr. Mill 43 , ' 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 simplicem, 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, admitted 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 
 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 
 
 13 Mill's Logic, Bk. III. ch. viii. 7.
 
 t 
 190 INDUCTIVE METHODS. 
 
 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 pro- 
 position known as the first law of motion.' 
 
 I 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 solid, liquid, or 
 aeriform) 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 solid 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 freeze or become solid if their heat could be sufficiently 
 reduced. In many we see this to be the case in ordinary 
 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 liquid 
 state by cold accompanied with violent pressure ; and, as our 
 means of applying these causes of condensation have im-
 
 METHOD OF CONCOMITANT VARIATIONS, 19! 
 
 proved, more and more refractory ones have successively 
 yielded. Hence we are fairly entitled to extend our con- 
 clusion 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 j 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 44 .' 
 
 An interesting application 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, cceteris 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 
 
 ** Herschel's Discourse on the Study of Natural Philosophy, 
 
 357 358. 
 
 Sir John Herschel's conjecture has been verified with regard to 
 aeriform fluids, and is now rapidly in course of being verified with 
 regard to liquids. The experiments of Cailletet and Pictet (an 
 account of which may be found in the Academy of Jan. I2th, 1878, 
 and in Nature of Jan. 3rd and i7th of the same year) have conclusively 
 shown that even oxygen, hydrogen, and nitrogen admit of liquefac- 
 tion. Thus, the old distinction between permanent and non-per- 
 manent gases has been entirely effaced. And the application of 
 the very low temperature which can now be so readily procured has 
 lessened the number of those liquids which, till quite recently, it was 
 thought could not be solidified. For example, it has been observed 
 that disulphide of carbon solidifies at 116 and fuses again at 
 about 110, that pure ether solidifies at 129, and absolute 
 alcohol becomes viscid at 129 and solidifies at 130-5. See 
 Ganot's Physics, 13th ed. 343.
 
 192 INDUCTIVE METHODS. 
 
 the temperature at day and night is comparatively slight, 
 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 por- 
 tion of the heat they have absorbed during the day. 
 
 ' A freedom of escape,' says Professor Tyndall * 5 , ' 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 ren- 
 dered entirely uninhabitable by beings like ourselves through 
 the operation of this single cause ; with a radiation, uninter- 
 rupted 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 temperature of this region. 
 Humboldt has dwelt upon the "frigorific 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 temperature. But, not 
 knowing the influence which we are now studying, Humboldt, 
 I imagine, omitted the most potent cause of the cold. The 
 
 tt Tymlall's Heat a Mode of Motion, 492.
 
 METHOD OF CONCOMITANT VARIATIONS. 193 
 
 refrigeration at night is extreme 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 thermometric range will be great. This, how- 
 ever, 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 
 denudation, 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 Lyell's Principles 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 
 
 o
 
 194 INDUCTIVE METHODS. 
 
 the famous temple of Jupiter Serapis, at Pozzuoli, on 
 the Bay of Naples. 
 
 ' We can scarcely avoid the conclusion, as Mr. Babbage 
 
 has 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 boiling springs and ancient volcanos of Ischiaon one side 
 
 and Vesuvius 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 connexion 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 condition 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 Nuovo 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.
 
 METHOD OF CONCOMITANT VARIATIONS. 195 
 
 '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 
 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 46 .' 
 
 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 4 V 
 
 Physiology (so far as it is based on Anatomy, as 
 distinct 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 
 
 16 Lyell's Principles of Geology, tenth edition, cb. xxx. 
 
 47 Whewell's Novum Organon 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 confounded witb 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. 
 
 O 2
 
 196 INDUCTIVE METHODS. 
 
 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 
 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* 8 , 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 Mammalian 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 
 
 48 Carpenter's Principles of Human Physiology, sixth edition, 
 1864.
 
 METHOD OF CONCOMITANT VARIATIONS. 197 
 
 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 
 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, 
 with regard to the general correspondence between the 
 development of the Cerebrum and the manifestations of 
 Intelligence ; very decided evidence of which is furnished 
 by the great enlargement of the Cerebrum, and the corre- 
 sponding alteration in the form of the Cranium, which present 
 themselves in those races of Dogs most distinguished for 
 their educability, when compared with those whose con- 
 dition approximates 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 49 , taking the brain-weights of ten dis- 
 
 49 On the Weight of the Brain, by John Thurnam, M. D. London, 
 J. E. Adlard. 1866.
 
 198 INDUCTIVE METHODS. 
 
 tinguished men, who died between the ages of fifty and 
 seventy, calculates the average weight of their brains 
 to have been 547 ounces. The average weight of the 
 brains of ordinary men, dying between the same ages, 
 is 47 'i ounces. These facts give in favour of ' cultivated 
 and intellectual man ' an excess of 7*6 ounces, or 15 per 
 cent. Though, as a general rule, the connexion between 
 intellectual and cerebral development appears to be sub- 
 stantiated, we must, however, be very cautious in drawing 
 any inferences as to particular cases. Megalocephaly, 
 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 investigation 
 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 argu- 
 ments 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
 
 METHOD OF CONCOMITANT VARIATIONS. 199 
 
 take it is called Formed IViaterial. The former is living 
 matter, capable of growth and germination ; the latter 
 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. In 
 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 rrfatter 
 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 50 . 
 
 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 
 
 50 The student will find this subject fully treated in Dr. Lionel 
 Beale's Lectures on the Simple Tissue of the Human Body, and in 
 other works of the same author.
 
 200 INDUCTIVE METHODS. 
 
 that one is cause and the other effect. They may both 
 be common effects of the same cause. Thus, though the 
 prevalence of some disease might be constantly attended 
 by the appearance of certain low forms of organic life, 
 such as what we now call microbes, it would by no means 
 follow that these microbes were the cause of the disease, 
 unless, by direct experiment on healthy organisms, we 
 could establish that, all other circumstances remaining 
 the same, the introduction of the microbe was followed 
 by the appearance of the disease. 
 
 The Method of Concomitant Variations 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 tran- 
 sition from the one word to the other gradual and 
 natural. From this circumstance 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 divergence. ' Thus, at first 
 sight,' says M. Brachet B1 , ' 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 aneme, in the tenth antme, which 
 leads us straight to the Latin anima.' In this case there 
 can be no doubt of the truth of the conclusion. 
 
 51 M. Brachet's Historical Grammar of the French Tongue, Dr. 
 Kitchin's Translation, p. 42. Seventh Edition, p. 53.
 
 METHOD OF CONCOMITANT VARIATIONS, 2CI 
 
 Similarly, the loss of declension in the transition from 
 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 com- 
 pletely regular declension : subject, murs, murus j object, 
 mur, murum: and people said " ce murs est haut;" "j'ai 
 construit un mur" 
 
 1 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
 
 202 INDUCTIVE METHODS. 
 
 language, which look like so many insoluble exceptions, but 
 find their explanation and historic justification in our know- 
 ledge of the Old French declension 5 V 
 
 Here the conclusion is that French Grammar is derived 
 from Latin Grammar, certain peculiarities 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 suis and the Greek 
 word elftt 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 f'o-/xi, the 
 connexion of the two words and their ultimate deriva- 
 tion from a common root becomes a certainty. Here 
 the divergence may be definitely accounted for by the 
 various 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 
 
 52 M. Brachet's Historical Grammar of the French Tongue, Dr. 
 Kitchin's Translation, p. 88. Seventh Edition, pp. 98-100.
 
 METHOD OF CONCOMITANT VARIATIONS. 203 
 
 methods have been stringently fulfilled. In any but 
 the Experimental Sciences it is always extremely difficult 
 to assure ourselves that we are acquainted with all the 
 circumstances 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 
 account, and the value of the conclusion will depend on 
 the extent to which we have ascertained that these other 
 points of difference are not pertinent, or not equally perti- 
 nent with those which we have taken into account, to the 
 circumstance 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 rate 
 of acceleration, however, is a very difficult and delicate 
 problem to solve. By means of the oscillating pendulum 
 or Atwood's machine (which it is unnecessary to describe 
 here) it is shown (i) that gravity is an uniformly acceler- 
 ating force, that is, that the increments of velocity in 
 equal times are equal ; (2) that the rate of increase varies
 
 204 INDUCTIVE METHODS. 
 
 slightly at different places on the earth's surface ; (3) that, 
 in the latitude of Greenwich, in vacuo, 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 quan- 
 tity, so that the spaces traversed in successive units of 
 time vary as the odd numbers i, 3, 5 .... (2n i). 
 A slight degree of attention will show that it is by the 
 Method of Concomitant Variations that all these con- 
 clusions are obtained 6S . 
 
 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 phe- 
 nomena, as, for instance, deficient education and crime, 
 may be expected to remain constant. 
 
 A very important application of the Method of Con- 
 comitant Variations is what is now commonly known 
 as the Historical Method. The Method designated by 
 this name is, in fact, simply the Method of Concomitant 
 Variations applied to facts furnished by history or to 
 a record of observations on the same classes of facts as 
 those with which history deals. It is specially applicable 
 to those sciences which deal with man as a progressive 
 
 ** The student who wishes for more detailed information on this 
 subject is referred to Professor Price's Infinitesimal Calculus, vol. iii. 
 chap. viii. sect 3.
 
 METHOD OF CONCOMITANT VARIATIONS. 205 
 
 being, or, at least, a being capable of progress. Thus, 
 a certain institution, custom, or opinion is traced through- 
 out various stages of society, and its growth or decline 
 is connected with that of some other institution, custom, 
 or opinion, or with the general state of civilisation pre- 
 valent throughout these periods, it being argued, in the 
 latter case, 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, 
 art, and language 6 * ; and it is sufficient to refer the 
 student for examples to works such as those of Sir 
 Henry Maine, Sir John Lubbock, Professor Max Miiller, 
 and Dr. Tylor. The gradual process by which the or- 
 ganisation of the family passes into that of the state, 
 or by which the primitive feeling of resentment is de- 
 veloped into that strict sense of justice which distin- 
 guishes 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 stating a priori what might be expected 
 from a general knowledge of human nature, it is called 
 by Mr. Mill the Inverse Deductive Method. Under this 
 head I shall briefly advert to it again, in the chapter on 
 the Relation of Induction to Deduction 65 . 
 
 '* The instances given on pp. 200-202 are examples of the appli- 
 cation of the Historical Method to the Science of Language. 
 
 55 There is one objection to the employment of the Historical 
 Method, which at least demands an answer. The progress, say, of
 
 2C6 INDUCTIVE METHODS. 
 
 The Method of Concomitant Variations, especially 
 when applied to subjects other than physical, such as 
 law, morals, language, social statistics, &c., is often called 
 vaguely the Comparative Method. 
 
 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 attained. 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 extreme 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 circumstances which 
 we call civilisation are far from being constant. Moreover, they are all 
 so intertwined with one another that almost any one of them varies 
 directly as almost any other. Amongst these various circumstances, 
 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 the best index to the state 
 of the other constituents 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 leams, in an infinite variety of ways, to adapt him- 
 self 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 intellectual faculties and 
 the aggregate of circumstances which constitute civilisation, the 
 student may consult Mr. Mill's Logic, Bk. VI. ch. x. 7. 
 
 The term ' Historical,' as designating this Method, is somewhat
 
 SUMMARY OF RESULTS. 207 
 
 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 
 over 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 distinc- 
 tion exists between those cases in which the induction 
 indicates the precise character of the causal connexion 
 which subsists between two or more phenomena and 
 those in which it simply points out that there exists a 
 causal connexion of some kind or other. In the latter 
 case a new induction is required in order to show what 
 the nature of the causal connexion 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- 
 misleading, because, though the facts to which the Method is ap- 
 plied may be mainly supplied by history, they are also, to a large 
 extent, taken from the contemporary observation of tribes and peoples 
 living in different stages, or different phases, of civilisation with 
 reference to the matters of enquiry.
 
 208 INDUCTIVE METHODS. 
 
 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, 
 though employed in an inductive enquiry, being rather of 
 the nature of a deductive than an inductive method. 
 
 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,8,6, 
 &c., the effects being regarded as heterogeneous and not 
 homogeneous. But, suppose the effect of A to be a, of B to 
 
 be -, of C to be y, of D to be -, and of E to be - the 
 2 32 
 
 total effect of A, B, C, D, E will be - + ^. It is obvious 
 
 2 6 
 
 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 
 effect. We might have, in fact, as in mechanical action 
 and reaction, A producing a and B producing a, each 
 cause thus neutralising 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
 
 INTERMIXTURE OF EFFECTS. 209 
 
 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 56 , and on the nature of 
 the assistance rendered by Deduction, the reader may con- 
 sult Mr. Mill's Logic, Bk. III. 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 
 
 16 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 compli- 
 cations. 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, that a muscle grows during exercise and loses bulk during 
 the subsequent rest.' Bain's Logic, Bk. III. ch. viii. 6.
 
 210 INDUCTIVE METHODS. 
 
 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 of 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. 
 
 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 on the Study of Natural Phi- 
 losophy, 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
 
 ANTICIPATED BY BACON. 211 
 
 the Second Book of Bacon's Novum Organum, we find 
 some approximations, very rough, it is true, to formal 
 inductive methods. The c instantiae crucis ' have already 
 been adduced as examples of the Method of Difference, 
 and the ' instantiae solitariae ' as comprising 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 ' instantige 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 67 ,' corresponding pretty 
 nearly, at least in this connexion, with 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- 
 blance is to state the conditions with 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 ' 58 were 
 
 87 On the meaning attached by Bacon to the word ' Form/ and 
 its relation to ' Essence ' and ' Cause,' see the Introduction to my 
 Edition of the Novum Organum, 8. 
 
 58 Novum Organum, Lib. II. Aph. xi. 
 
 P 2
 
 212 INDUCTIVE METHODS. 
 
 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 (' Instantise in 
 proximo, quse privantur natura calidi ') 59 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 effect), or a 
 necessary part of the cause, of heat. We should here 
 have the Method of Difference. 
 
 If, in the ' Tabula graduum, sive comparative in 
 calido 60 ,' we could discover some one phenomenon which 
 increased and diminished proportionately with the increase 
 and diminution of heat, that phenomenon would be the 
 cause or the effect of heat, or, at least, connected with it 
 through some fact of causation, and the conditions would 
 thus conform with 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 
 
 5 * Navum Crganum, Lib. II. Aph. xxii. '" Id. Aph. xiii.
 
 ANTICIPATED BY BACON. 213 
 
 be proved to be either the cause or the effect of heat, 
 and would conform with the requirements of the rider to 
 this last Method (p. 186). 
 
 The ' Exemplum exclusive, sive rejectionis naturarum 
 a forma calidi ' 6l (which is based on the foregoing Tables) 
 bears some, though, it must be acknowledged, a very 
 slight, resemblance to the Method of Residues. These 
 ' rejectiones ' consist in excluding some possible explana- 
 tion of the phenomenon, either because an instance, 
 which does not present the phenomenon, does present 
 the assigned cause, or because an instance, which does 
 present the phenomenon, does not present the assigned 
 cause ^ (and similarly with regard to increase and de- 
 crease). As an example of the former case, we may 
 take the following ' rejectio ' : ' Per radios lunae (which 
 were then supposed to be cold) et aliarum stellarum rejice 
 lucem et lumen.' As examples of the latter, we may take 
 the two following : ' Per radios solis, rejice naturam ele- 
 mentarem (that is, ' terrestrial nature,' which is composed 
 of ' the four elements ') ; Per ignem communem, et 
 maxime per ignes subterraneos (qui remotissimi sunt, et 
 plurimum intercluduntur a radiis coelestibus) rejice na- 
 turam coelestem.' By a succession of these ' rejectiones,' 
 we limit the number of possible explanations, amongst 
 which we are to look for the true one. Bacon's ' rejec- 
 
 61 Novum Organum, Lib. II. Aph. xviii. 
 
 63 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. See my notes on Novum Organum, Lib. II. Aph. xvi.
 
 214 INDUCTIVE METHOD 
 
 tions,' 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 antecedents 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 63 . 
 
 Note 3. Dr. Whewell (in a pamphlet published in 
 1849, which is now embodied in the Philosophy of Dis- 
 covery**) questions the utility of the Four Methods. 
 
 83 It must be understood that, in this note, I am simply comparing 
 the ' Tables ' of Bacon with the ' Methods ' of Mr. Mill. On the 
 relation of the ' Tables ' to each other and on the special importance 
 attached by Bacon to the 'Rejections,' the student may consult 
 9 of the Introduction to my edition of the Novum Organum 
 (Clarendon Press) and my notes to the earlier aphorisms of the 
 Second Book. 
 
 In comparing the logical procedure of Bacon and Mill, it should 
 be carefully borne in mind that Bacon contemplated the concurrent 
 use of all the Tables, as preparatory to his Method of Rejections, 
 and regarded the construction of the Tables and the subsequent ap- 
 plication to them of the Method of Rejections as constituting only 
 one process. On the other hand, each of Mr. Mill's Methods may 
 be worked independently, and lead to a final conclusion. 
 
 * See Philosophy of Discovery, ch. xxii. The criticism of Mr.
 
 CRITICISMS OF THEM. 215 
 
 ' Upon these methods,' he says, ' the obvious thing to 
 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 
 formation ; 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 success, without 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 fact does not obviate the necessity of 
 submitting them to a test. Nor is it a more real objec- 
 
 Mill's Methods will be found in 38-48. Mr. Mill replies in a 
 note at the end of Bk. III. ch. ix.
 
 INDUCTIVE METHODS. 
 
 tion that men, who know nothing of the technical rules 
 of Logic, often reason faultlessly themselves, and show 
 remarkable acuteness in detecting inconclusive reasoning 
 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 
 formulas, 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
 
 CRITICISMS OF THEM. 21 7 
 
 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 
 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, I 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 in- 
 vestigation must be either inductive or deductive, or 
 both. But, so far as it is inductive, it must conform 
 with the requirements of the Inductive Canons, or else it 
 will not result in positive proof, or even approximate
 
 2l8 INDUCTIVE METHODS. 
 
 closely to it. As in the former case, unless the dis- 
 coverer has, consciously or unconsciously, reasoned in 
 strict conformity with the requirements of Logic, he has 
 no right to feel any confidence in the result of his 
 researches. 
 
 It may be added that appropriate conceptions, pro- 
 mising 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 unconscious, of the laws of reasoning. Originality is 
 not a quality, as some seem to think, which admits of no 
 psychological explanation. 
 
 I have not thought it desirable to discuss more recent 
 criticisms of the Inductive Methods, because, apart from 
 the stress which they lay on the difficulty of satisfying 
 the conditions of the Canons (a difficulty which is ac- 
 knowledged on all sides to exist, at least in many cases), 
 I cannot think that they have added materially to the 
 objections raised by Dr. Whewell. 
 
 ' . ' The student is particularly requested to read, in 
 connexion with this chapter, the ' Preface to the Third 
 Edition,' reprinted at the beginning of the Book. This 
 Preface deals with certain controverted points respecting 
 the certainty of Inductive Reasoning and the nature of 
 the assumptions made in it, with which, though they 
 could not conveniently be introduced into the body of 
 the book, it is desirable that the student should acquaint 
 himself.
 
 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- 
 mends itself as possessing more or less of probability. 
 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 Inductio per enu- 
 merationem simplicem. 
 
 The Inductio per enumerationem simplicem is, as already 
 noticed ', when complete \Inductio Completa], a deductive, 
 and not an inductive, argument. When incomplete, it is 
 an inductive argument, for it is an inference of the general 
 from the particular or the unknown from the known. ,' 
 This form of Induction 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, 
 
 1 See p. 125, note 2, and Deductive Logic, Part III. chap. i. ap- 
 pended note 2.
 
 220 IMPERFECT INDUCTIONS. 
 
 it is grounded 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 Inductio per enumerationem simplicem affords 
 only a presumption, sometimes very slight, sometimes 
 tolerably strong, in favour of the position which it is 
 adduced to establish. I perceive, say in five, ten, or 
 twenty cases, that the phenomenon a is attended by the 
 phenomenon b, and, knowing of no cases in which the 
 one phenomenon is not attended by the other, I begin 
 to suspect that a and b are connected together in the 
 way 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 enumerationem simplicem, 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 
 likelihood, if there be any negative instances, of our 
 having met with them. The first of these considerations 
 deserves little weight, unless supported by the other. A 
 native of the North of Europe, some centuries ago, 
 might, if the mere accumulation of positive instances 
 were sufficient, have taken it for a certain truth that all 
 men had white complexions. His own personal observa- 
 tion, as well as the reports of travellers and the traditions
 
 INDUCTIO PER ENUM. SIMP. 221 
 
 of his race, would have furnished numberless instances 
 in favour of the position. But, before drawing the in- 
 ference, 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 supposing 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 ca- 
 pacity 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 enumeratio simplex, 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 qua procedit per enumerationem 
 simplicem res puerilis est.' But if the enumeratio simplex 
 be accompanied by a well-grounded conviction that there 
 are no instances to the contrary, it may afford a very
 
 222 IMPERFECT INDUCTIONS. 
 
 high degree of probability, and, if we can assure our- 
 selves that there are no instances to the contrary, to us 
 individually it will afford certainty. 
 
 It might seem that an Inductio per Enumerationem 
 Simplicem is always an employment of the Method of 
 Agreement. But there is this essential difference. The 
 Method of Agreement is a method of elimination, select- 
 ing some and rejecting other instances, and founding its 
 conclusion not on the quantity but on the character of 
 the instances which it selects. The Inductio per Enu- 
 merationem 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 
 instances. 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
 
 INDUCTIO PER ENUM. SIMP. 
 
 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 uni- 
 versally 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 I have already pointed out in the First 
 Chapter 2 , by means of an Inductio per Enumerationem 
 Simplicem that we establish what have been called 
 1 Inductions of Co-existence.' This is the case, when, 
 as the result of a wide experience, two phenomena 
 
 9 Pp. 7-9-
 
 224 IMPERFECT INDUCTIONS. 
 
 are found to he 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 connexion, 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 connexion, the 
 uniformity would be transferred to another category, 
 and would rank amongst the inductions discussed in 
 the last chapter. Meanwhile, these inductions, de- 
 pending simply on uncontradicted experience, and being 
 at present inaccessible to the Methods of Elimination, 
 must be regarded as generalisations awaiting further 
 investigation 9 . 
 
 The term ' Empirical Generalisation ' or ' Empirical 
 
 J For a further discussion of the Uniformities of Co-existence, the 
 reader is referred to Mr. Bain's Logic, Bk. III. ch. iii. I am disposed 
 to estimate more highly than Mr. Bain the probability that these 
 uniformities 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.
 
 EMPIRICAL LAWS. 
 
 Law' might be conveniently appropriated to express 
 those secondary laws (as distinct from Ultimate Laws 
 of Nature 4 ) which are the result of an Inductio per 
 Enumerationem Simplicem. Though these expressions 
 are employed with great latitude, it is usually regarded 
 as characteristic of an Empirical 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 6 . 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 
 
 * Some of these Ultimate Laws of Nature, such as the Law of 
 Universal Causation, the Law of the Conservation of Energy, the 
 invariable co-existence of Inertia with Gravity, &c., appear to rest 
 simply on uncontradicted experience, that is to say, on an Inductio 
 per Enumerationem Simplicem, and still it would seem paradoxical 
 to speak of them as merely ' Empirical Laws.' An Empirical Law 
 might, perhaps, be defined as a secondary law, the causal derivation 
 of which is not yet known or even surmised with any probability, or 
 as a subordinate generalisation arrived at by an Inductio per Enu- 
 merationem Simplicem ; definitions which, it will be perceived, are 
 really identical. I have, however, avoided any special discussion of 
 what are called ' Empirical Laws,' both on account of the extremely 
 indeterminate use of the expression, 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. 
 
 s See Herschel's Discourse on the Study of Natural Philosophy, 
 187, and Mill's Logic, Bk. III. ch. xvi. 4. 
 
 Q
 
 226 IMPERFECT INDUCTIONS. 
 
 Methods, but it is peculiarly applicable to the results 
 of the Inductio per Enumerationem Simplicem, and it 
 would be extremely 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 pre- 
 sently) on the other. Instances of Empirical Laws in 
 this restricted sense are such generalisations as that 
 certain animals or flowers 6 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 Enumerationem Simplicem or by an im- 
 perfect application of the Method of Agreement, that is to 
 say, whether it is based on instances taken indifferently, 
 or on selected instances. 
 
 Another form of imperfect induction is the Argument 
 from Analogy 7 . Here we do not argue from a number 
 
 4 The colours of flowers, however, seem to be in a fair way of 
 being accounted for by the peculiarities of their mode of fertilisation. 
 See a most interesting work on the Colours of Flowers, by Mr. Grant 
 Allen, published in Macmillans' Nature Series, 1882. 
 
 7 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 (Iff6r^ 
 \6yoav'). 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.
 
 ANALOGY. 227 
 
 of instances, as in the case of Inductio per Enumerati- 
 onem Simplicem, 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, c, 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, b, 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 
 
 Archbishop Whately defines Analogy as a resemblance of Rela- 
 tions. This definition, if intended to represent the ancient signifi- 
 cation 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 (vof/s) bears to the living 
 principle (^'I'X'?) tne same relation that the faculty of vision (ctyas) 
 bears to the body (crw/za) : us yap kv <rw/m o\f/is, kv if^v\y 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 
 ava\oyia, 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 : ' Analogic quam proxime ex Grseco transferentes 
 in Latino m. proportionem vocaverunt, haec vis est : Ut id, quod dubium 
 est, ad aliquid simile, de quo non quseritur, referat ; ut incerta certis 
 probet.' I am indebted for this quotation to Mr. Austin's Lectures 
 on Jurisprudence, vol. iii. p. 255. 
 
 Q 2
 
 228 IMPERFECT INDUCTIONS. 
 
 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 
 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.
 
 ANALOGY. 229 
 
 In the first place, we must have no evidence that there 
 is any causal connexion 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 
 ordinarily attached to those terms, are not to be found on 
 the moon's surface 8 . 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- 
 
 * See the essay Of the Plurality of Worlds (usually attributed to 
 Dr. Whewell), ch. ix. sect. 7-9. The whole of this essay furnishes 
 excellent examples of the employment of the Argument from Analogy, 
 and also illustrates the extreme caution and delicacy which are 
 requisite in estimating its value.
 
 230 IMPERFECT INDUCTIONS. 
 
 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 
 enquiring whether this property is more likely 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, b, 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
 
 ANALOGY. 231 
 
 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 
 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
 
 232 IMPERFECT INDUCTIONS. 
 
 B, because they are both of them vain and selfish, we 
 shall 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 them- 
 selves are mainly dissimilar, or points of dissimilarity 
 where the 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 distributed into land and water, and probably 
 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 sus- 
 taining 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
 
 ANALOGY. 233 
 
 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 
 resemblance to (i) the ascertained points of difference, 
 (2) the entire assemblage of the properties of the ob- 
 jects compared. If the ascertained resemblances are 
 numerous, the ascertained differences few, and we have 
 reason to think that we are well acquainted with the 
 objects compared, the argument from analogy is very 
 forcible. If, on the other hand, the ascertained resem- 
 blances 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 unacquainted, 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 complete 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
 
 234 IMPERFECT INDUCTIONS. 
 
 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 9 , '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 
 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 follow- 
 ing 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 10 , 
 while combating the once fashionable doctrine of elec- 
 trical fluids, brings into juxta-position two very interest- 
 ing instances of hasty analogies. 
 
 ' The progressive stages,' he says, ' in the History of Phy- 
 sical Philosophy will account in a great measure for the 
 adoption by the early electricians of the theories of fluids. 
 
 Mill's Logic, Bk. III. ch. xx. 2. 
 10 Fifth edition, p. 135.
 
 ANALOGY. 235 
 
 ' 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 Archasus). Air and gases were 
 also at first deemed spiritual, but subsequently became 
 invested with a more material character ; and the word 
 gas, from geist, 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 char- 
 acter 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 
 mode of reasoning ensued, and now aeriform fluids were 
 shown to be analogous in many of their actions to liquids or 
 known fluids. A belief in the existence of other fluids, 
 differing 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 con- 
 necting it with others ; the mind, once possessed of the idea 
 of a fluid, soon invested it with the necessary powers and 
 properties, and grafted upon it a luxuriant vegetation of 
 imaginary offshoots.' 
 
 Most of my 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
 
 236 IMPERFECT INDUCTIONS. 
 
 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 akin 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 u , ' 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 
 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 (Cam's 
 aureus) inhabits Africa, the warmer parts of Asia, and 
 Greece ; while the isatis (Cant 'slagopus) 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 
 
 11 Lyell's Principles of Geology, ch. vi. (ninth edition) ; ch. x. 
 (tenth edition).
 
 INCOMPLETE INDUCTIONS. 237 
 
 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 Hima- 
 laya by two great chains of mountains, each covered with 
 perpetual snow, the chain of Kuenlun, lat. 35 N., and that 
 of Mouztagh, 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 J, was in a 
 climate colder than that of Petersburg and Stockholm.' 
 
 Neither through Analogy nor through Induction by 
 Simple Enumeration can we establish a fact of Causa- 
 tion, 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 circum- 
 stances is the cause or the effect of another, or con- 
 nected 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 considerably short of a rigorous fulfilment 
 of these conditions may still lead to a conclusion, pos- 
 sessing more or less of probability. We may, for in-
 
 238 IMPERFECT INDUCTIONS, 
 
 stance, 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 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 probability of the con- 
 clusion. 
 
 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
 
 INCOMPLETE INDUCTIONS. 239 
 
 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 con- 
 clusion may be considered absolutely certain. But if, 
 on any grounds, we suppose one of these alternatives 
 to be more probable than the others, and we state this as 
 our conclusion, the inference is, of course, only a pro- 
 bable one, and should rank as an Imperfect Induction. 
 
 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.
 
 240 IMPERFECT INDUCTIONS. 
 
 Briefly to sum up the contents of this chapter, Im- 
 perfect Inductions are the results either of an Inductio 
 per Enumerationem Simplicem (to which I propose to 
 appropriate the expression ' Empirical Generalisations '), 
 or of the Argument from Analogy (which I call Ana- 
 logies), or of an imperfect fulfilment of one or other 
 of the Inductive 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 Deduction, 
 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 1 , 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 
 
 1 'H p\v 5r) iirayaayfi dpxri kan nal rov Ka96\ov, 6 8J <rv\A.o7r/xos 
 IK ruv Ka9u\ov. Elalv dpa a.pxo.1 Siv 6 <n/AAo7T/^s, Siv OVK tan 
 <n>\Ao7r/ior tirafajyj) apa. Eth. Nic. vi. 3 (3). Cp. Eth. Nic. vi. 
 6, 8 (9) ; Metaphysics, i. I ; Posterior Analytics, ii. 19. 
 
 R
 
 242 RELATION OF INDUCTION TO DEDUCTION, 
 
 many 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 an- 
 other.' But this proposition, if not referred directly to 
 induction, is classed under the head of intuitive con- 
 ceptions, the most probable, though perhaps not the 
 most commonly received, explanation of which is that 
 which derives them from the accumulated experience of 
 generations, transmitted hereditarily from father to son. 
 
 A Deductive Inference combines the results of pre- 
 vious inductions or deductions, and evolves new pro- 
 positions as the consequence, or, to put the matter in 
 a slightly different point of view, as expressing the total 
 result, of these combinations. I append a few easy ex- 
 amples of the manner in which the results of induction 
 are employed in a deductive argument. 
 
 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 o, B produces /3, C pro- 
 duces |, 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 /3 + 4 j. In this case
 
 AND VERIFICATION. 243 
 
 the simple rules of Algebra, governing the addition and 
 subtraction of quantities, combined with the special 
 data here furnished, are the premisses from which our 
 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 trans- 
 mit 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 ex- 
 pressed 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 
 
 R 2
 
 244 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 
 determined, on the other side of the surface, is derived 
 from a combination of the experimental truth, gained 
 by induction, that 'the angle of reflexion is equal to 
 the angle of incidence ' with the geometrical propositions 
 stated in Euclid i. 8 and i. 29. 
 
 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 experi- 
 ence, namely, (i) that land varies in value, and (2) that 
 there is some land either so bad or so disadvantageously 
 situated as to be not worth the cultivating 2 . 
 
 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 : 
 
 1 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 ad- 
 vantages of situation, such as proximity to a market, and regarded 
 the value of land as depending solely on its fertility.
 
 AND VERIFICATION. 245 
 
 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
 
 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 it. 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 Mamial of Political 
 Economy, Bk. II. ch. xi.
 
 AND VERIFICATION. 247 
 
 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, Mer- 
 cury, as the other inferior planet] should appear sometimes 
 horned like the moon. To this he answered by admitting the 
 conclusion, and averring that, should we ever be able to see 
 its actual shape, it -would 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 especially 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 succeeded 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, 399.
 
 248 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 be- 
 comes 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 
 continuously up to a certain point, and that from that 
 point the process of deduction should proceed equally 
 uninterruptedly. We may, and in fact should, frequently 
 pause to consider to what deductive conclusions our in- 
 ductive inferences lead, or to try whether they may not 
 be connected by a chain of deductive reasoning with 
 wider truths previously ascertained 5 . 
 
 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, 
 
 8 On this subject, see the excellent criticism on Bacon in Mr. 
 Mill's logic, Bk. VI. ch. v. 5.
 
 AND VERIFICATION. 249 
 
 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 
 frequently 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 ela- 
 borate 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,
 
 250 RELA TION OF IND UCTION TO DED UCTION, 
 
 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. The dis- 
 covery of the planet Neptune affords an excellent 
 
 / instance of the same kind. 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 employ the Method of Difference in order 
 to supplement the characteristic uncertainty attaching to 
 the employment of the Method of Agreement. Of the 
 process denoted by this looser sense of the word, in- 
 stances will readily occur to every one. Thus, the 
 diminution in the periods of Encke's comet has been 
 regarded by some astronomers (though, perhaps, errone- 
 ously) as a verification of the theory that space is filled 
 with an interstellar medium ; or, to take an instance 
 from a very different class of subjects, the recent break- 
 ing-up of the slave-system in the Southern States of
 
 AND VERIFICATION. 251 
 
 America may be regarded as a verification of the pre- 
 diction that slave and free institutions could not long 
 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, I may refer back to the 
 enquiry into the cause of crystallization, already adduced 
 in my discussion of those two methods 6 . 
 
 There is a still wider application 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- 
 cludes 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 induc- 
 tively, 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 method. 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 surface, which 
 had already been proved inductively, were, from the time 
 of Newton, brought under the law of universal gravita- 
 tion, and proved deductively from it. The same was 
 also the case with Kepler's Laws, when they were proved 
 See pp. 145, 146, 157, 158.
 
 252 RELATION OF INDUCTION TO DEDUCTION, 
 
 deductively from the theorem of the Central Force. This 
 mode of Verification is recommended by Mr. Mill, under 
 the name of the Inverse Deductive or Historical Method, 
 as specially applicable to generalisations on society which 
 have been inferred inductively from the study of history 
 or the observation of mankind. These generalisations 
 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 7 . It is 
 thus shown that the generalisations of history are such as 
 we might have anticipated a priori from a general know- 
 ledge of human nature, and each branch of the enquiry 
 is made in this manner to afford a striking confirmation 
 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 
 
 7 See above, pp. 204-207, 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 psychology, we may, and sometimes do, begin with psycho- 
 logical generalisations, 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. 
 
 accounted for by the law of the development of heat by 
 compression, this law acquired so novel and striking a 
 confirmation as to leave no doubt of its truth or univer- 
 sality. 
 
 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 with 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. 
 It must also be borne in mind that the term is not in- 
 frequently employed to designate simply the confirma- 
 tion of a hypothesis by an appeal to facts. 
 
 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 Mai-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. 255 
 
 was long ago pointed out by Bacon 1 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 explana- 
 tion of these 'curious coincidences' is that our at- 
 tention is arrested by the affirmative instances, whereas 
 
 1 ' Intellectus humanus in iis quse semel placuernnt (aut quia 
 recepta sunt et credita, ant quia delectant) alia etiam omnia trahit 
 ad suffragationem et consensum cum illis : et licet major sit instanti- 
 arum vis et copia, quse occurrunt in contrarium ; tamen eas aut non 
 observat, aut contemnit, aut distinguendo summovet et rejicit, non 
 sine magno et pemicioso prejudicio, quo prioribus illis syllepsibus 
 auctoritas maneat inviolata. 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 Deoram numen agnosceret, qusesivit denuo, " At 
 ubi sunt illi depicti qui post vota nuncupata perierint ? " Eadem 
 ratio est fere omnis superstitionis, ut in astrologicis, in somniis, omini- 
 bus, nemesibus, ethujusmodi ; in quibus homines delectati hujusmodi 
 vanitatibus advertunt eventus, ubi implentur ; ast ubi fallunt, licet 
 mnlto frequentius, tamen negligunt et praetereunt. At longe subtilins 
 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 humano intellectui error est proprius et perpetuus, 
 ut magis moveatur et excitetur affirmativis, quam negativis ; cum 
 rite et ordine sequum se ntrique praebere debeat : quin contra, in 
 omni axiomate vero constituendo, major est vis instantise negatives.' 
 Novum Organum, Lib. I. Aph. xlvi.
 
 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 connexion 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 warj 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 
 I shall speak in a subsequent part of this chapter 2 . 
 
 1 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, 257 
 
 This tendency is considerably intensified, if the af- 
 firmative instances are regarded as illustrations of some 
 preconceived theory 3 , or if the evidence afforded by 
 them be supplemented by some powerful affection of 
 the mind 4 . It seldom happens that men can hold 
 themselves entirely indifferent with respect to two rival 
 
 ' We would strongly recommend any of our readers whose occu- 
 pations 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-occurrence 
 of the expected consequent, 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 comparison 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 im- 
 pressed by the fulfilment than by the failure of a prediction, and it 
 is only, when thus placing ourselves face to face with fact and ex- 
 perience, that we can fully divest ourselves of this bias.' Familiar 
 Lectures on Scientific Subjects, Lecture IV. 
 
 3 ' Habet enim nnusquisque (prseter aberrationes naturae humanse 
 in genere) specum sive cavemam quandam individuam, quae lumen 
 
 naturae frangit et corrumpit ; vel propter differentias impres- 
 
 sionnm. prout occurrunt in animo praeoccupato et prsedisposito, aut in 
 animo sequo et sedato.' Bacon's Novum Organum, Lib. I. Aph. xlii. 
 
 4 ' 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 Or- 
 ganum, Lib. I. Aph. xlix. 
 
 S
 
 258 FALLACIES INCIDENT 
 
 opinions and apply themselves to the comparatively 
 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 5 , and the truth of which could 
 * When a person was convinced that he was subject to the evil
 
 TO INDUCTION. 259 
 
 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, 
 
 practices of a witch, this conviction would, of course, sometimes 
 produce the 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. 
 S 2
 
 260 FALLACIES INCIDENT 
 
 there is absolutely no support whatever in fact. Thus, 
 the theory which prevailed down to the time of Galileo 6 , 
 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, especially if it be 
 of a denser material, reaches the ground in a 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 observa- 
 tions 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 7 . 
 
 In Sir Thomas Browne's Enquiries into Vulgar and 
 Common Errors*, we have an examination of the propo- 
 
 8 Galilai Systema Cosmicum, Dial. II. 
 
 T This theory appears to have originated in a mistaken interpreta- 
 tion of a passage in Aristotle, De Generatione et Corruptions, II. 6. 
 See my note on Bacon's Novum Organum, Lib. I. Aph. xlv. 
 
 Bk. IV. ch. vii.
 
 TO INDUCTION. 261 
 
 sition that ' men weigh heavier dead than alive, and before 
 meat than after.' Here are two extraordinary paradoxes 
 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.
 
 262 FALLACIES INCIDENT 
 
 Another extraordinary instance of a statement which 
 obtained acceptance without any foundation whatever in 
 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- 
 ma/ium, Bk. I. ch. vii. Cp. Bk. III. 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 9 . 
 
 Vol. i. p. 394.
 
 TO INDUCTION. 263 
 
 'Aristotle, the greatest naturalist of Greece, had observed 
 that it was a curious fact, that on the sea-shore no animal 
 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.' 
 
 I 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 
 GlanvilPs Scepsis Scientifica^ published in i665 10 : 
 
 ' 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 the other, 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], 
 
 10 Scepsis Scientifica, ch. 24.
 
 264 FALLACIES INCIDENT 
 
 thence to [M], and so on, till I had finisht what I intended 
 to make known.' 
 
 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
 
 TO INDUCTION. 265 
 
 times it has frequently led, and still 'leads, men to embark 
 in the most desperate speculations, which no scientific 
 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 quite 
 a recent period, 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 12 , instead of care- 
 
 11 ' Axiomata, quae in usu stint, ex tenui et manipulari experientia, 
 et paucis particularibus, quse ut plurimum occurnmt, fluxere ; et sunt 
 fere ad mensuram eorum facta et extensa.' Nmwm Organum, Lib. 
 I. Aph. xxv. 
 
 13 ' Intellectns humanus illis, quae simnl et subito mentem ferire et 
 subire possunt, maxime movetnr ; 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
 
 266 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 1S . 
 
 obsidetur ; ad ilium vero transcursum ad instantias remotas et hetero- 
 geneas, per quas axiomata tanquam igne probantur, tardus omnino 
 intellectus est et inhabilis, nisi hoc illi per duras leges et violentnm 
 imperium imponatur.' Novum Organum, Lib. I. Aph. xlvii. 
 
 1S The history of the French language furnishes a striking instance 
 of non-observation and of the curious and baseless theories to which
 
 TO INDUCTION. 
 
 The student must have already perceived that I am 
 trenching on Fallacies of Generalisation. When we 
 proceed to treat insufficient evidence, or the absence of 
 evidence, or popular beliefs which run counter to all 
 
 it may lead : ' It is well known that before certain feminine sub- 
 stantives, such as messe, mire, soif, faim, peur, &c., the adjective 
 grand keeps its masculine termination, grand messe. grand mtre, &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 leamt 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 prolongation of Latin grammar ; consequently the 
 Old French adjectives followed in all points the Latin adjective ; 
 those adjectives which had two terminations 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 une 
 grand femme, grandis femina; une dme mortel, anima mortalis ; 
 une coutume cruel, consuetudo crudelis ; tine plaine vert, planities 
 viridis, &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, verte, forte, &c., after the pattern of bonne, &c. 
 A trace of the older and more correct form survives in such expres- 
 sions as grand'mere, grand'route, grand'fatm, grand'garde, &c., 
 which are the debris of the older language. In the seventeenth 
 century, Vaugelas and the grammarians 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, Dr. Kitchin's Transl., Preface, 
 p. vi ; Seventh Edition, pp. xxvi-vii.
 
 268 FALLACIES INCIDENT 
 
 the evidence available, as if they afforded perfectly suf- 
 ficient evidence, the fallacy is one of inference, and, if 
 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 infer- 
 ence itself. All the instances described above, I believe, 
 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 Enumerationem 
 Simplicem, 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 l4 , ' which 
 
 14 Herschel's Discourse on the Study of Natural Philosophy, 
 in.
 
 TO INDUCTION. 269 
 
 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 
 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.
 
 270 FALLACIES INCIDENT 
 
 The following examples, adduced by Mr. Mill 15 , are 
 so interesting and appropriate, that I take the liberty 
 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 hypo- 
 thesis (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 
 
 1S System of Logic, Bk. V. ch. iv. 4.
 
 TO INDUCTION. 2JI 
 
 be brought together, and carefully bound up with clean linen 
 rags, but, above all, to be let alone for seven days, at the end 
 of which period the bandages were removed, when the 
 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 
 first intention 16 ." ' 
 
 The next example I extract from Bp. Wilkins' very 
 curious tractate, entitled A Discovery of a New World, 
 or a Discourse tending to prove that 'tis probable there may 
 be another Habitable World in the Moon : 
 
 ' He [that is, ' a late reverend and learned Bishop,' writing 
 ' under the feigned name of Domingo Gonsales ' 1T ] supposeth 
 that there is a natural and usual passage for many creatures 
 betwixt our earth and this planet. Thus, he says, those great 
 multitudes 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 
 
 16 Dr. Paris' Pharmacologia, pp. 23-24. 
 
 17 The small tract here referred to is republished in vol. viii. of 
 the Harleian Miscellanies ( Park's Edition). The author was Francis 
 Godwin, afterwards Bishop of Hereford, and author of the well- 
 known book De Prasulibus Anglia Commentarius.
 
 272 FALLACIES INCIDENT 
 
 to obscure the day, and hinder the light of the sun. From 
 which, together with divers other such relations, he concludes 
 that 'tis not altogether improbable they should proceed from 
 the moon. Thus, likewise, he supposes the swallows, cuckoos, 
 nightingales, with divers other fowl, 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 18 .' 
 
 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 slovenliness 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. 
 
 II. Besides the errors which originate in the neglect of 
 instances or of some of the circumstances which are con- 
 18 Wilkins' Discovery of a New World, Fifth Edition, p. 160.
 
 TO INDUCTION. 273 
 
 nected with a given instance, there is another class of 
 errors derived from mistaking for observation that which 
 is not observation at all, but inference. To this class of 
 errors Mr. Mill gives the name of Fallacies of Mai- 
 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 we 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 visual perceptions of distance and 
 of form, the only perception proper is that of the various 
 tints of colour acting 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 19 , ' 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, 
 u Mill's Logic, Bk. V. ch. iv. 5. 
 T
 
 274 FALLACIES INCIDENT 
 
 many a scandalous anecdote, owes its origin to this in- 
 capacity. The narrator relates, not what he saw or heard, 
 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 observer 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 Mai-observation 
 can be given than what was called the common-sense 
 argument against the truth of the Copernican System.
 
 TO INDUCTION. 275 
 
 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- 
 
 T 2
 
 276 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 Mai-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 20 , 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 extremest 
 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 
 
 * Maudsley, The Physiology and Pathology of Mind, ch. iv. p.
 
 TO INDUCTION. 277 
 
 sensations are really experienced ; the error consists in 
 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. 
 
 To the head of Mai-observation, or the substitution 
 of gratuitous inference for accurate observation, may be 
 referred the fallacy which may, perhaps, best be designated 
 as Exaggerated Comparison. By the side of anything 
 very large, we are apt, being prepossessed by the idea of 
 largeness, to suppose that a small object is smaller than 
 it really is, and, on the other hand, by the side of any- 
 thing very small, being prepossessed by the idea of small- 
 ness, that a large object is larger than it really is. 
 Similarly, of things bright or dark, of periods and 
 distances long or short, of actions good or evil, of 
 evidence probable or improbable, and the like. We 
 are all familiar with the ' only half a mile off,' when we 
 are approaching a town, which we shall probably find to 
 be at least double or treble the distance named. The 
 countryman, of whom we enquire, knows that, in com- 
 parison with long distances, the distance is short, and 
 then, unconsciously exaggerating the shortness of the 
 distance, proceeds to name some definite distance which, 
 in his mind, is typical of shortness or which, he thinks, 
 will sufficiently reassure the weary traveller. Instead of
 
 278 FALLACIES INCIDENT 
 
 recurring to his own actual experience of the time he 
 takes to walk it, he draws a rapid inference from the 
 fact that the distance is comparatively short to the 
 particular distance which he names. In the same way, 
 men are apt to underrate the probability of an argument 
 as compared with certainty or a very high degree of 
 probability, or, on the other hand, to overrate its proba- 
 bility, as compared with very faint indications of evidence. 
 The concentration of our attention on one term of the 
 comparison perverts our judgment with reference to the 
 other term. 
 
 The description here given of the errors originating 
 in Non-observation or Mai-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.
 
 TO INDUCTION: 279 
 
 B. The fallacies incidental to the performance of the 
 inductive 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 
 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 little or no probability is 
 often adduced as affording highly probable evidence ; but, 
 as this kind of argument is very seldom 21 treated as 
 affording absolute certainty, the discussion of false ana- 
 logies may be reserved till I have completed the treat- 
 ment of the other 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 Enumerationem Simplicem 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, mistaken for a perfect induction. I shall first 
 
 21 The geological example on p. 236 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.
 
 280 FALLACIES INCIDENT 
 
 notice the case in which scientific induction is simu- 
 lated by the incomplete Inductio per Enumerationem 
 Simplicem 22 . 
 
 IV. When men first begin to argue from their experi- 
 ence 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 
 
 M 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 employed. The fallacies here treated are due to the un- 
 necessary or injudicious employment of the method.
 
 TO INDUCTION. 281 
 
 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 material 
 circumstances before they anticipate a similar effect. 
 But not only is the Inductio per Enumerationem Sim- 
 plicem the mode of generalisation natural to immature 
 and uninstructed minds ; it is the method which, till the 
 time of Bacon 23 , or at least till the era of those great 
 discoveries which shortly preceded the time of Bacon, 
 was almost universal. Aristotle, it is true, usually 2 * (for 
 
 23 Bacon seems to be never weary of condemning this unscientific 
 procedure. Thus, in addition to the aphorism already quoted (p. 
 125), we have, amongst others, the following emphatic passages: 
 ' Axiomata quoe in usu sunt ex tenui et manipulari experientia, et 
 paucis particularibus, quse ut plnrimnm 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 emendari ipsum verius foret.' Nov. Org. Lib. I. 
 Aph. xxv. ' At philosophise genus empiricum placita magis deformia 
 et monstrosa educit, quam sophistic-urn aut rationale genus ; quia non 
 in luce notionum vulgarium (quse licet tenuis sit et superficialis, 
 tamen est quodammodo universalis, et ad multa pertinens) sed in 
 paucorum experimentorum angustiis et obscuiitate fundatum est. . . . 
 Sed tamen circa hujusmodi philosophias cautio nullo modo prseter- 
 mittenda erat ; quia mente jam prsevidemus et auguramur, si quando 
 homines, nostris monitis excitati, ad experientiam se serio contulerint 
 (valere jussis doctrinis sophisticis), turn demum, propter prsematuram 
 et prseproperam intellectus festinationem et saltum sive volatum ad 
 generalia et rerum principia, fore ut magnum ab hujusmodi philo- 
 sophiis periculum immineat ; cui malo etiam nunc obviam ire 
 debemus.' Aph. Ixiv. 
 
 31 For exceptions, see An. Post. I. 31, p. 88, a. 4-5 ; Top. VIII. 8,
 
 282 FALLACIES INCIDENT 
 
 he is not consistent on this point) requires that an in- 
 duction should be based on an examination of all the 
 instances ; but this requirement being in the vast majority 
 of cases (even if we suppose Aristotle to be speaking of 
 species rather than individuals) impossible of fulfilment, 
 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 pas- 
 sage 25 in which he emphatically asserts that the minor 
 premiss of the inductive syllogism (for he represents 
 induction under the syllogistic form) should include all 
 the instances, he argues that all animals which are de- 
 ficient in bile are long-lived, because he finds this to be 
 the case with the man, the horse, and the mule. Aris- 
 totle's works, and especially those on Natural History, 
 abound in rash generalisations of this kind. 'It is a 
 fact,' says Mr. Lewes 26 , ' 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 observation 
 
 p. 160, b. 3. For further information on Aristotle's theory of Induc- 
 tion, I must refer the student to the beginning of 13, and, for a 
 more detailed account of the causes of his failure in his physical 
 researches than can well be given here, to 1 1 of the Introduction 
 to my edition of Bacon's Novum Organum. 
 
 * Analytica Prior a, ii. 25. 
 
 * Lewes' Aristotle, ch. xvi. 399. On the other hand, the student, 
 who is interested in the history of science, will do well to read, in 
 arrest of judgment on Aristotle, Dr. William Ogle's Introduction to 
 his translation of the De Partibus Animalium.
 
 TO INDUCTION. 283 
 
 thus : " The heart is destitute of bones except in horses 
 and in a species of ox ; these, however, in consequence 
 of their size, have something bony as a support, just as 
 we find throughout the whole bod\ """ His Spanish 
 follower Funes Y Mendoc.a improves on this statement 
 by saying that the bone acts like 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 ". 
 ' It is probable,' says the author of the review previously 
 quoted 29 , 'that Aristotle had got hold of the cranium 
 of an old individual in which the sutures had become 
 obliterated.' 
 
 The employment of the Inductio per Enumerationem 
 Simplicem prevailed so universally from the time of 
 Aristotle 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 30 , ' tried to establish a gene- 
 ralisation which has been much admired, namely, that all the 
 
 17 De Partibus Animalium, Bk. III. ch. iv. 
 
 M ^a. fitv yap l^fi /tovoffTtov ro Kpa^iov, uairtp 6 KVOIV, ra SI ffiry- 
 K(ifj.(vov, uairtp dvOpwiros. Historia Animalium, Bk. III. ch. vii. 
 
 " Quarterly Review, No. 233, Art. ii. The mention of the human 
 skull, which had no sutures, is evidently borrowed from Herodotus, 
 IX. 83. 
 
 " Lewes' Aristotle, ch. xvi. 399 d.
 
 284 FALLACIES INCIDENT 
 
 organs of Animal life are double and symmetrical, while all 
 the organs of Vegetal life are single and asymmetrical. 
 Unhappily the facts do not fit. In the commencement 
 almost every 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 ex- 
 ceptions 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 31 , 'that the sensible qualities of plants, such as colour, 
 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 Luridcz, which is indicative of their narcotic 
 and very dangerous qualities, as Datura, Hyoscyamus, 
 Atropa, and 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 when 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 ascribes too much importance to 
 such an indication, and his aphorisms are unsupported by 
 facts ; for instance, he says, " Color pallidus insipidum, 
 viridis crudurn, luteus amarum, ruber acidum, albus dulce, 
 niger ingratum, 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 
 31 Pharmacologia, ninth ed. pp. no, in.
 
 TO INDUCTION. 285 
 
 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 Lyell 32 , ' 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 
 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 im- 
 mediate 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 regard to basalt and other igneous rocks, Werner's 
 theory was original, but it was also extremely erroneous. 
 
 ** Lyell's Principles of Geology, ninth ed. Bk. I. ch. iv.
 
 286 FALLACIES INCIDENT 
 
 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 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 unprece- 
 dented 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 Enumerationem Simplicem. Averages of a suffi-
 
 TO INDUCTION. 387 
 
 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 reflexion ought to show 
 that the accuracy of these calculations depends on the 
 assumption that the causes in operation, so far as they 
 affect 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 univer- 
 sally and unconditionally. Mr. Venn, in his 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 illus- 
 tration of the point in question : 
 
 ' 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 
 
 ** Venn's Logic of Chance, chap. i.
 
 288 FALLACIES INCIDENT 
 
 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 life, 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 in- 
 fluence 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 per- 
 manent 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 ex- 
 amined 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 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 per- 
 sistent and invariable is scarcely to be found in nature 3 *.' 
 
 In these and similar cases, the fallacy arises from 
 ** Venn's Logic of Chance, ch. i. sect. 10, n.
 
 TO INDUCTION. 289 
 
 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, in- 
 stead 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 repeated, that we ought never to depend on fre- 
 quency 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 the physical 
 sciences, is still the common and received method of 
 induction in whatever relates to man and society. The 
 reason of this remark is to be sought in the extraordinary 
 difficulty 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 
 
 u
 
 FALLACIES INCIDENT 
 
 discover by elimination the true connexion 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 required to discover the cause of a given effect, our 
 materials 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 
 appreciable influence in the production of the effect in 
 question; 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 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 introduction of the new cause was not ac- 
 companied by other causes which may have wholly or 
 partially produced the supposed effect, (2) that the new
 
 TO INDUCTION. 29! 
 
 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 Enumerationem Simplicem, 
 or of a mere appeal to unsifted 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 little doubt that moral and social enquiries 
 are beginning to emerge from the chaotic state of con- 
 fusion 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 
 of the incomplete Inductio per Enumerationem Sim- 
 plicem may perhaps be referred the illegitimate use of 
 the Argument from Authority. The opinions or pre- 
 dictions of a certain man or of a certain class of men 
 upon some particular question or questions have been 
 subsequently found to be verified by the issue of events 
 or an examination of the facts. From this circumstance 
 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 
 
 U 2
 
 292 FALLACIES INCIDENT 
 
 accident ; but, not content even with this inference, 
 men are apt to draw the far more unwarrantable one 
 that this person or class of persons is to be accepted 
 a 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 trusting 
 to such a person than in trusting to himself. But the 
 same habit of mind, which is a virtue among uneducated 
 men and in primitive states of society, becomes one of 
 the most serious obstacles to progress and knowledge 
 when men, either individually or collectively, have at- 
 tained 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 is apt to become 
 tyrannical and irrational unless it is constantly con- 
 fronted with facts and subjected to the criticism of 
 others. 
 
 But an undiscriminating submission to the authority 
 of contemporaries, of which I have hitherto exclusively 
 spoken, has been but a slight source of error when com- 
 pared with undiscriminating submission to the authority 
 of past generations 36 . The latter involves a kind of com- 
 
 ** Of this tendency we have many ' glaring instances,' as Bacon 
 would call them. The error has been, so to say, canonised in the
 
 TO INDUCTION. 293 
 
 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 
 appear to us patently absurd, nor is it without effort 
 that we can realise the universality of their former re- 
 ception S6 . Instances of such propositions have already 
 
 proverb ' Mallem cum Platone errare.' There is a characteristic 
 anecdote of Schemer, who contests with Galileo the honour of 
 having been the first to observe the spots in the sun. ' Scheiner was 
 a monk ; and, on communicating 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 men- 
 tioned : be assured, therefore, that it is a deception of your senses, or 
 of your glasses." ' Baden Powell's History of Natural Philosophy, 
 p. 171. 
 
 36 The increasing unwillingness of men to accept a proposition on 
 mere authority is thus forcibly put by Bentham, Book 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 ex- 
 perience, the. mother of wisdom, shall have become barren), the
 
 294 FALLACIES INCIDENT 
 
 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 ST . But, in subjects lying 
 remote from ordinary observation, propositions almost 
 equally absurd have held their ground till quite recently ; 
 some continue still to maintain themselves, and others no 
 doubt will be propounded, from time to time, to take ad- 
 vantage of the credulity of mankind. 
 
 ' To give a general currency,' says Dr. Paris 38 , 'to a hypo- 
 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, 
 constitutional law, private law ; go back a few centuries, and you 
 will find argument consisting of reference to authority, not exclu- 
 sively, 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. 
 
 ****** 
 
 ' 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.' 
 
 37 It might appear that the illegitimate use of the Argument from 
 Authority should be classed amongst the Fallacies of Non-Observa- 
 tion ; but, though a blind devotion to authority is one of the most 
 powerful influences in leading men to neglect observation and ex- 
 periment, the disposition to bow thus unduly to it is itself a fact which 
 requires explanation, and one which it is here attempted to explain. 
 
 ** Dr. Paris' Pharmatologia, Introduction, p. 76, &c.
 
 TO INDUCTION. 295 
 
 thetical opinion, or medicinal reputation to an inert sub- 
 stance, nothing more is required than the talismanic aid of a 
 few great names ; when once established upon such a basis, 
 ingenuity, argument, and even experiment, may open their 
 ineffectual batteries ; the laconic sentiment of the Roman 
 satirist is ever opposed to remonstrance : " Marcus dixit f 
 ita est" A physician cannot err in the opinion of the 
 public, if he implicitly obeys the dogmas of authority. In 
 the most barbarous ages of ancient Egypt, he was pun- 
 ished 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 
 sys:em 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 estab- 
 lished custom 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 Chelidonium majus j and it is only within a few years 
 that the Theriaca Andromachi, in its ancient form, has been 
 dismissed from our Pharmacopoeia. The CODEX MEDICA- 
 MENTARIUS of Paris still cherishes the many-headed monster
 
 296 FALLACIES INCIDENT 
 
 of pharmacy, under the appropriate title of " Electuarium 
 Opiatum Polypharmacum? ' 
 
 ' 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 dan- 
 gerous malady by the use of the cold bath. The most frigid 
 water that could be procured was, in consequence, recom- 
 mended on every occasion : thus Horace, in his epistle to 
 Vala, exclaims 
 
 " Caput ac stomachum supponere 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, Marcellus ; an event which at once deprived the remedy 
 of its credit and the physician of his popularity.
 
 TO INDUCTION-. 
 
 '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 oblivion 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, Chifletius, 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,' 
 
 In discussing the Argument from Authority, I 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
 
 298 FALLACIES INCIDENT 
 
 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 39 . The latter, as was 
 once said by the late Bishop Thirlwall, may be regarded 
 as the ciphers after a decimal point 40 . 
 
 V. The errors incident to the employment of the 
 various Inductive Methods have already been pointed out 
 
 " ' Verns enim consensus is est, qui ex libertate jndicii (re prius 
 explorata) in idem conveniente consistit. At numerus longe maximns 
 eorum, qui in Aristotelis philosophiam consenserunt, ex prsejudicio 
 et auctoritate aliorum se illi mancipavit ; ut sequacitas sit potius 
 et coitio, quam consensus.' Bacon, Nov. Org., Lib. I. Aph. Ixxvii. 
 
 40 Cp. Glanvill's Scepsis Scientijica, ch. xvii. : ' Authorities alone 
 with me make no number, unless Evidence of Reason stand before 
 them : for all the Cyphers of Arithmetic are no better than a single 
 nothing.'
 
 TO INDUCTION: 299 
 
 in my 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 connexion between some 
 two phenomena, a and b, the connexion 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 b, 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 b 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 c ; (2) to have mistaken a for the sole cause, 
 when a and c are the joint causes, either (a) as both 
 contributing to the total effect, or (/3) as being both es- 
 sential to the production of any effect whatever 41 ; (3) to 
 have mistaken a for the cause of b t when they are really 
 
 41 The distinction may be illustrated by a familiar example. If a 
 cistern is filled by two pipes, the water passing through each con- 
 tributes 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.
 
 300 FALLACIES INCIDENT 
 
 both of them effects of c ; (4) to have mistaken a for 
 the proximate cause of b, when it is really only the re- 
 mote cause, c, 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* 1 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 
 :is 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 
 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 
 Vol. i. p. 383.
 
 TO INDUCTION. 301 
 
 former cause, ought properly to be referred to the 
 latter. 
 
 The above extract exemplifies this error as vitiating 
 an application of the Method of Agreement. In the 
 following extracts from Dr. Paris' Pharmaco/ogia, 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 43 ! ' 
 
 ' 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 
 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 
 
 43 Pharmacologia, p. 20.
 
 302 FALLACIES INCIDENT 
 
 enthusiasm declared that he already experienced the effect of 
 its benign influence throughout his whole body : the oppor- 
 tunity 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 per- 
 formed, 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 44 .' 
 
 ' 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 efforts 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 Greatricks, 
 performed in 1666, which were witnessed by contemporary 
 prelates, members of parliament, and fellows of the Royal So- 
 ciety, amongst whom was the celebrated Mr. Boyle, would pro- 
 bably, upon investigation, admit of a similar explanation. It 
 deserves, however, to be noticed that, in all records of extra- 
 ordinary cures performed by mysterious agents, there has 
 
 44 Pharmacologia, p. 28.
 
 TO INDUCTION. 303 
 
 always been a desire to conceal the remedies and other 
 curative means which might have been simultaneously ad- 
 ministered. Thus Oribasius commends, in high terms, a 
 necklace of peony-root for the cure of epilepsy ; but we learn 
 that he always took care to accompany 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 in- 
 formed, for the sole purpose of restoring the much-injured 
 character and use of the -vervain; in which the author 
 directs the root of that plant to be tied with a yard of white 
 satin riband around the neck; but mark during the period 
 of its application, he calls to his aid the most active medi- 
 cines 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 ad- 
 ministered with a sufficient portion of arsenic * 5 ." ' 
 
 ' 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 wire-drawn 
 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 timej the solution of 
 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 
 
 u Pharmacologia, p. 30.
 
 304 FALLACIES INCIDENT 
 
 the testimony of what they call experience, in justification of 
 their superstition 46 .' 
 
 Of a similar character was the old superstition, noticed 
 by Sir Thomas Browne 47 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 guain 
 recenti calidoque macerata, et sic quoque multis ictibus, tune 
 etiam praterquam eximias incudes malleosque ferreos fran- 
 gens. That is, it is broken with goat's blood, but not except 
 it be fresh and warm, 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 pp. 270-1) also illustrates this 
 class of fallacies 4S . 
 
 ** Pharmacologia, p. 88. 
 
 ** Enquiry into Vulgar and Common Errors, Bk. II. ch. v. Col- 
 lected Works, vol. ii. pp. 334, 335. 
 
 " These instances, .together with many others in this chapter,
 
 TO INDUCTION. 305 
 
 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 pro- 
 duced 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 perfectly 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 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 49 . 
 
 (2) When an effect is the joint result of two or more 
 
 illustrate 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 indif- 
 ferently to two or more sources of deception. ' From the elliptical 
 form,' says Archbishop Whately (Elements of Logic, Bk. iii. i), 
 ' in which all reasoning is usually expressed, 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. 
 49 See pp. 6, 23, 127-8, 131-4.
 
 306 FALLACIES INCIDENT 
 
 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 would perhaps be too great an innovation on 
 established language. 
 
 (a) An instance of supposing that a phenomenon is 
 entirely 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 M , ' 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 
 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- 
 
 50 Physiology of Common Life, vol. i. p. 322.
 
 TO INDUCTION. 307 
 
 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 im- 
 pelling force." On the other hand, an influence acting on 
 the capillaries 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 is sufficient for 
 my 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 51 each other's influence. This is a considera- 
 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 BS . 
 
 51 We sometimes speak of causes ' wholly or partially counter- 
 acting each other." It would be an advantage if we could appro- 
 priate the word frustration to express complete counteraction. 
 
 a P. 498. Vol. i. p. 386. 
 
 X 2
 
 308 FALLACIES INCIDENT 
 
 ' In ordering saline draughts as vehicles for active medi- 
 cines, 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 refer- 
 ence 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 carbonic acid may not invalidate the powers 
 of the remedies simultaneously given with them. I should 
 certainly recommend 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 carbonate? 
 
 ' 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 
 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 pre- 
 vented or retarded by certain peculiar and accidental circum- 
 stances. 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 pre-
 
 TO INDUCTION. 309 
 
 sumption that, but for the partial obstruction to the cause, it 
 would have operated in these as in the other instances where 
 no obstructions existed 54 .' 
 
 ' It 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 exceptional 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 probat regulam, a 
 maxim which is, of course, only applicable where the 
 exceptions are apparent, and where they admit of ex- 
 planation in conformity with the rule. 
 
 (3) 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. 13-16). Thus, the burning of a fire 
 
 54 Sir G. C. Lewis' Methods of Observation and Reasoning in 
 Politics, vol. i. p. 386.
 
 310 FALLACIES INCIDENT 
 
 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 con- 
 tains, 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 shown 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 similar and familiar phenomenon of the in- 
 creased brightness with which a fire burns on a frosty- 
 day, owing to the better draught. 
 
 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 (by which I mean pure water) boils depends 
 slightly on the nature of the vessel, but mainly upon two 
 causes or conditions, the temperature of the water and 
 the pressure of the atmosphere. Now, as the latter 
 varies at different heights and in different states of 
 weather, water does not always boil at the same tempera- 
 ture, the boiling-point being, as a rule, diminished by i 
 for every 590 feet that 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 bearing 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
 
 TO INDUCTION. 311 
 
 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 ad- 
 ministered, but Calomel, or some mercurial, when in com- 
 bination with it, appears to direct its influence to the kidneys, 
 and in some unknown manner to render these organs more 
 susceptible of its influence 55 .' 
 
 ' It has been determined by the most ample experience 
 that substances will produce effects upon the living system, 
 when presented in a state of simple mechanical mixture, very 
 different from those which the same medicinal ingredients 
 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 relative 
 effects of alcohol in the form of what is termed " spirit" and 
 in that of wine, may be explained upon the same principle ; 
 in the former case it is in a state of mixture, in the latter in 
 
 K Pharmacologia, p. 388.
 
 312 FALLACIES INCIDENT 
 
 that of combination. It has been demonstrated, beyond all 
 doubt, that a bottle of port, madeira, or sherry, actually con- 
 tains as much alcohol as exists in a pint of brandy ; and yet 
 how different the effect ! a fact which affprds a very striking 
 illustration of the extraordinary powers of chemical combina- 
 tion 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 relative agents, producing their effects 
 in reference only to the state of the living frame. We must, 
 therefore, concur with Sir Gilbert Blane in stating that the 
 virtues of medicines cannot be fairly essayed, nor beneficially 
 ascertained, 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 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 
 
 56 Pharmacologia, pp. 426, 427.
 
 TO INDUCTION. 313 
 
 of the other. By not reasoning upon such facts, physicians 
 have, in my opinion, very unphilosophically advanced to 
 conclusions respecting the inefficacy of certain agents. They 
 have administered 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 
 tris-nitrate of bismuth, a substance which, however powerless 
 in health, I am well satisfied, from ample experience, is 
 highly efficacious 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 irri- 
 tation of illness, and that, which without opposition is inert, 
 may act powerfully where it meets with an opponent. Ex- 
 periments should be made on the sick, in order to determine 
 how the sick will be affected, and nothing should be pro- 
 nounced feeble, merely because it has done nothing where 
 there was nothing to be done 5r .' 
 
 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 times to 
 be the joint result of a number of causes, the presence 
 of every one of which seems to be essential to the pro- 
 duction 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 circumstances, and 
 the addition of some one other circumstance seems to be 
 the spark which produces the conflagration. 
 
 57 Pharmacologia, pp. 133, 134.
 
 314 FALLACIES INCIDENT 
 
 'When we are told,' says Dr. Maudsley 88 , '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 individual, not neg- 
 lecting 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 concurrence of con- 
 ditions, 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 ex- 
 plosion 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 founda- 
 tions of the character, and the final outbreak is perhaps the 
 explosion of a long train of antecedent preparations.' 
 
 (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 ex- 
 citement or inordinate grief adduced as causes of 
 insanity, whereas these are probably merely incipient 
 
 M Physiology and Pathology of Mind, Part II. ch. i. p. 225.
 
 TO INDUCTION. 315 
 
 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, ulti- 
 mately 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 import- 
 ance, 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. 
 
 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 59 , '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, 
 
 59 Pharmacologia, p. 89.
 
 316 FALLACIES INCIDENT 
 
 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 philologists 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 familiar 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, Pro- 
 venc.al 61 , 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 Provencal only was the daughter of 
 Latin ; whereas French, Italian, Spanish, and Portuguese were 
 
 First Series. Lecture V. 
 
 l The exact relationship of French to Proven9al may be repre- 
 sented thus : the Peasant Latin became in the South of France the 
 Langue d'Oc (or Provencal), and in the North the Langue d'Oil, of 
 which the French (or the dialect of the Isle de France) was the 
 principal dialect, and has in its modem form become the language 
 of the nation. See Brachet's Historical Grammar (Dr. Kitchin's 
 Translation), p. 18; j-th ed. pp. 22-3.
 
 TO INDUCTION. 317 
 
 the daughters of Provencal. Hd maintained that Latin passed, 
 from the seventh to the ninth century, through an inter- 
 mediate stage, which he called Langue Romane, and which he 
 endeavoured to prove was the same as the Provengal of 
 Southern France, the language of the Troubadours. Ac- 
 cording to him, it was only after Latin had passed through 
 this uniform metamorphosis, represented by the Langue 
 Romane or Provencal, 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 Cornewall Lewis, can only be refuted by a 
 comparison of the Provengal grammar with that of the other 
 Romance dialects. And here, if you take the auxiliary verb 
 to be, and compare its forms in Provengal and French, you 
 will see at once that, on several points, French has preserved 
 the original Latin forms in a more primitive state than Pro- 
 vengal, and that, therefore, it is impossible to classify French 
 as the daughter of Provengal, and as the granddaughter 
 of Latin. We have in Provengal : 
 
 sent, corresponding to the French nous somntes, 
 etz vous etes, 
 
 son Us sont, 
 
 and it would be a grammatical miracle if crippled forms, 
 such as sent, etz, and son, had been changed back again into 
 the more healthy, more primitive, more Latin, sommes, etes, 
 sont; sumus, 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 modifica- 
 tion of Provengal. Keeping to the auxiliary verb to be, we 
 find that I am is in
 
 31 8 FALLACIES INCIDENT 
 
 Sanskrit Grtek Lithuanian 
 
 asmi 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 
 
 But here Sanskrit, as far back as its history can be traced, 
 has reduced assi to asij 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-tij and, with the loss of the final /, 
 we recognise the Latin est, Gothic ist, and Russian esf. 
 
 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 singular, 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 regular form would be as-anti; this, in Sans- 
 krit, is changed into santi. In Greek, the initial s is dropped, 
 and the ^Eolic enti is finally reduced to eisi. The Latin, on 
 the contrary, has kept the radical s, 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 removal
 
 TO INDUCTION. 319 
 
 of the proximate cause may only temporarily remove the 
 effect, and the primary cause may, after a time, repro- 
 duce it ; or, again, the removal of the primary cause may 
 still leave the proximate cause in full action. This error 
 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 con- 
 tinue 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 
 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 tran- 
 sitory 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 
 remove that condition, the relief of the Systemic sensation 
 not immediately producing relief of the local sensation, never-
 
 320 FALLACIES INCIDENT 
 
 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 hope- 
 less 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 62 .' 
 
 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 English words which have been de- 
 rived from the Latin through the French, as, for instance, 
 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 
 had no Latin equivalents, as seraphim, Gehenna, pascha, &c. ; 
 from Latin they passed at a later time into French (straphin, 
 gene, pdgue). 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, bey, cadi, caravane, derviche, 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 
 
 62 Lewes' Physiology of Common Life, vol. i. pp. 45-47.
 
 TO INDUCTION. 321 
 
 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 lan- 
 guage with many words belonging to the three sciences 
 which the Arabians cultivated successfully : in astronomy it 
 gave such words as azimuth, nadir, zenith; in alchemy, 
 alcali, alcool, alambic, alchimie, elixir, strop ; in mathe- 
 matics, alglbre, 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 63 .' 
 
 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 connexion 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- 
 nexion of the most diverse races. 
 
 I 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. 
 
 93 Historical Grammar, Translation, p. 22, note 2 ; jth ed. p. 27, 
 note 2.
 
 322 FALLACIES INCIDENT 
 
 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 64 . 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. 
 
 I have, thus far, discussed those errors which originate 
 in overlooking the presence of some third circumstance. 
 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 neglecting to 
 take account of their mutual action and reaction 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 65 : 
 
 64 See Mill's Political Economy, Bk. II. ch. xi. 2. 
 85 On Methods of Observation and Reasoning in Politics, vol. i. 
 P- 375-
 
 TO INDUCTION. 323 
 
 '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 acuteness 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 intelligence and good sense of the people may pro- 
 mote its good government, and the goodness of the govern- 
 ment may, in its turn, increase the intelligence of the people, 
 and contribute to the formation of sound opinions among 
 them. Drunkenness is in general the consequence of a low 
 degree of intelligence, 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 improves nature, and nature facilitates 
 education. National 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 insti- 
 tutions strengthen, perpetuate, 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, 
 Y 2
 
 324 FALLACIES INCIDENT 
 
 organises military institutions : these institutions promote 
 and maintain a warlike 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 66 ) 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 
 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 
 
 <* Pp. 181-2.
 
 TO INDUCTION. 325 
 
 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 life 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 ought not to be left out of account. 
 
 (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
 
 326 FALLACIES INCIDENT 
 
 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 G7 ) maintains that 
 it is the effect, and argues thus : 
 
 ' Whatever may be the state of the ultimate molecules of 
 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 constituent 
 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 volume. 
 The diameter will be only 10, and the surface loo times 
 
 87 Herschel's Meteorology, 135, 137.
 
 TO INDUCTION. 327 
 
 increased. But the electric contents, being the sum of those 
 of the elementary globules, will be increased one thousand- 
 fold, and, being spread entirely over the surface, will have a 
 tenfold density (i. e. tension). 
 
 ******* 
 
 ' It will easily be seen that, when thousands of these 
 electriferous globules again further coalesce into rain drops, 
 a great and sudden increase of tension at their surface must 
 rake 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 
 question, long persisted, and even yet persists, with few ex- 
 ceptions, 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 
 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
 
 328 FALLACIES INCIDENT 
 
 marriage within the tribe. Sir John Lubbock 68 , on the 
 other hand, opposes this opinion, and regards exogamy 
 as arising from marriage by capture, not marriage by 
 capture frofn exogamy. 'Mr. M'Lennan's theory,' says 
 he, ' seems to me quite inconsistent with the existence 
 of tribes which have marriage by capture and yet are 
 endogamous. The Bedouins, for instance, have un- 
 mistakeably 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 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. 
 
 ' 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 ex- 
 
 M Origin of Civilization and Primitive Condition of Man, ch. 3. 
 " P- 153-
 
 TO INDUCTION. 329 
 
 isted 70 ? To make increased population the cause of im- 
 proved agriculture is to commit the absurd blunder of 
 confounding cause and effect.' 
 
 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 ' mutuality ' of cause 
 and effect, noticed a few pages back, than of inverting 
 their relation. 
 
 VI. The Argument from Analogy, as has already been 
 stated, consists in drawing the conclusion that, because 
 two or more phenomena resemble each other in certain 
 observed points, they also resemble each other in certain 
 other points beyond the range of our observation. The 
 conditions with which such an inference, in order to be 
 legitimate, must conform, need not be here repeated. If 
 the conditions be not fulfilled, we may commit the error 
 
 ro This question appears to ignore the fact that a population may 
 have an insufficient supply of food, though what it does possess maj 
 be just competent to sustain life.
 
 330 FALLACIES INCIDENT 
 
 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 
 used against, 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
 
 TO INDUCTION. 331 
 
 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, d, c t 
 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 a, b, c, there is no room for any 
 inference whatever. The whole force of the Argument 
 from Analogy consists in the chance of d being causally 
 connected with a, b, or c: if we have reason to believe 
 that this is the case, the argument becomes more than 
 analogical ; if we have reason to believe that it is not 
 the case, we are debarred from employing the argument 
 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-
 
 332 FALLACIES INCIDENT 
 
 flexion or observation would lead to the belief that there 
 is probably no connexion 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, I 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 resem- 
 blance and many of difference between the precious metals 
 on the one hand, and corn, coal, &c. on the other : but the 
 important circumstance to the supposed argument is that the 
 utility of gold and silver (as coin, which is far the chief) 
 depends on their value, 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 sovereign would be twice as large ; if only 
 
 71 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. 333 
 
 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, ' that 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 belief 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 
 Enumerationem Simplicem. 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 
 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
 
 334 FALLACIES INCIDENT 
 
 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 TO , 
 
 7a Novtim Organum, Lib. I. Aph. Ixxxiv. In the first edition of 
 this work I suggested that the reference might possibly be to 
 ^Eschylus, Prometheus Vinctus, 1. 981 : a\\' fHSiSaaxei vavO' <5 
 ~fT)pa.ffK<vv \p6vos. Through the courtesy of the Rev. E. Marshall, 
 I am now enabled to supply the true reference, which is to Aulus 
 Gellius, Nodes Attica, Lib. XII. cap. u : ' Alius quidam veterum 
 poetarum, cujus nomen mihi nunc memorise non est, veritatem tem- 
 poris filiam esse dixit.' It has also been pointed out to me that 
 ' Veritas temporis filia ' is the legend on the groats of Queen Mary, 
 which were doubtless in use in Bacon's time. The following sen- 
 tences occur in the same Aphorism of the Novum Organum : ' De 
 antiquitate autem opinio, quam homines de ipsa fovent, negligens 
 omnino est, et vix verbo ipsi congrua. Mundi enim senium et 
 grandsevitas pro antiquitate vere habenda sunt ; quse temporibus 
 nostris tribui debent, non juniori setati mundi, qualis apud antiques 
 fuit. Ilia enim setas, respectu nostri, antiqua et major; respectu 
 mundi ipsius, nova et minor fuit. Atqne revera quemadmodum 
 majorem rerum humanarum notitiam, et maturius judicium, ab 
 homine sene expectamus, quam a juvene, propter experientiam, et 
 rerum, quas vidit, et audivit, et cogitavit, varietatem et copiam ;
 
 TO INDUCTION. 335 
 
 'veritas temporis filia dicitur, non auctoritatis.' 'Anti- 
 quitas saeculi juventus mundi 73 .' 
 
 Bishop Wilkins' Discovery of a New World contains 
 
 eodem modo et a nostra setate (si vires suas nosset, et experiri et 
 intendere vellet) majora multo quam a priscis temporibus expectari 
 par est ; ntpote setate mundi grandiore, et infinitis experimentis et 
 observationibus aucta et cumulata.' Bentham in his Book of Falla- 
 cies, Part I. ch. ii., and Sydney Smith in his review of that work 
 {Edinburgh Review, No. Ixxxiv, reprinted in his Collected Works), 
 have some very apposite and amusing remarks on this subject. 
 
 73 De Augmentis Scientiarum, Lib. I. Dr. Whewell in his 
 Philosophy of Discovery (chap. xiii. 4) appears to think that this 
 celebrated Aphorism 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 inter- 
 locutors, 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 we 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 1' 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 piu lunga eta, che i nostri predecessori.' 
 Mr. Spedding, however, in his edition of Bacon, questions whether 
 Bacon intended the aphorism as a quotation, and thinks it probable 
 that he did not derive it from any earlier writer. See Ellis and 
 Spedding's edition of Bacon, vol. i. p. 458, n. 4.
 
 336 FALLACIES INCIDENT 
 
 the following curious extract, translated from the work 
 of Cardinal Nicolb de Cusa De doctd, Ignorantid, 7 * : 
 
 ' 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 
 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 
 
 74 Wilkins' Discovery of a New World in the Moon, p. 128 ; 
 Cusanus, De doctd IgnorantiA, Lib. II. ch. xii.
 
 TO INDUCTION. 337 
 
 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" 5 
 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 ; turn demum philo- 
 sophise Aristotelis et Platonis, tanquam tabulae ex 
 materia leviore et minus solida, per fluctus temporum 
 servatse 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 
 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,' 
 
 75 Lib. I. Aph. Ixxvii. 
 Z
 
 338 FALLACIES INCIDENT 
 
 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 
 1 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 reflexion, 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 76 : 
 
 74 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 : ' 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 into an analogy are 
 not found in the same classes of existence. Individuals 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
 
 TO INDUCTION. 339 
 
 ' 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 nineteenth, as compared with Italy in the four- 
 teenth and sixteenth centuries it does not necessarily lose 
 its civilisation. A political community is renewed by the 
 perpetual succession of its members; new births, immigra- 
 tions, 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 in- 
 evitably ends in death : whereas a community might, con- 
 sistently with the laws of human nature, have a duration 
 co-extensive with that of mankind. 
 
 ' The supposed analogy between the existence of a political 
 community and the life of a man seems to have contributed 
 to the formation of the belief in a liability to corruption, 
 inherent in every society. It was a favourite doctrine among 
 
 but moral essences. They are artificial combinations, and, in their 
 proximate efficient cause, the arbitrary productions of the human 
 mind. \Ye 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. 
 Z 2
 
 34 FALLACIES INCIDENT 
 
 some writers of the last century that every civilised com- 
 munity 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 in- 
 dividual, therefore, tends not only to prevent the deterioration 
 of the society, but to promote its improvement.' 
 
 Ancient medicine was full of false analogies. I select 
 the following examples from Dr. Paris "" : 
 
 ' 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.'" 
 
 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- 
 
 77 Pharmcuologia, p. 64.
 
 TO INDUCTION. 341 
 
 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 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 contamination ; and hence the origin 
 of the epithet base, as applied to such metals. This hypo- 
 thesis 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 belief, still prevalent even amongst persons of 
 intelligence, that the weather changes with the ' changes ' 
 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 78 ,' the 
 
 78 On this subject the reader will find some very curious informa- 
 tion in Mill's Logic, Bk. V. ch. v. 6, and Whewell's History of the 
 Inductive Sciences, Bk. IV. ch. iii. 2.
 
 342 FALLACIES INCIDENT 
 
 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 abundantly illustrate the nature of False 
 Analogy and its frequency in the reasoning of early 
 speculators. 
 
 The Argument from Final Causes 79 , in that un- 
 
 79 'Turn vero, ad ulteriora tendens [intellectus humanus], ad 
 proximiora recidit, videlicet ad causas finales, quse sunt plane ex 
 natura hominis, potius quam universi : atque ex hoc fonte philo- 
 sophiam miris modis corruperunt.' Bacon, Nov. Org. Lib. I. Aph. 
 xlviii. 
 
 To prevent misconception, I may at once state that there is an 
 employment of the Argument from Final Causes which I believe to 
 be not only perfectly legitimate, but the highest expression of scien- 
 tific truth. The process of Natural Selection (for an explanation of 
 which I must refer my readers to the works of Darwin, Wallace, 
 and Herbert Spencer), by eliminating unfit types and imperfect 
 organisms in the struggle for existence, has a constant tendency, in 
 the course of evolution, to produce exactly those results which best 
 correspond with the conditions of existence (a proposition, I may 
 remark in passing, which, in some measure, may be extended from 
 the biological to the moral and mental spheres). Hence there is a 
 sense in which it is true that ' Nature always acts for the best,' and 
 that ' Nature does nothing in vain,' but we are not, therefore, justi- 
 fied in ascribing to Nature the attributes of rationality, in crediting 
 it with conscious design, or in assimilating its processes to those of 
 man. If, however, we believe in an intelligent Supreme Cause from 
 whom all Nature and Nature's laws have proceeded, and by whom 
 they are still sustained, it seems inevitable to suppose that the 
 results of the Universe, in their totality, are effecting the designs of 
 this all-powerful Being, numerous and inexplicable as may be the 
 apparent exceptions, when regarded in isolation. Moreover, the
 
 TO INDUCTION. 343 
 
 scientific form of it, once, and even now in some 
 circles, so widely prevalent, 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 arti- 
 ficer, and the argument appears to rest on the assump- 
 tion that the motives, conceptions, 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 pur- 
 pose.' These and similar maxims express the general 
 principle on which the argument rests. Of its applica- 
 tion 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 
 
 marvellous results which not only the material but the spiritual 
 world reveals to us, especially when viewed in comparison with the 
 humble and simple beginnings to which many now believe that they 
 can be carried back, can hardly fail to serve as an indication of the 
 existence of that Supreme Cause and to suggest the attributes of 
 supreme wisdom, power, and goodness with which it has been the 
 habit or instinct of the more cultured races of mankind to invest 
 Him. Theories of evolution may be so stated as not to impair, but 
 indefinitely to exalt, our ideas of the power, wisdom, and benevo- 
 lence of the Being in whom Nature had its source. 
 
 80 Advancement of Learning, Bk. II. (Ellis and Spedding's edition, 
 vol. iii. p. 358). Cp. De Augmentis, iii. 4. It should be noticed, 
 however, that Bacon allows the use of Final Causes in what he calls 
 ' Metaphysic.' Of the foregoing instances, ' and the like,' he says 
 that they are ' well enquired and collected in Metaphysic ; but in
 
 344 FALLACIES INCIDENT 
 
 against the employment of Final Causes in physical en- 
 quiries, 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 
 
 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.' 
 What Bacon appears to mean (and the distinction is important) is 
 that, in extra-physical speculations, as are those of Natural Theology 
 (for the study of ' Metaphysics,' in the ordinary sense of the term, 
 he repudiated), we may argue from an ascertained case of adaptation 
 to the wisdom or goodness of the Creator, but that we are not justi- 
 fied in assuming adaptation or design as a datum in physical investi- 
 gation. 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 enquiring 
 into their purpose) have been suggested by the idea of adaptation 
 (which, it may be noticed, does not necessarily include the idea of 
 design). See Sir H. Acland's Harveian Oration for 1865, and 
 Dugald Stewart's Philosophy of the Human Mind, Part II. ch. xi. 
 (Sir W. Hamilton's edition of Stewart's Works, vol. iii. p. 335, 
 &c.). This fact may be, and, indeed, must be, admitted with 
 respect to physiological enquiries (however the adaptation may 
 be accounted for), and hence Bacon's prohibition is certainly too 
 absolute. 
 
 I have discussed the subject of Final Causes, with special reference 
 to the views of Bacon, in the Introduction to my edition of the 
 Novum Organum, 10.
 
 TO INDUCTION. 345 
 
 watering 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. 
 
 In the Timaus of Plato 81 , 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 Plato 82 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 
 
 81 Of Plato, Bacon says truly, that he ' ever anchoreth on thai 
 shore.' 
 
 M Vol. iii. pp. 272-275.
 
 346 FALLACIES INCIDENT 
 
 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 
 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 connexion 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
 
 TO INDUCTION. 347 
 
 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. 
 
 ' 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
 
 348 FALLACIES INCIDENT 
 
 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. 
 
 1 Moreover, the liver was made to serve another purpose. 
 It was selected as the seat of the prophetic agency ; which 
 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
 
 TO INDUCTION. 349 
 
 or excessive accretions or accumulations, and thus to pre- 
 serve it clean and pure.' 
 
 Aristotle constantly employs this method of reasoning. 
 Thus, in a familiar passage of the Ethics 93 , he says that 
 ' if it is better for men to attain happiness through their 
 own exertions than through chance, it is reasonable to 
 suppose that this will be the case, since everything that 
 depends on Nature M 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 
 
 83 Eth. Nic i. 9 (5). E2 5' tariv ovrca f}*\nov r\ Sia TVXV tvSai- 
 ftovttv, (vkoyov tx (tv OVTOIS, tivtp TO, Kara <f>vaiv, os dlov re Ka\\iffra 
 X e<I/ OVTQJ iri<pvKfv. 
 
 81 The student will notice the transition from the Demiurgus and 
 inferior gods of Plato to the ' Nature ' of Aristotle. ' And in this,' 
 says Bacon, ' 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 (Translation of the De Augmentis), Bk. III. ch. iv. (Ellis 
 and Spedding's edition, vol. iv. p. 364.)
 
 35 FALLACIES INCIDENT 
 
 the body ' in a mean state 8 V On this account, he 
 supposed, all animals which have blood are furnished 
 with a brain, while bloodless animals, having little heat, 
 require nothing to cool them, and are, therefore, with- 
 out one. Moreover, in order to temper the coldness of 
 the brain, blood is conveyed to the membrane which 
 envelopes 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 86 . 
 
 ' 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 necessarily 
 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 down- 
 wards, and rather in front than behind : for Nature is accus- 
 
 85 Compare the extraordinary fancy (De Partibus 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 
 
 <po)v avdpcjwos txd KarCfvyfifva rcL dptffT(pa). 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 with Aristotle's theories. 
 
 w De Partibus Animalium, ii. 7. Cp. Lewes' Aristotle, 164, 
 p. 1 80.
 
 TO INDUCTION. 351 
 
 tomed to seat the noblest in the noblest place, unless any 
 stronger reason prevails : ov //q 
 
 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 88 . 
 
 'Though there are some who think mountains to be a 
 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 89 .' 
 
 ' 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 produced in 
 vain ; and what more probable meaning can we conceive 
 there should be, than to make that place convenient for 
 habitation 90 ?' 
 
 ' 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 
 
 87 De Partibus Animalium, iii. 4. I here quote Mr. Lewes' 
 summary, given in 395, p. 310, of his Aristotle. 
 
 88 Bishop Wilkins was one of the founders of the Royal Society, 
 and enjoyed one of the highest scientific reputations of his time. 
 
 89 A Discovery of a New World in the Moon, p. 77. * Id. p. 91.
 
 352 FALLACIES INCIDENT 
 
 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 their heads. And Nature hath thus provided for 
 those in Peru, with the other inhabitants under the line 9 V 
 
 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 92 : 
 
 ' 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 every natural substance, 
 which possesses any medicinal virtues, indicates, by an ob- 
 vious and well-marked external character, the disease for 
 which it is a remedy, or the object for which it should be 
 employed. This extraordinary monster of the fancy has been 
 principally adopted and cherished by Paracelsus, Baptista 
 Porta, and Crollius, although traces of its existence may cer- 
 tainly be discovered in very ancient authors. 
 
 ******* 
 
 ' The conceit, however, did not assume the importance of 
 
 tl A Discovery of a New World in the Moon, p. 121. 
 w Pharmacologia, pp. 47-50.
 
 TO INDUCTION. 353 
 
 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, 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 uni- 
 versal. Thus, the lungs of a fox must be a specific for 
 asthma, because that animal is remarkable for its strong 
 powers of respiration. Turmerick has a brilliant yellow 
 colour, which indicates that it has the power of curing 
 jaundice ; by the same rule, Poppies must relieve diseases of 
 the head ; . . . and the E^^phras^a (eye-bright) acquired fame 
 as an application in complaints of the eye, because it exhibits 
 a black spot in its corolla resembling 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 infundi- 
 bulum cerebri, and pituitary gland; in the next place, the 
 three membranes, of which its leaves are composed, an- 
 nounce their value to the stomach, which has three mem- 
 branes." 
 
 ' 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 
 
 A a
 
 354 FALLACIES INCIDENT 
 
 from the nose ; the 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 
 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 93 , 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 
 connexion, as only another name for God, the argument, 
 as employed in the above and similar examples (I am 
 
 93 The following example (taken from Plutarch, De Stoicorum 
 Repugnantiis, p. 1042, by Mr. Lecky, in his History of European 
 Morals, fiom Augustus to Charlemagne, vol. ii. p. 174, note 2) is 
 perhaps unsurpassed in absurdity : ' Chrysippus maintained that 
 cock-fighting was the final caus^e of cocks, these birds being made 
 by Providence in order to inspire us by the example of their courage.'
 
 TO INDUCTION. 355 
 
 not here discussing the more refined employment of it), 
 seems to rest on the three following assumptions : 
 
 (1) 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. 
 
 (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 94 . 
 
 w The 'principle' laid down by Descartes (De Printipiis Philo- 
 sophies, i. 28) supplies an appropriate commentary on this assump- 
 tion : ' 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 parti- 
 cipes nos esse putemus.' 
 
 It is interesting to compare the following extracts from Galileo's 
 Systema Cosmiatm, 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 adsequate 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 usele>s, as 
 likewise that so great an immensity for receipt of the fixed stars as 
 exceeds our utmost comprehension would be superfluous, I would 
 A a 2
 
 356 FALLACIES INCIDENT TO INDUCTION. 
 
 Of these three assumptions, the first and second are, 
 as I 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, involves 
 a generalisation from a very narrow range of experience 
 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, which is concerned with deductive 
 reasoning. 
 
 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 whatso- 
 ever thing in the Universe is not subservient 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 superfluous, yea more, that there are no such things in 
 rerum "
 
 INDEX. 
 
 Adaptation and Design, p. 344. 
 
 Adaequata causa, why the ex- 
 pression is not here em- 
 ployed, 121. 
 
 Adequate hypotheses, 106-112. 
 
 Affirmative instances, tendency 
 of the mind to notice, rather 
 than negative instances, 
 
 255-259. 
 Analogy, argument from, 226- 
 
 337- 
 
 different meanings of the 
 
 word, 226-227. 
 
 false, fallacy of, 329-356. 
 Antiquitas soeculi juventus mundi, 
 
 origin of the apophthegm, 
 
 335- 
 
 Antiquity, illegitimate use of the 
 argument from, 333-335- 
 
 Aristotle pointed out the de- 
 pendence of deduction on 
 induction, 241. 
 
 his defective observation, 
 
 362-263. 
 
 his constant employment of 
 
 inductio per enumerationem 
 simplicem, 281-283. 
 
 his constant employment of 
 
 the argument from final 
 causes, 349-35 1 - 
 
 Assumptions made in reasoning, 
 xi-xvi, xix-xx. 
 
 Astronomy, a science of observa- 
 tion, 42, 44. 
 
 peculiarly rich in examples 
 
 of the Method of Residues, 
 
 175- 
 Authority, illegitimate use of the 
 
 a'gument from, 291-298. 
 Average of observations, 47, 48. 
 Averages, undue extension of 
 
 conclusions based upon, 
 
 286-289. 
 
 Bacon, his condemnation of in- 
 ductio per enumerationem 
 simplicem, 125, 281. 
 
 his instantm solitaria:, 144, 
 
 M5- 
 
 his instanti<z crncis, 151-154. 
 
 his 'approximation to the in- 
 
 ductive methods, 211-214. 
 
 difference between his pro- 
 
 cedure and that of Mr. Mill, 
 in the use of the Tables and 
 Methods respectively, 214. 
 
 bis error with regard to the 
 
 relation between the induc- 
 tive and deductive pro- 
 cesses, 248.
 
 INDEX. 
 
 Bacon, his notice of the tendency 
 to take account of affirma- 
 tive rather than negative 
 instances, 255. 
 
 his criticism of the argument 
 
 from final causes, 342-345. 
 Bain, Professor, referred to on 
 uniformities of co-existence, 
 8, 9, 224. 
 
 his view of the origin of uni- 
 
 versal beliefs, 34. 
 
 quoted with reference to the 
 
 Intermixture of Effects, 209. 
 Botany, reasons for the excellence 
 of its classifications, 55. 
 
 nomenclature of, 89-91. 
 
 terminology of, 92-94. 
 Brown, Dr. Thomas, his view of 
 
 the origin and nature of our 
 conception of cause, 24-26. 
 
 his objection to one of Hume's 
 
 definitions of cause, 23. 
 
 Causal relations, various kinds 
 of, 126-129. 
 
 Causation, can only be estab- 
 lished by the Experimental 
 Methods, 7-9, 224, 237. 
 
 Cause, relation of, to the con- 
 ditions of a phenomenon, 
 13-16. 
 
 nature of our conception of, 
 
 18-30. 
 
 origin of our conception of, 
 
 25-28. 
 
 definition of, 23-25. 
 
 : is an idea sui generis, 23. 
 
 error originating in mistaking 
 
 a joint cause for a sole cause, 
 
 305-3I4- 
 
 Cause, error originating in mis- 
 taking joint effects for cause 
 and effect, 314-318. 
 
 error originating in the con- 
 
 fusion of the proximate with 
 the primary or remote cause 
 of a phenomenon, 318-322. 
 
 error due to neglecting to 
 
 take into account the mu- 
 tual action and reaction 
 (mutuality) of cause and 
 effect, 322-325. 
 
 error due to the inversion of 
 
 cause and effect, 325-329. 
 Causes, exciting, 15-16. 
 
 predisposing, 15-16. 
 
 final, illegitimate employment 
 
 of the argument from, 342- 
 
 356. 
 Certainty, the question whether 
 
 it be predicable of inductive 
 
 inferences, ix-xx. 
 Characteristick, 84, 85. 
 Chemistry, nomenclature of, 91. 
 
 method of difference exten- 
 
 sively employed in, 154. 
 Classification, 52-89. 
 
 scientific, distinguished from 
 
 that employed in the affairs 
 of ordinary life, 52-55. 
 
 scientific, regarded as sub- 
 
 sidiary to induction, defini- 
 tion of, 54-55. 
 
 a natural system of, distin- 
 
 guished from an artificial 
 system of, 55-57.
 
 INDEX. 
 
 359 
 
 Classification, natural, rules for 
 the right conduct of, 74-80. 
 
 Classifications, though subsidiary 
 to inductions, themselves de- 
 pend on inductions per enu- 
 merationem simplicem, 54. 
 
 Co-existence, Inductions of, 7-9, 
 54, 223-224. 
 
 Colligation of facts, a hypothesis 
 serves for, 99-100. 
 
 Comparative Method, 206. 
 
 Comparison, P'allacy of Exag- 
 gerated, 277-278. 
 
 Conditions, relation of, to the 
 cause of a phenomenon, 1 3- 
 16. 
 
 Consent, Universal, argument 
 from, 297-298. 
 
 Conservation of Energy, Law of, 
 6, 129. 
 
 Consilience of inductions, 119- 
 121. 
 
 Continuity, law of, 82-84. 
 
 Crucial instances, 151-154. 
 
 Darwin, Mr., quoted on the sig- 
 nification of the word ' spe- 
 cies,' 81-82. 
 
 referred to on the Theory of 
 Final Causes, 342. 
 
 Deduction, its relation to induc- 
 tion, 241-249 ; cp. xvii-xx. 
 
 Definition, are natural classes 
 determined by definition or 
 type, 85-89. 
 
 Descartes,his criticism of the argu- 
 ment from final causes, 355. 
 
 Diagnosis, 84, 85. 
 
 Empirical generalisations or 
 laws, 224-226. 
 
 Energy, Law of the Conserva- 
 tion of, 6, 129 ; cp. xix. 
 
 Evolution, . course of, indicates 
 the existence and attributes 
 of the Supreme Cause, 342- 
 
 343- 
 Exaggerated comparison, fallacy 
 
 of, 277-278. 
 Exceptio probat regulam, the 
 
 maxim explained, 309. 
 Exceptions to rules, 210, 308--* 
 
 309- 
 
 Experiment, 39-51. 
 
 how far employed by the 
 
 Greeks, 40. 
 
 distinguished from observa- 
 
 tion, 39 40. 
 
 general superiority of, over 
 
 observation, 40-42. 
 
 not open to us in the attempt 
 
 to ascertain the cause of a 
 given effect, 42-43. 
 
 and observation, rules for 
 
 the right conduct of, 45-5 1 . 
 Explanation, in the scientific 
 sense, what, 98-99. 
 
 Fallacies incident to induction, 
 
 254-356. 
 
 of generalisation, 279-356. 
 
 common to the employment 
 
 of the various inductive 
 methods, 298-329. 
 
 the same instance may often 
 
 be indifferently ascribed to 
 several, 305.
 
 3 6 
 
 INDEX. 
 
 Fallacy of non-observation, 254- 
 272. 
 
 arising from confusion be- 
 
 tween absolute and relative 
 frequency, 259. 
 
 of non - observation of in- 
 
 stances, 254-268. 
 
 of non-observation of circum- 
 
 stances attendant on a given 
 instance, 268-272. 
 
 of mal-observation, 272-278. 
 
 of exaggerated comparison, 
 
 277-278. 
 
 arising from treating the in- 
 
 dnctio per enumerationem 
 simplicem as if it were a 
 valid induction, 279-298. 
 
 of ' non causa pro causa,' 
 
 300-305. 
 
 due to the neglect of a joint 
 
 cause, 305-314. 
 
 due to mistaking joint effects 
 
 for cause and effect, 3 1 4-3 1 8. 
 
 due to the confusion of the 
 
 proximate with the primary 
 or remote cause of a phe- 
 nomenon, 318322. 
 
 due to neglecting to take 
 
 into account the mutual 
 action and reaction (mu- 
 tuality) of cause and effect, 
 
 322-325- 
 
 due to the inversion of cause 
 
 and effect, 325-329. 
 - of false analogy, 329-356. 
 
 due to the illegitimate employ- 
 
 ment of argument from final 
 causes, 34 2 -35 6 - 
 
 Final causes, fallacy due to the 
 illegitimate employment of 
 the argument from, 342-356. 
 
 legitimate employment of the 
 
 argument from, 342-344. 
 Frequency, confusion between 
 
 absolute and relative, 259. 
 Frequency of occurrence does not 
 
 always furnish an argument 
 
 for the recurrence of an 
 
 event, 288-289. 
 Frustration of Effects, 307-309. 
 
 Galileo, quoted on the theory of 
 Final Causes, 355-356. 
 
 Geology abounds in instances 
 of the employment of the 
 method of concomitant vari- 
 ations, 193. 
 
 God ; see Supreme Cause. 
 
 Nature often used indefinitely 
 
 f or, 354-356- 
 
 Hamilton, Sir W., his criticism 
 
 of Hume's theory on the 
 
 nature of cause, 22. 
 Herschel, Sir John, distinctly 
 
 recognises the inductive 
 
 methods, 210. 
 
 quoted on our tendency to 
 
 notice affirmative rather 
 
 than negative instances, 
 
 256-257. 
 Historical Method, 204-207, 
 
 252. 
 Hume, his view of the nature of 
 
 our conception of cause, 18- 
 
 30-
 
 TNDEX. 
 
 361 
 
 Hume, injustice done to him by 
 quoting from his treatise of 
 Human Nature, 29-30. 
 
 Hypothesis, xviii-xix, 11-13, 
 97-123, 248-249. 
 
 always suggested by facts 
 
 within our experience, xviii, 
 248. 
 
 distinction between, and in- 
 
 duction, 11-13, 112-115. 
 
 description of, 97-99. 
 
 conditions of a legitimate, 
 
 100-113. 
 
 difference between Mr. Mill 
 
 and Dr. Whewell as to the 
 functions of, 115-121. 
 
 views of Professor Jevons on 
 
 the relation of hypothesis 
 to induction, xvi-xix, 117. 
 
 gratuitous, 122-123. 
 Hypothetical, all reasoning is in 
 
 a sense, xi-xvi ; cp. xix. 
 
 Imaginative Faculty, Formation 
 
 of Hypotheses the work of, 
 
 100. 
 Indued o per enumerationem sim- 
 
 plicem, 7-9, 124-126, 219- 
 
 226. 
 
 complete, 125, 219. 
 
 distinction between complete 
 
 and incomplete, 219-220. 
 
 distinguished from the Method 
 
 of Agreement, 222, 226. 
 
 fallacy arising, in certain 
 
 cases, from its employment 
 as if it were a scientific in- 
 duction, 280-298. 
 
 Inductio per enumerationem sim- 
 plicem, its employment by 
 Aristotle, 281-283. 
 
 instance of its employment 
 
 in the Science of Proba- 
 bility, 286-288. 
 
 is still commonly employed 
 
 in social speculations, 289- 
 2.91. 
 
 Induction, ambiguous use of the 
 word, 3. 
 
 the nature of, 3-10, 124-126 ; 
 
 cp. xviii, xix. 
 
 defined, 9-10. 
 
 does it admit of certainty, 
 
 ix-xx. 
 
 distinction between, and hy- 
 
 pothesis, 11-13. 
 
 question whether it be from 
 
 the particular to the general, 
 or from particulars to ad- 
 jacent particulars, 16-18. 
 
 its relation to deduction, 241- 
 
 249; cp. xvii-xx. 
 
 fallacies incident to, 254-356. 
 Inductions of Co-existence, 7-9, 
 
 54, 223-224. 
 
 of Causation, 8-9, 125-126, 
 
 224. 
 
 of Equality, 8-6. 
 
 imperfect, 219-240. 
 
 incomplete, 237-240. 
 Inductive Methods, 124-218, 
 
 222-223. 
 
 their object, 126, 216, 222- 
 
 223, 299. 
 
 reducible to two only, 207-208. 
 
 distinctly recognised by Sir
 
 362 
 
 INDEX. 
 
 John Herschel, though the 
 importance now attached to 
 them is mainly due to Mr. 
 Mill, 210. 
 
 Inductive Methods, approxima- 
 tions to, in the Novum Or- 
 ganum, 210-214. 
 
 defended against the attacks 
 
 of Dr. Whewell, 214-218. 
 
 imperfect applications 0^237- 
 
 240. 
 
 fallacies common to the em- 
 
 ployment of the various, 
 398-329. 
 
 Intentional Species, 123. 
 
 Intermixture of effects, 208-210. 
 
 Invariable conjunction, 130, 137- 
 138,145-147,163-164,170; 
 cp. 48-49, 134. 
 
 Inverse Deductive Method, 205, 
 252. 
 
 Isolation of phenomena, im- 
 portance of, 50-51. 
 
 Jevons, Professor, referred to on 
 the question whether induc- 
 tion be from the particular 
 to the general, or from par- 
 ticulars to adjacent par- 
 ticulars, 17. 
 
 on rules for legitimate hy- 
 
 potheses, IOI; 
 
 on the relation of Hypothesis 
 
 to Induction, xvi-xix. 
 
 on the uncertainty attaching 
 
 to inductive inference,ix-xx. 
 on the nature of inductive in- 
 ference, ix-xx, 117. 
 
 Kant, his criticism of Hume's 
 account of causation, 26-27. 
 
 Law of uniformity of nature, 5- 
 
 9> 30-38. 
 
 of universal causation, 4-9, 
 
 30-38- 
 
 Laws of Thought, xix-xx. 
 
 Lewes, Mr., criticism of his 
 statements on the belief in 
 the law of universal causa- 
 tion, 30-32. 
 
 Locke, his account of the idea of 
 power, 19-20. 
 
 Maine de Biran, M., his view of 
 the nature of our conception 
 of cause, 27. 
 
 Malebranche, his idea of causa- 
 tion, 18. 
 
 Mansel, Dr., his view of the na- 
 ture of our conception of 
 cause, 27-28. 
 
 his view of the origin of our 
 
 beliefs in the laws of uni- 
 versal causation and the 
 uniformity of nature, 36. 
 
 Material and immaterial circum- 
 stances, 48-49, 134-135. 
 
 Medicine,*distinction of exciting 
 and predisposing causes in, 
 15-16. 
 
 Method of Agreement, 130-148. 
 
 of difference, 148-159. 
 
 double, of agreement (or joint 
 
 method of agreement and 
 difference), 160-173. 
 
 of residues, 173-182.
 
 INDEX. 
 
 3 6 3 
 
 Method of concomitant varia- 
 tions, 183-206. 
 
 of concomitant variations, Mr. 
 
 Bain quoted on its applica- 
 tion in the case of Inter- 
 mixture of Effects, 205-209. 
 
 comparative, 206. 
 
 historical, 204-207, 252. 
 
 Method of Agreement distin- 
 guished from Inductio per 
 Enumerationem Simplicem, 
 222, 226. 
 
 Methods, inductive or experi- 
 mental, 124-218, 222-223. 
 
 Mill, James, quoted on the origin 
 of our belief in the law of 
 universal causation, 34-35. 
 
 Mill, J. S., referred to on the re- 
 lation between the cause and 
 the conditions of a pheno- 
 menon, 14-15. 
 
 question between him and Dr. 
 
 Whewell, as to whether in- 
 ductive inference be from 
 the particular to the general, 
 or from particulars to adja- 
 cent particulars, 16-18. 
 
 his definition of cause criti- 
 
 cised, 24. 
 
 his answer to Reid's objection 
 
 to Hume's account of causa- 
 tion, 24-25. 
 
 his view of the origin of uni- 
 
 versal beliefs, 34-36. 
 
 difference between him and Dr. 
 
 Whewell as to the function 
 of hypotheses, 115-121. 
 
 importance now attached to 
 
 the inductive methods main- 
 ly due to his influence, 210. 
 
 Mill, J. S., on the Law of Iden- 
 tity, xx. 
 
 Mineralogy, mainly a classifica- 
 tory science, 55. 
 
 Natural distinguished from arti- 
 ficial classification, 55-57. 
 
 classification, rules for the 
 
 right conduct of, 74-80. 
 
 groups, arrangement of, in a 
 
 natural series, 77-80. 
 
 groups, constant recognition 
 
 of new, 82-84. 
 
 Selection, its relation to doc- 
 
 trine of Final Causes, 342- 
 343- 
 
 Nature, substituted by Aristotle 
 for God, 349-351. 
 
 vague employment of the 
 term, 354-356 5 cp. 342-343- 
 
 Newton, his demonstration of a 
 central force, 113-115. 
 
 his employment of the ex- 
 
 pression ' Vera Causa,' 121- 
 
 122. 
 
 Nomenclature, 89-91. 
 Non causa pro causa, 305. 
 
 Observation, 39-51. 
 
 distinguished from experiment, 
 
 39-4- 
 
 general employment of, pre- 
 
 ceded that of experiment,40. 
 
 alone open to us in the at- 
 
 tempt to ascertain the cause 
 of a given effect, 42-43.
 
 3 6 4 
 
 INDEX. 
 
 Observation, sciences wholly or 
 mainly dependent on, at a 
 great disadvantage, as com- 
 pared with those in which 
 we can largely employ ex- 
 periment, 43-45. 
 
 and experiment, rules for the 
 
 right conduct of, 45-51. 
 
 Observations, importance of 
 taking an average of, 47-48. 
 
 Ogle, Dr. William, his Intro- 
 duction to the De Parttbus 
 Animalium referred to, 282. 
 
 Physiology frequently employs 
 the method of concomitant 
 variations, 195-196. 
 
 Plato, his employment of the 
 argument from final causes, 
 
 345-349- 
 
 Plurality of causes, 6, 23, 127- 
 128, 131-134. 
 
 fallacy arising from neglect- 
 
 ing to take into account, 305. 
 Post hoc, ergo propter hoc, 305. 
 Power, question whether the 
 
 idea of is involved in our 
 
 conception of cause, 18-30. 
 Prediction, value to be attached 
 
 to, 117-121. 
 
 Read, Mr. Carveth, his expres- 
 sion ' Vicariousness of 
 Causes,' 127. 
 
 Reid, his criticism of Hume's ac- 
 count of causation, 21-25. 
 
 his view of the nature of our 
 
 conception of cause, 27. 
 
 Reid, his view of the origin of 
 universal beliefs, 32-33. 
 
 Social questions, the extreme dif- 
 ficulty attendant on their in- 
 vestigation, 289-291. 
 
 Species, practice of naturalists in 
 stopping at, open to ques- 
 tion, 80-82. 
 
 and varieties, constant recog- 
 nition of new, 82-84. 
 
 Spencer, Herbert, his view of the 
 origin of universal beliefs, 
 
 referred to on the Theory of 
 
 Final Causes, 343. 
 Statistics, conclusions based on, 
 
 are instances of the appli- 
 
 cation of the method of 
 
 concomitant variations, 204. 
 Stewart, Dugald, his view of the 
 
 nature of our conception of 
 
 cause, 27. 
 Subordination of characters, prin- 
 
 ciple of, 74-75. 
 Supreme Cause, the course of 
 
 evolution an indication of 
 
 His existence and attributes, 
 
 34 2 -343. 
 
 Terminology, 92-97. 
 
 Theory, two meanings of the 
 word, 13. 
 
 Thermotics, Science of, furnishes 
 good examples of the Me- 
 thod of Difference, 155. 
 
 Type, persistency of, 83-84.
 
 INDEX. 
 
 365 
 
 Type, are natural classes deter- 
 mined by definition or, 85- 
 
 Ultimate laws of nature, 225. 
 Uniformity of nature, law of, 
 
 5-9- 
 
 converse does not hold true, 6. 
 
 vaguer and more precise mean- 
 
 ings of the expression, 9. 
 
 universality of the belief in, 
 
 30-32 ; cp. xi-xvi. 
 
 origin of the belief in, 7-9, 
 
 30-38. 
 
 Universal beliefs, various theo- 
 ries as to the origin of, 30- 
 38. 
 
 Universal causation, law of, 4-9. 
 
 universality of the belief in, 
 
 30-32 ; cp. xv-xvi. 
 
 origin of the belief in, 30-38. 
 
 Variation of circumstances, im- 
 portance of, 49. 
 
 Venn, Mr., referred to on a com- 
 mon fallacy in the calcula- 
 tion of probabilities, 286- 
 288. 
 
 Vera causa, why the expression 
 
 is not here employed, 121- 
 
 122. 
 
 Verification, 249-253. 
 Veritas temporis filia dicitur, non 
 
 auctoritatis, origin of the 
 
 apophthegm, 334-335. 
 
 Whewell, Dr., question between 
 him and Mr. Mill as to whe- 
 ther inductive inference be' 
 from the particular to the 
 general, or from particulars 
 to adjacent particulars, 16- 
 18. 
 
 his view of the origin of 
 
 universal beliefs, 33. 
 
 his position that natural 
 
 classes are determined not 
 by definition but by type, 
 85-89. 
 
 his remarks on terminology, 
 
 92-96. 
 
 difference between him and 
 
 Mr. Mill as to the function 
 of hypotheses, 115-121. 
 
 his criticism on the inductive 
 
 methods, 214-218. 
 
 Zoology, reasons for the excel- 
 lence of itsclassifications,55. 
 
 THE END.
 
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